Elliptical Core and D-Shape Fibers

This is a continuation from the previous tutorial - Metal-coated fibers.

 

1. OVERVIEW

Elliptical Core Optical Fiber

Most polarization-maintaining \(\textbf{(PM)}\) fibers work on the basic principle of creating two decoupled paths by introducing anisotropic stress generated by the different thermal expansions of the glass materials across the optical core region.

In comparison, the elliptical core single-mode fiber employs the distinct property of geometry or form birefringence, rather than stress, to achieve its polarizationpreserving characteristics. By separating the propagation constants of the two fundamental modes, the elliptical core fiber is able to reduce intermodal coupling.

As a result, the polarization is maintained over a significant distance to be used in interferometric sensors.

In 1961 the first solution of an elliptical dielectric rod was published by Lyubimov et al. Later the next year, Yeh outlined the extensive analysis of the elliptical core waveguide.

When fiber optics emerged as the likely candidate for long-distance transmission lines, Dyott and Stern analyzed the slightly elliptical core optical fiber as an annoying limitation in telecommunication links based on the group delay difference between the two orthogonal fundamental modes, which was followed by a study by Schlosser of delay distortion due to elliptical deformation.

Ramaswamy et al. and Dyott et al.  soon realized that when the ellipticity and the core-to-cladding index difference are made sufficiently large, intermodal coupling is reduced, polarization is maintained, and elliptical core fiber applications eventually emerged generally concentrated in interferometric sensors.

This larger core-to-cladding index contrast is useful not only to maximize the birefringence, but also to prevent radiation when the fiber is bent around a small radius.

Another requirement particularly useful in interferometers is that extraneous light launched into the cladding is rapidly attenuated, even in short fiber lengths, minimizing spurious interference.

This is satisfied by a nonguiding cladding, a cladding with an index lower than the surrounding medium, often referred to as a depressed index cladding. The elliptical fiber’s azimuthally stable modes are exploited in a new set of higher order mode sensors not available with the standard circular core fiber.

 

D-Shape Elliptical Core Fiber and Variations with Assessable Regions

The \(D\)-shape elliptical core fiber satisfies two additional and important requirements for polarization-preserving fiber: the accurate angular location of the birefringent axes and access to the optical fields.

Because the flat is close to the cladding, the evanescent optical fields are assessable after removing only a small amount of silica material. The \(\text D\) shape with the flat of the \(\text D\) parallel to the major axis of the elliptical core is generally preferred because of the tighter mode field of the \(\textbf{eHE}_{11}\) mode, compared to the \(\textbf{eHE}_{11}\) mode.

The axes of birefringence are positioned by locating the flat of the \(\text D\) typically against a flat surface or by the glint from the reflection off of the flat. This inherent feature of the D-shape fiber locates the birefringence axes no matter how far down the fiber from a reference point and circumvents the lack of angular reference exhibited by circular clad commercial \(\textbf{PM}\) fibers that exhibit some degree of internal twist.

These unique features of the \(\text D\)-shape fiber facilitate \(\textbf{PM}\) component fabrication described in subsequent sections.

Several key shape and orientation variations of the standard D-shape fiber find interesting applications. Figure 1a and b show the standard orientation and 90-degree rotated elliptical core versions of the \(D\)-shape fiber.

The vertical core orientation \(\text D\)-shape fiber is used in partially etched replaced core devices. The rotated core orientation near 45 degree (Fig. 2c) was investigated with surface relief Bragg gratings. The quadrant fiber (Fig.1d) was proposed in 1985 to make co- and cross-polarized couplers.

Because much of the work in integrated optics is based on Si substrate platforms, modified circular clad (Fig. 1e), and \(\text D\)-shape fiber with the flats at the appropriate 70.5-degree (Fig. 1f) mate perfectly with the standard anisotropic wet etched \(\text{Si}\;V\) groove.

The main advantage is coupling to integrated optics without the need for active polarization alignment. A notched D-shape fiber (Fig. 1g) enables higher electric fields across the core region for all fiber electro-optic devices.

 

 

 

 

2.  MANUFACTURING OF ELLIPTICAL CORE AND D-SHAPE FIBERS 

One method to manufacture an elliptical core preform is to fabricate a tube with non-uniform thickness and collapse the tube by heating it to the softening point. The surface tension in the shaped walls during the collapse and subsequent draw cause the fiber core to be nearly elliptical in cross-section.

In this way, a familiar method to make circular core fiber using modified chemical vapor deposition is tailored to create a noncircular core. Referring to Fig. 2, the initial circular silica tube is ground with two opposing slight flats on the outer 

 

 

 

periphery. Then, after cleaning the inner surface, a series of fluorine-doped silica glass layers are deposited inside to create the depressed index cladding. The cladding index is approximately 0.003 less than the index of pure silica, which is enough to prevent interaction between the guided light and the undesirable cladding modes.

A final deposition of germania-silica is deposited for the core before the preform collapse. The nominal core-to-cladding index difference is 0.035. During the outer collapse of the preform, surface tension pulls the outside surface circular and the resulting inner index profile exhibits a noncircular crosssection.

The depth of the opposing ground flats and the magnitude of the vacuum control the geometry of the core during the preform collapse. The target is an approximate ellipse with the core’s major to minor axis ratio of 0.5.

A small vapor spot or dip in the index profile centered on the fiber axis occurs during the preform vacuum collapse. Subsequently, some diffusion of the core–cladding boundary occurs during the fiber pulling.

To produce \(\text D\)-shape fibers and other custom-shaped fibers, the circular preform is mounted, with the proper angular orientation of the elliptical axis, inside a grooved surface plate fixture and ground.

The initial coarse grind removes the bulk of the material. Several fine grinds allow for a smooth finish on the flat of the \(\text D\)-shape preform, thereby reducing the potential for scattering and generally improving the polarization holding.

Usually the flat does not intersect the outer edge of the depressed-index cladding boundary. With the noncircular outer surface of the preform and the core in a predetermined geometric relationship to the core, the drawing rate and temperature are controlled to produce a fiber with a cross-section similar to that of the preform.

 

3.  ELLIPTICAL CORE FIBERS: CHARACTERISTICS AND PROPERTIES

The core boundary is defined by an elliptical cross-section with major and minor radii, \(a\) and \(b\), and with ellipticity \(b/a\).

Using \(n_1\) and \(n_2\) for the core index and cladding index, respectively, the normalized frequency is defined by 

\[\tag{1}V_b=k_ob\sqrt{(n^2_1-n^2_2)},\]

where \(k_o=2\pi/\lambda_0\). Exact closed-form solutions to calculate propagation constants of the elliptical core step-index fiber modes are not available because of the azimuthally asymmetry of the elliptical geometry. Instead, the propagation constant of each mode is solved by setting up a determinant of a truncated set of infinite Mathieu functions.

Other approaches using equivalent rectangular waveguide or equivalent circular guide approximations are established as well. Although the results from these approaches agree fairly with the measurements, it is commonplace to employ modern numerical techniques to solve for the propagation constants and mode fields.

The fundamental circular core \(\textbf{HE}_{11}\) mode splits into two modes: odd \(\textbf{HE}_{11}\textbf({oHE}_{11})\) and even \(\textbf{HE}_{11}\textbf{(eHE}_{11})\) derived from the odd and even Mathieu functions, respectively, as the ellipticity is introduced. Both \(\textbf{eHE}_{11}\) and \(\textbf{eHE}_{11}\) modes have no cutoff.

The \(\textbf{eHE}_{11}\) mode has transverse electric fields along the major axis of the guide. Likewise, the \(\textbf{eHE}_{11}\) mode has transverse electric fields along the minor axis, as shown in Fig. 3. The propagation constant of the \(\textbf{eHE}_{11}\) modes is greater than that of the \(\textbf{eHE}_{11}\) mode because the \(\textbf{oHE}_{11}\) is bound tighter inside the core compared to the \(\textbf{eHE}_{11}\) mode. A greater percentage of

  

 

 

power is in the core for the \(\textbf{oHE}_{11}\) mode. Consequently, the \(\textbf{eHE}_{11}\) evanescent tails extend further into the cladding than those of the \(\textbf{oHE}_{11}\) mode.

These features are exploited in many useful devices. The \(\textbf{oHE}_{11}\) mode is usually preferred because its smaller velocity is more resistant to bend-induced radiation. Frequently, these two fundamental modes are referred to as the slow and the fast mode, for the \(\textbf{oHE}_{11}\) and the \(\textbf{eHE}_{11}\) mode, respectively.

In the elliptical core waveguide, all of the modes are hybrid, \(\textbf{HE}_{nm}\) or \(\textbf{EH}_{nm}\), in comparison to the circular core waveguide that allows circular symmetrical nonhybrid modes \(\textbf{TE}_{0n}(H_{0n)}\) and \(\textbf{TM}_{0n}(E_{0n)}\). 

 

Birefringence

The difference between the normalized propagation constant of the two fundamental modes, \(_0\bar\beta=_0\bar\beta/k_0\;\text{and}\;_e\bar\beta=_e\beta/k_0\) is the fiber birefringence,

\[\tag{2}\Delta\bar{\beta}=_0\bar\beta-_e\bar\beta.\]

The fiber birefringence is of great value serving to de-couple the propagation constants and maintain the polarization. For most practical fibers, \(\boldsymbol{\Delta\beta}\) is proportional to the square of the index difference between the core and the cladding.

Therefore, elliptical core fibers with large core–cladding index differences will exhibit higher birefringence. Usually the beat length characterizes this birefringence, \(L_B=\lambda_0/\boldsymbol{\Delta\bar\beta}\). Elliptically core fiber has a birefringence strongly dependent on wavelength .

The maximum achievable normalized birefringence is based on the ellipticity and \(V_b\), as shown in Fig 4. \(\textbf{KVH}\) Industry’s elliptical core fiber typically exhibits a normalized birefringence of at least \(1.5\times10^{-4}\).

Zhang and Lit investigated the temperature and strain sensitivities of the birefringence between three types of \(\textbf{PM}\) fibers. The two stress-induced birefringence fibers exhibited temperature sensitivities that were seven times larger than

 

 

 

that of the elliptical core fiber. This residual sensitivity of the elliptical core fiber is due to the small component of stress-induced birefringence caused by the expansion mismatch between the core and the cladding during manufacturing as the fiber cools.

The variation of the locked-in stress with temperature changes the birefringence. In regards to the strain sensitivity, the two stress-induced birefringence fibers were 27 times more sensitive than the elliptical core fiber. Because the birefringence is based on the shape of the core, the elliptical core fiber exhibits stable characteristics under adverse conditions of bending, twisting, and wide temperature variations, which can seriously degrade the performance of stressinduced birefringence fibers. Similar measurements of modal birefringence and its sensitivity to temperature and hydrostatic pressure have been reported. 

The difference in the group index \(n_\text g=\frac{c}{\text{vg}}\) for each fundamental mode is termed the group birefringence, \(\Delta n_g=_e n_g-_0n_g\) and is related to the birefringence, as shown in Eq. (3): 

\[\tag{3}\Delta n_g=\left[\Delta\bar\beta+V_b\frac{\partial(\Delta\bar\beta)}{\partial V_b}\right]\]

Elliptical core fibers exhibit a group birefringence that is highly dependent on the operating wavelength.

The group birefringence is used to calculate the differential time delay between the two fundamental modes for a given length of fiber. The point of vanishing group birefringence, where \(\Delta\bar\beta=-V_b\frac{\partial(\Delta\bar\beta)}{\partial V_b}\), is always in the overmoded region for the elliptical core fiber regardless of the ellipticity.

 

Polarization Holding

\(\textbf{PM}\) fibers are important to fiber sensors, integrated optic interconnections, fiber jumpers, source pigtails, and many other devices. An important characteristic of birefringent fibers is the ratio of the power leakage into the unexcited mode to that of the total input power.

The statistical determination of the polarization transfer as a function of length is characterized by the h parameter. The inverse \(1/h\) is the characteristic distance for the polarization transfer. Measurements of the h parameter of \(\textbf{KVH’s}\) elliptical core fiber are routinely 50 \(\text{dB/m}\).

The elliptical core fiber generally has a reduced intrinsic sensitivity because the birefringence axes are controlled during the drawing process.

 

Ellipticity and Higher Order Modes

Elliptical core fibers have nearly twice as many modes as the circular core counterpart because of the broken circular symmetry. The first set of higher order modes, the \(\textbf{TE}_{01}\) \(\textbf{(H}_{01})\), and \(\textbf{TM}_{01}\;\textbf(E_{01})\) modes of the circular core fiber, transform into \(\textbf{eHE}_{01}\) and \(\textbf{oEH}_{01}\) hybrid modes without circular symmetry. The first higher order mode of the elliptical core fiber, \(\textbf{eHE}_{01}\), depends on the ellipticity and the normalized cutoff wavelength is defined by an empirical expression from Dyott:

\[\tag{4}V_{bcutoff}=2.405(b/a)^{0.6275}\]

The second higher order mode depends on the ellipticity and \(\Delta n\). For practical values of \(\Delta n\) and ellipticity \(0.38<b/a<1\), the \(\textbf{oEH}_{01}\) mode is the second higher order mode.

However, when b/a<0.38, a mode is borrowed from the third set of higher order modes. The third set of higher order modes is based on the splitting of the circular \(\textbf{HE}_{21}\) mode into the \(\text{eHE}_{21}\) and \(\text{oHE}_{21}\) modes.

Consequently, when b/a<0.38, the \(\textbf{eHE}_{21}\) mode is the second higher order mode. The power distributions and transverse electric fields of the pertinent modes are shown in Fig. 3. The power distribution splits from a central region for the \(\textbf{eHE}_{11}\) and \(\textbf{oHE}_{11}\) modes into double regions for the \(\textbf{eHE}_{01}\) and \(\textbf{oEH}_{01}\) modes.

These double regions are aligned with the major axis of the ellipse. The first two sets of common modes are grouped together and often called the \(\textbf{LP}_{01}\) and even \(\textbf{LP}_{11}\) modes.

The sequence of modes of an elliptical core fiber for two values of ellipticity, \(b/a=0.8\) and \(b/a=0.375\), were experimentally confirmed (Fig. 5). 

When operating a two-mode device, usually the dominant modes and the first set of higher order modes are used.

The next higher order mode is avoided by proper selection of the ellipticity and the operating wavelength with the largest bandwidth noted near b/a=0.5. The main advantage of the elliptical core fiber is that the higher order mode-field pattern orientations are stable.

In a circular core fiber, the modes are degenerate and the small external perturbations or waveguide perfections introduce phase shifts and uncontrollable coupling between the modes. The differences in the propagation constants between the dominant modes and the first higher order modes with common polarizations, are proportional to the core-to-cladding index, \(\Delta n\).

 

 

4.  D-SHAPE FIBERS: CHARACTERISTICS AND PROPERTIES

The extraordinary advantage that the \(D\)-shape fiber supplies is the opportunity for manufacturing all fiber optical components, which in general possess intrinsic benefits such as reduced back-reflection, low insertion loss, and yet polarization preservation.

These components and devices are so-called evanescent field devices that can be constructed on a \(D\)-shape optical fiber waveguide

 

 

 

substrate. Wet-etching away the silica-based cladding materials enables access to the guiding waveguide field.

 

Accessing the Optical Fields: Fiber Etching 

The field of the propagating wave distributed in the elliptical core extends beyond the core–cladding interface decaying exponentially from the interface into the cladding.

Generally, a waveguide with a small \(V\) value has larger magnitude of the field in the cladding. For instance, the diameter of \(\textbf{KVH’s}\) standard \(D\)-shape fiber used in \(\textbf{FOG}\) is 85 \(\mu m\) and the distance of the flat from the core center is 10 \(mu m\).

Wet etch removes the cladding silica and fluorine-doped silica isotropically. By fine control of the etching process, the tail of the evanescent wave can be accessed from the direction of the fiber flat.

By modifying the cladding material close to the core–cladding interface, the waveguide characteristics will be changed and consequently the propagation characteristics and that of the guiding light will be also changed.

Besides the wet-etching fiber method, there are several other techniques to access the evanescent wave in \(D\)-shape fibers, which include: tapering the fiber in heat, heating the fiber to defuse the dopants in the core (e.g., germanium) into cladding, etching to reduce the whole cladding diameter, and side-polishing a region of the one side of \(D\)-shape or circular fiber.

Among all these techniques, wet-etching the \(D\)-shape fiber is convenient and accurate. The degree of the evanescent wave access is among the best, as explained in the following subsections.

 

Wet Etching of Silicon Dioxide–Based Cladding and Germanosilicate Core

Hydrofluoric \(\textbf{(HF)}\) acid and buffered oxide etch \(\textbf{(BOE)}\) are widely using in the fabrication of micro-electromechanical systems, integrated circuits, fiber probes for near-field optics, and all-fiber devices.

The exact chemical mechanisms are complex. The main reaction between silicon dioxide and HF acid are

\[\tag{5}\text{SiO}_2+6\text{HF}\rightarrow\text{H}_2\text{SiF}_6+2\text{H}_2\text O.\]

The etch rate depends on etchant concentration, agitation, time, and temperature. Addition of ammonium fluoride \(\textbf{(NH}_4\textbf F)\) creates a buffered \(\textbf{HF}\) solution \(\textbf{(BFH)}\), or \(\textbf{BOE}\), that maintains a more stable etching rate, because addition of ammonium \(\textbf{NH}_4\textbf F\) to \(\textbf{HF}\) controls the \(\textbf{pH}\) value and replenishes the depletion of fluoride ions.

\[\tag{6}\text{NH}_4\text F\leftrightarrow\text{NH}_3+\text{HF}\]

In a \(\textbf{BOE}\) solution, the \(\textbf{H}_2\textbf{SiF}_6\) further react with \(\textbf{NH}_3\) as the following:

\[\tag{7}\text H_2\text{SiF}_6+2\text{NH}_3\rightarrow(\text{NH}_4)_2\text{SiF}_6\]

Similarly, \(\textbf{GeO}_2\) undergoes analogous reactions. Nevertheless, the rates of reactions and the dissolution of germanium-related products—\(\textbf{H}_2\textbf{GeF}_6\), \(\text{(NH}_4)_2\) \(\textbf{GeF}_6\), and so on—are different with those of silica ones, which results in the different etching rate in the \(\textbf{GeO}_2\)-doped region depending on the proportion of the constituents of the etchant.

\(\textbf{BOE]\) consists of a mixture of 40% ammonium fluoride and 49% \(\textbf{HF}\) solution in a ratio of \(X:1\), etching characteristics of different regions of the fiber depends on this ratio. For lower values

of \(X(X<5)\), the \(\textbf{GeO}_2\)-doped core etches at faster rate compared to fluorinedoped silica cladding and pure silica cladding.

As the concentration of HF in the mixture decreases \((X>5)\), \(\textbf{GeO}_2\)-doped core etches at a slower rate. The fluorine-doped silica region etched at a faster rate than \(\textbf{GeO}_2\)-doped core and pure silica cladding and the rate is independent of the proportion of the constituents of the etchant.

The relatively different etch rates enable a selective etch to the cladding and core according to the needs.

 

Standard Etching (Etch to Reach Evanescent Field)

Because the etching rate is strongly dependent on the etching conditions, accurate control of the degree of the etching to the fiber is crucial for a predictable manufacturing process.

The etching conditions, such as acid concentration and temperature, have to be maintained accurately. To relieve the requirements for the strict condition control, a real-time monitor of the etching process was proposed.

The \(\textbf{PM}\) properties of the \(\textbf D\)-shape fiber enables this type of monitor by the use of an in situ optical polarimetric measurement.

The etching setup with an optical monitor is shown diagrammatically in Fig. 6. Light from a coherent source is launched at 45 degrees to the birefringent axes of the fiber, exciting both fundamental modes equally.

The source wavelength is chosen to produce a strong evanescent field in the fiber, that is, the \(\text V\) value should be at the lower end of its operating range. The coherence length

 

 

 

\(L_s\) of the source should be long enough so that the de-coherence length \(L_D\) is much longer than the fiber length \(L\), where

\[\tag{8}L_D=\frac{L_s}{\Delta\boldsymbol{\bar\beta}+V\frac{\partial(\Delta\boldsymbol{\bar\beta})}{\partial V}}.\]

Light emerging from the other end of the fiber passes through a Soleil–Babinet compensator and another polarizer onto a detector and amplified using a lock-in amplifier. The data are then stored and displayed in a \(\textbf{PC}\).

During the etch, first the silica boundary layer and then the cladding of the fiber-guiding region (having a refractive index of \(\sim1.5)\) are replaced by the acid/ water solution with an index of about 1.33.

When the acid reaches the evanescent field region, the phase velocity of both fundamental modes is increased. However, the even \(_\text{eHE}{11}\) mode has an evanescent field extending further than that of the odd \(_\text{oHE}{11}\) mode so that a phase shift is introduced between the modes causing a rotation of the polarization of the light emerging from the fiber, which is converted by the output polarizer into a change in amplitude of the detected signal.

Figure 7 shows a typical plot of detector output versus time. The periodic variations become more and more closely spaced until eventually the acid reaches the core and the amplitude of the signal becomes zero.

 

 

 

The method can control the etching depth very accurately with excellent repeatability. The accuracy of etching also depends on the length of the etched section. Estimated accuracy for etching \(\textbf D\)-shape fiber of 3-cm long is several tens of nanometers. 

The polarimetric monitor provides a sensitive measurement on the relative etching degree so long as the cladding-water interface reaches the evanescent field tail. As described later, the degree of etching required to manufacture fiber polarizers and couplers is slight, as only the tail of the evanescent field is barely exposed.

On the other hand, to achieve a better manipulation of the guided light, a deeper and selective etching on the fiber cladding enables the exposure of the fiber core.

 

Exposing the Core

Using a \(\textbf{BOE}\) of \(\textbf{NH}_4\textbf F:\textbf{HF}\) ratio of \(20:1\), the etch rate of the cladding is more than 10 times larger than that of the core. The upper half of the cladding can be removed and the core can be exposed from the upper side of the fiber.

A typical cross-section of a core-exposed \(\textbf D\)-shape fiber is shown in Fig.8. The etching was done in two steps. The first step is to pre-etch the \(\textbf D\)-shape fiber

 

 

 

using 25% HF acid to remove the relatively bulky cladding material quickly because the etch rate is high for \(\textbf{HF}\) acid to the fluorine-doped and pure silica. The second step is a fine-etch of the cladding material to expose the core using \(\textbf{BOE}\), which has a relatively slower etch rate to cladding than the \(\textbf{HF]\) acid.

Figure 9 shows the polarimetric etch monitor output as a function of etch time during the second step. The periodic variation continues to become more closely separated at the first five recorded periods, and then the spacing of the peaks becomes eventually larger.

At this time, the fiber flat position is etched close to the position of the major axis of the core ellipse, and the group velocity of odd \(_\textbf{oHE}11\) mode is more influenced by the removal of the cladding than that of the even \(_\textbf{eHE}11\) mode. 

Because the air in the core-exposed section replaces approximately half of the upper side of the cladding material, the \(\text V\) value of the section is significantly raised. The insertion loss increase is mainly due to the mode-field mismatch at the two transition areas, although surface scattering loss from the core–air interface also contributes.

If a material with a refractive index close to the original \(\textbf F\):\(\textbf{SiO}_2\) cladding is used to replace the cladding, the waveguide characteristics can be recovered. This creates an exciting opportunity for novel on-fiber devices.

 

 

 

Partial and Full Core Removal

In principle, the wave-guiding field can be further manipulated if the fiber core is fully, or partially, removed, and the empty core is refilled with certain functional material that replaces the removed core and rebuilds the waveguide characteristics. The method and technique for partially and fully removing the core of the \(\textbf D\)-shape fiber have been proposed.

This technique enables new and exciting opportunities in the field of in-fiber electro-optic devices by refilling the removed core with an electro-optic active polymer to fabricate, for example, all-fiber modulators. The selective removal of the core is based on the differential etching of \(\textbf{HF}\) acid to the fiber materials. The pure \(\textbf{HF}\) acid etches the germa-nosilicate core with a rate \(\textbf{11}\) times faster than the rate for etching the pure thermal silica and approximately 8 times faster than the fluorine-doped silicon dioxide cladding.

When the cladding is etched away and the interface is tangent to the core ellipse, the \(\textbf{HF}\) etches the germanosilicate core with a much higher rate than the cladding, and the core is selectively removed.

During the core removal, the relatively higher refractive index core \((n_\text{core}=1.4756)\) is gradually replaced by the lower index etchant \((\text{n}_\text{HF}=1.33)\).

The decrease of effective index of refraction of the waveguide also decreases the \(\text V\) value of the waveguide and the power transmission decreases correspondingly, because of transition and scattering loss. Finally, the transmission is thoroughly terminated. Although the polarimetric etching monitor technique explained in Section Standard Etching (Etch to Reach Evanescent Field) is applicable in this situation as well (Fig. 7), an easier method to control the in situ etching process is to monitor the power change directly because of the dramatic power change during the core removal.

Figure 9. shows a recorded transmission of power as a function of etching time. The power starts to rapidly decrease when the core etching begins.

The etching rate is then hindered by the so-called vapor spot, which is relatively poor in germanium, and resumes to the high rate until the whole core is removed. The cross-sections at different intermediates are shown as inserts in Fig. 9.

 

 

5.  D-SHAPE FIBER COMPONENTS

The elliptical core \(\textbf D\)-shape fibers are used to create rudimentary \(\textbf{PM}\) components. These components are used extensively in all types of interferometers; however, a long list of other applications includes fiber amplifier pump couplers, reflectors, filters, polarization monitors, and various sensors.

The use of elliptical core \(\textbf D\)-shape fiber opens the possibilities of constructing spliceless interferometers and fiber optic assemblies that eliminate additional losses, spurious reflections, and any distinct polarization coupling points at the splices.

 

Couplers

A true evanescent field coupler can be made by two \(\textbf D\)-shape fibers positioned flat-to-flat in comparison to the tapered optical fiber couplers with a small-diameter pulled-down region acting as the core with a free space cladding. The main advantages of the \(\textbf D\)-shape fiber couplers are that the light remains guided completely in the cores and the guiding regions are completely enclosed.

As a result, there is no coupling dependence or loss due to the surrounding materials.

\(\textbf{PM}\) couplers are characterized by insertion loss, power split ratio, and extinction ratio. Practical \(\textbf{PM}\) couplers exhibit stable properties over temperature.

Performances of \(\text D\)-shape elliptical core couplers include less than 0.3-\(\textbf{dB}\) loss and better than 25-\(\textbf{dB}\) extinction ratio. With tuning, the coupling is typically held to within 1–2% of the desired splitting ratio.

One method of tuning the coupler is by heating and pulling to slightly reduce the diameter of the fibers and extend the evanescent fields. Another method, diffusion tuning, is preferred. With diffusion tuning, heat is applied to the coupler to diffuse the germania-doped cores into the common cladding region.

The power ratio between the two output coupler legs is monitored at the desired wavelength to determine when to terminate the diffusion process.

The thin outer layer of silica between the depressed index cladding and the flat of the \(\text D\)-shape fiber and a small portion of the depressed index cladding are removed typically by wet etching throughout the coupler region before coupling.

In this way, the amount of required diffusion to produce a 50/50 coupler is reduced. Excessive diffusion of the cores enlarges the effective optical mode fields, which will eventually overlap with the silica index cladding outer boundary resulting in high insertion loss. Index-matched–clad \(\textbf D\)-shaped fibers can be used to make both types of couplers, diffusion, and pulled tapered types, without the preliminary wet etching step.

With the \(\textbf D\)-shaped flats aligned and fused together using a heat source, the temperature stability and thermal mismatch concerns are addressed. Surrounding the coupler in a \(\text{Vycor}\) glass tube or channel mitigates variable coupling and polarization performance due to a change in the refractive index of the coupling region from mechanical strain.

Such mechanical strains are inherent with bending or twisting of the fiber leads and when using packing materials with mismatched coefficients of thermal expansion. Because the Vycor glass softens approximately \(100^\circ\) lower than silica and exhibits a thermal coefficient of expansion matching that of silica, the surrounding Vycor fixes and protects the fiber coupler leads.

Figure 10. shows the cross section of a \(\textbf D\)-shaped elliptical core diffusion tuned fiber coupler in a vacuum-collapsed Vycor tube.

 

 

 

Loop Mirrors 

A \(\textbf D\)-shaped elliptical core fiber is particularly suitable to fabricate a polarization preserving all fiber loop mirror or reflector by looping back the flats of the fiber to make a 50/50 coupler.

If the 50/50 coupler is lossless then all of the incident power is reflected along the input fiber. The loop acts as a wavelength dependent reflector that is sensitive to the variation in coupling with wavelength.

In one application, the loop mirror at the end of a fiber laser will let the pump power in and block the light at the lasing wavelength. The \(\textbf D\)-shape elliptical core fiber is the perfect candidate to be used in the construction of birefringent all fiber cascaded higher order filters and all fiber reflection Mach–Zehnder interferometers.

 

Polarizers 

A fiber optical polarizer is one of the fundamental components in all-fiber optical interferometers and many other fiber systems that are highly dependent on the polarization of the light guided by the optical fiber.

Various methods to make relatively short fiber polarizers often involve grinding or polishing circular clad fiber laterally and exposing the core to a birefringent crystal, a birefringent film, or using a thin metal film or a thick metal film to induce differential attenuation in the orthogonal modes of a birefringent fiber.

Another type of all-fiber polarizer is based on longer lengths of single-polarization fibers often wrapped in small-diameter coils to induce differential polarization bending loss.

When a proper birefringent crystal is used to replace the portion of removed cladding, the refractive index of the crystal is less than that of the effective index of the waveguide for the transmitted mode and greater than that of the orthogonal mode, causing the unwanted light to escape into the bulk crystal.

Birefringent properties of liquid crystals have been used to make an all-fiber polarizer in this manner.

A similar approach, but without the birefringent material, uses a thin multimode planar dielectric overlay of zinc sulfide, vacuum deposited directly onto the fiber, and relies on differential coupling between the \(\textbf{TE}\) and \(\textbf{TM}\) like modes of the asymmetrical structure.

In this arrangement, the \(\textbf{TE}\) and \(\textbf{TM}\) resonances are sufficiently shifted to act as a polarizer across a limited wavelength range.

Thick metal film polarizers with a low index dielectric buffer layer between the optical fiber core and the metal interface rely on bulk absorption caused by the imaginary part of the refractive index of the metal at optical frequencies above the plasma resonance frequency.

Other types of fiber polarizers use very thin layers of single metal or bimetal film configurations (5–30 nm) in close proximity to the core (1–2 \(\mu m)\) to create surface-plasmon waves, which selectively couple the waveguide’s evanescent waves.

Fiber polarizers of varied configurations using aluminum, chromium, gold, silver, nickel, indium, and platinum have been constructed with high polarization extinction ratios.

Polishing even short lengths of circular clad fiber consistently to the required submicron accuracy and simultaneously aligned with the birefringent axes to maintain low loss and high polarization extinction is difficult. One of the most efficient and easiest ways to manufacture fiber optical polarizers is based on the \(\textbf D\)-shape elliptical core fiber.

An etched \(\textbf D\)-shape fiber, typically 30–70 mm long, covered with a thin, yet optically thick, metal of indium film will selectively suppress modes with the electric field orthogonal to the fiber metal surface and results in high extinction ratio (>50 \(\text{dB})\) and low-loss (0.5 \(\text{dB})\) fiber optic polarizers.

The polarizer can be fabricated at any point along the fiber and cascaded with other \(\textbf{PM}\) fiber components. 

 

Butt Coupling to Active Devices

The first step for all the fiber optic applications is to couple a maximum amount of light from a single-mode laser diode to the fiber. For a \(\textbf{PM}\) fiber, the coupling efficiency is dependent not only on the regular alignment parameters such as lateral, axial, and angular offsets, but also on the rotational alignment between the major axes of the mode fields of fiber and laser.

\(\textbf D\)-shape elliptical core fiber is beneficial for this type of alignment.

Commonly used techniques to coupling laser diodes to standard circular fibers use either a focusing lens or a microlens fiber tip. The latter is preferable because it produces highly efficient coupling and compact packaging. Chemical etching and subsequent heat melting generally form the fiber end microlenses.

However, these techniques have practical problems for the fibers with stress-induced birefringence, such as bowtie and \(\textbf{PANDA}\)-type fibers.

The microscale stresses at the core region do not allow the uniform etching and melting required for making quality microlenses. Several techniques have been proposed and demonstrated to overcome the problems, but processes were cumbersome or offered limited coupling efficiency.

For the \(\textbf{KVH}\) \(\textbf D\)-shape elliptical fibers, the birefringence is significantly attributed to the geometric factor (i.e., the elliptical shape of the core), and the contribution from the local stress is minor.

Therefore, the non-uniform etching and melting problem induced by stress is not as critical as the other types of \(\textbf{PM}\) fibers. One practical issue to overcome is that the axis of microlens formed through the wet-etching and flame, or laser, melting does not coincide with core axis of the asymmetrical \(\textbf D\)-shape fiber.

Although there is a possible solution for this problem, making the fiber symmetrical by wedge polishing the opposite side of the flat of a \(\textbf D\)-shape fiber tip before etching, more procedures are required and reproducibility is a concern. Instead of the commonly used pig-tailing techniques, direct butt-coupling to the facet of a laser diode has proven to be a simple and convenient technique to make a highly efficient and stable laser coupling to a \(\textbf D\)-shape fiber.

The pigtail efficiency can be estimated as coupling two elliptical mode fields that are represented by two mismatched Gaussian beams. If the major axes of the two elliptical mode fields are overlapped as \(\text x\)- and \(\text y\)-axes and the coupling efficiency can be treated as composed of two coupling components in the \(\text x\) and \(\text y\) directions as

\[\tag{9}\eta=\eta_\text x\eta_\text y,\]

where

\[\tag{10}\eta_a=\frac{\int^\infty_0\psi^*_{1a}(a)\psi_{2a}(a)da}{\sqrt{{\int^\infty_0}|\psi_{1a}(a)|^2|\psi_{2a}(a)|^2da}},a=\text x,\text y\]

where, \(\psi_{1,2}(a)=\text{exp}(-a^2/\omega^2_{1a,2a})\) and \(\omega_{1a,2a}\) are the \(1/e\) amplitude radii of the field of the two beams in the \(\text x\), or \(\text y\), direction. The power coupling efficiency is expressed as

\[\tag{11}|\eta|^2=\frac{2\omega_{1x}\omega_{2x}}{\omega^2_{1x}+\omega^2_{2x}}\frac{2\omega_{1\text y}\omega_{2\text y}}{\omega^2_{1\text y}+\omega^2_{2\text y}}.\]

If we directly butt-couple a fiber that has a mode-field size of \(\omega_{1x}=4.2\mu\text m\) and \(\omega_{1\text y}=2.8\mu\text m\) to a laser that has a mode-field size of \(\omega_{2x}=3.8\mu\text m\) and \(\omega_{2\text y}=1.0\mu\text m\), the theoretical power coupling efficiency is \(|\eta|^2=\)63%, according to Eq. 11, in which the limitation from the modal asymmetry is outstanding because \(|\eta_x|^2=\)99% and \(|\eta_\text y|^2=\)63%.

The influences of the astigmatism of the diode lasers on the coupling efficiency are also studied theoretically.

It is found that the astigmatism is important only at high coupling efficiencies. The influence is negligible for coupling efficiencies less than 50%.

A \(\textbf UV\)-curable epoxy is used as an adhesive to attach a \(\textbf D\)-shape fiber to the laser diode facet. The epoxy has a refractive index close to that of silica, \(n\sim\;1.45\) at 820 nm.

With the outer medium changed from air to epoxy, the outer index of refraction changes from 1.00 to 1.46. Therefore, the reflection of the output cavity of the laser diode changes to some extent.

This reflection change results in furthering the lasing threshold change to a certain degree.

It has been demonstrated at \(\textbf{KVH}\) that a direct butt-couple of \(\textbf D\)-shape fiber to the facet of a laser diode results not only in a reasonable high efficiency but also good thermal stability.

This method has resulted in a 65% coupling efficiency. The pigtail is also reasonably stable over temperature. Figure 11 shows a typical pigtail stability evaluation chart measured in \(\textbf{KVH}\) production. The horizontal axis is temperature and the vertical axis is a normalized output

 

 

 

power with respect to the backward power measured from the photodiode attached with the laser diode. The normalized power changes 0.5 \(\textbf{dB}\) when the temperature change spans \(-46\) to \(62^\circ C\) due to the small change on the reflection when operating below threshold. With the proper choice of adhesives, the lifetime of the laser does not degrade as tested over several years.

Fiber-to-waveguide connection is one of the key technologies in the realization of guided-wave optical devices. Optical telecommunication systems are the leading force for these technologies.

Most of the applications in optical telecommunication are based on the use of random polarized light, because the available \(\textbf{PM}\) fibers are impractical and expensive for long transmission. Inside the network nodes, devices of well-defined polarization are one option to handle the polarization problems such as polarization-dependent loss \(\textbf{(PDL)}\) and the polarization mode dispersion \(\textbf{(PMD)}\).

The field of optical fiber sensors is another area where PM coupling to integrated optics is also needed. In such components using polarization modes, the rotational alignment between the devices and the inputs—and to a lesser extent the outputs—\(\textbf{PM}\) fibers must be very accurate.

Furthermore, when using different \(\textbf{PM}\) components in the systems, all the interconnections must be rotationally aligned with high precision to minimize polarization cross-talk between different polarization modes. The circular outer shape of the regular \(\textbf{PM}\) fiber does not give enough alignment accuracy through visual examination.

Several methods for rotational alignment of a \(\textbf{PM}\) fiber have been proposed. They are typically based on changing the phase difference between the polarization modes continuously and simultaneously rotating a polarizer in from the fiber. The phase difference can be varied to generate strain on the fiber such as heating, stretching, and pressing or by tuning the wavelength.

Accuracies between 0.2 and 1.0 degree are typically achievable with these methods. Slightly improved accuracy—less than 0.1 degree—was demonstrated with an interferometric technique using a broadband source. All of these methods are somewhat complicated and time consuming. 

The \(\textbf{D}\)-shape fiber guarantees a good alignment between the elliptical core axes and the flat. The accuracy can be controlled within 1 degree during preform grounding. This makes the rotational alignment simple and accurate according to the alignment of the fiber flat visually.

For a sensing system using interferometric architectures, for instance, in a fiber optic interference gyroscope, the spurious sub-interferometers are particularly harmful.

These spurious signals are created by Fresnel back-reflections due to the index mismatch between the integrated optics circuit and the fiber coil. In practice, a slant angle of 10 degrees on the \(\text{LiNbO}_3\) modulator circuit reduces power with respect to the backward power measured from the photodiode attached with the laser diode.

The normalized power changes 0.5 \(\textbf{dB}\) when the temperature change spans \(-46\) to 62\(^\circ C\) due to the small change on the reflection when operating below threshold. With the proper choice of adhesives, the lifetime of the laser does not degrade as tested over several years.

 

Coupling to Integrated Optics

Fiber-to-waveguide connection is one of the key technologies in the realization of guided-wave optical devices. Optical telecommunication systems are the leading force for these technologies. Most of the applications in optical telecommunication are based on the use of random polarized light, because the available \(\textbf{PM}\) fibers are impractical and expensive for long transmission.

Inside the network nodes, devices of well-defined polarization are one option to handle the polarization problems such as polarization-dependent loss (PDL) and the polarization mode dispersion \(\textbf{(PMD)}\). The field of optical fiber sensors is another area where \(\textbf{PM}\) coupling to integrated optics is also needed.

In such components using polarization modes, the rotational alignment between the devices and the inputs—and to a lesser extent the outputs—\(\textbf{PM}\) fibers must be very accurate. Furthermore, when using different \(\textbf{PM}\) components in the systems, all the interconnections must be rotationally aligned with high precision to minimize polarization cross-talk between different polarization modes.

The circular outer shape of the regular \(\textbf{PM}\) fiber does not give enough alignment accuracy through visual examination. Several methods for rotational alignment of a \(\textbf{PM}\) fiber have been proposed.

They are typically based on changing the phase difference between the polarization modes continuously and simultaneously rotating a polarizer in from the fiber. The phase difference can be varied to generate strain on the fiber such as heating, stretching, and pressing or by tuning the wavelength. Accuracies between 0.2 and 1.0 degree are typically achievable with these methods.

Slightly improved accuracy—less than 0.1 degree—was demonstrated with an interferometric technique using a broadband source. All of these methods are somewhat complicated and time consuming. 

The \(\textbf{D}\)-shape fiber guarantees a good alignment between the elliptical core axes and the flat. The accuracy can be controlled within 1 degree during preform grounding. This makes the rotational alignment simple and accurate according to the alignment of the fiber flat visually.

For a sensing system using interferometric architectures, for instance, in a fiber optic interference gyroscope, the spurious sub-interferometers are particularly harmful. These spurious signals are created by Fresnel back-reflections due to the index mismatch between the integrated optics circuit and the fiber coil.

In practice, a slant angle of 10 degrees on the \(\textbf{LiNbO}_3\) modulator circuit reduces the back-reflected power to below \(-60\) \(\textbf{dB}\). Because the axis of the butt-coupled fiber must be oriented according to refraction laws to preserve a low loss connection, the slant-polished angle of 15 degrees of \(\textbf{SiO}_2\) fiber is required.

During the preparation of the input and output fiber subassemblies, a small tube or block is attached to the end of each fiber. This tube is angle-cut and polished to minimize back-reflections from the interfaces.

The tube increases the surface area and bond strength of the pigtail and liability. \(\textbf{UV}\) or thermal curable adhesives are used to attach the fiber subassemblies to the chips. To de-couple the strain induced by the differential thermal expansion among the integrated optic chip, the fiber, and the packaging material, subassemblies with a strain-absorbing bow and a compliant adhesive are used.

 

 

6.  SPLICING

\(\textbf D\)-Shape to \(\textbf D\)-Shape Fiber Splicing

The \(\textbf D\)-shaped elliptical core fiber can be readily fusion spliced to itself with low loss, high strength, and excellent polarization properties. The flat is used for polarization alignment of the PM fiber core without the usual cumbersome fiber side-viewing techniques to align the birefringent axes.

The \(\textbf D\)-shape of the \(\textbf{PM}\) fiber aids in orientation alignment when the components are spliced into a fiber optic gyroscope and other interferometers that require high polarization extinction levels. Using an industry standard fusion splicer—the Ericsson Model 975—the \(V\)-groove chucks and the mechanical flat top clamps perfectly aligning both fibers with the flats upright.

As a result, the splice insertion losses are, at most, 0.5 \(\textbf{dB}\) with the best splice losses being too low to measure. Typically, the splice extinction ratios are better than 25 \(\textbf{dB}\).

The \(\textbf D\)-shape fiber’s self-aligning feature enables efficient and economical fusion-spliced \(\textbf{PM}\) fiber assemblies. The orientation of the major axis of the fiber core is readily recognized and aligned for the splice because the fiber flat has been ground parallel with the major axis of the elliptical core during the preform fabrication.

 

\(D\)-Shape to Circular Clad Fiber Splicing

Connection to other types of optical fibers is sometimes necessary. Splicing \(\textbf D\)-shaped fiber to circular clad fiber is feasible as well. Dissimilar optical fiber cross-sections are difficult to splice together with simultaneous high-strength and low-loss properties.

Large transverse movements or offsets with respect to the optical mode-field size between the two fibers result because of the asymmetrical forces from surface tension during the fusion molten glass stage.

Furthermore, if a tolerable insertion loss is achieved, the fusion splice is weak because the dissimilar cross-sections are subject to high stresses at the junction.

One straightforward method to remedy these difficulties is to edge-polish the cleaved end of the circular clad fiber before the fusion process. In this way, the circular clad fiber takes on the \(\textbf D\) shape just at the cleaved surface. Figure 12 shows the edge of the circular clad fiber undergoing polishing. The cleaved end of the fiber extends a predetermined distance from the holder and is lowered gradually to meet the polisher.

After the initial setup, the edge-polishing process is very reproducible. The resultant edge-polished fiber is shown in Fig. 13. In Fig. 14, the side-view of the edge-polished circular clad fiber is shown mated up to the \(\textbf D\)-shape fiber. The splice loss, which usually depends on the mismatch between the fiber mode fields (Eq. [11]), is lessened because of thermal diffusion of the core to clad boundary of the higher index difference optical fiber.

Routine splice losses less than 0.8 \(\textbf{dB}\) are achievable when splicing \(\textbf{KVH}\)’s elliptical core \(\textbf D\)-shaped fiber to Corning’s \(\textbf{SMF}\)-28 fiber. To maintain the polarization through a splicebetween aD-shapeandacircular cladPMfiber, the angular orientation of the circular \(\textbf{PM}\) fiber must be prealigned with the fiber holder before edge-polishing.

 

 

7.  IN-FIBER DEVICES

Three unique characteristics of the elliptical core \(\textbf D\)-shape fiber facilitate the developments of in-fiber devices: The \(\textbf D\)-shape fiber clad simplifies a long-distance access to the evanescence field through selective wet etching, the 

 

 

 

 

 

 

elliptical core maintains light polarization, which is crucial for interferometric sensors and devices, and the high-level germania constituent enhances the photosensitivity to the grating on the fiber core. Utilizing one, or a combination, of these characteristics, different types of the devices and sensors have been proposed and demonstrated. 

 

 

 

Electro-Optic Overlay Intensity Modulators

Extensive theoretical and experimental studies have been carried out on the fiber optic components based on the principle of asymmetrical directional coupling. In these devices, one of the waveguides can be a \(\textbf D\)-shape fiber with its flat etched, or an optical fiber with its side cladding polished, to close proximity of the core, and the other is a planar waveguide, which regularly has higher refractive index.

Efficient evanescent coupling from the fiber to the overlay waveguide occurs when one of the film waveguide modes, usually highest order mode, is matched to that of the fiber. Light coupled into the planar waveguide might not return back to the fiber waveguide and is absorbed, scattered, or irradiated away.

The theoretical analysis on the coupling between a curved fiber and a planar waveguide is conducted either analytically using the coupled-mode theory or numerically using the beam propagation method. 

To understand the modulator characteristics governed by the physical parameters, let us omit the structure details such as the fiber curvature and derive analytical fields in the two compound waveguides using coupled-mode equations

\[\tag{12}\begin{array}\frac{\partial}{\partial_z}A_f(z)=-ikA_\text{wg}(z)\text{exp}(i\Delta\beta\text z)\\\frac{\partial}{\partial z}A_\text{wg}(\text z)=-ikA_f(\text z)\text{exp}(-i\Delta\beta\text z)-a_\text{wg}A_\text{wg}(\text z)\end{array}\]

where, \(A_f\) is the amplitude of the field in the fiber, \(A_\text{wg}\) is the amplitude of the field in the planar waveguide, \(\Delta\beta=\beta_f-\beta_\text{wg}\) is the difference between the propagation constant in the two waveguides, \(k\) is the coupling coefficient between the waveguides, and \(a_\text{wg}\) is loss coefficient induced by the planar waveguide.

Assuming that all the light is in the fiber initially, that is, \(A_f(0)=1\) and \(A_\text{wg}(0)=0\), the solution to Eq. (12) is

\[\tag{13}A_f(z)=\frac{1}{K_r}\text{exp}[-(z/2)(a_\text{wg}-i\Delta\beta)]\cdot[(a_\text{wg}-i\Delta\beta)\sinh(zK_r/2)+K_r\cosh(zK_r/2)]\]

\[A_\text{wg}(z)=\frac{-2i}{K_r}\text{exp}[-(z/2)(a_\text{wg}+i\Delta\beta)]k^*\sinh(zK_r/2),\]

where, \(K_r=[(a_\text{wg}-i\Delta\beta)^2-4|k|^2]^{1/2}\). The dependence of the modulator transmission, \(A_f(L)\) on Db at different coupling efficiencies, \(\textbf k\), calculated according to Eq. (13) is plotted as Fig. 15.

The transmission dip happens when the two waveguide modes match, \(\Delta\beta\). The planar waveguide mode can be changed by varying one of the waveguide parameters such as thickness, refractive index, or wavelength.

For \(\textbf{EO}\) modulation, by altering the refractive index of the \(\textbf{EO}\)

 

 

 

waveguide, the phase-matching condition is changed, resulting in the modulation of the electric field in the fiber. Applied voltage \(V\) alters the refractive index \(n\) as \(\Delta n=(1/2)_{\pi n^3}\lambda r(V/d)\), where \(r\) is the \(\textbf{EO}\) coefficient and d is the electrode’s gap. 

The overplayed \(\textbf{EO}\) waveguides were reportedly using polymer, lithium niobate crystal, liquid crystal, and a GaAs/AlAs multiple quantum-well waveguides. Figure 16. shows a wavelength and switching response of this type of modulator.

A polished fiber half-coupler was made from a standard single-mode 1.3-\(\mu m\) optical fiber and a 1.5-mm thick corona poled \(\textbf{EO}\) polymer film, sandwiched with \(\textbf{ITO}\) electrodes, was fabricated on the flat. The indices for \(\textbf{TM}\) and \(\textbf{TE}\) polarization are 1.626 and 1.6339, respectively.

The intensity dips correspond to the resonant phase matching of the fiber mode with the highest order mode of the film. Applying 400 V across the 1.5-\(\mu m\) thick film results in a 12-nm red shift on the resonant dip of the \(\textbf{TM}\) mode and gives a modulation depth of 15.5 dB (Fig. 16.).

 

Replaced Cladding Phase Modulators

The idea for a replace-clad modulator on a core-exposed \(\textbf D\)-shape fiber is that the phase of the guiding light can be electrically manipulated if the material that replaced the original cladding material is \(\textbf{EO}\) active.

 

 

 

The insert of Fig. 17 shows the structure of the phase modulator. The upper half of the fiber clad of length \(\text L\) is replaced by an \(\textbf{EO}\) material, and two parallel metal electrode strips are fabricated along each side of the core with a separation gap \(d\). When a modulating voltage, \(V\), is applied between the electrodes, a phase delay \(\Delta\phi\)  is induced as 

\[\tag{14}\Delta\phi(V)=\pi n^3\lambda r\Gamma L(V/d).\]

To achieve a low insertion loss and a desirable phase modulation, the refractive index of the new cladding material should be lower than the index of the core but still reasonably large to maintain a low \(V\) value.

The \(\Gamma\) value \((<1)\) is determined by overlaps among the evanescent fields, the \(\textbf{EO}\) cladding material, and the applied electric field. If the value of \(V_b\) is close to 1, up to 30% of the modal power can be distributed in the upper \(\textbf{EO}\) material replaced cladding.

Either reducing the core size through wet-etching or replacing the cladding with a relatively higher index material can realize a lower \(V_b\) value waveguide.

Using a fluorine-containing polymer that incorporates \(\textbf{EO}\) chromophores \(\textbf{(DR1)}\) as a cladding material, low insertion loss phase modulators are fabricated. The phase modulation produced by this modulator was measured using an open-loop interference fiber optic gyroscope \(\textbf{(FOG)}\).

A \(\pi\)-phase modulation on a 25-mm long modulator was achieved. In this type of \(\textbf{FOG}\) configuration, a phase modulator is incorporated within the Sagnac interference loop asymmetrically with respect to the directional coupler. A sinusoidal modulating voltage

 

 

 

\(V=V_0\sin(\omega t)\) is applied to the modulator and results in a time-varying phase modulation according to Eq. (14) and can be expressed as \(\phi(t)=\phi_0\sin(\omega t)\).

A differential phase delay between the counter-propagating waves is generated: 

\[\tag{15}\Delta\phi=2\phi_0\sin(\omega\tau/2)\sin(\omega t).\]

where \(\tau\) is the light transition time through the loop. The interference signal induced by Sagnac phase shift \(\phi_s\), at the modulating frequency, \(\omega\), is

\[\tag{16}I(\omega)/I_{01}=2J_1(\Delta\phi)\cos(\omega t)\sin\phi_s,\]

where \(I_{01}\) is the light intensity propagating in one direction of the fiber and \(J_1\) is the first order of Bessel function of first kind.

The output of the \(\textbf{FOG}\) is a function of the phase modulation \(\Delta\phi\) and the Sagnac phase shift. The gyro output is shown in Fig. 17. The intensity modulation in the phase modulation is better than 100 ppm.

The \(D\)-shape of the elliptical core fiber also implies opportunities to make infiber devices by replacing the core by a functional material.

The techniques for partial and full core removal by \(\textbf{HF}\) acid wet-etch have been demonstrated.

To fabricate this type of device, the core of a section of the \(\textbf D\)-shape fiber is removed by dipping into the \(\textbf{HF}\) acid etchant. To deposit the new functional material, usually a polymer, into the core trough, a spin-coating technique is used to generate a smooth finishing surface (Fig.18).

Because regularly the refractive index of the material is higher than that of the fiber core, the process should be optimized for a low insertion loss device. It was discovered, through waveguide simulations and experiments, that a partially etched and partially filled core with high index polymer reduces the insertion loss.

The etch depth of the core is chosen to allow for the formation of a single-mode polymer waveguide near the center of the fiber. The thickness of the polymer in the core should not be too thick; otherwise, a slab mode might be launched in the

 

 

polymer film coated on the flat. The experiments also demonstrated that long transition distances between the unetched fiber and the polymer waveguide section reduce the transition loss, because the graduated transition allows an adiabatic energy transfer between two waveguides with different \(\text V\) values. 

A 2-cm long partially removed core fiber was filled with a dispersed red 1 (DR1) chromophore blended polymethylmethacrylate \(\textbf{(PMMA)}\). The best loss achieved is approximately 1.6 dB.

The polymer blend used is of \(\textbf{DR1}\) : \(\textbf{PMMA}\) ratio of 0.075:1 by weight and has a refractive index of 1.54 at a wavelength of 1550 nm. Figure 18. shows the \(\textbf{SEM}\) images of the cross-sections of the waveguides filled with different viscosities when the polymers are spin-coated. The insertion loss for (a), (b), and (c) are 1.6, 36, and \(\infty\) dB, respectively.

Once the low-loss replaced core fiber has been achieved, the device can be used for phase, birefringence, or intensity modulation.

 

Fiber Bragg Grating Devices

The benefits of using \(\textbf D\)-shape fibers for fiber Bragg grating \(\textbf{(FBG)}\) fabrication and applications are twofold: The relative high germanium doping level in the fiber core is sensitive to the \(\textbf{UV}\) irradiation and etching the cladding from the flat direction enables direct access of the evanescent light. Both characteristics of the D-shape fiber are used to fabricate \(\textbf{FBG}\) devices.

Bend sensors with direction recognition based on long-period gratings (LPGs) written in D-shape fiber is demonstrated. The fiber was photosensitized by \(\textbf H_2\) loading before the inscription of a \(\textbf{LPG}\) structure with a period of 381 mm by use of a 244-nm \(\textbf{UV}\) laser and the point-by-point method.

The inscription results in two series of transmission peaks, corresponding to those of the two polarization modes. The retained transmission peak for the light polarization in the fast axis is at 1629.66 nm and has an extinction ratio of 8.48 dB. The transmission peak for the orthogonal slow axis is at 1645.43 nm and has an extinction ratio of 8.34 dB.

The spectral positions of the peaks shifted when the grating fiber is bended, and the shifts linearly depend on the curvature of the bending (Fig. 19). The slope of the shift-curvature lines was found to be strongly dependent on the fiber orientation, because of the asymmetrical location of the core relative to the geometrical center of the cladding cross-section.

Short-period FBGs were etched on the flat of D-shape fiber for high-temperature sensing. To fabricate these gratings, the flat side cladding was first removed by wet etching to reach to the evanescent wave using \(\textbf{BOE}\), to an extent that the distance from the flat to the top of the core is approximately 0.4 \(\mu m\).

A grating pattern of 534-nm period was written on a previously spun photoresist layer on the flat, by means of a two-beam interference using a 363.8-nm laser.

 

 

The developed grating pattern was dry-etched using DRIE, and the sinusoidal pattern was then transferred onto the flat of the fiber (Fig. 20).

The short-period gratings degenerate the two retained transmission peaks corresponding to the two light polarizations into one peak, which is spectrally located at 1552.6 nm with a extinction ratio of approximately 8 dB. In the temperature range 200–1100 8C, the temperature sensitivity of the spectrum shift is 16.2 \(\text{pm}/^\circ\text C\). 

High-sensitivity optical chemsensors based on the \(\textbf{LPG}\) on \(\textbf D\)-shape fiber have also been demonstrated. The guided light was made accessible through wet-etching the \(\textbf D\)-shape fiber with \(\textbf{LPG}\) written to the core. As the flat is etched to a distance of 7.8 \(\mu m\) from the center of the core, the retained transmission peak shifts when the surrounding-medium refractive index changes.

This characteristic enables concentration measurements of known chemicals when the index-percentage relation is calibrated. The peak location changes from 1545.4 to 1546.5 nm when the concentration of aqueous solutions of sugar changes from 0 to 60%, which corresponds to the refractive index from 1.33 to 1.44.

 

 

 

Variable Attenuators 

 

An in-fiber variable attenuator can be built on a \(\textbf D\)-shape fiber as a type of the evanescent field device. If a bulky external material, whose refractive index is greater than the mode effective index, replaces a part of the evanescent field reachable cladding, the mode can become leaky and some of the optical power can be radiated.

If the index of the external material can be changed with a controllable mean, through the effects such as thermo-optic, electro-optic, or acoustic-optic, a device with controllable attenuation is achievable. 

The combination of the fiber and the external bulk overlay has been modeled as an equivalent planar four-layer waveguide structure, so that the circular fiber can be replaced with an equivalent planar waveguide if the modal fields and propagation constant of the planar waveguide match those of circular fiber. Analytical expressions for the real and the imaginary parts of the propagation constant of the complex leaky mode have been derived.

Chandani and Jaeger have studied the power-loss dependency on the refractive index of the external medium on a \(\textbf D\)-shape elliptic core fiber. The fiber has indices of 1.441 and 1.475 at the operation wavelength of 1550 nm for cladding and core, respectively.

Figure 21a.  shows the calculated power loss for this fiber according to Sharma et al. [120] and Thyagarajan et al. A 1-cm long section of a \(\textbf D\)-shape fiber is wet-etched in a 10% \(\textbf{HF}\) solution until the flat is

 

 

 

4–6 \(\mu m\) from the center of the elliptical core. The etched fiber was then immersed into oil with its index and its thermo-optic coefficient known. By controlling the oil temperature, the index of the oil is fine-tuned.

The loss-temperature, therefore, loss-index, curve is well fitted using Sharma’s theory in a temperature range of 10 \(\sim\) \(90^\circ C\) which corresponds to the index change of 1.4808 \(\sim\) 1.4499, respectively.

The distance of the flat from the core center (4.705 \(\mu m)\) has been determined as a least-fit parameter. The power loss for the fast mode is approximately 0.2 dB larger than that for the slow mode in the whole index range, as shown in Fig. 21b. The purpose of the study is for a temperature sensor, although in-fiber optic attenuators have been proposed under the same principle.

 

Optical Absorption Monitoring

The \(\textbf D\)-shape fiber, with its evanescent field accessible by exposing the fiber core, is a reasonable approach to monitor the absorption spectra of gas and contaminations of an aqueous solution.

Fiber optic evanescent wave absorption spectroscopy has been of research interest because of the many potential advantages over the conventional chemical-monitoring methods such as speed of response, selectivity, in-situ testing, and safety.

In the design of the sensors, several basic aspects have to be considered. First, most of the gases of interest for the environmental and safety measurements possess much stronger absorption lines in the mid-infrared \(\textbf{(MIR)}\) than in the near infrared. Although the low attenuation transmission window of silica-based optical fibers is in the range 0.6–2 \(\mu m\)—with particularly good transparency between 1 and 1.8 \(\mu m\)—special fibers, such as unclad silver halide fibers, chalcogenides, and fluoride glass fibers, were fabricated to extend an \(\textbf{MIR}\) transparent window to the gas absorption region, such as hexane, trichlorotrifluoro- ethane, methane, acetone, and others.

On this \(\textbf{Mid}\)-\(\textbf{IR}\) and Infrared Fibers tutorials describes these types of fibers. However, the technological benefits then point towards the near-infrared system as offering many advantages when compared to the \(\textbf{MIR}\) equivalent despite the radically stronger line strengths in the longer wavelength region. Second, most systems operate with fairly small values of absorption and the detected strength is linearly proportional to the value of the line strength.

The short exposure length of the side-clad polished fibers does not supply enough sensitivity. \(\textbf D\)-shape fibers enable a much longer length and higher degree of core exposure, which enhances the sensitivity in the sense of gas-field overlap and interaction length.

It is also possible to draw \(\textbf D\)-shape fibers that make the evanescent field intrinsically exposed by grinding the flat of the preform to close proximity to the core. Bending a \(\textbf D\)-shape fiber further increases the sensitivity.

A methane-sensing sensitivity at 1.66 \(\mu m\) is calculated to be increased as much as 30% by bending a \(\textbf D\)-shape fiber to a 12-cm radii curvature with its flat surface to the outside.

An alternative method to enhance the sensitivity is by using air-guiding photonic band-gap \(\textbf{(PBG)}\) fibers. The gaseous species filled into the air holes of the fiber absorb the guided light through a long interaction length.

A drawback of the \(\textbf{PBG}\) fiber sensors, comparing to the \(\textbf D\)-shape fiber sensors, is that the response time for the former should be much longer because of the small diameter of the air holes for the gas to be filled in. Third, the sensitivity also depends on the resolution or the spectral detection scheme.

A narrow line width and wavelength-tunable light source of a high spectral resolution spectrometer is crucial. When the source line width exceeds the absorption line width, the maximum detected signal expressed as a fraction of the detected optical power decays linearly with the increase in source line width signal. Diode lasers with distributed feedback \(\textbf{(DFB)}\) architectures are the most convenient. However, their tuning ranges are relatively modest.

The extended cavity air path tunable laser facilitates source tuning throughout the entire usable gain of the optically active elements. In the tunable fiber laser, the long cavity ensures narrow line widths and low noise operation.

Culshaw et al. used a \(\textbf D\)-shape fiber evanescent wave optical fiber gas sensor to realize distributed methane detection using the single absorption line of 1.66 \(\mu m\) with resolutions of the order of 100 ppm methane.

The \(\textbf D\)-shape fiber used was 5 m in length and specially designed with near-zero core/flat distance. The dependency of the detection sensitivity on the core size and the core/clad index difference was investigated.

 

Intrinsic Fiber Sensors

A unique characteristic of the highly elliptical core fibers is their supporting to two spatial modes in a range of wavelength in the two polarization direction, respectively. The two modes experience different phase shifts when the fiber is strained. The interference between the output lights in two modes supplies a sensitive way to measure the strain.

The two-mode optical fiber is useful for building new types of fiber devices such as sensors that selectively sensitized for perturbations of interest and were immune to others. These perturbations may include strains, twists, temperature change, and so on.

 

Strain Sensor

In a range of wavelength elliptical core fibers exclusively support the fundamental \(\textbf{LP}_{01}\) and even \(\textbf{LP}_{11}\) spatial mode with Eigen-polarizations of both modes parallel to the major and minor core axes. When the \(\textbf{LP}_{01}\) and \(\textbf{LP}_{11}\) modes are launched equally in an elliptical core fiber, the far field output pattern is a superposition of the contributions from the two modes as a double loped modal interference pattern, and the its intensity distribution is depended on the phase difference, \(\Delta\phi\), between the two modes (Fig. 22).

Applied strain alters the differential phase and gives rise to a corresponding change in pattern. Because the orientation of the double lopes is determined by the orientation of the core axes, and both modes in the identical fiber without separate reference arms as needed in Mach–Zehnder or Michelson interferometers, the interference pattern is stable and less susceptible to the environmental noises. These make this type of sensor applicable for the remote sensing in the harsh conditions.

For a strain measurement, light with a known polarization state is launched into an elliptical core two-mode fiber with approximately equal intensities in each of the two spatial modes.

After passing through the stretched section of the fiber, the light is projected onto a screen for the far-field interference pattern. The local variation of the intensity, as a function of differential phase, of the interference pattern can be written as

\[\tag{17}I\sim1+v\cos(\Delta\phi),\]

where \(v\) is the fringe visibility, depending on the launching conditions, detection area, and the location. The differential spatial modal phase \(\Deltta\phi\) is modified upon  

 

 

 

the applied stretch and related to the modal birefringence \(\Delta\beta=\beta_{01}-\beta_{11}\) and the length of the sensing fiber, \(l\), by 

\[\tag{18}\delta(\Delta\phi)=\Delta\beta\delta l+l\delta(\Delta\beta),\]

where the subscript \(01\) and \(11\) stand for the \(\textbf{LP}_{01}\) and the \(\textbf{LP}_{11}\) mode for a two-mode fiber, respectively.

For a change in \(\Delta\phi\) of \(2\pi\), there will be one complete oscillation of the intensity pattern. Measurement of the elongation \(\delta l_{2\pi}\) required in a sensing fiber for a \(2\pi\) change in \(\Delta\phi\) calibrates the measurement sensitivity, the coefficient \(\delta(\Delta\phi)\) is then calculated from the measurement \(2\pi/\delta l_{2\pi}\). Because \(\delta\beta\) is a function of deformation \(\delta l\), under a stable ambient temperature, the light intensity is solely a function of deformation dl, under a stable ambient temperature, the light intensity is solely a function of \(dl\)

\[\tag{19}I\sim1+V\cos\left(2\pi\frac{\delta l}{\delta l_{2\pi}}+\Delta\phi_0\right),\]

where \(\Delta\phi_0\) is the unperturbed phase difference between the two spatial modes at the fiber end. Huang et al. have measured \(\beta\) and \(\Delta\beta\) as functions of the fiber elongation, \(dl\), and the wavelength on an elliptical core fiber.

By launching the two modes into both Eigen polarizations of the elliptical fiber, two independent spatial mode interferometers were effectively built, one for each polarization state. Because the strains coefficients induced by stretch and temperature change on the two spatial mode interferometers are different, simultaneous measurement for both fiber elongation and temperature change are possible.

Devices based on the two-mode optical fiber sensing are reported using the selective measurement of one type of strain perturbations, or simultaneous measurement of two types of the perturbations.

Bohnert et al. used two dual-mode fibers in tandem acting as unbalanced sensor and recovery interferometers. Using homodyne phase tracking, small optical-phase modulations induced by periodic strain were recovered.

A stability of the detected AC signal is achieved to within \(\pm 10^{-3}\) in the presence of additional quasi-static phase drift of large amplitude.

The minimum detectable differential modal-phase modulation is 5 \(\mu\)rad rms/\(\surd Hz\) at 70 \(Hz\).

A piezoelectric quartz high-voltage transducer has been demonstrated. A simultaneous strain and temperature measurement was realized by incorporation of both polarimetric and two-mode differential interferometric schemes in an elliptical core fiber.

Using elliptical core fibers, strains due to stretch and temperature change can be measured simultaneously with resolutions of 10 \(\mu m/m\) and \(5^\circ C\), respectively.

A technique based on the evaluation of the condition number of a matrix is shown to be useful in evaluating comparative merits of multi-parameter sensing schemes.

Individually measuring the polarization changes in the \(\textbf{LP}_{01}\) and \(\textbf{LP}_{11}\) modes of an elliptical core fiber, a simultaneous recovery of temperature and the strain was realized.

To couple only the \(\textbf{LP}_{11}\) mode out of the fiber, an in-line mode splitter was developed by side-polishing the fiber and overlaying a prism with film interlay.

When the index of the interlay is chosen correctly, 35-dB modal separation was enabled while preserving the polarization properties of both modes. The polarization changes of both modes were analyzed by inserting a polarizer with 45 degrees with respect to the core axes, respectively. The scheme has been demonstrated to be sensitive to changes of \(1^\circ C\) and \(5\mu\varepsilon\).

 

Twist Sensor

Twisting fiber induces circular birefringence, which can be used to measure angular displacements,

\[\tag{20}\Delta a=\text g\tau(\text{rad/m})\]

where \(\text g\) is a photoelastic coefficient, \(\text g=-0.5n^2_0(p_{11}-p_{12})\approx0.146\) for silica fibers, \(p_{11}\) and \(p_{12}\) are components of the strain-optical sensor of the fiber, and \(n_0\) is the average refractive index of the fiber.

The polarization evolution of the fundamental mode in a twisted single-mode fiber was obtained by using either the Poincare´ sphere or the coupled-mode equations.

If \(\text x’,\text y’\) is the local coordinate that follows the principle axes of the twisted fiber, and x,y is that for the fixed principle axes of the fiber. Under assumptions that there is no coupling between the \(\textbf{LP}_{01}\) and \(\textbf{LP}_{11}\) modes and that fiber is uniformly twisted with a rate \(\phi\). The electric field components \(E'_\text x\) and \(E'_\text y\) for each spatial mode, at the output end of the fiber, are represented as

\[\tag{21}\begin{array}&E^i_{x'}=\text{exp}\left(\frac{-j}{2(\boldsymbol\beta_{i\text x}-\boldsymbol\beta_{i\text y})l}\right)\times\left[E^i_{x0}\cos\frac{K_i l}{2}-j\frac{\Delta\boldsymbol\beta_i}{K_i}E^i_{xo}\sin\frac{K_i}{2}l+\frac{\boldsymbol\phi(2-\text g_i)}{K_i}E^i_{\text y0}\sin\frac{K_il}{2}\right]\end{array}\]

and 

\[\tag{22}E_{\text y'}^i\text{exp}\left(\frac{-j}{2(\boldsymbol\beta_{i\text x}-\boldsymbol\beta_{i\text y})l}\right)\times\left[E^i_{\text y0}\cos\frac{K_il}{2}+j\frac{\Delta\boldsymbol\beta}{K_i}E^i_{\text y0}\sin\frac{K_il}{2}-\frac{\boldsymbol\phi(2-\text g_i)}{K_i}E^i_{\text x0}\sin\frac{K_il}{2}\right]\]

with \(K_i=\sqrt{(\Delta\beta_i)^2+[\tau(2-\text g_i)]}^2\), \(I=1,2,\) where \(l\) is the fiber length and \(\text g_i\) is a photoelastic coefficient for \(i\)th mode.

The \(E^i_{x0}\) and \(E^i_{\text y0}\) are electric fields in the two polarizations for the \(i\)th mode at the input end of the fiber. The local intensity at the output fiber end is

\[\tag{23}I=I_{x'}+I_{\text y'}=|E^1_{x'}+E^2_{x'}|^2+|E^1_{\text y'}+E^2_{\text y'}|^2,\]

where \(I\) is a function of the twist rate, \(\tau\). Huang et al. calculated and measured \(I_{\text y0}\) of one lope of the pattern as a function of twist rate f, on a 19.3-cm long elliptical core two-mode fiber, when only \(LP^x_{01}\) mode was excited. With the twist rate \(\phi\) increase, \(LP^\text y_{01}\) and \(LP^\text y_{11}\) modes were coupled and form interference fringes (Fig. 23).

Mancier et al. developed an optical fiber twist sensor for measuring angular displacements at low temperature.

The sensing part is composed of a fiber coil rotated between two points, which induces a twist of two sections of the fiber. It is demonstrated that the sensor was able to take angular measurement over a 100-degree range with an accuracy of 0.2 degree.

The thermal sensitivity is studied and it was concluded that the sensor has to work in stabilized temperature environments so \(\Delta T<5^\circ C\) to keep the 0.2-degree accuracy.

 

\(\textbf D\)-Shape Fiber Opto-Electronic Devices

Novel \(\textbf D\)-shape fiber–based opto-electronic devices have been proposed and patented. For example, two-dimensional (2D) photonic crystal structures can be microfabricated on the \(\textbf D\)-shape fiber.

If the silica vacant locations are filled with functional materials, exciting new opportunities for the \(\textbf D\)-shape fibers are expected. Fiber optic filters and modulators based on the \(\textbf D\)-shaped fiber

 

 

 

 

are patented. A photonic crystal structure as an overlay on the side-polished \(\textbf D\)-shape fiber is proposed. The devices can be tunable if electro-optic active materials are used. A method to fabricate electrodes on \(\textbf D\)-shape fibers has also been proposed and patented. 

 

 

8.  RARE EARTH-DOPED ELLIPTICAL CORE FIBER

Among the several methods reported to introduce rare earth dopant into the fiber, the solution doping technique, developed by Townsend et al. in 1987, is the simplest and, therefore, the most popular.

The \(\textbf{MCVD}\) process for the germania core deposition is carried out at a reduced temperature so that a partially sintered germania layer inside the quartz tube is formed.

A solution of salt of the rare earth (usually aqueous or alcoholic solutions of nitrate of chloride salts) soaks into porous soot and then is glassed at a higher temperature. The tube is then collapsed to form preform. Passing chlorine through the heated tube before the glassification reduces the \(\textbf{OH}\) content considerably.

The concentration is limited by the clustering of the rare earth ions, which quench the photo-excited ions. Co-doping with aluminum isolates the rare earth ions by forming a salvation shell at each neodymium ion and allows for a high doping level of the rare earth ions without clustering.

A 33-dB small signal gain was reported on a 23-m long Al–Nd co-doped fiber under 50-\(m\textbf W\) pump power, whereas the small signal gain was only 7 dB for the Nd-only–doped fiber under the same pumping conditions. 

Several milliwatts of superfluorescent light at approximately 1080 nm were measured when a 9-m long fiber was forwardly pumped by an 820-nm LD that delivers approximately 20-m\(\textbf W\) pump power into the fiber.

A fiber optic gyroscope for finding true north was demonstrated at \(\textbf{KVH}\) using this superfluorescent light source. Gain anisotropy was observed in a 300-ppm Nd-doped fiber with core size of 2.5 by 1.25 \(\mu m\) and core-cladding index difference of 0.032.

Under the measurement conditions of 21-\(\text m\)\(\textbf W\) pump power at 810 nm and 450 \(\mu W\) seeding power at 1088 nm, the small signal gains were 3.4 and 3.1 dB, respectively, when the polarization directions for the pump and seeding light are in both the major and the minor axes.

The anisotropic behaviors of the gains are consistent with a model based on stronger confinement of the odd \(\textbf{HE}_{11}\) mode. Microsecond optical-optical switching in this type of fiber was demonstrated.

In this device, the effective indices of a two-mode fiber interferometer operated at 633 nm were resonantly modulated using an 807-nm pump laser, which results in switching between the two interferential lopes.

Erbium- and ytterbium-doped \(\textbf{PM}\) fibers were fabricated and studied, mainly motivated as a potential, but expensive, candidate to solve signal distortion problem caused by the polarization dispersion. A 14-dB net gain reported in a 27-m long erbium-doped \(\textbf{PANDA}\)-type \(\textbf{PM}\) fiber.

The fiber transmitted only one polarization mode in the emission wavelength of 1.535 \(\mu m\) while supporting two polarization modes at the pump wavelength of 1.485 \(\mu m\).

A high-power \(\textbf{PM}\) amplifier was demonstrated using an \(\textbf{Yb}\)-doped bowtie fiber. Backward-pumped by a high-power 974-nm diode bar, a 9.5-m long fiber had an amplified seed signal at a wavelength of 1050 nm with approximately 40 dB small-signal gain. The saturated output power of 2.3 W and extinction ratio of 17 dB was demonstrated at pump power of 5.7 \(\textbf{W}\).

One of the important applications of the rare earth-doped fiber is as a broadband superfluorescent light source, particularly for navigation-grade \(\textbf{FOG}\). The advantage of the rare earth-doped, especially erbium-doped, fiber over the other existing broadband light sources is its excellent mean wavelength stability.

Together with its low pump power requirement, the broadband light produced by rare earth-doped fiber meets the stringent requirements for inertial navigation-grade \(\textbf{FOG]\).