Rare Earth-Doped Fibers

This is a continuation from the previous tutorial - retardation plates.

 

1. Introduction

Rare earth (RE) doping of optical fibers dates back to the 1960s and was one of the forces driving development of guided wave optical fibers. The goal was to exploit the long path length provided by wave-guiding media to improve operation of Nd, Er, and Er/Yb fiber lasers.

Then, as now, the fiber consisted of regions with raised refractive index to guide light and some distribution of RE ions that interacted with this light. Very simply, the goal remains to exploit the optical activity of the RE elements to create a laser or amplifier.

From its inception to the late 1980s, such fibers were primarily a research platform for study of various optical phenomena, which, though interesting, did not mature into commercial products. There were no compelling applications or needs that were filled by fiber lasers.

This changed very quickly and very dramatically with the discovery of the erbium-doped fiber amplifier (EDFA) because a critical need for optical amplification arose, and because the EDFA was able to fulfill that need exceptionally well.

The success of the erbium-doped fiber spawned an industry driven to improve and surpass its performance. This included the search for alternative dopants and hosts, as well as improved fiber designs.

Naturally, these efforts morphed into other uses and applications for amplifier fiber technology, the most active one being the quest for very high power fiber lasers and amplifiers for industrial materials processing applications.

RE-doped silica fibers play an important role in a variety of modern technologies. Fiber lasers and amplifiers using such fibers are extensively used in basic and applied research, medicine, and military applications. They are replacing gas and solid state devices in industrial materials processing and are used in a variety of fiber optic sensors.

Many of these applications take advantage of unique properties of silica-based glasses, such as excellent optical transmission from ultraviolet (UV) to near-infrared wavelengths (with some of the lowest losses possible), isotropy of optical properties of the glass, excellent refractive index homogeneity with a low nonlinear refractive index, small strain birefringence, a very low coefficient of thermal expansion, very high thermal stability, very high chemical and environmental durability, high mechanical strength, and resistance to radiation.

Although the field is by no means new, quickly developing military and commercial applications, particularly involving high-power lasers and amplifiers, put new and demanding requirements on quality and long-term reliability of such fibers, as well as stimulate further research and development in the field of RE fiber fabrication.

This tutorial discusses two main categories of RE-doped fibers: fibers for telecommunications applications and fibers for high-power source applications.

The former comprises Er and Er/Yb fibers while the latter covers a broader range of RE elements (Er, Er/Yb, Yb, Tm, Ho, etc.) and fiber architectures.

 

2. Motivation

Why put RE elements in an optical fiber? Because RE ions in glass are optically active, meaning they absorb light at one wavelength and emit light at another. This can be useful in creating a laser, a broadband source, or a signal amplifier at the emission wavelength.

Figure 7.1 illustrates this concept using the well-known example of an erbium-doped amplifier.

Figure 7.1 shows the absorption spectrum of Er in a silica fiber, while the inset shows the bottom three levels of the energy level diagram. When light at a wavelength near 980 or 1480 nm is incident upon Er ions in the fiber, the photons are absorbed, causing excitation into higher energy levels.

These relax to the lowest excited level whereupon final relaxation back to the ground state is accompanied by emission at a wavelength around 1530 nm.

This light is quickly reabsorbed by ions in the ground state, but if a population inversion exists (number of ions in upper state exceeds that in ground state), emission will exceed absorption and gain about 1530 nm results.

 

 

The spectra and optical behavior are the result of a quirk in the electronic levels of the REs, which include the lanthanide and actinide series (atomic numbers 57–103).

Using the classic description of an atomic nucleus surrounded by shells of electrons, for most of the periodic chart, as the atomic number increases, the electron shells are filled with progressively increasing radius.

However, beginning with lanthanum (atomic number 57), the situation changes. Lanthanum has filled 5s and 5p shells and addition of another electron occupies the 4f shell, which has a smaller radius than the 5s and 5p shells.

The filled outer 5s and 5p shells of the RE elements effectively shield the unfilled bands and cause the ions to exhibit atomic-like properties. Although many RE ions can exist in a divalent state, they are most commonly incorporated in glasses as trivalent ions in which two electrons are absent from the 6s shell and one from the 4f shell.

The resulting electron structure is similar to xenon with only partially filled electron orbital \(f^{N-1}\). Normally, elements doped into a solid give up an electron to the matrix because the outermost wave functions are delocalized. For RE elements, shielding results in relatively well-defined energy levels, which are exhibited as narrow absorption and emission bands.

The incompletely filled 4f energy levels are composed of states that are spread in energy due to spin–spin and spin–orbit coupling. These levels are spread still further when the ions interact with a host material such as a crystal or solid because the degeneracy of levels is lifted somewhat by slight asymmetry of the environment.

This Stark splitting gives rise to multiple transitions, which comprise the spectra of the REs. In Er, for example, the ground state has eight Stark levels and the first excited state has seven, so the emission around 1530 nm results from an ensemble of 56 individual transitions.

Although transitions within the 4f shell are strictly forbidden in an electric dipole because the initial and final states have the same parity, asymmetry from the local environment causes some admixture of higher lying states with opposite parity and strongly influences the oscillator strength.

The local environmental asymmetry present in glasses causes crystal field splitting of the energy levels and results in spectra that are much broader than found in a crystalline host, but considerably more narrow than that exhibited by other elements, such as transition metals in glass. This is evident in the spectrum of Fig. 7.1 and is true of all of the lanthanide series.

 

3. Host Glasses for Rare Earth Ions

The highly polymerized structure of pure silica glass does not allow easy accommodation of RE ions even at low concentrations. Trivalent RE ions do not substitute for silicon in the glass network easily, if at all, and at the same time they need six to eight oxygen ions for their coordination.

Silica has very few nonbridging oxygen ions that can provide such coordination and RE ions are forced to cluster together to share those few oxygen ions that are present in the network.

Such clustering can lead to enhanced energy transfers between \(f^{N-1}\) energy levels of neighboring RE ions, concentration self-quenching of luminescence even at low doping, and rapid phase separation at higher doping levels.

For example, the formation of Nd-O-Nd bonds was directly observed in silica glass doped with 2400 ppm of Nd₂O₃ by the extended x-ray absorption fine structure (EXAFS) spectroscopy with Nd-Nd and Nd-O distances similar to those found in crystalline Nd₂O₃.

Such close pairing can result in luminescence self-quenching due to very efficient cooperative energy transfers, which cause losses of ion excitations. The signature of concentration quenching is the decrease of luminescence lifetime with increasing RE concentration.

To increase RE solubility in silica and decrease the negative effects of clustering, co-doping is most often used in all fabrication methods. Co-dopants also provide the index modification needed for creating a wave-guiding structure and are often used to alter spectroscopic properties, such as increasing the emission bandwidth or shifting undesirable excited state absorption features.

A special category of co-dopants consists of other lanthanides such as lanthanum and lutetium that tend to cluster together with optically active ions shielding them from one another, increasing the distance between neighboring optically active ions, and therefore decreasing efficiency of cooperative energy transfers. This can allow higher active RE concentration or improved device performance.

The most popular solubilizer is aluminum. Aluminum can be incorporated into the silica network either in tetrahedral coordination as a network former or in octahedral coordination as a network modifier.

The four coordinated aluminum shares nonbridging oxygen ions with RE ions, therefore reducing RE ion clustering. As an illustration, direct probing of neodymium-doped aluminosilicate glasses using EXAFS spectroscopy showed a breakup of Nd-O-Nd linkages and the formation of Nd-O-Si/Al bonds at their expense.

From the solution chemistry point of view, alumina dissolves well in silica, while RE oxides dissolve well in alumina. Therefore, alumina forms a solvation shell around RE ions, allowing them to become soluble in a silica network.

Arai et al. showed that a molar ratio Al/Nd of 10 was enough to make a neodymium-doped glass suitable for laser applications, as confirmed by Magic Angle Spinning (MAS), Nuclear Magnetic Resonance (NMR), and Electron Paramagnetic Resonance (EPR) measurements, while a similar impact for Er has been confirmed.

Phosphorus is another popular co-dopant, and in fact, phosphate glasses provide an excellent matrix into which high concentrations of RE ions can be readily incorporated.

High gain coefficient phosphate glass fiber amplifiers with high gain per unit length were demonstrated, although their poor compatibility with high silica telecommunication fibers and low mechanical and thermal stability are still known issues.

When co-doped into silica, phosphorus plays a role similar to aluminum and incorporates in two tetrahedral configurations P₂O₅ and P₂O₄, with the second configuration attracting charge compensation cations, such as RE ions.

A solvation shell is formed around RE ions, allowing their accommodation within silica network without clustering. A molar ratio P/Nd of 15 or more was shown to be sufficient for laser applications.

Similar to use of Al, addition of P can be used to solubilize the RE or alter the spectral properties. Phosphorus is essential for efficient operation of Er/Yb–co-doped systems, as is discussed in detail later in this tutorial.

Other less common dopants that were used for co-doping RE-doped fibers include alkali and alkaline earth metals. Quite often, a combination of several dopants both from the first and second groups are used in order to obtain desired wave-guiding and spectral properties.

The primary goals in altering the host glass for RE ions for photonic applications is to tailor the absorption and emission spectra, influence excited state properties, and improve the glass-forming characteristics.

Unfortunately, the atomic structure, which confers unique optical properties on RE ions, also conspires to make these properties relatively immune to changes in local glass environment.

A huge literature has been developed on hosts for RE ions for solid state lasers and other optical and nonoptical applications, but relatively little of this has been (or can be) applied to optical fiber. Many glass systems are not appropriate because of difficulty in creating the required index structure to produce wave guiding or because of optical attenuation, which would be excessive in a fiber device that has a path length of meters.

The dominant host has been silica, but the range of compositions is small because of glass-forming limitations. Even use of modest dopant levels is problematic because most elements cause excess optical attenuation and must be avoided, whereas the remaining few have only modest influence. Some, such as phosphorus as a codopant for Er, cause undesirable changes in the spectrum, such as spectral narrowing.

More radical modification requires use of other hosts, such as phosphates, borates, tellurites, and fluorophosphates, as well as nonoxygen hosts such as fluorides, sulfides, and other chalcogenides.

For these, there are several benefits. The dominant influence is a profoundly altered phonon energy spectrum, which reduces nonradiative excited state decay and allows radiative emission, which would be quenched in silica.

In addition, other host glasses allow lasing transitions that occur beyond the 2.0-μm absorption edge of silica. These glasses are mainly nonoxides and heavy oxide materials like TeO₂. Glasses such as phosphates are useful because the dopant concentration can be very high.

Finally, some hosts are chosen because the high polarizability enhances Stark splitting and creates a more desirable spectrum. The range of possibilities is too broad for this discussion, but nonsilica materials are discussed briefly in the following sections.

 

4. Fabrication of Rare Earth-Doped Fibers

4.1. Overview of Optical Fiber Fabrication

Fabrication of low-loss optical fiber requires very pure precursor materials and a method to produce the cylindrically symmetrical preform from which the fiber is drawn.

To achieve the current level of transparency for optical communications transmission fiber, the concentration of impurities such as iron (which gives window glass its characteristic green color) must be reduced to less than one part per billion (ppb).

Hydroxyl (\(\text{OH}^-\)) impurities from water contamination create a characteristic absorption band at 1.39 μm and are typically reduced to less than 10 ppb. Amazingly, such high purity is readily achieved in large-scale manufacturing using several vapor-phase processes practiced globally.

All possess the similar characteristic that silicon-containing vapor (such as SiCl₄) is reacted with oxygen to form small particles of silica (SiO₂), as first reported in 1973. Such vapor-deposition processes have been refined to comprise two categories: outside vapor deposition (OVD) and internal deposition processes such as modified chemical vapor deposition (MCVD).

In MCVD, the first process for commercial fabrication, this reaction occurs inside a silica tube, as shown schematically in Fig. 7.2.

 

 

Vapor of silicon tetrachloride is delivered into a rotating silica tube and reacted with oxygen at approximately \(1300^\circ\)C to create submicron silica particles. The composition of the particles is determined by the composition of the gas phase, so the addition of GeCl₄, for example, will produce Ge-doped particles.

These particles are driven to the cooler glass wall by thermophoresis, where they deposit on the inner surface of the tube. The reaction hot zone is produced using an external torch, such as an oxy-hydrogen burner.

As this burner traverses down the tube, the deposition zone also translates. As the torch passes over the previously deposited ‘‘soot,’’ the particles are sintered to form clear glass.

Because the glass is formed at high temperature in the presence of chlorine, the primary impurities (transition metals and water) remain as volatile chlorides and exit the tube. This allows purification by many orders of magnitude and is a critical aspect of the process. If the precursors contain contaminants such as hydrogen, each layer must be purified before being fully consolidated.

To build the desired wave-guiding structure in the glass, multiple layers are deposited, each of appropriate composition to either raise (e.g., using germanium) or depress (using fluorine) the refractive index relative to silica.

The tube is collapsed to a solid rod by surface tension when heated to approximately \(2300^\circ\)C. The result is a cylinder of glass with a doped region at the center.

Alternative techniques for making this rod entail creation of the silica particles in a flame through hydrolysis rather than oxidation. In OVD, the flame traverses along a mandrel and the silica particles are collected as porous soot. Multiple passes of the torch build up the soot (and the index structure) radially. After the mandrel is removed, the soot is purified in a chlorine-containing atmosphere in a furnace and sintered to clear glass.

In vapor-phase axial deposition (VAD), the chemistry is similar, but the flame is directed at the end of a rotating rod. As the rod is gradually withdrawn, a long soot boule is grown axially. Multiple torches are used to form the Ge-doped core and the pure silica cladding.

Because porous boules created by outside processes are purified before sintering, the glass precursors may contain hydrogen or other impurities. This allows a wider range of starting chemicals to be used, such as organometallic precursors instead of SiCl₄.

For all of these processes, after the core rods are formed, they are overclad or jacketed to build up the outer diameter and then drawn into fiber. These aspects of the process are unchanged when producing RE-doped fibers.

 

4.2. Incorporation of Rare Earth Elements

A key feature of the preceding discussion is that the glass precursors are vapors formed from high vapor pressure compounds such as the chlorides. In addition, the use of vapor methods precludes transport of transition metal ions and other contaminants to the reaction zone during deposition and allows for the routine fabrication of fiber approaching the theoretical minimum loss in silica.

However, these same properties prohibit incorporation of many potentially useful dopants and only several elements (such as Si, Ge, P, B, Ti) can be conveniently incorporated from liquid phase through vapor deposition at relatively high levels.

Because the desired RE elements do not possess suitable high vapor pressure compounds, a host of alternative doping methods have been developed for use with OVD, VAD, and MCVD.

The most widely used techniques are discussed here. Several other methods exist such as rod-intube, seed fiber, and various vapor-delivery techniques, but none of these is practiced on a wide scale. 

4.2.1 Vapor-Phase Methods

All-vapor delivery avoids contamination of the system, accelerates the glass formation process, and allows superior control of the refractive index profile. Vapor delivery may be accomplished by heating RE chlorides to around \(1000^\circ\)C to generate sufficient vapor.

Such an apparatus is shown in Fig. 7.3 and consists of an ‘‘injector’’ containing a suitable RE halide or nitride situated inside a rotating MCVD silica substrate tube and heated by an external furnace.

 

 

Because the vapor pressure of the RE precursor increases with temperature exponentially, however, such a process is difficult to control. Note that the understanding of early work using RE halides situated on the inside surface of the substrate tube was flawed because the halides quickly react with oxygen at elevated temperature to form refractory materials and are not delivered as halides.

While heated RE halides produce enough vapor to obtain modest glass doping levels, their vapor pressure is still quite low (well under 1 Torr at \(600^\circ\)C).

However, it is well known that aluminum chloride readily complexes with many metal chlorides, forming a high vapor pressure complex. Thus, by passing aluminum chloride over erbium chloride, the complex Al_xErCl_3(x+1) will be generated, increasing the delivery rate by seven orders of magnitude at \(600^\circ\)C and reducing the variation of vapor pressure with temperature.

Using this technique, many core layers may be deposited and dehydration is not required. However, it becomes complicated if multiple dopants are desired, such as for Er/ Yb–doped fibers, which is discussed later in this chapter.

The surface plasma chemical vapor deposition (SPCVD) technique is a modification of the MCVD technique that allows a lower deposition temperature. In a further development, vapor phase SPCVD deposition of erbium and aluminum from heated anhydrous salts allowed fabrication of erbium-doped fibers with 5700 ppm weight of erbium.

An amplifier made from this fiber demonstrated a 0.5-dB/cm gain when pumped at 980 nm. It was argued that the lower deposition temperature that the SPCVD provides decreases RE clustering, leading to the higher gain.

Chelates

Vapor phase delivery is also possible with certain metal organic compounds of RE metals heated to around \(200^\circ\)C. Such methods were used for the fabrication of optical waveguides and fiber optic preforms using both OVD and MCVD.

The precursor materials are typically \(\beta\)-diketonate complexes, which are fluorinated to increase volatility. To aid processing of high Nd³⁺ and Yb³⁺ MCVD preforms, unfluorinated \(\beta\)-diketonate compounds have been used.

In these processes, a carrier gas of helium or argon is used to transport the vaporized material to the OVD or MCVD preform being processed. Although this requires heated delivery lines and careful metering of gas flows, the process is readily controlled and is suitable for multiple RE dopants.

With any metal organic delivery, hydrogen is present in the precursor material, so the deposited glass must be dehydrated in the same manner as for solution doping.

4.2.2. Nonvapor Methods

The first neodymium-doped optical fiber was fabricated by the ‘‘rod-in-tube’’ method from a multicomponent silicate glass rod overclad with a soda-lime silicate tube. The same approach was used to fabricate RE-doped fibers with core glass that was compatible with a pure silica overcladding tube.

Similar to these methods, the powder-in-tube technique allowed fabrication of ultrahigh RE concentration silica fibers (54 wt% of Tb₂O₃) for Faraday isolator applications.

The technique allows a single draw directly to the final fiber with a small core diameter, so a much higher thermal expansion mismatch can be handled than would ever be possible in regular preform fabrication methods.

Vapor methods that were described earlier offer significant advantages over these ‘‘bulk glass’’ techniques, which suffer from poor dimensional control and high background attenuation. In addition, they may require significant modifications of existing standard equipment. However, multiple co-dopants can be easily incorporated and they allow high levels of RE and other dopants.

Various nonvapor-delivery methods were developed to circumvent limitations of both of the vapor phase approaches earlier bulk glass methods. Contamination from transition metal ions and hydroxyl complexes can generally be avoided by a careful choice of high-quality dopants and an appropriate drying/sintering treatment.

Solution Doping

The simplest and most widely used method for doping optical preforms with alternative dopants is solution doping or molecular stuffing. In this process, as applied to MCVD, the torch temperature during glass deposition is reduced so that sintering of the soot is incomplete and the glass layer left behind the torch remains porous.

The tube is then soaked in a liquid that contains the desired dopant to permeate the porous glass. As the body is dried, the dopants are adsorbed or precipitate in the pores of the glass and become incorporated in the glass when it is finally sintered. Additional doped layers can be built up sequentially.

Conventional dopants such as germanium, phosphorus, and fluorine are incorporated from the gas phase while other elements such as AlCl3 and low-vapor pressure precursors such as RE chlorides or nitrates are dissolved in the liquid.

Virtually any solvent and any soluble precursor free of impurities may be used. A wide range of elements have been successfully incorporated. Because the porous glass soot is sintered at high temperature (\(\gt2100^\circ\)C if necessary), crystallization of the glass is avoided. This allows high concentration of dopants such as Al to be incorporated readily without crystallization.

Although solution doping is easy to implement, control of dopant concentration, which depends on surface adsorption, solute concentration, soot density, and dehydration conditions, is difficult.

For example, the soot density is controlled by glass viscosity, which varies exponentially with temperature and the concentration of dopants such as Ge. In addition, to achieve uniform doping, the solution must be drained and dried evenly, avoiding a buildup of material at the bottom or on one side of the body due to gravitational settling.

Dehydration, which is most effectively accomplished by treating the body in an atmosphere containing Cl₂ at \(800^\circ\)C for about an hour, may alter the composition by volatilizing the dopants as chlorides.

Finally, it is difficult to build up large or complex cores because each layer requires considerable time to deposit, cool, soak, dry, dehydrate, and then sinter each layer, with the probability of forming a defect in the soot increasing with each pass.

The soot processes, VAD and OVD, lend themselves readily to solution doping because the glass boule is already in the form of a porous body. However, there are several critical limitations that complicate the process.

Because the porous boule is typically many millimeters in diameter, soluble dopants migrate to the surface as the solvent evaporates. This creates a pronounced radial gradient in dopant concentration.

The effect of this gradient can be reduced by removing the outer regions of the cylinder. Alternatively, the solute can be immobilized using hypercritical drying, freeze-drying, or precipitation. Because dehydration and sintering of the boules occurs below about \(1400^\circ\)C, there is a strong tendency for the doped bodies to devitrify before densification is complete.

This can limit aluminum concentration to only a few percent to avoid formation of mullite. As is shown later in this chapter, Er-doped fiber has optimum spectral properties when the Al concentration is greater than 10 mol%. This level is difficult to achieve with outside processes.

The solvents most commonly used are water and alcohols. Water is often preferred because it provides higher solubility limits and lower viscosity at high concentration, which is important for faster adsorption.

Various acids can also be used as a solvent and may provide an added advantage of lower pH, which can potentially enhance dopant adsorption. For example, phosphoric acid was used to prepare fiber RE concentration up to 2.8 mol% while serving as a precursor for phosphorus.

Despite the relative simplicity of water and alcohol solution doping, questions of glass homogeneity and the influence of process variables on glass quality remain and little published experimental data exist to clarify the issue.

It is possible that evaporation of the solvent leaves a crystalline residue of hydrated RE salts in the pores of the frit, which form clusters or microcrystallites of refractory RE oxide upon heating and sintering.

Even if the halide residue is washed away with acetone or other solvents, the ion adsorption preferentially occurs inside the pores of the frit, so it is possible that areas of highly doped glass are formed after these pores collapse during sintering. This doping technique would then be inherently prone to some initial nonuniformity, with the frit nanostructure and pore size playing an important role.

Adsorption during solution doping can be of a physical or chemical nature, with indirect experimental evidence supporting the prevalence of the latter. For example, efficiency of adsorption strongly depends on the type of metal ion. While some ions such as lanthanides are incorporated quite easily, others like transition metal ions are hardly adsorbed at all.

There exists incorporation interdependence between ions of different species, with aluminum, for example, enhancing the adsorption efficiency of the RE ions. The ion size does not seem to play a role, as would be expected if only physical trapping was taking place.

Solution acidity is also quite important with the pH range over which maximum adsorption occurs, strongly depending on the cation in question. Surface cation sorption onto silica is often explained by an ion-exchange mechanism, with silica acting as an ion exchanger of the weakly acid type.

Assuming that chemical bonding and ion-exchange reactions are mostly responsible for cation adsorption during solution doping, a linear dependence between solution strength and cation adsorption efficiency implies the existence of equilibrium of the exchange reaction between ‘‘free’’ cations in the solution and cations bonded to the frit.

The equilibrium is determined by both relative concentration of cations and the bond strength between them and the frit. Saturation of the cation incorporation at higher solution strengths may suggest a decrease of available bonding sites.

4.2.3. Aerosol Doping

The limited availability of volatile glass reagents led to the development of liquid aerosol methods that do not rely on the vapor pressure of the precursors. Bulk glasses, including silicates, were made by flame hydrolysis of the vapors of glass precursors while being co-doped with various metal ions through aerosol delivery of nebulized solutions to the reaction zone.

The same approach using flame hydrolysis of chloride vapors and aerosolized aqueous solutions of metal salts was used for fabrication of passive optical silica fibers.

It was observed that in bulk glasses, because of poor mixing of glass precursor vapors and aerosol, the presence of large aerosol particles in the aerosol stream lead to non-uniformity and solid inclusions of the final glass.

For the fiber fabrication, a specially designed multiconduit burner was used to improve the mixing of incoming reagent streams and to increase the dopant content of fiber preforms.

In these techniques, vapors of liquid glass-forming chlorides, such as SiCl₄, GeCl₄, and POCl₃, were used as glass-forming precursors. This, in addition to the observed inhomogeneity due to the poor mixing with aerosol, may also hinder efficient incorporation of metal oxides because of the production of high amounts of chlorine as a byproduct of the oxidation reaction.

These problems are avoided using an aerosol-doping technique that combines all glass components in one solution without significant amount of chlorine. It can be applied to both MCVD and OVD. For the MCVD setup, an ultrasonic nebulizer filled with a solution produces fine (4-10 μm) aerosol mist that is delivered by a carrier gas to the reaction hot zone.

In Fig. 7.4, we see the results of nebulization from a 1.6-MHz transducer. The nebulization rate from a single transducer can be as high as 2 g/min, which is more than adequate for core doping of single-mode preforms.

 

 

Similar to the arrangement shown in Fig. 7.3, an injection tube carries the aerosol from the nebulizer into the substrate tube. To maintain constant spacing between the injector exit and the hot zone, the tube is moved axially along with the burner. This produces a more uniform deposit.

As with other nonvapor methods, some post-deposition processing is required before sintering. Depending on the nature of solution, post-processing steps may include removal of residual carbon from the soot and drying.

Because this is carried out with a substrate tube on the glass MCVD lathe, processing is trivial and far less complex than the drying process necessitated by OVD fabrication. Dry and low-loss fibers with high RE concentrations of 10 wt% and higher can be routinely fabricated.

Unlike solution and sol-gel doping, aerosol doping does not require removal and subsequent remounting of the substrate tube on the lathe. Other additional steps like soaking, draining, and drying for solution doping are also unnecessary.

At the same time, the deposition efficiency depends on the physical and chemical properties of a particular solution, whereas axial uniformity requires control of process parameters, just as in vapor deposition.

The same technique was modified for use in the OVD. While the described high-frequency nebulizer can be successfully used in both MCVD and OVD setups, in the OVD it can be replaced with a lower frequency ultrasonic atomizer that produced larger (up to 70mm) aerosol droplets, providing higher delivery rates of material.

Because the solution is fed directly into the nozzle and immediately atomized at the nozzle tip, the requirements on solution viscosity and solvent evaporation rates are greatly relaxed.

Two basic kinds of solutions are normally used: inorganic and organic. Inorganic solutions with metal halides and organic solutions with metal alkoxides and salts are similar to the solutions used for solution doping and the sol-gel method, respectively.

Tetraethyl-orthosilicate (TEOS) is most often used as a silica precursor in organic solutions. It is normally mixed with organic solvents used to dissolve various metal organic compounds, including precursors for aluminum, REs, phosphorus, boron, germanium, or any other chemical elements and their combinations.

This makes the process extremely accommodating as to which chemical element can be doped in the glass because almost any element can be successfully put in a solution with the appropriate combination of a solute and solvent.

For example, TEOS can be combined with other precursors for glass-forming oxides, such as germanium and boron ethoxides, for fabrication of photosensitive fibers from one solution.

Fibers co-doped with both boron and germanium oxides were successfully fabricated with concentrations estimated to be more than 10 mol% of each oxide. Simultaneous co-doping of such glasses with RE ions is also possible.

It is also to be noted that many organic precursors do not have distinct boiling points, so when they enter the hot zone in either MCVD or OVD, they decompose.

Thus, the oxides are formed from partially dissociated precursors. This, along with initial homogeneity at the molecular level in the precursor liquid, leads to a more homogeneous glass structure and tends to minimize clustering.

There are several important general constraints on choice of solution chemistry. In addition to mutual solubility and miscibility, solutions should have low viscosity and surface tension to enable efficient mist formation.

The material transport of chemicals from the solution to the reaction zone should predominantly proceed through the aerosol and not the vapor phase, so the vapor pressures of the components should be low.

In the aerosol process, evaporation of components with relatively high vapor pressure leads to changes in solution composition over time and may affect nebulization and deposition efficiencies, as well as glass composition. Low mutual reactivity is also quite important, especially if such reactions in the solution lead to precipitations or increased viscosity.

4.2.4. Nanoparticle Doping

A process very similar to the aerosol approach as applied to the outside process OVD has been termed direct nanoparticle deposition (DND). It, too, is based on the combustion of gaseous and atomized liquid raw materials in an atmospheric oxy-hydrogen flame.

As shown in Fig. 7.5, the reagents include both the standard refractive index changing materials such as aluminum and germanium, as well as other dopants such as the REs.

 

 

Oxidation and hydrolysis in the flame produce doped glass particles, which are collected on a target and then sintered using conventional methods. The particle formation process depends on parameters such as the vapor pressure of the metals, the temperature and temperature distribution in the flame, gas velocities, droplet route through the flame, and the Gibbs free energy of the raw materials.

Particle size measurements show a single-peaked particle-size distribution, which indicates that the particles are formed through evaporation–condensation process with a narrow size distribution, which can be adjusted between 10 and 100 nm.

The large number of layers deposited onto the target rod allows accurate and independent control of the radial index difference and active dopant profiles in the fiber core.

 

4.3. Summary of Rare Earth-Doped Fabrication Techniques 

A review of RE-doped fiber fabrication methods was published in the early days of RE fiber commercialization. This work included a chart showing a comparison of the various methods. In Table 7.1, we present a somewhat updated version of this chart.

 

 

5.  Erbium-Doped Fiber 

Before the invention of EDFAs, the effects of optical loss in a transmission system were compensated every few tens of kilometers by an electronic repeater. At each repeater, the signal was detected, electronically filtered, and retransmitted by a new laser diode.

This architecture is expensive and restricted to a single channel at a single wavelength. Network architecture changed dramatically when single-mode EDFAs for direct optical amplification of 1.5-μm signals were simultaneously developed by AT&T Bell Laboratories and the University of Southampton in 1987.

The efforts directed at development of techniques for producing high-quality RE fibers suddenly bore fruit as Er amplifiers emerged to fill a critical need. Optical amplifiers are a tremendous advantage because they directly amplify the optical signal, support multiple wavelengths, and are independent of bit rate.

By 1989, the first EDFA pumped by an efficient semiconductor laser had been demonstrated, and in 1994, the first undersea optical amplifiers were deployed by AT&T Submarine Systems in a communication system between Florida and St. Thomas.

By 1995, the first trans-Atlantic communication system using optical amplifiers was deployed, followed soon by trans-Pacific systems and the ubiquitous deployment of EDFAs in terrestrial communication systems.

The development of EDFAs enabled an explosion in the capacity of fiber optic communication systems. When the first optically amplified systems were deployed, the aggregate data rate per fiber was only a few gigabits per second. Current communications systems now transmit hundreds of gigabits per second while many laboratory demonstrations have exceeded 10 terabits/sec (Tbps).

The need for facile amplification of optical signals arose as transmission bandwidth began to outstrip the performance of electronics and erbium-doped amplifiers filled this niche.

This occurred just as the industry was migrating from signal wavelength of 1310 to 1550 nm to exploit the lower fiber attenuation that resulted from improved fiber manufacturing. It is a wonderful coincidence of nature that erbium fits this wavelength window and performs with simplicity and efficiency.

 

5.1 Principles of Operation

As illustrated in Fig. 7.1, erbium-doped silica can be pumped around 980 or 1480 nm to excite the Er ions and produce emission about 1530 nm. Emission can be stimulated by injecting a signal around 1530 nm, allowing creation of a traveling wave amplifier, as illustrated in Fig. 7.6

 

 

A simple optical amplifier consists of a signal source, a short length (5–20 m) of Er-doped fiber, a pump diode, a multiplexer for combining a signal and the pump, and optical isolators to prevent undesirable effects from backward- scattered light. Because the system is all optical, amplification is independent of bit rate and can operate over many channels simultaneously.

Because the signal is continually reabsorbed by the ground state of the Er ion, the spectral shape of emission depends critically on the details of the population inversion of the Er ions, as illustrated by the emission spectra shown in Fig. 7.7.

 

 

Note that the spectra nicely cover the lowest loss region of silica around 1550 nm, shown in Fig. 7.1. The broad emission of Er readily extends from 1530 to 1565 nm and defines the so-called ‘‘amplifier C-band.’’

Because the emission spectrum extends to long wavelength, slight changes in amplifier architecture and the population inversion can extend the spectrum into the L-band, from 1565 to about 1615 nm. The number of channels supported over this bandwidth obviously depends on channel spacing, but more than 80 channels at 10 Gbps can be readily accommodated in a single fiber. Tighter channel spacing can increase this even further.

The excellent performance of EDFA is a direct consequence of the energy level diagram. Because the transitions are strictly dipole forbidden but allowed due to slight crystal field asymmetries caused by the local environment of Er in a solid, the excited state lifetime is quite long, around 10 ms.

In addition, because there are no states below \(^4I_{13/2}\), the only way for the ion to relax back to the ground state is either radiatively by emission of photon or nonradiatively by coupling energy into the vibrational modes of the glass network.

However, since the average phonon energy of silica is about 1100 cm\(^{-1}\), bridging the energy gap requires five phonons. Because the probability of decay decreases exponentially with the number of phonons, the nonradiative lifetime is very long. As a consequence, Er is an excellent energy storage medium and optical conversion efficiencies very close to theoretical maximum are readily achieved.

The optical gain experienced by the signal can be represented as

\[\tag{7.1}G=4.343\Gamma{L}N_0[\sigma_e(\lambda)-(\sigma_a(\lambda)n_2-\sigma_a(\lambda))]\]

where gain is expressed in decibels, \(\Gamma\) is the spatial overlap between optical field and dopant distribution, \(L\) is fiber length, \(N_0\) is the concentration of RE, \(\sigma_e\) and \(\sigma_a\) are the emission and absorption cross-sections, and \(n_2\) is the population of excited RE ions.

This simple equation illustrates the impact of several fiber parameters, which make up the discussion in this section:

• The overlap integral, which is determined by waveguide design
• The absorption and emission cross-sections, which are determined by glass composition
• Excited state population, which is determined by the first two bullets plus device architecture.

The goal of fiber design is to optimize the transfer of energy from pump to signal and to control the spectral characteristics of gain, including both the overall bandwidth and the flatness of the spectrum.

A critical aspect for telecommunications applications is generation of noise due to spontaneous emission, but this is highly dependent on the specifics of amplifier architecture and is beyond this discussion.

 

5.2.  Fiber Design Issues

The energy level diagram in Fig. 7.1 illustrates the three-level nature of the Er system. That is, the ground state is also the terminal emission level, which means that the signal is constantly reabsorbed as it transits the fiber and full population inversion (\(n_2=0\)) cannot be achieved.

Without pump light to excite the ions, the fiber is highly absorbing, with about 5–10 dB/m absorption given typical dopant levels. As pump power increases, however, the population of ions in the ground state, and hence, the absorption, decreases.

At the threshold power for a particular wavelength, the fiber is transparent (\(G=0\)), with just as many photons absorbed as emitted. This competition between absorption and emission implies that high optical intensity will more fully invert the erbium population and increase gain.

In the early days of amplifier development, the limited available pump power (tens of milliwatts) put a premium on the gain slope efficiency, expressed as dB of gain per mW of pump power.

Achieving high slope efficiency is readily accomplished by maximizing the pump intensity seen by the Er. The most effective route is to increase the index of the core (expressed as \(\Delta\), the difference between core and cladding refractive index normalized by the core index) to reduce the mode field diameter. For example, \(\Delta\) of 2%, compared to 0.35% for standard fiber, are typical and are realized simply by increasing the germanium concentration.

In addition, for maximum pump efficiency, the cutoff wavelengths are tuned to minimize mode-field diameter. Optimum cutoff wavelengths occur at 800 and 900 nm for pumping at 980 and 1480 nm, respectively, and are roughly independent of \(\Delta\).

Further increase in slope efficiency is provided by confining Er doping to the central part of the core, as illustrated in Fig. 7.8. Such high \(\Delta\)-confined dopant cores are useful for application with limited pump power, such as remotely pumped or battery-operated amplifiers, because slope efficiency can exceed 12 dB/mW.

 

 

However, there are several impairments of such designs. High \(\Delta\) cores have an anomalous scattering loss, which varies as \(\Delta^2\) as \(\Delta\) exceeds about 1.2%.

This loss is due to scattering from thermodynamic fluctuations in dopant concentration and irregularities at the core–clad interface, and although it can be reduced by grading the index profile of the core and drawing the fiber at lower temperature, it cannot be eliminated.

Although a typical required length of erbium-doped fiber is only about 20 m, losses can approach 0.01 dB/m, causing a noticeable penalty in performance. The impact of higher background loss is exacerbated by the longer fiber length required for high \(\Delta\) designs. Because the overlap between pump light and doped region is reduced by a factor of more than two for such fibers, the fiber length must be proportionally increased.

A second concern raised by the high-delta small-core fiber is increased loss when spliced to a standard fiber. Because of the small mode-field diameter of erbium-doped fibers, typically less than 3 μm, losses of more than 3 dB may be incurred upon butt coupling to dispersion-shifted fibers.

However, the mode-field diameter can be altered during fusion splicing by extending the duration of the arc to tens of seconds. The extended exposure time at high temperature allows significant diffusion of the highly doped core, reducing the effective index and increasing the core diameter.

The mode-field diameter of the standard fiber will also increase, but at a slower rate. For each pair of fibers, there is an optimum splicing schedule to minimize splice loss. Splice losses less than 0.1 dB are readily achieved.

Finally, although high \(\Delta\) fiber is efficient at low power, at higher power several excited state interactions come into play and create additional loss mechanisms. This is illustrated in Fig. 7.9, which shows gain as function of pump power for a range of core \(\Delta\).

 

 

At high pump intensity, the rate of nonradiative decay from the \(^4I_{11/2}\) state to the \(^4I_{13/2}\) state becomes a limiting factor, and excited state absorption from \(^4I_{11/2}\) promotes the Er ion to higher energy levels. These levels relax nonradiatively back to the \(^4I_{11/2}\), resulting in loss of one photon.

In addition, since Er is never homogeneously distributed in the glass, energy can migrate from ion to ion until it finds a suitable trap to decay nonradiatively. The higher pumping intensity increases the probability that this can occur. As can be seen in Fig. 7.9, these effects occur even for modest pumping powers, so optimum fiber design depends on the operating power level.  

As available pump power has increased over time, the requirement on reduced mode-field diameter has relaxed, so \(\Delta\) is typically in the range of about 1%, although communications applications with higher optical output signal power use fiber with even lower \(\Delta\).

These designs do not require confined dopant distribution to improve efficiency. On the contrary, the distribution of Er may be reduced at the center of the core or extended into the cladding to manipulate the interaction between pump and signal intensities to control the population inversion.

As illustrated in Fig. 7.7, since the emission spectrum is highly dependent on the population inversion, such schemes can be used to tailor the emission spectrum.

 

5.3. Fiber Composition Issues

The amazing initial success of optical amplifiers inspired considerable effort to further improve fiber performance. The primary goals were to broaden the emission bandwidth to support even more signal channels, and to flatten the gain spectrum so that each channel behaves similarly.

Despite heroic efforts, however, the technology remains dominated by the first materials explored: Al-doped silica, with Ge used to produce the desired index profile. The atomic structure of Er, which produces the long excited state lifetime, and well-defined absorption and emission spectra also conspire to make these features relatively immune to changes in local glass environment.

Many elements of the Periodic Table have been explored, with most eliminated because they cause excess optical attenuation in silica. The remaining few such as alkalis, alkaline earths, and P, Sb and Bi have only modest influence, and many co-dopants, such as phosphorus and the alkalis, narrow rather than broaden the spectrum.

Despite much work, the dominant tweaks beyond waveguide design discussed in the previous section remain refinement of the Er and Al concentrations.

The most critical feature of doping Er into silica is the detrimental effect of clustering of Er ions. In particular, RE ions have low solubility in silica, which means they tend to cluster and even crystallize at concentrations of fractions of 1%.

Close physical proximity of the ions allows energy exchange and several excited state and quenching phenomena, which invariably reduce amplifier performance. The different phenomena come into play under different amplifier operating conditions, but in all cases, the driving design direction is to reduce Er concentration and increase the length of fiber needed in the amplifier.

The choice of ion concentration requires a balance between the detrimental clustering effects and the benefits of reduced fiber length, including less impact from background loss and lower fiber cost and package size.

The high field strength of RE ions results in low solubility in silica and a tendency for the ions to cluster together, even at concentrations of less than 1%. Even before outright crystallization occurs, these clusters exhibit several long-range optical interactions that cause loss of energy.

The most serious effect is a cooperative upconversion process called ‘‘pair-induced quenching’’ in which pairs of ions in the \(^4I_{13/2}\) state combine their energy to promote one ion to a higher level while the other goes to the ground state.

Decay back to the \(^4I_{13/2}\) state is nonradiative and results in loss of one photon. This mechanism is unsaturable and behaves as a strongly wavelength-dependent attenuation. Energy may also be lost through concentration quenching in which excited state energy migrates from ion to ion until it finds a suitable trap to decay nonradiatively.

A higher fraction of clustered ions increases the probability for such decay. Aluminum co-doping is the silver bullet used to homogenize the glass to inhibit scattering losses due to crystallization and inefficiency due to concentration quenching, only a small amount is necessary to improve clustering effects.

However, because the ion–ion interaction occurs over long distance (up to 3 unit cells in the silica matrix), quenching will occur at some concentration even in a homogeneous glass. The onset of quenching typically occurs at a concentration of Er of about 500 ppm.

An additional significant benefit of aluminum doping is the modification of the emission spectrum, as shown in Fig. 7.10.

 

 

Aluminum flattens and broadens the emission spectrum around 1550 nm, thereby decreasing the sensitivity to signal wavelength, and increases the absorption at the pumping wavelength of 1.48 μm. The flatter spectrum is very beneficial for high channel count operation. In this case, very high concentration of Al is most desirable.

Although aluminum doping is beneficial, only limited modification occurs in a silica host. More radical modification requires use of other hosts, such as phosphates, borates, tellurites, and fluorophosphates, as well as nonoxygen hosts such as fluorides, sulfides, and other chalcogenides.

The first of these to be explored in earnest were fluorides. These glasses, of the base composition ZrF₄-BaF₂-LaF₃-AlF₃-NaF (ZBLAN), were discovered in the late 1970s and investigated very actively because they offer the potential of very low attenuation (<0.001 dB/km at 2.6 μm) because of reduced Rayleigh scattering and a low vibrational energy spectrum, which pushes the phonon attenuation edge to long wavelength.

To date, this potential has not been realized because of contamination issues and scattering resulting from the low threshold for crystallization during fiber processing. Contamination is the result of batch melting methods used for preform fabrication, which contrast sharply with gasphase methods used for silica fiber processes, which are free from contact with solid containers and provide intrinsic purification during glass formation.

The lowest losses achieved are in the range of 2 dB/km, which is inadequate for long-distance transmission but suitable for fiber device applications such as amplifiers, which require only tens of meters of fiber length.

As a host for Er, since RE elements may simply substitute for some of the LaF₃ in the base glass network, solubility is not an issue as it is for silicates. Fluorides produce an inherently broader and flatter emission spectrum because of details of crystal field splitting, but the change is only modest and has been insufficient to justify the added cost and complexity of using fluoride fibers.

However, the low phonon energy of fluorides provides an advantage over silica for other RE systems. The vibrational frequency of the glass network is in the range 600-400 cm\(^{-1}\) (compared to 1100 cm\(^{-1}\) for silica), and because the probability of phonon relaxation from an excited state decreases exponentially with the number of phonons required to bridge the energy gap, radiative emission is possible for transitions that would otherwise be quenched. For example, optical amplification can be achieved in Pr at 1310 nm and Tm at 1460 nm.

Because the emission spectrum of REs is dictated by Stark splitting of the intraband transitions, the most effective way to manipulate the spectrum is to increase the polarizability of the local environment.

To this end, heavy elements such as tellurium, antimony, and bismuth are effective, although these are not compatible with standard glass-formation methods. In particular, chlorine is typically used to remove hydroxyl ions (OH\(^{-1}\)) during silica fabrication, but this also removes these elements and makes fabrication of low-loss silica fibers difficult.

In addition, because the allowable dopant concentration must remain low to maintain glass stability, the contribution from these elements is limited. Therefore, it is more effective to abandon use of high silica glass and explore other glass hosts with high polarizability.

Erbium doping of tellurite glasses (TeO₂) fully leverages such an environment, and wideband operation extending almost 80 nm in a single amplifier has been demonstrated.

Although the tellurites are good glass formers and optical amplification is reasonably efficient, the added cost and complication of using such glasses has inhibited further development.

One of the more effective approaches has been to produce a multicomponent antimony silicate glass (MCS) using batch processing to prepare the low-temperature base glasses and a crucible approach to draw the fiber.

As shown in Fig. 7.11, the spectrum is broader than achieved in typical Al-doped silica. Output power exceeding 20 dBm with greater than 80% quantum efficiency has been demonstrated.

Interestingly, the bandwidth is also extended beyond 1610 nm, offering the possibility for adding channels to the L-band, where fiber attenuation is still reasonably low. This occurs because of reduced excited state absorption from the \(^4I_{13/2}\) state. Despite superior spectral properties, this technology lies dormant because current applications do not justify the added complexity of this approach.

 

 

5.4. Short Wavelength Amplifiers

The low-loss transmission window of silica fiber shown in Fig. 7.1 is considerably wider than the spectrum covered by C- and L-band optical amplifiers. This suggests the opportunity for broadening the Er-gain spectrum to lower wavelength or using other RE elements.

The Er emission spectrum in Fig. 7.7 certainly shows the potential for gain far shorter than 1500 nm, but competing emission at the gain peak near 1530 nm renders such amplifiers inefficient and noisy.

A clever solution to quench the amplified spontaneous emission from this peak is to create a waveguide design that cuts off the fundamental mode beyond about 1500 nm. An index profile such as shown in Fig. 7.12 uses a deep trench of carefully controlled width to make the loss of the fundamental mode very sensitive to bending.

This can create a sharp increase in attenuation with wavelength so the fiber operates like a short-pass filter. By tuning the design and bend diameter, the loss edge can be placed to extinguish unwanted 1530-nm emission with little impact on gain at shorter wavelengths.

Such an approach has produced efficient low-noise amplifiers operating in the so-called ‘‘S-band’’ from about 1488 to 1508 nm. This allows amplification of 27 additional transmission channels, and long-haul transmission over 100 km has been demonstrated.

 

 

RE elements other than Er can provide amplification in the S-band. In particular, Tm shows efficient gain in a four-level scheme, as shown in Fig. 7.13, as long as low-phonon energy glasses such as fluorides are used.

Although the terminal \(^3F_4\) state for 1470-nm emission has relatively long lifetime, multiwavelength pumping can be used to manipulate the excited state populations to achieve efficient gain.

The figure shows upconversion pumping at 1100 nm to empty the \(^3F_4\) level. Amplifiers based on such pumping schemes are well studied and have demonstrated excellent performance.

 

 

If amplification around the 1550-nm transmission window is readily accomplished, what about amplification at 1310 nm, a wavelength that is still being actively deployed?

Several possibilities exist for such amplifiers, the dominant ones being Nd and Pr. In silica, emission from Nd is poor because of competition from excited state absorption. However, low-phonon energy glasses such as fluorides and fluoroberyllates have better performance. Unfortunately, however, the peak emission is at slightly longer wavelength, and performance at 1310 nm is rather poor for all-glass hosts.

Significantly better performance can be achieved using a Pr-doped fluoride glass. The energy level diagram in Fig. 7.14 illustrates the four-level nature of the transition responsible for emission around 1300 nm and the close spacing of the intermediate levels.

 

 

In silica, the \(^1G_4\) state would rapidly decay nonradiatively down this ladder, with no optical emission, but the low phonon energy of the fluoride host inhibits nonradiative decay, lengthens the \(^1G_4\) lifetime to about 0.1 ms, and provides relatively efficient gain.

Performance of such amplifiers has been reasonably good, with predictions of high small-signal gain exceeding 40 dB, excellent saturated output power, and quantum conversion efficiency greater than 30%. Although Pr amplifiers were available commercially for a brief period, the applications for 1310-nm transmission are extremely price sensitive and could not justify use of such an amplifier.

 

6. The Co-Doped Er/Yb System

Erbium-doped amplifiers require pumping in narrow wavelength bands around 980 or 1480 nm. To extend pumping into the 1060- to 1100-nm band and allow use of higher power pumps such as solid state lasers made from crystals of Nd:YAG or Nd:YLF, Er may be ‘‘sensitized’’ by addition of Yb.

Pump wavelength from about 900 to 1100 nm may be absorbed by Yb\(^{3+}\), which can transfer the energy to erbium if the glass contains both dopants. Absorption of Yb\(^{3+}\) peaks around 975 nm and populates the \(^2F_{5/2}\) level, as shown in Fig. 7.15.

 

 

Energy may transfer to the \(^4I_{11/2}\) band of erbium, from which nonradiative relaxation populates the \(^4I_{13/2}\) state. Emission and signal amplification is then quite similar to standard Er-doped fiber. Such energy transfer was first demonstrated in an alkali silicate host and later in a phosphate glass.

The efficiency of this sensitization process depends on several factors. The ions must be in close physical proximity for energy transfer to occur, meaning that the dopant concentrations of Er and Yb must be considerably higher than in standard erbium-doped fibers.

In particular, Er concentration is typically approximately 2000 ppm. Note that the pair-induced quenching process described in previous sections results in strong unsaturable absorption peaked around 1530 nm, which effectively shifts the gain spectrum to longer wavelength than in erbium-doped fiber by about 10 nm.

To facilitate energy transfer, the lifetime of the Yb\(^{3+}\)\(^2F_{5/2}\) level must be sufficiently long to avoid spontaneous Yb emission and the lifetime of the Er\(^{3+}\)\(^4I_{11/2}\) state must be short enough to inhibit back-transfer. Both effects occur in phosphate glasses and phosphorus-doped silica, allowing remarkable efficiency. Typical fibers have about 10 mol% P₂O₅. Addition of Al is found to be detrimental, presumably because it associates more closely with the RE ions and diminishes the influence of phosphorous.

Whereas the Er system is well understood and can be simulated with excellent accuracy, the Er/Yb system is more complicated and modeling of amplifier performance is more uncertain.

Simulation involves treatment of more energy levels and the details of energy transfer, but the higher RE concentration also brings more ion–ion interactions into play. At the same time, because the goal of the Er/Yb system is to allow operation at higher power, additional excited state phenomena begin to dominate.

Despite this complexity, current models now have adequate accuracy for most high-power applications. There is limited use for Er/Yb fiber lasers or amplifiers in single-mode operation in telecommunications because the efficiency and operating bandwidth are inferior to erbium-doped fibers.

However, the high pump absorption, around 915–975 nm, allows pumping with very high power diodes, and utility has shifted to architectures that can leverage these broad area pumps, which have single emitter power levels exceeding 6 W.

 

7. Double-Clad Fiber

In the fibers discussed earlier, pump light must be launched into the single-mode core, placing a significant limitation on diode power because of the amount of current coupled into the active area of the diodes and restrictions on facet intensity to minimize damage.

A clever solution to these limits is to break the constraint on single-mode diode pumping. By surrounding the fiber cladding with a second cladding that has a lower index than the inner cladding, the entire inner cladding region becomes a waveguide, as shown schematically in Fig. 7.16.

Pump light introduced into this region propagates along the fiber, occasionally crossing the core where it is absorbed by, and transfers energy to, an optically active RE dopant.

This allows high-power strongly multimode pump light to be efficiently converted to a diffraction-limited output beam, with an enormous increase in optical brightness. Such a design, called a ‘‘double-clad’’ or ‘‘cladding-pumped’’ device, was first demonstrated as a 1060-nm neodymium laser pumped by a collection of 807-nm broad-area diodes.

 

 

To collect the greatest amount of pump light, the second cladding should have as low an index as possible. This is best achieved using a low index polymer cladding directly on a silica fiber, for which the numerical aperture (NA) is around 0.45.

With a modest facet intensity of only 5mW/μm\(^2\), more than 500 W could theoretically be coupled into a 180-μm diameter fiber with NA = 0.45.

In a double-clad laser, multimode pump power must cross the core to be effective. In circular fiber, this is inefficient because much of the light follows helical paths and is not absorbed. To prevent this, the fiber is made noncircular so that fewer helical modes are supported and all rays eventually cross the core.

An alternative and more accurate viewpoint is that the cladding waveguide supports more modes that have nonzero power at the centerline, so a larger fraction of the supported modes experience absorption.

Because only the core absorbs pump light, the effective absorption rate of the fiber, \(\alpha_{clad}\), is roughly equal to the core absorption times the ratio of core area to cladding area, \(\alpha_{clad}=\alpha_{core}\cdot{A}_{core}/A_{clad}\). This relation assumes that the cross-section of the fiber is uniformly illuminated and that all available optical modes are excited.

Because the core absorption at the pump wavelength is typically several decibels per centimeters for common dopants (Yb, Tm, Nd), laser lengths are typically less than 100 m and in many cases only a few meters.

Note that the large pumping area results in relatively low pump intensity compared with the signal intensity, which is guided in the central core. This poses limits on fiber and amplifier design if there is significant ground state signal absorption. For example, Yb-doped double-clad lasers operating at 980 nm where there is high absorption require very short fiber lengths and high pump intensity to achieve population inversion because Yb at 980 nm is a three-level system.

Operation in regimens with minimal ground state absorption, such as Yb at 1060–1120 nm or Nd at 1060 nm, is much more efficient and has greater design flexibility, because in this wavelength regimen, they are quasi-four level systems.

The basic double-clad structure may consist of a laser if a resonant cavity is present, such as provided by fiber Bragg gratings as shown in Fig. 7.17a, or a signal amplifier if a suitable pump-signal multiplexer is provided.

In either case, pump light from high-power broad-area diodes must be coupled into the cladding of the active fiber. Multiplexing may be accomplished using lenses in conventional free-space optics, whereas an all-fiber architecture may use a fused-fiber pump combiner, as shown in the figures, V-groove pump injection, or side-pumping in which the pump and signal fibers lie side-by-side in a common low-index polymer coating.

Each method has its advantages and proponents. The amplifier architecture can have one or more stages and an array of interstage components depending on the required operation.

 

 

The pump combiners and double-clad fibers should preserve pump brightness as efficiently as possible, where brightness is approximated as the product of fiber area and the square of NA, \(A_{clad}\cdot{NA}^2\).

This puts a premium on the NA of the inner pump cladding. For silica-based fiber, materials constraints limit the NA if both the inner and the outer claddings are glass. Higher NA requires use of a low-index polymer to define the outer cladding in addition to protecting the glass surface from mechanical damage.

Fluorinated acrylate and silicone polymers replace the standard fiber coating, achieving NA from 0.45 to 0.60 with no compromise in mechanical properties. To pump these fibers, broad-area diodes are commonly pigtailed with fibers with NA approximately 0.22, allowing reduction in cladding area of a factor of more than 4 in multiplexing to the gain fiber.

This means that in the fused bundle approach, the pigtails of 19 broad-area diodes with 0.22 NA pigtails can be bundled together, fused, and tapered to an output diameter only about 1.6 times the diameter of an individual pigtail fiber. At the fiber exit, the beam is typically diffraction limited and the fiber can be spliced to other fibers using conventional techniques.

Double-clad fiber lasers and amplifiers based on the aforementioned concept are increasing in performance and continue to penetrate wider markets and applications.

Fiber lasers, in particular, offer several very attractive benefits over more conventional lasers, the most notable being better heat dissipation and relative immunity to detrimental wave-guiding effects.

Fiber lasers can be compact, rugged, reliable, and efficient and have low cost of ownership. Pushing fiber technology to higher performance in terms of average and peak power will allow greater penetration into existing markets and enable new directions.

This requires new developments in fiber and component design if fibers are to replace established solid state technology or create new niche applications.

 

7.1. Limitations of Fiber Lasers

Design of a fiber laser capable of generating high pulse energies with high average and peak power requires careful attention to limitations from the extractable energy of the gain medium and nonlinear limits of the fiber.

The saturation energy of the gain medium is a key parameter for determining how much energy can be stored in an amplifier and is given by

\[\tag{7.2}E_{sat}=\frac{h\nu_sA_{eff}}{(\sigma_{es}+\sigma_{as})\Gamma_s}\]

where \(\sigma_{es}\) and \(\sigma_{as}\) are the emission and absorption cross-sections at the signal wavelength, \(h\nu_s\) is signal energy at frequency \(\nu_s\), \(A_{eff}\) is area of the active doped region, and \(\Gamma_s\) is signal overlap with the active dopant.

Although long fiber length is beneficial in managing heat dissipation and increasing pump absorption, long length becomes an impairment because of nonlinear interactions.

Two deleterious nonlinear effects of concern are stimulated Brillouin scattering (SBS) and stimulated Raman scattering (SRS). Both rob power from the signal and can cause catastrophic damage if allowed to build uncontrollably.

For SRS, the threshold for peak power \(P_{th}\) before onset of serious Raman scattering in passive fibers is given by

\[\tag{7.3}P_{th}=\frac{16A_{eff}}{g_RL}\]

where \(A_{eff}\) is the effective mode area of the fiber, \(g_R\) is the Raman gain coefficient, and \(L\) is the fiber length.

For example, for a fiber with 25-μm core diameter, \(P_{th}\cdot{L}\sim70kWm\). Because typical fiber lengths exceed 5 m, this indicates peak powers of about 20 kW before Raman scattering becomes severe.

SBS arises from interaction of the signal with longitudinal acoustic modes of the fiber, causing part of the signal to be reflected backwards. Similar to the case of SRS, the threshold condition for SBS can be written as

\[\tag{7.4}P_{th}=\frac{21A_{eff}}{g_BL}\left(1+\frac{\Delta\nu}{\Delta\nu_{SiO_2}}\right)\]

where \(g_B\) is the Brillouin gain coefficient, \(\Delta\nu\) is the bandwidth of the signal, and \(\Delta\nu_{SiO_2}\) is the Brillouin bandwidth of the fiber (~50MHz for silica).

If the signal has bandwidth comparable to \(\Delta\nu_{SiO_2}\), then for a fiber with 25-μm core diameter, \(P_{th}\cdot{L}\sim350Wm\). This is obviously a severe constraint and mitigation is necessary for narrow line-width lasers.

Although narrow line width is important for many applications in spectroscopy and frequency conversion, for materials processing, the line width is less important and the threshold can be increased considerably.

 

7.2. Methods to Improve Performance 

7.2.1. Core Design

For both SBS and SRS impairments, as well as other limits like four-wave mixing and self-phase modulation, mitigation is possible by increasing the modal area and decreasing the fiber length.

To increase mode area, the core diameter can be increased while the core index is decreased to maintain single-mode operation. For example, a core with \(\Delta{n}=0.0012\) will remain single mode at 1060 nm up to core diameter of about 20 μm. At such a low core index, the fiber becomes sensitive to external perturbations, which can cause excessive bend loss. This is generally considered the lower limit in index before severe problems with fiber handling and fixturing set in.

For larger core diameter, the fiber will support multiple modes. In some cases, this is acceptable, but generally single-mode performance is preferable, especially where the output beam requires diffraction-limited focus, a high level of collimation, or where the beam is to be used for frequency conversion.

In such cases, because the higher order modes are inherently more sensitive to bending than the fundamental mode, they can be stripped by coiling the fiber without incurring excessive loss of the fundamental mode.

To enhance the ‘‘leakiness’’ of the higher order modes, cladding features such as holes or raised index rings can be used. If the effective index of an unwanted core mode is matched to that of a cladding mode supported by the added features, energy can mix between the regions and cause high mode extinction. This method was successfully applied to a fiber with effective mode area of about 1400 μm\(^2\).

However, as core diameter increases, the difference in propagation constant or effective index between modes decreases and mode mixing becomes severe. Because the number of modes and the power transfer rate between modes vary quadratically with core diameter, there is a practical limit in core size dictated by excessive power transfer, as is well known from studies of multimode transmission fiber.

A practical limit is about 25 μm if the refractive index contrast between core and cladding are kept as low as permitted by bend loss. Thus, there is a practical limit to increasing core diameter while maintaining effectively single-mode operation. Use of microstructured fiber to increase the mode area has been discussed, but the mode diameters are not significantly larger than has been achieved in solid fibers with comparable effective refractive indices.

As core diameter increases, the mode-field diameter also increases, but at a slower rate, as shown in Fig. 7.18. Around 15 μm, the mode-field and core diameters are approximately equal, but for a 40-μm core, the mode field occupies only about half the core area.

The effect is relatively insensitive to core index. This poor overlap between the mode and the core can generate excessive amplified spontaneous emission if the entire radius of the core contains RE dopant. However, as explained for erbium-doped fibers in Fig. 7.8, confinement of the RE dopant can improve efficiency, in some cases by up to 10 percentage points.

 

 

A further problem with large mode-area designs is the well-known but often overlooked property of bend-induced mode distortion. From a mode propagation point of view, bending of a fiber is analogous to tilting the refractive index profile, transforming a step index, for example, into a profile. This is illustrated in Fig. 7.19, which shows the mode-field diameters for bend (solid lines) and unbent (dotted lines) configurations.

Because the mode is increasingly sensitive to features at large radius, bend distortion increases with core diameter. As seen in the figure, the 30-μm core experiences little change on bending, whereas the 50-μm core shows almost 50% reduction with even a modest 20-cm diameter bend.

This distortion has profound implications for packaging of large mode-area fibers. This effect can be avoided using non–step-index profiles. For example, a parabolic core profile is immune to such distortion (a tilted parabola is still a parabola).

 

 

Modification of the core index profile can also be used to resolve many of the other issues discussed earlier. For example, step-index designs produce Gaussian mode profiles that do not fully fill the core and have high intensity at the center.

By adding a high index ring to the periphery of the core, as shown in Fig. 7.20, the mode is drawn outward and flattened. This increases the effective mode area, reduces the peak intensity, and provides better overlap between the mode and the core. Such mode-flattened designs achieve a five times increase in nonlinear threshold.

Despite this improvement, several additional problems arise. While the fundamental mode has better overlap with the core, the higher order modes, such as LP\(_{11}\) and LP\(_{02}\) are stabilized by the high index ring and become more difficult to remove by bending.

These features also exacerbate the distortion caused by bending because the ring becomes a more dominant feature on one side of the profile. As a consequence, mode-flattened designs have the greatest mode distortion sensitivity of any other design.

In addition, because the mode profile is highly non-Gaussian, coupling to a conventional step-index fiber can result in exceedingly high loss and is often undesirable for the output beam. Although this is problematic, solutions exist and are discussed in the following subsections.

 

 

7.2.2. Microstructure Fiber

The design constraints discussed in the previous section can be relieved by adding air holes to the cladding. First used in 1974, holes add a degree of freedom in waveguide design for controlling cladding index and mode propagation.

This can open the design space for achieving higher performance with larger core area, shorter fiber length, better mode purity, and potentially more robust device operation.

Microstructure fiber has been used to demonstrate an assortment of waveguide phenomena, including supercontinuum generation in small-core, extremely high index waveguides, endlessly single-mode operation in which higher order modes are suppressed, extremely bend-insensitive fiber designs, microfluidics, and even true photonic band-gap operation. Applied to RE-doped gain fibers, the primary design goal has been to increase the effective area beyond levels practical with solid fibers.

The addition of holes to the cladding reduces the average refractive index of the cladding and can render the cladding index wavelength dependent. For suitable structures in which the ratio of hole diameter to hole spacing is less than about 0.4, the cladding index approaches that of the core index and prohibits propagation of any higher order modes.

In essence, the fiber can become single mode at all wavelengths, a feature not possible in solid fibers. This phenomenon was also thought to allow operation at arbitrary mode-field diameter, offering breakthrough performance for fiber amplifiers.

However, for large core size, the effect of the holey cladding is simply to reduce the average index and the fiber behavior is very similar to a conventional low NA waveguide. Thus, addition of holes in this design regimen does not provide relief from bend sensitivity or mode-coupling issues plaguing solid fiber.

To overcome these issues, the fibers can be made very rigid to inhibit microbending and held straight to avoid bend loss. Such rodlike fibers have achieved very high levels of performance, but their practicality remains questionable because of packaging and free-space alignment issues.

A second design regimen using holes can be defined based on higher order mode suppression. If the holes are large and few, higher order modes experience significantly greater bend loss than the fundamental mode, allowing large core operation with an effectively higher core index. This reduces the bend loss of the fundamental mode and inhibits mode coupling.

Fibers based on this principle offer a practical improvement over conventional fiber, with core area around 1417 μm\(^2\) and excellent immunity to bend loss having been achieved. However, just as for conventional large core solid fibers, this design still suffers from severe bend-induced mode distortion described earlier.

 

 

7.2.3. Concentration-Induced Problems

As discussed earlier, in addition to increasing the effective area of the signal, high-power devices can avoid nonlinear limitations by using shorter fiber lengths. This is readily achieved by increasing the concentration of RE dopants.

Unfortunately, just as erbium-doped fibers suffer from pair-induced quenching if the ion concentration is too high, other RE ions show deleterious concentration-induced problems as well.

For example, Tm is known to photo-darken in an aluminum-doped host when exposed to 1064-nm light. The rate of photo-darkening depends on the light intensity to the power of 4.7. Also, in neodymium-doped silica fibers, if the Nd concentration exceeds about 7 wt%, phase separation occurs, resulting in high scattering losses.

Even for relatively low concentrations, however, an excited Nd ion can transfer part of its energy to an ion in the ground state, placing both ions into an intermediate energy level from which nonradiative decay occurs. This cross-relaxation process limits the concentration of Nd in a silica host to only a few hundred parts per million.

In Yb-doped fibers, the workhorse of high-power fiber lasers, because the energy levels in a dielectric host consist of only two manifolds, there are few possibilities for quenching phenomena.

However, when a highly Yb-doped fiber is exposed to intense pump radiation, the signal degrades over time. This photodarkening is likely due to formation of a color center in the glass and appears as a strong absorption at visible wavelengths, accompanied by a strong absorption around 975 nm.

Although the mechanism for photo-darkening has not been fully resolved, a number of studies have probed various aspects of the problem. Similar to other RE ions at high concentration, excited state decay of Yb can be decomposed into an initial rapid decay, followed by a long fluorescence lifetime. The latter is associated with isolated Yb\(^{3+}\) ions in the glass matrix, with lifetimes from 0.8 ms in an aluminum-rich host to about 1.2 ms in a phosphorus-rich host.

The fast component with lifetime of less than 200 μs appears to be independent of host composition and is likely the result of a nonradiative transition. The fast component is not found in fibers with low Yb concentration.

Although Yb exhibits cooperative luminescence in which two excited ions combine energy to produce emission from a virtual excited state, the fast component of lifetime indicates that the behavior of Yb is more complex than expected from a simple ion embedded in a dielectric host.

When exposed to only 150 mW of pump light at 975 nm, a single-mode core with 8-μm diameter can exhibit a rapid reduction in transmitted power, even with fiber length as short as 30 cm. Note that this optical intensity is equivalent to about 100 W of pump launched into a double-clad fiber with a 200-μm outer diameter.

The time trace of 975-nm transmission through two fibers of different hosts and roughly the same Yb concentration is shown in Fig. 7.22a.

 

 

Note that pump throughput normalized to the initial power, \(T_0\), initially decays very rapidly and appears to saturate. This behavior suggests a kinetic process that depletes a population of precursors and creates some form of defect, perhaps a color center.

Based on the behavior of similar phenomena such as decay of UV-written Bragg gratings, it is likely that the population of precursors has a distribution of activation energies, with higher optical intensity reaching deeper into the distribution to form more color centers. For the Ge + F composition shown in the figure, the activation energy for defect formation apparently is relatively low.

Although the decay of 975-nm transmission is accompanied by strong absorption in the visible (Fig. 7.22b), the correlation in attenuation between both spectral regions is very sensitive to host composition.

Note that the Ge + F doped fiber has relatively little change in visible attenuation despite catastrophic attenuation at 975 nm. Because of this, it can be misleading to use the change in visible attenuation as a metric for photo-darkening.

This is unfortunate because the visible spectrum is quite easy to measure or monitor, but it does indicate that the color center is very sensitive to glass host, unlike the usual spectra of typical RE ions, which behave like isolated trivalent ions embedded in a glass host.

Note also in Fig. 7.22b that the tail of the absorption feature in the visible does not extend into the pump or signal wavelengths and, thus, is not responsible for the degradation in amplifier or laser performance. This suggests some phenomenon related to the Yb-excited state.

The dependence of photo-darkening on optical intensity has been studied using several methods. Early work indicated a strong unsaturable absorption associated with the 975-nm absorption peak in Yb.

Also, because photo-darkening appears to result from the incidence of pump light rather than signal light at wavelengths beyond about 1020 nm, the \(^2F_{5/2}\) state must be involved in defect formation.

By exposing sets of fibers to varying intensity of 920-nm light at constant temperature and using a numerical model to calculate the Yb population inversion, the change in attenuation at 633 nm is found to vary with population inversion to the seventh power.

Thus, CW fiber lasers with limited population inversion are much less susceptible to degradation than pulsed lasers, which experience high inversion between pulses. As described earlier, the degree of photo-darkening also increases with increasing Yb concentration.

To further probe the defect state, photo-darkened fibers were heated to 500\(^\circ\)C in air and found to recover completely. On the other hand, unexposed fibers heated in H\(_2\) gas showed growth of a strong absorption band in the visible, which was not altered by exposure to intense 975-nm light and which could not be annealed by heating in the absence of H\(_2\).

The spectral changes induced by reaction with H\(_2\) were different from those induced photolytically, but one would expect a difference caused by the presence of H\(^+\) near the defect site.

The change in attenuation shown in Fig. 7.23 indicates several emission peaks. The location of these peaks does not agree with those found from cooperative luminescence or other contaminant RE ions and is likely due to fluorescence from the color center.

 

 

These observations, and the ones described earlier, are consistent with a model in which Yb\(^{3+}\) is reduced to Yb\(^{2+}\). The reduced state is responsible for the strong broad absorption band in the visible, which is very sensitive to glass host composition (including the presence of H\(^+\)).

It is also responsible for the fluorescence of photo-darkened fiber. Yb\(^{2+}\) has been studied in several types of fluoride crystals in which it exhibits similar spectral absorption and emission features. Based on this model, Yb\(^{3+}\) is reduced to form a metastable exciton composed of Yb\(^{2+}\) and a trapped hole. Multiphoton excitation for this transformation is likely aided by the presence of nearby excited Yb\(^{3+}\) ions, which contribute energy.

As illustrated in Fig. 7.24, during operation of a fiber amplifier, energy transfer from excited Yb\(^{3+}\) ions to Yb\(^{2+}\) ions results in loss of a pump photon through nonradiative decay at the defect.

The formation of color centers and the degradation of the amplifier, thus, increase with Yb concentration because of the formation of pairs or clusters, which enable migration of energy from the excited state.

Note that the pair shown on the right in Fig. 7.24 will appear spectroscopically as an unsaturable absorption feature composed of the superposition of the two spectral absorptions. This model explains all the observed features of photo-darkening and indicates why reduction of Yb concentration has been effective in reducing the effect.

It also suggests a possible route to eliminating the effect if one can create a glass host in which holes are not available to stabilize the formation of Yb\(^{2+}\). To date, it does not appear that this problem has been solved because all known fibers have exhibited similar levels of photo-darkening despite the attempts at the usual glass modifications.

 

 

7.2.4. Cladding Design

Given the limitations in design of the fiber core waveguide and composition, an additional means of decreasing fiber length is to decrease the pump area by increasing the NA of the pump waveguide.

Recall that for double-clad designs, conservation of brightness dictates that the product of pump NA times the diameter of the pump region cannot exceed that of the pump diodes or the fiber pigtail that delivers the light.

Typical low-index polymers used as the pump cladding allow NA of about 0.45, while all-glass structures have an even lower NA, typically about 0.22, because of the limited amount of fluorine that can be incorporated into silica to reduce the refractive index.

An alternative approach is to surround the pump region with air in a microstructured fiber, as shown in the photo in Fig. 7.25.

 

 

In such an air-clad structure, the NA can be increased to 0.6–0.8, allowing reduction in fiber length by almost a factor of 2. An additional advantage of this design is that the outer glass region can be made quite thick because it is not part of the wave-guiding structure. This reduces external mechanical perturbations that can cause deleterious mode mixing.

Air-clad designs offer the additional benefit of higher pump intensity. This can be beneficial for lasers or amplifiers that operate as three-level laser systems. Because such systems have non-negligible ground state absorption at the signal wavelength, to achieve significant gain, the population inversion must be maintained as high as possible.

Air-clad designs are useful and even imperative for obtaining emission at moderate pump powers from Yb at 980 nm, Nd at 940 nm, or even Er at 1530 nm.

 

7.2.5. Device Assembly

In most cases, it is essential that the large mode area signal be preserved in the components and through the fusion splices of the device. The key issue is development of components and assembly methods that preserve the purity of the signal mode with low signal and pump attenuation.

For high-power lasers, however, the fiber designs discussed earlier depart radically from traditional core index profiles and sizes. Large area fibers support propagation of many optical modes and should have maximum possible mode area and optimum overlap between the signal mode-field and the gain material.

Although the conventional techniques for fusion splicing are used, it can be quite difficult to understand the mode content after the splice and verify that the region can reliably handle tens of watts of power.

To maintain signal integrity, mode transformation technology allows facile coupling between conventional step-index single-mode fiber with Gaussian mode shape and large mode area fiber with non-Gaussian mode shape.

This allows the gain fiber design to be optimized for peak performance independent of concerns for signal launch and output beam quality. With suitable mode transformation methods, the construction shown in Fig. 7.26 is most desirable.

 

 

In this example, the output beam is near Gaussian, has very high mode purity, and a mode-field diameter of about 15mm at 1550 nm. Depending on the specific fiber designs, the mode transformers can have losses less than 0.1 dB. Similar results have been achieved with output mode-field diameter of 28mm at 1080 nm using different pigtail fiber.

Much of the published literature on double-clad devices uses free-space coupling into and out of the fibers. Although this is acceptable for laboratory demonstrations or fiber and amplifier performance, it is generally unsuitable for robust commercial applications.

A fused approach such as discussed earlier will be essential for this technology to have significant commercial impact. As fiber designs become increasingly exotic, this aspect becomes quite a challenge and novel methods for mode transformation and multiplexing of pump and signal will be required.

 

The next tutorial discusses in detail about the Rabi frequency.