Polarization Maintaining Fibers
This is a continuation from the previous tutorial - nondispersive prisms.
The purpose of this tutorial is to provide a practical, technical introduction to the field of polarization maintaining (PM) fiber that will equip the reader with the basic knowledge and understanding necessary to use or specify this category of specialty fiber.
The tutorial begins by explaining how PM fibers work and provides brief examples of their various applications in sensing, medicine, and telecommunications, before describing the main fiber designs and the fabrication techniques used to produce them.
The relatively new technology of ‘‘holey’’ or ‘‘microstructure’’ fibers is addressed briefly, as is one of PM fiber’s more exotic cousins, polarizing fiber.
The second half of the tutorial moves into the more practical areas of performance criteria, measurements, and environmental effects.
To the novice, this tutorial provides a clear framework to assist the acquisition and development of knowledge gained from practical experience, and to the more experienced individual, it provides insight to stimulate deeper understanding and more effective problem-solving when using PM fibers.
1. What is a polarization maintaining fiber?
‘‘Polarization maintaining,’’ ‘‘PM,’’ ‘‘polarization preserving,’’ ‘‘HiBi,’’ or even occasionally ‘‘polarization retaining fiber’’ are all different names to describe the same thing—any optical fiber that will faithfully preserve and transmit the polarization state of the light that is launched into it, even when subjected to environmental perturbations.
2. Why use PM fibers? - Applications
PM fiber is used in any application that requires the transmission and delivery of polarized light.
2.1. Interferometry
The applications of PM fibers cover a broad spectrum encompassing telecommunications, medicine, and sensors. Most typically, these applications are interferometric and take advantage of the fiber’s ability to prevent signal fade by ensuring that the light traveling in the signal and reference arms of the interferometer always recombines with the same state of polarization, ensuring optical constructive interference, as depicted in Fig. 8.1.
If conventional single-mode fiber were used, the polarization state of the light traveling within each arm would vary independently with time, causing the recombined signal to fade between a maximum and zero as the relative polarization state of the two waveforms varied over 360 degrees. In broad terms, this basic principle is relevant to the interferometric techniques used in all three of the main application areas.
2.2. The Fiber Optic Gyroscope
The interferometric fiber optic sensor that has achieved the most commercial success is the fiber optic gyroscope (FOG). In essence, a FOG is a rotation and rotation-rate sensor that comprises up to three coils of PM fiber, one for each degree of freedom required (in aircraft terms: roll, pitch, and yaw).
Light is launched into both ends of each coil simultaneously and recombined at a detector. If the coil experiences a rotation, the light will undergo a Doppler-shift (the Sagnac effect) with the result that the counter-propagating beams will recombine out of phase, creating interference that may be analyzed to determine the degree and rate of rotation.
The basic design of a FOG ably illustrates the key benefit of using fiber as an intrinsic optical sensing element; the fiber’s ability to guide light enables exceptionally long path lengths to be confined within small physical volumes.
These long path lengths magnify relatively weak optical effects, enabling the manufacturing of very compact high-precision sensors. Typical FOG coils contain between about 100 and 5000 m of PM fiber, depending on the desired performance, and are capable of challenging the precision of the very best spinning-mass or ring-laser gyros.
It is interesting to note that the original experiments that demonstrated the basic principle by which the FOG operates were performed in the early 1920s using free-space optics, deployed over an area of several square kilometers; in stark contrast, the same measurements could be performed today using a FOG that would not be much bigger than a teacup.
2.3. Coherent Communications
PM fibers have also been used in telecommunications since the earliest days of specialty fiber technology. Coherent communications, or ‘‘Cocomms,’’ used interferometric detection techniques that could improve both receiver sensitivity and selectivity by around two orders of magnitude, when compared with the conventional state of the art of the 1980s.
Unlike conventional direct detection, where the optical signal is converted directly into a demodulated electrical output, a coherent receiver first adds a locally generated optical wave and then detects the combination.
The resultant signal carries all of the information of the original yet is at a frequency low enough to allow further signal processing to be performed using conventional electronics.
The technique is described as ‘‘coherent’’ because some degree of coherence between the signal and locally generated waveforms is essential; if the phase relationship between the two waves were to vary with time, then the data would become corrupted.
The development of commercial coherent communications systems for broad-area networks effectively ceased in the early 1990s, as the advent of the erbium-doped fiber amplifier (EDFA), combined with dense wavelength division multiplexing (DWDM) presented a simpler and more versatile solution to high-bandwidth repeaterless transmission.
However, Cocomms has survived as a specialized technology for use in applications that require vast amounts of data to be processed in real time, particularly to enable antenna remoting in military phased-array radar deployments.
2.4. Integrated Optics
Signal processing in interferometric sensors and transmission or detection in both conventional and coherent communications both use another significant technology that is enabled by PM fiber: integrated optics (IO).
Today, IO is most often encountered in the lithium niobate (LiNbO3) modulators used in telecommunications transmitters. A typical modulator consists of a lithium niobate chip into which titania-doped waveguides, flanked by gold electrodes, have been diffused. A PM fiber pigtail delivers a stable polarization state, aligned to the birefringent axes of the chip.
The device functions because of the Pockel effect; in other words, when a voltage is applied to the electrodes, the refractive index of the substrate is changed in proportion to that voltage.
The resulting change in effective optical path length can be used to generate interference that, depending on the precise design of the titania-doped waveguides, may be manipulated to provide modulation of phase, frequency, or amplitude or even to switch optical power between channels.
2.5. Laser Doppler Anemometry and Velocimetry
Whereas some interferometers may be constructed entirely of PM fiber, through the use of fused or polished all-fiber components, in many instances, the main function performed by the PM fiber is merely to provide a flexible delivery system that enables fragile optics and signal processing electronics to be isolated from the delivery point.
Examples of this sort of application are laser Doppler velocimetry (LDV) and laser Doppler anemometry (LDA)—noncontact techniques for flow velocity measurement, for example, air-flow in wind tunnels or even blood flow in veins and arteries. In LDA and LDV, flow velocity is determined by measuring the Doppler shift of the light scattered from the fluid.
To make a measurement, linearly polarized light from a laser source is split into two equal components and transmitted to the measurement site through two identical lengths of PM fiber.
At the output of these fibers, lenses focus the two beams down to a small spot within the moving fluid. At this point, the two beams converge to form interference fringes. Small particles within the fluid scatter light from each beam at slightly different Doppler frequencies because of their motion relative to the two beam directions.
Some of this scattered light is then collected by a large-core multimode fiber and transmitted to a photodetector where the two frequencies combine to form a temporal beat frequency. This beat frequency is linearly related to the difference in the Doppler frequencies created from each laser beam and, therefore, to the particles’ velocities.
2.6. EDFA Pump Combiners, Reflection- Suppression Schemes, Current Sensing, and Optical Coherence Tomography
The use of PM fiber to enable the flexible and remote delivery of polarized light extends to a variety of other applications across the full spectrum of industries.
Developments in telecommunications systems’ architectures over the last few years have demanded ever increasing power outputs from EDFAs that, in some designs, have been achieved through the polarization multiplexing of 980- or 1480-nm pump diodes. Similarly, pump diodes have also been pigtailed in PM fiber to enable polarization-based schemes for the suppression of back-reflection.
In sensing, the Faraday effect current sensor is experiencing something of a renaissance. As a polarimetric device, the current sensor relies on the delivery of a stable and known polarization state to the sensor head, and typically, this is achieved via PM fiber.
Finally, in medicine, coronary heart disease patients suffering from the condition known as ‘‘total occlusion,’’ where a blood vessel is totally blocked, are being treated with the assistance of a special catheter, or ‘‘guidewire,’’ that uses PM fiber. The PM fiber enables the surgeon to differentiate between the vessel wall and the blockage itself through the technique of optical coherence reflectometry (OCR), thereby facilitating its safe removal.
3. How do PM Fibers Work?
Under laboratory conditions, polarization maintenance may be demonstrated in virtually any single-mode fiber—provided that it is kept short enough, straight enough, and isolated from any form of environmental perturbation. The problems tend to occur when it becomes necessary to use the fiber in more practical situations.
The fundamental (TEM00) mode that propagates within a single-mode fiber is actually a degenerate combination of two orthogonally polarized modes.
In a conventional telecommunications-type fiber, these two components have the same propagation constant (i.e., they travel at the same velocity). This property makes it very easy for optical energy to transfer, or ‘‘cross-couple,’’ from one of these modes to the other, if it encounters any sort of perturbation within the fiber.
These perturbations may be intrinsic, caused by microscopic geometric variations within the core or residual thermal stress, locked-in by the fiber fabrication process, or extrinsic, induced by the environment in which the fiber has been deployed.
Extrinsic perturbations are usually mechanical stress-related phenomena caused by microbending or macrobending, typically in combination with the effects of the thermal behavior of the fiber coating (buffer) material.
In essence, these are the same phenomena that generate polarization mode dispersion (PMD), for the simple reason that birefringence and PMD are essentially one and the same thing.
In the real world, in which fibers cannot reasonably be protected from environmental stress (temperature fluctuations, etc.), it is necessary to use a purpose-designed PM fiber.
PM fibers are engineered in such a way that the two orthogonally polarized modes are forced to travel at different velocities (i.e., with different propagation constants). This difference in velocities makes it very difficult for optical energy to cross-couple, with the result that the polarization state of the transmitted light is preserved.
This difference is created through the introduction of anisotropy within the core of the fiber, either geometric, by making the core elliptical, or, more typically, through the application of a controlled uniaxial stress. These two designs are described as form birefringent or stress birefringent.
4. PM Fiber Types: Stress and Form Birefringent
4.1. Stress-Birefringent Fibers: Bowtie, PANDA, and Elliptical Jacket
The vast majority of PM fibers used today have one of the three basic stress-birefringent geometries: bowtie, PANDA, and elliptical jacket.
All three designs function in the same way; the cores are flanked by areas of high-expansion glass that shrink-back more than the surrounding silica, as the fiber is drawn, and freeze the core in tension.
This tension induces birefringence (i.e., it creates two different indices of refraction: a higher index parallel and a lower index perpendicular to the direction of the applied stress).
In essence, the phenomenon is very similar to that which creates visible interference fringes when transparent plastics are stressed except that, in a PM fiber, the effect is highly controlled and its magnitude is at least an order of magnitude lower than may be achieved in an organic glass (polymer/plastic).
In any of these designs, when polarized light is launched along the ‘‘slow axis,’’ it is forced to travel at a lower velocity than if it had been launched along the ‘‘fast axis’’ and vice-versa.
The cross-coupling of light from one axis to the other, therefore, becomes very difficult because it would require a perturbation capable of making a significant change in the velocity of the transmitted light. The greater the applied stress, the greater the difference in propagation constant (light velocity) between the two axes and the higher the birefringence. PM ability is enhanced because a larger perturbation is, therefore, needed to generate cross-coupling from one axis to the other.
It should be clarified at this stage that polarization maintenance is not a loss mechanism, as is sometimes believed; under the vast majority of practical circumstances, there is no measurable difference in attenuation between the fast and slow axes. However, to this day, most applications use the slow axis exclusively. Although the origins of this practice are thought to lie in the theoretically superior resistance to bend-induced loss provided by the slight increase in numerical aperture (NA) on this axis, the principal benefit has been to provide a useful degree of standardization.
Each of the three designs is capable of generating sufficient birefringence for even the most demanding of applications, so the precise choice of fiber is typically determined by other criteria, ranging from handling characteristics to history.
In telecommunications applications, the fiber of choice is usually the PANDA design, invented by Nippon Telegraph and Telephone in the early 1980s, then developed and commercialized in the United States and Europe throughout the 1990s. In essence, PANDA is a telecommunications fiber, modified through the insertion of stress rods (usually referred to as stress applying parts [SAPs]) to provide PM properties.
The fiber was conceived in support of the large volume of Japanese work in the area of coherent communications that had been driven by that country’s unique geography (i.e., a series of islands interlinked by stretches of ocean that could be 100 km or more in width).
This topography challenged the direct detection technologies of the day, but provided an ideal test case for the improved receiver sensitivity of Cocomms. Fiber attenuation and mode-field diameter (MFD) were well matched to those of single-mode telecommunications fibers so that, when Cocomms was overtaken by the EDFA in the late 1980s, it was a natural extension to continue using the fiber in conjunction with the IO modulators that successfully made the transition between the two technologies.
To this day, bowtie fibers are most typically encountered in sensor applications, and indeed, the majority of FOGs worldwide use a fiber of this design. It should, therefore, come as no surprise that the fiber was conceived in the early 1980s as a sensor fiber, developed at the University of Southampton Optical Fiber Group in support of the FOG program at British Aerospace.
Without the constraints of a telecommunications fiber design, bowtie was introduced with a high NA to provide increased resistance to the bend-induced loss that could arise in small-diameter sensor coils, and the elliptical core generated by its fabrication process was accepted readily for sensor use.
In extremis, the bowtie design can be shown capable of creating more birefringence than any other stressed design, simply because it is based on two opposing wedges, the simplest and most efficient means of applying stress to a point.
However, in all but the most exotic of applications, the fundamental design is implemented in a suboptimum condition in the interests of manufacturing yield and consequent cost.
It is interesting to note that although redesigned variants of both PANDA and bowtie have subsequently been introduced to address the sensor and telecommunications markets, respectively, more than 20 years later, both designs continue to dominate the applications for which they were originally conceived. The bowtie fiber has been developed and commercialized by Fibercore Limited, a spinout company from the University of Southampton Optical Fiber Group since the fiber’s invention in 1983.
The elliptical jacket fiber also had its origins in Japan, but this time with Hitachi. In common with PANDA, the original interest was in a fiber suitable for coherent communications use. However, the fiber was manufactured in the United States initially by a company called Eotech that was subsequently acquired by 3M, who is probably best known for the commercialization of this product as a sensor fiber throughout the United States and Europe.
Whereas the elliptical jacket fiber is capable of similar levels of birefringence to the PANDA and bowtie designs, this performance is achieved at the expense of handling characteristics.
As can be seen from the Fig. 8.7, this fiber is unique in that the SAP extends all around the core, generating a significant amount of parasitic stress that serves to reduce the fiber’s birefringence. The oversized stress member necessitated by this characteristic can compromise performance in the reduceddiameter fibers used in many sensor applications, for the simple reason that there can be insufficient room to locate a SAP of the necessary dimensions. Furthermore, levels of parasitic stress can be considerable, leading to uneven fracture when cleaved and reducing fusion splice yields.
4.2. Elliptical Core, Form-Birefringent Fiber
In conventional single-mode fibers, core ellipticity is undesirable simply because it creates birefringence (a.k.a. PMD) that reduces performance in high data-rate systems. In a form-birefringent fiber, this effect is taken to the extreme.
Form-birefringent fibers, with their simple design of a highly elliptical core, combined with a very high NA and small mode, predate stress-birefringent fibers and may be traced back to Hitachi in the late 1970s.
However, the high levels of attenuation and lack of compatibility, created by their highly germania-doped cores and consequent small modes, made them unsuitable for telecommunications use.
However, they did find some application in sensors as the ‘‘E-core’’ fiber manufactured by Andrew Corporation and sold throughout the 1980s, and the original Hitachi designs were developed by Corning as its PMF38 fiber throughout the latter part of the 1990s.
However, despite best efforts to demonstrate how the basic incompatibility caused by the small mode and high loss could be overcome, and very attractive pricing, the product failed to gain market acceptance. Today, form-birefringent fibers, tracing their lineage back to the original Andrew E-core fiber, are still used in KVH’s range of FOGs.
4.3. Microstructure (’’Holey’’) Fibers
Although the original form-birefringent technology may have been sidelined to a significant degree, it is interesting to note that in the future, form-birefringent designs, in the guise of microstructure fibers (also referred to as ‘‘holey’’ or sometimes ‘‘photonic crystal’’ or ‘‘photonic band-gap’’ fibers), may prove to offer the ultimate in terms of PM performance.
Although there has been much debate about the precise mechanism by which these fibers work, it is now generally accepted that the vast majority of examples function because of the index difference created by the microstructure of air-gaps within the cladding, making PM variants effectively form birefringent.
By virtue of the unitary index of the air that makes up the bulk of the optical cladding, a huge degree of anisotropy may be generated, with correspondingly huge levels of birefringence, up to an order of magnitude greater than has been achieved from conventional stress-birefringent designs.
4.4. Polarizing Fiber
A type of very highly birefringent fiber that has been known since the earliest years of the technology but remains a rather rare and exotic variant of PM fiber, is polarizing fiber, also known as ‘‘zing’’ or simply ‘‘PZ.’’
Zing fibers take advantage of the fact that light polarized along the slow axis is guided slightly more strongly than that polarized along the fast axis and will, therefore, be less sensitive to bend-induced optical loss. For this reason, a bend diameter may be found at which the fast axis is attenuated very strongly and only the slow axis propagates.
With the correct choice of fiber length, bend diameter, cutoff, and transmission wavelengths, a significant degree of polarizing behavior may be demonstrated in virtually any standard PM fiber.
However, in practical sensor applications, it is typically advisable to use a purpose-designed polarizing fiber to ensure environmentally robust performance over a sufficiently broad operating window.
Zing fibers are typically designed with short cutoff wavelengths (\(\lambda_c\)) relative to the intended polarizing window, together with low NAs. These design characteristics weaken the strength of optical guidance and, therefore, ‘‘encourage’’ both the fast and the slow mode to radiate.
To ensure that the slow mode remains guided for an operating window extending perhaps 50 nm beyond the wavelength at which the fast mode is lost, the birefringence of the fiber is also increased by about 40% over values usually encountered in PM fibers. As a refinement to this basic design, structures may also be incorporated within the inner cladding to preferentially attenuate the fast mode.
Although there is no fundamental reason that both form- and stress-birefringent designs may be used to create polarizing fibers, and indeed, microstructure designs may be highly suited due to the extreme levels of birefringence that have been demonstrated, to date only stress-birefringent configurations have been used commercially, primarily the zing bowtie fiber introduced by York VSOP in the mid 1980s and the PZ elliptical jacket fiber commercialized by 3M around 1990.
5. PM Fiber Fabrication Methods
In common with their more conventional counterparts, the manufacturing process for PM fibers comprises two parts: preform fabrication and fiber drawing.
The fiber drawing process is practically identical for all fiber types, both PM and non-PM. For this reason, only the preform fabrication stage is addressed in this section.
5.1. Bowtie Fibers
Bowtie preforms are fabricated on a lathe using inside vapor-phase oxidation (IVPO) with stress members created by the process of gas-phase etching. First of all, a ring of boron-doped silica (effectively boric oxide B2O3 mixed with silica SiO2) is deposited within a high-purity, synthetic-silica substrate tube by the oxidation of boron tribromide (BBr3) in combination with silicon tetrachloride (SiCl4).
When a sufficiently thick layer has been created, the rotation of the lathe is stopped to allow two diametrically opposed sections to be etched away. The material is etched by passing a suitable etchant (typically sulfur hexafluoride SF6) through the center of the tube and activating it by means of a narrow-zone etching burner. The final shape of the bowtie SAPs may be controlled and stress levels optimized by varying the arc through which the etching burner is rotated.
After the completion of the etching stage, rotation is recommenced and inner-cladding, followed by core layers, are deposited. The inner-cladding is typically fused silica containing a suitable viscosity modifier (usually phosphorus pentoxide P2O5, synthesized by the oxidation of phosphoryl chloride POCl3, and index matched using fluorine). The core is germanosilicate (a mixture of germania GeO2 and SiO2), created through the oxidation of a combination of SiCl4 and GeCl4.
Preform fabrication is completed with a controlled collapse process. An overpressure of dry nitrogen is introduced to balance the surface-tension forces that gradually overpower the viscosity of the material as the process temperature is increased to almost 2000\(^\circ\)C.
The characteristic bowtie shape is created as the central hole is collapsed to form a solid cylindrical preform. When this preform is drawn, surface tension forces also ensure that the geometry of the preform is faithfully reproduced in the fiber.
5.2. PANDA Fiber
As benefits its origins as a modified telecommunications fiber, the starting point for a PANDA fiber is a circularly symmetric ‘‘telecoms-type’’ preform, into which two diametrically opposed holes have been drilled ultrasonically.
The PANDA preform is then completed by the insertion of a boron-doped stress rod into each hole. These stress rods may be fabricated either by vapor deposition or by a sol-gel process. When drawn, the low melt viscosity of these stress rods relative to the surrounding silica ensures that the boron-doped material entirely fills the holes to form the characteristic PANDA shape.
Whereas the fabrication process for PANDA may appear relatively straightforward, the drawing process must be well controlled to prevent distortion of both the stress rods and the fiber itself and achieve the exceptional geometric precision for which the design is renowned.
Similarly, despite various proposals for alternative PANDA fabrication methods, the tight machining tolerances and tool stability necessary to drill side-holes of significant depth have continued to make the manufacture of very high-yielding preforms technically challenging.
5.3. Elliptical Jacket Fiber
The fabrication method for elliptical jacket preforms combines processes from both bowtie and PANDA manufacture: boric oxide deposition by MCVD and ultrasonic machining. The initial fabrication steps are identical to those for a bowtie preform, except that the gas-phase etching is omitted, leaving an unbroken circular annulus of boron-doped material surrounding the core.
After this circularly symmetric preform has been completed, its symmetry is broken by the machining of two flats, one on each side of the core. Although it is possible to use conventional mechanical grinding techniques, the associated force and vibration would make the highly stressed preform vulnerable to fracture. For this reason, a more benign ultrasonic machining process is typically used.
When drawn, the high surface tension forces within the molten glass force the preform to circularize, thereby creating the characteristic elliptical jacket shape.
5.4. Elliptical Core, Form-Birefringent Fiber
Some degree of ellipticity may be induced in the core of any single-mode fiber if process controls are inadequate. For example, in MCVD, if the surface tension forces within the collapsing preform are not accurately balanced by pressurizing the substrate during the final stages of the fabrication process, then the preform will ‘‘pull flat’’ to some degree and create an elliptical core.
To fabricate a core that is deliberately elliptical, it is necessary to take this phenomenon to an extreme by also removing the circularizing effect of the rotation of the lathe, depositing the core (by MCVD/IVPO) within a stationary substrate tube, then collapsing it under vacuum to create the characteristic high-ratio ellipse.
The resulting cladding ellipticity is low because of the very small amount of material movement actually taking place, relative to the total volume of the preform, and any residual cladding ellipticity can either be removed by including an additional high-temperature ‘‘rounding’’ step during preform fabrication or even during the fiber drawing process itself.
5.5. Microstructure (‘‘Holey’’) Fibers
The fabrication technique for PM microstructure fibers bears little resemblance to that of any other PM fiber because it does not rely on direct chemical vapor deposition to create the preform.
Microstructure fiber performs are fabricated by building a close-packed arrangement of silica tubes around a central silica rod that replicates the desired fiber structure.
Precision-machined jigs are used to facilitate this process and the completed preform is typically held together with platinum wire during drawing. Exceptional precision is essential during the assembly of the preform, together with fine control of all drawing conditions to ensure that viscous forces do not distort the fiber during formation.
Please note that chemical vapor deposition may still be used to fabricate the high-purity, fused silica components that make up the preform.
6. Key Performance Parameters
This section introduces the important optical and physical parameters that influence a PM fiber’s performance. It is intended to act as a practical guide to specifying a PM fiber for any specific application.
Explanations are provided where these parameters differ from those of more conventional fibers, particularly in cases in which these differences should raise practical concerns, and in doing so, some popularly held myths are dispelled.
6.1. Attenuation (\(\alpha\))
Attenuation values for PM fibers are typically higher than those encountered in other single-mode fibers for three reasons: transmission wavelength, the proximity of the SAPs, and core dopants.
Many PM fibers are designed to operate at wavelengths outside the second (1310 nm) or third (1550 nm) telecommunications windows. At short wavelengths, the components of attenuation contributed by both Rayleigh Scattering (\(\lambda^{-4}\)) and electronic transitions (\(e^x\)) are still substantial resulting in attenuation values as high as 50 dB/km in the blue (488 nm), falling to approximately 30 dB/km at 514 nm, around 12 dB/km at 633 nm and roughly 4 dB/km in the first telecoms window around 850 nm. These relatively high values are no reflection of the quality of the fiber itself, merely a practical illustration of the fundamental physics that underpins the spectral attenuation cure of the silicate glasses involved.
Even at 1550 nm, the losses of sensor-optimized PM designs tend to be significantly higher than the 0.2-dB/km theoretical limited that has become the norm for use in telecommunications, typically around 1.5 dB/km.
Once again, the explanation here does not lie with the quality of the fiber, but in the influence of boric oxide (B2O3) used to increase the expansion coefficient of the SAPs. Boron has a very strong vibrational absorption overtone centered close to 1550 nm. The 2000\(^\circ\)C temperatures—and above—prevalent during both the final stages of preform fabrication and throughout the fiber drawing process cause this boron to diffuse into the inner-cladding. If the SAPs have been located very close to the core (say, within 4 μm or so) to generate additional birefringence, this diffusion will bring the strong absorption of the boron into contact with the edge of the optical field, resulting in a higher value of fiber attenuation.
6.2. Numerical Aperture (NA)
To cope with the small-diameter bends often encountered in sensor coils, many PM fibers are designed with higher NAs than generally found in telecommunications fibers.
Typical NA values of 0.16 or 0.20 are achieved by incorporating higher levels of germania (GeO2) within the fiber core. Whereas germania, like silica, is a transparent amorphous glass, it is also susceptible to the formation of defects when subjected to the high (~1800–2200\(^\circ\)C) temperatures of both preform fabrication and fiber drawing.
These defects are created when thermal energy knocks electrons from the material lattice to create empty sites, the presence of which intensifies the contribution from the electronic absorption edge (or Urbach edge) to the attenuation of the fiber.
This contribution can be significant, particularly at wavelengths in the ultraviolet and visible spectrum, where it may reach several tens of dB/km in extremis. Although careful attention to fabrication conditions, and in particular, by drawing the fiber at the lowest viable temperature, can minimize the creation of these defects, it is difficult to eliminate them entirely.
For this reason, the tolerances on attenuation for PM fibers designed for the blue and green (488 nm/514 nm) or the red (633 nm/ 680 nm) tend to be significantly broader than those designed for the infrared, particularly for fiber designs that preclude drawing at reduced temperatures.
Another unique aspect of PM fibers is that birefringence creates a lower and a higher value of NA for the fast and slow axes, respectively. In normal PM fiber designs, this difference is perhaps 2.5% with the result that there is no practical difference between the two axes in terms of resistance to bend-induced loss.
However, if taken to extremes, for example, in a polarizing fiber, a bending condition may be found for which the slow axis continues to guide, yet the fast axis does not. In this case, the guidance of the slow axis is also assisted, to a small extent, by the presence of the low refractive index regions formed by the SAPs.
Fast and slow axes are clearly visible in the aforementioned refractive index profiles, identified as sections through the relevant axes. The presence of the SAPs is indicated by the low index regions that flank the core in the slow axis view.
NAs for PM fibers are typically determined directly from the fiber refractive index profile using the equation
\[\tag{8.1}\text{NA}=\sqrt{n_1^2-n_2^2}\approx\sqrt{2n_2\delta{n}}\]
where
- \(n_1\) core refractive index
- \(n_2\) cladding refractive index
- \(\delta{n}\) refractive index difference between core and cladding.
Please note that for the slow axis, the value of \(n_2\) is that of the inner-cladding only—not that of the SAP. It should also be borne in mind that this method of measuring NA directly from the fiber refractive index profile will typically generate a value higher than that derived from taking the sine of the half-angle of the output cone due to the influence of cutoff wavelength.
6.3. Is There a Connection Between Polarization Maintenance and Attenuation?
One question that is often asked is What is the difference in attenuation between the fast and slow axes? The answer, in all but the most extreme applications, is Nothing.
Theoretically, the slow axis is more strongly guiding and has been both the transmission axis of choice in the majority of applications and the axis most often ‘‘keyed’’ in PM connectors, but the truth is that you can use either axis, to equally good effect, most of the time. The attenuation of a PM fiber is certainly influenced by the presence of the SAPs, but polarization maintenance is fundamentally not a loss mechanism.
6.4. Cutoff Wavelength (\(\lambda_c\))
To address their many and varied applications, PM fibers have been available across a broad range of cutoff wavelengths since their commercial introduction in the early 1980s. Most manufacturers offer standard specifications optimized for 488–532 nm in the blue and green, 633–680 nm in the red, 780–850 nm in the first telecommunications window, 940–1100 nm for YAG, YLF, and semiconductor EDFA pump lasers, 1310–1550 nm in the second and third telecommunications windows, and 1530–1610 nm for the so-called S-, C-, and L-bands.
All of the basic rules that apply to conventional telecommunications fibers also apply to PM fibers. Progressively fewer modes are supported as the cutoff wavelength is approached, reducing to only a single mode when cutoff is reached. The fiber will then continue to support this one remaining mode, usually for at least 200 nm beyond cutoff. This single-mode waveband will increase if the fiber follows a relatively straight physical path and gradually reduce as the fiber is deployed in smaller and smaller diameter coils. This waveband is also extended by the increased NAs of many ‘‘bend-insensitive’’ PM fiber designs, with an NA of around 0.2 capable of providing practical single-mode transmission over perhaps 500 nm or more.
A theoretical complication introduced by PM designs is that the cutoff wavelength is actually fractionally shorter for the fast axis than it is for the slow, because of the difference in index difference (\(\delta{n}\)) created by the birefringence. However, in practice, this difference amounts to only a few nanometers (in fact, it is typically within the limits of measurement accuracy)—unless, of course, it has been deliberately accentuated through a polarizing fiber design deployed at a relatively small diameter.
6.5. Mode-Field Diameter (MFD)
The MFD, or sometimes ‘‘spot size,’’ is simply the diameter of the optical field within the fiber. Since the distribution of energy within the fundamental mode (TEM00) is Gaussian in shape, this diameter may be defined in a number of different ways including \(1/e^2\), \(1/e\), and full width half maximum (FWHM) (i.e., the diameter at which the optical intensity falls to \(1/e^2\) of its peak value, etc.). Most typically, it is the \(1/e^2\) value that is quoted in product specifications. The MFD is always larger than the actual ‘‘physical’’ core diameter, defined at the point at which the refractive index falls to that of the cladding, because the tail of the Gaussian penetrates into the inner cladding, typically by up to 1 micron.
The higher NAs and shorter cutoff wavelengths used in many PM designs generate MFDs that are significantly smaller than those of more conventional single-mode fibers. For example, MFDs of typical PM fibers may vary from as little as 2.75 μm, for a fiber designed for 488 nm, up to around 8.0 μm for a 1550-nm fiber; these figures compare with 8–10 μm for standard telecommunications fibers.
Although users are often concerned about handling difficulties that may result from the smaller MFDs of many PM fibers, and it is true that alignment for connectorization or fusion splicing is far more critical in these designs, it should be noted that it is not possible to design a fiber with a larger MFD without reducing its resistance to bend-induced loss, perhaps significantly. For this reason, the MFD of a custom-designed fiber is often determined by the relative importance of bend-induced or splice/connector loss within the intended application.
Another aspect of MFD in which some PM fibers also differ is mode shape. Both form-birefringent fibers and most bowtie geometry stress-birefringent fibers have elliptical cores that generate elliptical modes.
In the case of the form-birefringent fiber, this shape is intrinsic to the fundamental mechanism by which the fiber functions. However, in bowtie fibers, the ellipse is created by the flow of the SAP and inner-cladding materials during the collapse phase of preform fabrication. The shape is not the result of applied stress, as is sometimes believed, or even a design factor intended to enhance PM performance by creating additional form birefringence; in fact the very small amount of form birefringence generated in this way actually works against the primary stress birefringence within the fiber, but to an insignificant degree.
One interesting phenomenon associated with elliptical modes is that the shape reverses from the near to the far field. In the near field, the mode shape matches that of the core, whereas in the far field, the major and minor axes of the ellipse correspond to the ‘‘slow’’ and ‘‘fast’’ axes, respectively.
This phenomenon has frequently led users to believe that the mode of these fibers is indeed circular for the simple reason that the human eye is relatively insensitive to ellipticity and the mode will appear circular if projected onto a screen positioned close to the midpoint of its transition.
Users accustomed to the perfectly circular modes of conventional fibers are sometimes resistant to the idea of an elliptical mode, particularly in telecommunications. However, in the vast majority of applications, mode shape has absolutely no impact on performance, and in fact, elliptical modes can even be beneficial when pig-tailing to devices that also have noncircular modes, including planar waveguides and some semiconductor lasers.
The only true exceptions to this rule that are generally encountered are in LDA and in the fabrication of fiber-based depolarizers. In LDA, an elliptical mode will generate different particle transit times in the two orthogonal directions, thereby creating potential problems in data analysis, and in depolarizers, the insertion loss of the 45-degree splice will be increased because of the incomplete overlap of the elliptical modes.
6.6. Beat Length (\(L_p\))
Beat length is arguably the parameter that best represents the fundamental ability of a PM fiber to preserve polarization. Beat length is particularly useful because, unlike H-parameter or extinction ratio (ER), it is independent of fiber length or the way in which the fiber has been deployed. H-parameter and ER will both be affected adversely by high winding tensions, small coil diameters, point intrusions, or multilayered winds, whereas beat length will remain constant. For this reason, beat length is an invaluable tool that enables you to compare the PM properties of different fibers; put quite simply, the shorter the beat length, the better the performance.
When light is launched into a PM fiber with a linear component along each of its two birefringent axes, the difference in velocities of these two components causes the resultant polarization state to vary along the length of the fiber. The beat length is the distance over which this polarization rotates through 360 degrees. The greater the birefringence within the fiber, the greater the difference between the two velocities and the shorter the beat length.
Beat length is related to birefringence (B) by the following equation:
\[\tag{8.2}L_p=\frac{\lambda}{B}\]
where \(\lambda\) is the wavelength at which the beat length is measured, and birefringence (B) is the difference between the refractive indices of the fast and slow axes (\(n_\text{slow}-n_\text{fast}\)).
From this equation, it may be seen that beat length varies with wavelength in a linear fashion. For example, a beat length of 1.3 mm measured at 633 nm would increase to approximately 2.7 mm at 1310 nm and 3.2 mm at 1550 nm.
The most direct way of measuring beat length is to launch light into the fiber at 45 degrees to its birefringent axes so that equal amounts of optical power are coupled into each axis. Rayleigh scattering within the fiber causes beats to appear as alternating regions of light and dark as the two modes interfere as they move in and out of phase along the length of the fiber. In this instance, the beat length is merely the distance between two successive light or dark regions.
In many cases, the simplest thing to do is to use red light (typically 633 or 680 nm) in the measurement so that these beats may be observed with the naked eye and measured on a millimeter scale. Alternatively, an infrared diode laser may be used (say, at 830 nm), but in this case, a scanning photodiode is required to measure the beats.
This simple and direct technique does have limitations, primarily that it is relatively coarse because it relies on an operator counting the number of beats within a relatively short distance and is, therefore, susceptible to rounding errors caused by partial beats, but its precision is sufficient for the vast majority of applications. Furthermore, because it is possible to engineer launch conditions so that a single mode at 633 nm may propagate for a few meters in virtually any fiber, irrespective of cutoff wavelength, the technique is exceptionally versatile.
If a more precise measurement of beat length is required, then this may be achieved by, once again, exciting both axes of the fiber equally but this time capturing the output on a spectrum analyzer.
Interference between the two modes may be seen in the fringe pattern and the beat length calculated in the following manner:
\[\tag{8.3}L_p=\frac{\text{Fringe Width}}{\text{Central Wavelegnth}\times\text{Fiber Length under Test}}\]
The wavelength dependence of beat length is also clearly indicated in the steady increase in fringe width visible throughout the spectrum. Whilst this technique is more accurate than direct visual measurement, its suitability is limited by the wavelength range of available spectrum analyzers, together with that of suitable polarizers and sources. For this reason, the technique is usually restricted to measurement at 1550 nm (see Fig. 8.21).
6.7. Extinction Ratio (ER)
Whereas beat length provides an invaluable means by which the PM performance of different PM fibers may be compared, the influence of environment is so significant that absolute performance may only be determined experimentally— by deploying the fiber in a way that is representative of the intended application and measuring the purity of the output polarization.
One of the most frequently used measures of the PM performance of a PM fiber is the ER. If a ‘‘perfect’’ PM fiber were used under ideal conditions, all transmitted optical power would remain within the same birefringent axis that it was originally launched into (i.e., light polarized along the fast axis would remain entirely in the fast axis and vice-versa).
In practice, this does not happen. Instead, some energy will always transfer into the orthogonal axis, causing a degraded state of polarization to emerge from the delivery end of the fiber. The ER is merely the ratio of this ‘‘unwanted’’ power, to the amount of power remaining in the launch axis, typically expressed in decibels:
\[\tag{8.4}\text{ER}=10\log_{10}(P_u/P_w)\]
where
- \(P_u\) = optical power transferred to the unwanted axis
- \(P_w\) = optical power remaining in the launch (wanted) axis.
In other words, an ER of \(-30\) dB indicates a ratio of wanted to unwanted optical power of 1000:1, \(-20\) dB is 100:1, \(-10\) dB is 10:1, and so on.
6.8. H-Parameter
Another frequently used measure of PM fiber’s performance is the so-called H-parameter. The H-parameter is simply an ER, expressed as a decimal (not to be confused with decibel) per unit length of fiber. For example, an ER of \(-30\) dB, achieved over 1000 m of fiber is the same as an H-parameter of
\[\frac{1}{1000\times1000}\text{ per meter}\]
Typically written as simply \(10^{-6}\). Similarly, an ER of \(-20\) dB achieved over 100 m is the same as an H-parameter of
\[\frac{1}{100\times100}\text{ per meter}\quad\text{ or }10^{-4}\]
6.9. Effect of Test Conditions and Environment on Polarization Maintaining Performance
One of the most frequently asked questions about PM fibers is What is the H-parameter (or ER)? Despite its apparent simplicity, this question is perhaps one of the most difficult to answer satisfactorily.
The fact that H-parameter is expressed normalized to a unit length may lead one to believe that PM performance and length have a linear relationship and indeed, straight-line graphs of PM performance against length appeared on a number of fiber data sheets published during the late 1980s.
However, in practice, PM performance is dictated by a combination of test conditions, deployment conditions, packaging, and beat length. Put quite simply, under the ‘‘right’’ conditions, ERs of \(-30\) dB may be achieved over perhaps 5 km of fiber (an H-parameter of \(2\times10^{-7}\)), whereas, under the ‘‘wrong’’ conditions, even the best PM fiber could struggle to preserve any polarization at all, even over a few meters.
The fundamental mechanism by which most PM fibers work is birefringence created by uniaxial stress generated within the fiber structure; the greater the stress, the better the fiber in terms of PM performance.
It should, therefore, come as no surprise that this internal stress may be reduced, along with the fiber’s ability to preserve polarization, by any externally induced stress that the fiber may be subjected to.
By far the most common and the most damaging sources of externally induced stress are point defects (essentially microbends) that occur when the fiber is inadvertently tensioned over any small rigid object. In a sensor coil, these point defects may occur where irregularities within the wind cause fibers to cross over each other or where leads cross un-radioed corners within the package or even where air or gas bubbles are entrapped within potting compounds.
This last type of point defect is also frequently encountered in PM connector manufacture or in device pig-tailing where the fiber must be cemented into a ferrule of V groove. The physical size of these defects is typically on the same order as the fiber diameter, or smaller. Differential thermal expansion and changes in the Young modulus of different materials used within these systems also conspire to exacerbate the effect.
The damaging effects of these point defects may be reduced through careful attention to both the fiber design itself and that of its packaging. Fibers with a shorter beat length (in the range 1.0–1.3 mm at 633 nm) have greater levels of internal stress and are, therefore, intrinsically more resistant to the effects of externally generated stress than those with longer beat lengths.
However, because of the very high levels of localized stress that can be generated by point defects, it is also essential that the coating package (buffer) be capable of isolating the fiber from their penetration over the full operating temperature range of the sensor coil or component.
To achieve this isolation, it is necessary to use a primary coating that is very soft and that remains soft throughout the desired temperature range. Primary buffer materials are typically urethane acrylates that, in common with all polymer glasses, get significantly harder at temperatures below 0\(^\circ\)C. In this context, ‘‘soft’’ should be interpreted as maintaining a Young modulus of less than 100 MPa for the majority of the required operating temperature range and less than 1000 MPa for the entire range.
At room temperature, these primary materials have a typical modulus in the region of 1 MPa and, for this reason, must be protected with a secondary coating that is significantly harder to impart strength and abrasion resistance. Young’s modulus should also be taken into account when selecting ferrule cements, with softer urethane-based materials being more suitable for use in conjunction with PM fibers than the harder yet more popular epoxies.
In general, the environments and packaging in which PM fibers designed for sensor applications tend to be used are significantly more challenging than those encountered in telecommunications.
In sensors, longer lengths of fiber tend to be packaged in smaller volumes and used over much wider temperature ranges. For example, it is not unknown for 200 m of PM fiber to be coiled to a diameter of 20 mm and expected to perform down to - 55\(^\circ\)C, whereas even in telecommunications components, bends smaller than 40 mm are rarely encountered and room-temperature operation is often the norm.
The more aggressive deployment environments of sensors should always be reflected in the choice of coating materials for a PM fiber, and for this reason, care should be taken when specifying fibers for these applications.
It should also be noted that the fundamental PM properties of stress-birefringent fibers are also temperature dependent. This phenomenon may be explained intuitively by reference to the mechanism by which the birefringence is generated—the mismatch in thermal expansion coefficients between the boron-doped SAPs and the silica that makes up the bulk of the fiber structure.
At lower temperatures, this mismatch is accentuated, with a corresponding reduction in beat length. Conversely, at elevated temperatures, the beat length increases, with birefringence disappearing completely at around 600\(^\circ\)C.
In theory, this effect helps to provide some compensation for the hardening of buffer materials at low temperatures. In practice, the effect is negligible for the vast majority of applications. However, there are some sensor applications in which it may be advantageous to use a PM with reduced temperature sensitivity.
For example, situations in which it is difficult to differentiate the effects of temperature from those of the desired measurand. In these cases, the use of a form-birefringent fiber should be considered because the lack of reliance on thermal stress within these designs reduces their temperature coefficients to practically zero.
When winding sensor coils, avoidance of crossovers and the maintenance of a constant and low tension (typically a few grams) are essential if good values of H-parameter are required.
When these points are considered, it becomes clear why values of ER or H-parameter measured on a standard shipping spool provide little or no indication of fundamental PM performance. The main considerations when spooling fiber for shipment are speed and robustness, to minimize cost and ensure that the fiber stays firmly on the reel during transit. To optimize PM performance, you need a low-tension precision wind.
One area of PM fiber measurement often overlooked is the fundamental limitations of the test equipment used. Any commercially available PM fiber should be able to demonstrate an ER in excess of \(-35\) dB, if tested under ideal conditions and using suitable equipment.
Something that may easily be forgotten is that PM and polarizing fiber are very different things: PM fiber is designed merely to maintain the state of polarization launched into it, and only a polarizing fiber can improve it.
What this means is that in practice, any polarization measurement performed on a PM fiber will be limited by the ER of the worst component, so if the source, or polarizer used at launch is capable of only \(-20\) dB, then that is the best result that could be expected from the fiber, even if it may be theoretically capable of \(-35\) dB or better.
When assembling equipment to make these measurements, you should consider that most ER or H-parameter rigs put together from nonoptimized components will struggle to measure better than about \(-25\) dB. Achieving \(-30\) dB or higher requires either a great deal of luck or the hand selection of top-quality components.
7. Mechanical and Lifetime Properties
7.1. Strength Paradox I: Fragile Preforms Make Exceptionally Strong Fibers
In all stress-birefringent fibers, it is the preform fabrication stage that provides the greatest challenge to process yields—particularly for the bowtie and elliptical jacket fibers.
As stressed structures formed from brittle materials, both bowtie and elliptical jacket preforms are highly vulnerable to brittle fracture. Process controls have evolved to minimize this risk, through optimization of fiber geometries and avoidance of mechanical or thermal shock, so very few preforms are lost in this way today.
Although there is some danger that the stress rods themselves may fracture within a PANDA preform, because the rods are mechanically decoupled from the surrounding material until the preform enters the hot zone of the drawing furnace, immediately before fiber formation, this risk is actually very small.
Paradoxically, although the fiber preforms themselves are very fragile, there is absolutely no danger that stress-birefringent fibers will shatter in use, as is sometimes feared. Although both the preform and the fiber are stressed brittle structures and, therefore, potentially unstable, the fibers themselves cannot shatter because their small dimensions hold insufficient surface energy to create a new crack surface. A stressed fiber’s inability to shatter is, in fact, a perfect illustration of Griffith’s Theory of Brittle Fracture.
In practice, PM fibers can exceed the tensile strength requirements set out in Telcordia GR-20-CORE by typical margins of 30% or more with dynamic stress corrosion parameters (\(n_d\)) in the low to mid 20s against a requirement of 18].
Advances in materials, particularly the availability of ultrahigh purity synthetic silica substrate tubes, combined with state-of-the art fabrication practices, including drawing in a Class 100 clean-room environment, mean that the Telcordia requirements for tensile strength have become extremely conservative and any fiber of quality manufacture should be expected to exceed them.
High though they are, the tensile strength values of stress-birefringent PM fibers are usually a few percentage points below those of standard telecommunications-grade singlemode fibers (see Fig. 8.22). This observation may be explained intuitively by reference to the fiber cross-sections; in PM fibers, a significant fraction of the cross-sectional area is composed of boro-silicate, a material with a tensile strength approximately 20% lower than that of pure silica.
In all practical applications, fiber tensile strength is relatively unimportant provided that it exceeds the GR-20-CORE minimum limits of 3.14 GPa/455 kpsi (unaged) and 2.76 GPa/400 kpsi (aged) because tensile failure (i.e., pulling a fiber too hard) is very rarely encountered.
Lifetime, as determined by a fiber’s resistance to static fatigue, is of far greater consequence, particularly for PM fibers that are used in sensors or components, because they are usually packaged in far smaller volumes and, therefore, are under far greater strain than would be encountered in typical telecoms installations.
Fibers subjected to a constant strain, typically induced by bending or coiling, will eventually succumb to static fatigue because strain causes intrinsic microflaws (cracks) located at the fiber surface to grow. When these cracks have grown beyond a critical limit, they will quickly propagate across the fiber and cause it to fracture.
In these circumstances, the stressed nature of PM fibers may actually increase fiber lifetime values because SAPs that place the core in tension also place the fiber surface in compression, thereby resisting crack growth. Hard evidence of this strengthening phenomenon is difficult to find because of the highly statistical nature of fiber lifetime data.
However, from reviewing reliability data drawn from several million meters of PM fiber destined for FOG applications—that values of \(n_d\) are typically in the upper range of what might be expected of a more conventional single-mode fiber.
7.2. Strength Paradox II: Thin Fibers Can Be Stronger Than Thicker Ones
Review of the PM fiber data sheets from any manufacturer will reveal that many specifications are available in both 125-μm and 80-μm variants. A 125-μm glass diameter is a standard that was originally developed for the telecommunications industry and that has a number of advantages, primarily it is big enough to be seen and handled easily while being small enough to enable multifiber cable designs of acceptable dimensions and, being a standard means that a wide variety of compatible components are available.
However, once again, the more aggressive service environments often encountered by PM fibers should always be considered before making a final choice on fiber diameter. Put very simply, if a PM fiber is to be used in a small-diameter sensor coil, an 80-μm glass diameter will offer a significant increase in lifetime because of its enhanced resistance to mechanical failure through static fatigue.
Static fatigue is a phenomenon by which optical fibers can fracture spontaneously if subjected to bending stress or an invariant tensile load. The stress induces intrinsic and microscopic flaws located on the fiber surface to grow, causing fracture as soon as any flaw grows beyond the critical limit for the material.
Fibers are made more resistant to static fatigue, typically by applying one or more of two methods: increased proof test level and reduced glass diameter. Proof test involves straining the fiber to destruction to screen out intrinsic flaws; the higher the proof test level, the smaller the size of intrinsic flaw that will remain in the surviving fiber and the lower the probability that the fiber will fail under static fatigue.
The telecommunications industry standard for proof test is 1% strain. Deploy such a fiber in a 20-mm diameter FOG coil and it could fracture within months. When analyzing the reliability data for any fiber, you should always consider that lifetime predictions represent the valid design constraint of the very worst case of what could happen—not what will happen.
If a fiber is proof tested to 1% strain (~100 kpsi), the resulting lifetime estimate will assume that the fiber still contains a flaw only fractionally below the size necessary to have caused spontaneous mechanical failure during that proof test. In truth, the fiber has only been tested to around one-sixth of its tensile limit, so this flaw probably does not exist. In other words, observations that ‘‘none of the 10 units made in the laboratory 5 years ago have broken yet,’’ is not a valid reason to discount these lifetime predictions when progressing to high-volume production.
A more direct way to enhance lifetime is to limit bending stress levels by reducing the outside diameter of the fiber itself. A typical FOG fiber has a diameter of 80 μm—a little more than two-thirds of that of a standard telecommunications fiber (125 μm). When bent, the induced stress within these fibers is around 40% lower than that of the larger fiber (Fig. 8.23), slowing growth of intrinsic flaws and boosting lifetimes from mere months to 20 years or more.
When used in the FOG or other intrinsic fiber sensors, reduced-diameter fibers have the added benefit of enabling more fiber to be coiled within a given volume, enhancing the sensitivity that may be achieved from a specific form factor.
In conclusion, if you intend to use a PM fiber in a small package or coil, due consideration should be given to the choice of both glass diameter and proof-test level in any reliability-critical application.
The next tutorial discusses in detail about laser pumping and population inversion.