This document summarizes a comparative study of different types of polarizing fibres for use in fibre-optic gyroscopes (FOGs). It compares Panda-type fibres with W-index profiles and depressed cladding, as well as microstructured fibres. It analyzes the spectral width of their single-polarization windows while considering bending, and their splice losses when spliced to conventional fibres. A new type of match-clad Panda fibre that polarizes without bending is also proposed. Simulation methods are described for modeling the mechanical stresses and optical properties of the different fibre designs.

1. 1
Comparative theoretical study of polarising Panda-type and
microstructured fibres for fibre-optic gyroscope
A. M. Kurbatov, R. A. Kurbatov
E-mail: romuald75@mail.ru
(originally published in Optical and Quantum Electronics, September, 48, paper 439)
Abstract Comparative study is fulfilled for different polarising fibres: Panda fibres with match-
clad and depressed-clad W-profiles, along with microstructured fibres. Comparison is made for
their spectral width of single-polarisation windows taking into account bending, and for their
splice losses with conventional fibres. A new type of match clad fibre is also proposed polarising
even without bending. It is shown that the optimal is W-fibre Panda. At the same time, truly
broadband polarising microstructured fibres demonstrate enormously large splice losses,
whereas those of them with relatively low splice losses could not be wound into the coil of
reasonable size due to large bend losses.
Keywords polarising fibre, W-profile, Panda fibre, microstructured fibre, bend loss, fibre optic
gyroscope.
1. Introduction
Polarisation non-reciprocity (PNR) is the fundamental limit of Sagnac fibre ring interferometer
(FRI) accuracy (Kintner 1981). It could be strongly suppressed by sensing coil of highly
birefringent (Hi-Bi) fibre together with broad-band optical source (Burns and Moeller 1983).
Further suppression is available due to highly birefringent (Hi-Bi) optical element before or after
FRI polariser (Jones and Parker 1986), which could be in the form of polarisation maintaining
(PM) fibre section (Cordova et al. 1996). However, in Ref. (Carrara et al. 1987) it is mentioned
that this suppression has its own essential limit, and in Ref. (Kurbatov 2011a) it is shown that
this is due to high order polarisation mode coupling in coil fibre and to optical axes
misalignments of spliced components. In this case, further dramatic PNR suppression could be
reached by sensing coil of polarising (PZ) fibre together with the lightguide at the input of ring
interferometer, when the following condition is fulfilled (Kurbatov 2011a)
𝛼𝐿𝑖𝑛 𝐵𝑖𝑛 𝐵 ≫ 1⁄ (1)
Here 𝛼 is the attenuation coefficient of rejected fundamental y-polarised mode (y-mode)
intensity in PZ-fibre of the coil with birefringence 𝐵, while 𝐿𝑖𝑛 and 𝐵𝑖𝑛 are the length and
birefringence of input lightguide. For 𝛼 ~ 30 dB/km, condition (1) means that 𝐿𝑖𝑛 value should
be order of 𝐿 (length of the coil fibre), but for 𝛼 ~ 0.1-1.0 dB/m one may use 𝐿𝑖𝑛 ≪ 𝐿. Input
lightguide may also be polarising with y-mode attenuation coefficient 𝛼𝑖𝑛. Note that term
“fibre” is reserved for FOG coil fibre, while the term “lightguide” is used for input fibre, for their
easy differing.
Basic parameter of PZ-fibre is the width of dichroism window, a spectral range, where the
loss of fundamental x-polarised mode (x-mode) is below 0.1 dB, and y-mode loss is above 30 dB
(rigid criterion of dichroism window). In the literature, х-mode loss is often set equal to 1 dB
(soft criterion). Also, according to (1), the α-value at 1.55 μm is considered as one more
dichroism criterion for coil fibre only.
Nowadays, FOG coils are usually wound of high-aperture match-clad (MC) fibre (Δn ~ 0.015).
It cannot be a broadband polariser, but the low-aperture (Δn < 0.005) MC-fibre can be

2. 2
(Varnham et al. 1983). The same is right for fibres having refractive index W-profile (Fig. 1),
which becomes MC-profile at Δn- = 0. In this case, the value Δn+ could be done much smaller
than 0.015.
Long polarising W-fibres (roughly speaking, of over 100 m length) are known with elliptical
stress cladding (Wang et al. 2009; Jacobsen et al. 2013), having small Δn+ and Δn- (Fig. 1), and
Panda fibre (Kurbatov et al. 2010 and 2013) with arbitrary Δn±. Shorter PZ-lightguides (less than
50 m) can be implemented at FRI input, they could be divided into bend-polarising MC-
lightguides and W-lightguides which can be polarising even without bending. For the first case,
bow-tie lightguides are known (Varnham et al. 1983, Hill et al. 2012), along with Panda
lightguides (Okamoto 1984). As for W-lightguides, the ones are known with elliptical stress
cladding (Simpson et al. 1983; Messerly et al. 1991, Wang et al. 2009; Jacobsen et al. 2013),
along with Panda fibres (Kurbatov 1990, 2004, 2010, 2011b). Finally, present paper offers one
more Panda-type MC-fibre which is polarising even without bending, where the reduced index
stress applying parts (SAP) play the key role.
Also, microstructured (MS) fibres are known as promising ones for a lot of fields (Zheltikov
2000), including PZ-fibres applications (Kubota et al. 2004; Saitoh and Koshiba 2005; Chen and
Shen 2007; Jian 2011; Lu 2013).
Below, three kinds of highly birefringent PZ-fibre are considered (straight and bent), having
the following refractive index profiles: 1) low-aperture MC-profile; 2) W-profile; 3) MS-profile.
For these kinds of fibres a comparative study is fulfilled, concerning the width of dichroism
window and splice losses with conventional fibres (for example, SMF-28), or with the
waveguides of integrated-optic chip (IOC), whose fields are approximated by Gaussian beams.
For FOG coil fibre, splice loss should be doubled because it is spliced from both ends with two
IOC waveguides.
Among the fibres with stress applying parts (SAP), present paper treats only Panda-type
ones, which are simulated realistically enough, taking into account the smoothed and
essentially asymmetric Panda-type refractive index profiles, along with their non-uniform
material birefringence distribution within fibre cross section. This simulation is the essential
development of that from Ref. (Kurbatov et al. 2013), and it is successfully tested
experimentally (including numerous experimental data from literature). To the authors
knowledge, no such realistic description has been published, and they believe that this is one of
the reasons why PZ-fibres are still often considered as hardly available for manufacturing. Also,
below presented consideration of bending properties of microstructured PZ-fibres is of primary
importance for fibre gyroscopy which never deals with straight fibres.
2 Mathematical simulation procedures
Rectangular configuration 1 at Fig. 2a illustrates the rectangular cross section of W-fibre with
boron-doped SAP and absorbing complex-index layer (black ring). Configurations 2 and 3 at Fig.
2a illustrate the alternative geometries for absorbing (black) region. For light absorption,
configurations 1 and 2 leads to the same result, while configuration 3 leads to the same result
Fig. 1 Refractive index W-profile, n1-3 are
refractive indices of the core, depressed cladding
and outer silica cladding, 2ρ and 2τ are diameters
of the core and depressed cladding.

3. 3
as considerably more complicated PML-method (Berenger 1994). We assume the real part of
absorbing region dielectric constant is equal to silica one, only correcting it as Re2
𝑛 − Im2
𝑛.
The width of this region was chosen equal to 10 μm. The axes x and y are the fibre slow and fast
optical axes, 𝐿 𝑥,𝑦 are the lengths of simulation region. Fig. 2b illustrates the angle 𝛳 of SAP
orienting relative to bending plane for bent fibre (axes xbend and ybend are parallel and
perpendicular to bending plane).
Fig. 2a W-fibre Panda cross section for simulation of mechanical stresses induced by boron-doped SAP, and
of the light absorption by different complex-index black regions (rectangular configurations 1-3).
Fig. 2b illustration of the angle 𝜭 of SAP orienting with respect to fibre bend plane (axes 𝒙 𝒃𝒆𝒏𝒅 and 𝒚 𝒃𝒆𝒏𝒅 are
parallel and perpendicular to bend plane), 𝑹 is the fibre bending radius.
In the similar manner, an absorption region and 𝛳-angle could be illustrated for MS-fibre.
Mechanical stresses are simulated by Goodier potential ψ(x,y) (Chu and Sammut 1984),
which satisfies the equation
(𝜕2
𝜕𝑥2⁄ + 𝜕2
𝜕𝑦2⁄ )𝜓(𝑥, 𝑦) = [(1 + 𝑣) (1 − 𝑣)⁄ ]𝜅(𝑥, 𝑦)𝛥𝑇,
Where 𝑣 is Poisson ratio, ΔТ is the difference of SAP melting temperature and fibre
temperature, κ(x,y) is the thermal expansion coefficient distribution. Temperature, Young
modulus Е and v are assumed to be the same everywhere. Stress components are calculated in
the following form (Chu and Sammut 1984):
𝜎𝑥 =
𝐸
(1+𝑣)(1−2𝑣)
[(1 − 𝑣)
𝜕2
𝜕𝑥2 + 𝑣
𝜕2
𝜕𝑦2] 𝜓, 𝜎 𝑦 =
𝐸
(1+𝑣)(1−2𝑣)
[(1 − 𝑣)
𝜕2
𝜕𝑦2 + 𝑣
𝜕2
𝜕𝑥2] 𝜓.
Goodier potential is represented in the form of Fourier decomposition:
𝜓(𝑥, 𝑦) = ∑ 𝜓 𝑚,𝑛 cos[𝜋(𝑚 + 1 2⁄ ) 𝑥 𝐿 𝑥⁄ ] cos[𝜋(𝑛 + 1 2⁄ ) 𝑦 𝐿 𝑦⁄ ]𝑚,𝑛 .
Values σх and σy are zero at external boundary of layer 1 at Fig. 2, and the profiles for x- and y-
polarised light could be written in the form (Okamoto et al. 1981)
𝑛 𝑥(𝑥, 𝑦) = 𝑛0(𝑥, 𝑦) + 𝐶1 𝜎𝑥(𝑥, 𝑦) + 𝐶2 𝜎 𝑦(𝑥, 𝑦),
𝑛 𝑦(𝑥, 𝑦) = 𝑛0(𝑥, 𝑦) + 𝐶1 𝜎 𝑦(𝑥, 𝑦) + 𝐶2 𝜎𝑥(𝑥, 𝑦).
Here 𝐶1,2 are elastooptic constants. Material birefringence field is defined as 𝐵(𝑥, 𝑦) =
𝑛 𝑥(𝑥, 𝑦) − 𝑛 𝑦(𝑥, 𝑦), the difference Δ𝜅 for SAP and silica is chosen for desired 𝐵(0,0) value,

4. 4
because for Panda fibres, 𝐵(0,0) is almost equal to modal birefringence 𝐵 𝑚𝑜𝑑 = (𝛽 𝑥 − 𝛽 𝑦) 𝑘⁄
(Section 3), which determines the dichroism window width (here 𝛽 𝑥,𝑦 are propagation
constants of х- and у-modes, 𝑘 is the vacuum wavenumber). This rough approach maintains the
basic features of stress distributions yielded by others (Chu and Sammut 1984). Similar to this,
one may also calculate the stress field in bow-tie and elliptical stress-clad fibres.
Panda fibres under consideration are weakly guiding, satisfying the scalar wave equation
implemented individually for x- and y-modes (Snyder and Young 1978):
[𝜕2
𝜕𝑥2⁄ + 𝜕2
𝜕𝑦2⁄ − 𝑘2
𝑛 𝑥,𝑦
2 (𝑥, 𝑦)]𝐸 𝑥,𝑦(𝑥, 𝑦) = 𝛽 𝑥,𝑦
2
𝐸 𝑥,𝑦(𝑥, 𝑦), (2)
where 𝐸 𝑥,𝑦 are electric fields of х- and у-modes. The solution of this equation is derived by
frequency domain finite difference method (FDFDM) (Stern 1988). For 125- and 80-μm
diameter fibres, meshes 300×300 and 200×200 are enough. This is due to the fact that realistic
profiles are smoothed.
For MS-fibres, FDFDM is implemented from Ref. (Zhu and Brown, 2002). Here the complex-
index layer is added, as for configuration 1 at Fig. 2a, and for silica index a Sellmeier equation is
used.
For all fibres, a supermode method is implemented, proposed in Ref. (Francois and Vassallo
1983), along with the procedure of necessary supermode searching (Kurbatov et al. 2013). For
bent fibre profile 𝑛 𝑏𝑒𝑛𝑡(𝑥, 𝑦), and for straight fibre profile 𝑛 𝑠𝑡𝑟(𝑥, 𝑦), one may wright the
following interrelation, starting from the result of Ref. (Heilblum and Harris 1975)
𝑛 𝑏𝑒𝑛𝑡(𝑥, 𝑦) ≈ 𝑛 𝑠𝑡𝑟(𝑥, 𝑦)[1 + 𝑥 𝑏𝑒𝑛𝑑(𝑥, 𝑦) 𝑅⁄ ] = 𝑛 𝑠𝑡𝑟(𝑥, 𝑦)[1 + (𝑥 cos 𝜃 − 𝑦 sin 𝜃) 𝑅⁄ ].
During the coil winding, the angle 𝛳 is out of control, so their bend loss calculations are done
for all 𝛳 from 00 to 900 with the step 2.50, and after that the averaged loss curve is calculated.
This method of simulation was verified experimentally (Kurbatov et al. 2013). As for MS-fibres,
only certain values of 𝛳 are considered, which fact is explained in Section 4 (however, 𝛳-
averaged calculations could be done).
Finally, splice losses are calculated by the overlap integrals of mode fields.
3 Polarising Panda fibres for FOG coils
In this section, comparative study is carried out of polarising fibres with low-aperture MC-
profile and with W-profile. Consider two groups of such fibres having MFD = 8 μm (fibres MC-8
and W-8) and with MFD = 10 μm (fibres MC-10 and W-10), where MFD is fundamental mode
field diameter.
MC-fibres are known as the basis for bend-type polarisers. However, in this case dichroism
occurs even in the absence of bending, because the fundamental mode cutoff of practical finite
clad fibre is also finite (Black and Bourbonnais 1986). Also, a pair of SAP with reduced index
shifts the dichroism window towards smaller wavelengths. In W-fibres, the fundamental mode
cutoff may be finite due to depressed clad only (even for infinite silica clad). In another cases,
the depressed clad only is not enough, so cutoff is finite due to finite silica clad and reduced
SAP index, similar to MC-fibres. Both situations occur for y- and x-modes of W-fibre from Ref.
(Messerly et al. 1991), respectively.
Table 1 contains the parameters of fibres W-8, MC-8, W-10 and MC-10.
Table 1
Geometrical parameters and calculated optical characteristics of fibres W-8, MC-8, W-10 and
MC-10

5. 5
Parameter MC-8 MC-10 W-8 W-10
Core diameter, 2ρ, μm 4.9 8.0 9.2 12.5
χ = τ/ρ (Fig. 2) - - 1.6 1.5
Material birefringence at fiber center B(0,0) 8×10-4 8×10-4 8×10-4 8×10-4
Δn+ 7.5×10-3 4.35×10-3 5×10-3 3.45×10-3
Δn- 0 0 9.0×10-3 9.0×10-3
Dichroism window (rigid criterion), μm 1.54-1.55 1.5-1.55 1.5-1.55 1.46-1.55
Dichroism window (soft criterion), μm 1.54-1.64 1.5-1.64 1.5-1.61 1.46-1.63
Attenuation of у-mode at 1.55 μm, dB/km 60 120 500 1000
Material loss in SAP, dB/km 0.44 0.6 0.09 0.28
Fig. 3а shows the spectral losses of x- and y-modes in straight 1000-m fibres MC-8 and W-8, Fig.
3b is the same for these fibres wound with diameter 100 mm.
Fig. 3а Spectral loss curves for straight fibres W-8 (black solid curves) and MC-8 (grey dashed curves), “y”
and “x” denote the graphs for y- and x-modes of corresponding fibres.
Fig. 3b The same as at Fig. 3(a) for fibres wound with 100-mm diameter.
Dichroism occurs in all cases, and the fibre W-8 has wider dichroism window than MC-8. What
is more important, loss of y-mode at 1.55 μm in fibre W-8 is almost 10 times larger than loss in
fibre MC-8, so only fibre W-8 satisfies the condition (1). This is due to sharper growth of loss
curve of fibre W-8. Also, material loss in SAP for fibre W-8 is 4.5 times lower than for fibre MC-
8. Loss in SAP was calculated taking into account their index reduced by 0.01 relative to silica.
This decreases the loss in SAP by 3-5 times comparing to the case when SAP index is equal to
silica one, as in Ref. (Tajima and Sasaki 1989).
Note, that in Ref. (Varnham et al. 1983) microbending losses of x- and y-modes are
considered as a reason of dichroism window in straight fibres at long wavelengths. These losses
also could be simulated by supermodes method taking into account the influence of SAP, as in
Ref. (Kurbatov et al. 2011b). However, there is no data for microbends statistical properties.
Fig. 4 illustrates the spectral graphs of 𝐵 𝑚𝑜𝑑 for fibres MC-8 and W-8. Up to 1.7 μm, they are
almost the same as 𝐵(0,0), and for fibre W-8 this differing from 𝐵(0,0) is much less due to
tight confinement of x- and y-modes within the core.

6. 6
Consider the cutoff of x- and y-modes for fibre W-8. Fig. 5а shows the graphs of x- and y-
modes effective indices.
Fig. 5а Spectral graphs of effective indices of x- and y-modes in fibre W-8.
Fig. 5b Spectral losses of x- and y-modes in fibre W-8 of length 1 m (dashed) and 1000 m (solid).
Their crossing points with silica index (it is set equal to 1.46) are the mathematical cutoffs of x-
and y-modes. Do they mean the beginning of the growth of these modes losses (physical
cutoff)? Arrows from Fig. 5а to Fig. 5b reveal that mathematical and physical cutoffs agree well
for 1-m fibre, unlike the 1000-m one. Thus, mathematical cutoff which may be calculated in a
simple manner (Kurbatov et al. 2011b) could not be considered for simulating the fibre for FOG
coil.
Bend polarisers of anisotropic MC-fibres are always considered as low-aperture (Δn < 0.005,
MFD > 10 μm). For this case, fibres MC-10 and W-10 were compared revealing the same
advantages of fibre W-10, as those from comparing the fibres W-8 and MC-8 (see Table 1).
Moreover, y-mode loss at 1.55 μm in fibre W-10 is even 2 times larger than in fibre W-8.
However, material loss in SAP is increased to 0.3 dB/km, because the distance between SAP is
the same as in W-8, while the core is larger.
4 Microstructured fibres for FOG coils
MS-fibres have significant advantages over MC- and W-fibres for large number of situations,
and often they have no alternatives (Zheltikov 2000). As for their application in FOG coils, their
extremely high birefringence is mentioned in literature, indistinguishable for fibres with SAP.
Consider the examples of three MS-fibres with fragments of cross section illustrated at Fig. 6.
Fig. 4 Dash-dotted horizontal line is the level of
material birefringence 𝑩(𝟎, 𝟎) at fibres center,
black solid curve and grey solid curve are the
spectral graphs of modal birefringence 𝑩 𝒎𝒐𝒅 in
fibres W-8 и MC-8, respectively.

7. 7
Fibre MS-I is the most known. The rest two MS-fibres, among other applications, are offered for
FOG PZ-coils. However, in Ref. (Kubota et al. 2004; Saitoh and Koshiba 2005; Chen and Shen
2007) they are treated only being straight. Because of their extremely high birefringence, it is
meant (although not stated explicitly) that dichroism window is also extremely wide. Let’s show
that this is not always so. Table 2 presents the geometrical parameters and calculated optical
characteristics of fibres considered here.
Table 2
Geometrical parameters and calculated optical characteristics of microstructured fibres
Parameter MC-I-1 MC-I-2 MC-II MC-III
Λ, μm 5.588 1.7 2.2 1.4
a/(2Λ) 0.35 0.5 0.5 0.48
b/(2Λ) 0.35 0.5 0.5 0.24
d1/(2Λ) 0.95 0.95 0.95 0.66
d2/(2Λ) 0.95 0.95 0.95 0.48
Splice loss with IOC (MFD = 8 μm), dB 1.65 8.5 11 12.5
Splice loss with IOC (MFD = 10 μm), dB 2.5 11.5 15 16
Dichroism window width (rigid criterion), nm 0 20 110 300
Dichroism window width (soft criterion), nm 0 60 160 > 400
4.1 Fibre MS-I
For this fibre, birefringence is due to the pair of large air holes. The indices of x- and y-modes
may be lower than that of the cladding of small holes (cutoff). In Ref. (Kubota et al. 2004) a first
practical PZ-fibre is described with MS-I structure. Its x- and y-modes losses are 28 and 196
dB/km at 1.55 μm. However, this fibre structure is not optimal (Ju et al. 2006), where four
different similar fibres are treated at 1.55 μm. Here we consider two kinds of fibre MS-I (MS-I-1
and MS-I-2, see Table 2), similar to fibres denoted as PCF-VI and PCF-VIII in Ref. (Ju et al. 2006).
Fig. 7 illustrates the spectral losses of x- and y-modes for 1000-m FOG coil of fibre MS-I-1,
wound with 25-cm diameter. Only one 𝛳-angle orientation is considered for holes structure
with respect to bend plane, because other orientations yield the same type of result. Clearly,
dichroism window does not satisfy even the soft criterion. One reason is that the phase
birefringence is only 2×10-4 at 1.55 μm, while its maximum (4.55×10-4) occurs at 2.3 μm, where
this fibre acts as 1-m PZ-fibre, similar to fibre PCF-VI from Ref. (Ju et al. 2006). This two-fold
reducing of birefringence is unavoidable for long fibres due to their operational wavelength
shift towards smaller wavelengths comparing to short fibres (similar to Fig. 6(b)). Fig. 7a also
illustrates the short-wavelength boundary 1 of bend loss, typical for MS-fibres (Nielsen et al.
2004), and long-wavelength boundary 2, typical to MC- and W-fibres. Oscillations in the region
1 are the resonances with modes of clad of small holes (Murao et al. 2009). Winding this fibre
with 100-mm diameter leads to overlapping of boundaries 1 and 2, so the loss exceeds 100
dB/km at all wavelengths.
Fig. 6 Fragments of cross sections of fibres MS-I,
MS-II, and MS-III. Grey background is silica;
white regions are the air holes.

8. 8
Fig. 7a Spectral losses of x- and y-modes of fibre MS-I-1, wound with 25-cm diameter (only for
one value of angle 𝜭). Regions 1 and 2 are the short- and long-wavelength limits of bend
losses.
Fig. 7b Spectral graph of phase birefringence, determined as 𝑩 𝒎𝒐𝒅 in section 2.
Situation is different for fibre MS-I-2. Even for winding with 20-mm (!) diameter its dichroism
window parameters are almost the same as for straight fibre (Fig. 8a) due to larger size of small
air holes.
Fig. 8a Spectral loss curves of x- and y-modes of fibre MS-I-2, straight (𝟐𝑹 = ∞, black solid
lines) and winded with diameter 𝟐𝑹 = 20 mm at fixed 𝜭 (grey dashed lines) for mesh
500×500.
Fig. 8b Spectral loss curves in straight fibre for meshes with 𝑵 = 𝟒𝟎𝟎 and 𝑵 = 𝟓𝟎𝟎.
Fig. 8c Spectral graph of phase birefringence.

9. 9
The worst case of holes structure orienting is considered relative to bend plane (upper inset at
Fig. 8a). The lower inset informs that FDFDM mesh is used with 𝑁𝑥 = 𝑁𝑦 = 𝑁 = 500. Fig. 8b
illustrates the spectral loss curves in straight fibre for 𝑁 = 500 and 𝑁 = 400. In the literature,
attempts are made to reduce the calculation error of such graphs below 1% (Guo et al. 2004).
Fig. 8b reveals much larger difference of graphs, at least for х-mode. However, for dichroism
window width, the difference is small due to sharp growth of loss curves, so there is no need in
very large N. Fig. 8c illustrates the spectral dependence of phase birefringence. It is
approximately 10 times larger than in all above considered fibres, but dichroism window is
narrower than even in MC-fibres Panda. Also, for this MS-fibre splice loss is very large (see
Table 2).
4.2 Fibres MS-II and MS-III
These fibres are described in References (Saitoh and Koshiba 2005; Chen and Shen 2007) in the
absence of bending. Here we’ll not present the graphs for bent fibres. Note instead that
winding the fibre MS-II with 60-mm diameter does not influence the dichroism window, similar
to Fig. 8a. This could be treated as extremely wide dichroism window, but splice loss is too large
(Table 2). For fibre MS-III, calculation reveals that its extremely wide dichroism window is
almost the same for winding diameters up to 20 mm, but with even larger splice loss (Table 2).
Another two extremely broad-band polarising MS-fibres are known (Jian et al. 2011; Lu et al.
2013), also with large splice loss. Thus, the wider the dichroism window in MS-fibre the larger
are splice loss. On the contrary, for smaller splice loss (fibre MS-I-1), FOG coil with required size
could not be wound.
5 Short polarising lightguides (~1 m)
Short polarising lightguides (~1 m) could be used at FOG ring interferometer input, where they
may act as polariser and depolariser (Kurbatov et al. 2011). Also, it effectively filters high-order
modes, because their cutoffs are below 1.0 μm. Finally, such lightguide suppresses half of
optical y-polarised intensity, which otherwise was suppressed by IOC PZ-waveguides, leading to
undesired additional IOC heating.
Here we’ll compare 1-m length sections of MC- W- and MS-lightguides. For MC- and W-
lightguides we assume that birefringence is 𝐵𝑖𝑛= 0.001, because their diameters are 125 μm
instead of 80 μm for coil fibre, which simplifies the birefringence enlarging (Chu and Sammut
1984). We start from the point that all these lightguides should be polarising, both being
straight or bent.
5.1 MC- and W-lightguides
Anisotropic MC-lightguides are known as bend polarisers (Varnham et al. 1983). Here another
kind of MC-polariser is considered with dichroism even without bending, due to the indices of
x- and y-modes shifting below the silica index by depressed index SAP. Fig. 9 presents six loss
graphs of х- and у-modes: 1) in straight lightguide (dashed lines); 2) in bent lightguide with 60-
mm diameter when the graphs are 𝛳-averaged within 𝛳 = 0-300 (solid lines); 3) in bent
lightguide with 95-mm diameter without any SAP orienting, so graphs are 𝛳-averaged within 𝛳
= 0-900 (dashed-dotted lines).

10. 10
Lightguide parameters are listed in Table 3. Clearly, this is PZ-lightguide even being straight. For
both bend diameters, x-mode loss is 0.1 dB/m. One may say that pair of depressed-index SAP
form W-profile along x-axis leading to dichroism without bending. However, it is not so,
because light tunnels basically along y-axis (Fig. 2a).
The advantage of this lightguide is that SAP are close to thin enough core, allowing enlarging
the birefringence even above 0.001. However, x-mode is deformed by SAP, so the splice loss
with SMF-28 fibre is 0.4 dB for double splice passing towards the coil and back. In Ref.
(Kurbatov et al. 2011 and 2013), a polarising W-lightguide is treated theoretically and
experimentally. Here we turn to some other W-profile (Table 3) for which Fig. 10 presents the
same six loss graphs as at Fig. 9. One may see that W-lightguide characteristics are similar to
those of MC-lightguide. However, х-mode of W-lightguide is almost circular, so splice loss with
SMF-28 fibre are 0.07 dB for splice double passing. Here a slight х-mode field squeezing by SAP
still occurs, but SAP could be surrounded by silica layer, or/and their index could be raised. This
spreads х-mode between SAP, and according to calculations, allows decreasing of splice loss to
0.02 dB for splice double passing. Of course, the loss value 0.4 dB for MC-lightguide is not
Fig. 9 Spectral losses of y- and x-modes
of MC-lightguide. Dashed curves are
for straight fibre, solid curves are for
fibre wound with 60-mm diameter and
with SAP orienting within 𝜭 = 0-300
,
dash-dotted curvesare for fibre
winded with diameter 95 mm without
SAP orienting.
Fig. 10 The same graphs as at
Fig. 9 for W-lightguide.

11. 11
critical, but W-profile allows reducing the MFD at least up to 8 μm (Kurbatov et al. 2013) for
polarising lightguides, which are still broadband, unlike the MC-fibres.
Table 3
Parameters of MC- and W-lightguides for mathematical simulation
Parameter MC-lightguide W-lightguide
Core diameter (μm) 8.4 9.5
χ = τ/ρ (Fig. 2) - 1.8
Δn+ 0.003 0.0031
Δn- 0 0.0033
Linear birefringence 0.001 0.001
5.2 MS-lightguides
Basic advantage of MS-lightguides, according to the literature, is their extremely large
birefringence, unavailable for fibre with SAP. However, this means small MFD and unavoidable
large asymmetry of x-mode field, i.e. large splice loss. Thus, there is the reason to consider only
the lightguide МS-1 (Fig. 6), similar to PCF-VI from Ref. (Ju 2006). In Ref. (Ju 2006) the optimal
structure has the dichroism window width 0.0 and 103.5 nm, according to rigid and soft criteria,
with 6-dB splice loss for double passing.
6 Conclusions
Comparative study is fulfilled for different types of polarising fibres for fibre optic gyro (FOG)
sensing coil and for input polarisation/modal filters for FOG ring interferometer. Three kinds of
fibre are considered: Panda fibres with matched-clad (MC) and W-profile, along with
microstructured (MS) fibres. It is shown that W-fibres Panda are the optimal for high-accuracy
FOG, having broad-band dichroism and minimal splice losses with other fibres and IOC
waveguides. Also, a new MC-profile fibre is proposed polarising even without bending. As for
polarising MS-fibres, they may be extremely anisotropic. But they don’t demonstrate similar
several times wider dichroism window. MS-fibres with widest dichroism window are extremely
bend resistant, but have too large splice loss. This makes such fibres not to be so promising for
FOG, at least with modern FOG element base.
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