Polarisation maintaining fibre with pure silica core and two depressed claddings for fibre optic gyroscope

Kurbatov A. M. a, Kurbatov R. A. a, Voloshin V. V. b, Vorob’ev I. L. b, Kolosovsky A. O. b.

aKuznetsov Research Institute for Applied Mechanics, Moscow

bFryazino Department of Institute of Radio Engineering and Electronics of RAS, Fryazino, Moscow Region

E-mail address: romuald75@mail.ru (Kurbatov R.)

(Originally published in Optical Fiber Technology, V. 32, (December 2016))

ABSTRACT Polarisation maintaining (PM) fibre is described with pure silica core and two depressed

claddings for fibre optic gyro (FOG) sensing coil. Detailed mathematical simulation is presented by supermodes method, which is extremely necessary for such fibre. Simulation is fulfilled by frequency domain finite difference method (FDFDM), taking into account all details of realistic index profile with stress applying parts, while the leakage/bend loss occur in the region with complex index, surrounding the fibre. Cutoff and small bend loss are theoretically predicted and experimentally measured with excellent agreement between theory and experiment. Polarisation maintaining ability is measured in the form of conventional h-parameter (7.1∙10-6 1/m) for 90-μm diameter fibre with birefringence value only 3.9∙10-4.

Keywords: pure silica core fibre, depressed clad fibre, polarisation maintaining fibre,

bend resistant fibre, fibre optic gyroscope, supermodes, finite difference method.

1. Introduction The basic problem of fibre optic gyro (FOG) space applications is radiation induced

attenuation (RIA) in sensing coil fibre. Implementing the pure silica core fibre, one may overcome this problem [1]. Fig. 1 illustrates some refractive index profiles of such kind. Profile 1 has a wide depressed cladding (DC) and external silica cladding [2]. For bend loss decreasing, profile 2 has a depressed index outer tube instead of silica cladding [3], profile 3 is the pure silica core match-clad (MC) profile [4]. Finally, double-DC pure silica core fibre with profile 4 (Fig. 1) is described in ref. [5].

The listed fibres are isotropic, so their implementing for FOG requires a double-

depolarised configuration of Sagnac interferometer [1], which possesses the larger polarisation non-reciprocity than the one with the coil of polarisation maintaining (PM) fibre. However, nowadays, pure silica core high birefringent (Hi-Bi) fibres are considerably less widespread than isotropic ones. We’ll mention two following pure silica core Hi-Bi fibres: 1) Panda-type fibre [6] with MC-profile 3; 2) elliptical stress-clad fibre [7] with dichroism value 15 dB/km. In Ref. [6], it is established that Hi-Bi pure silica core fibre has approximately ten times larger RIA comparing to isotropic one, but this is still not critical for FOG.

Fig. 1. Pure silica core profiles.

In the present manuscript, Hi-Bi double-DC fibre is described drawn from preform with index profile corresponding to profile 4 at Fig. 1. In section 2, a detailed mathematical simulation is provided for leakage/bend losses and high-order modes suppression (modal filtering), which is extremely necessary for double DC-profile, unlike MC-profile 3 at Fig. 1. In section 3, experimental results are presented for insertion loss, h-parameter, bend loss, and cutoff wavelength, revealing very good agreement with theory.

2. Mathematical simulation of propagation and absorption by supermodes method Fig. 2 illustrates the rectangular configuration 1 of size 𝐿𝑥 × 𝐿𝑦 containing Panda-type

double-DC fibre cross section with black complex index absorbing ring around it. This ring has complex refractive index 𝑛 = Re𝑛 + 𝑖 × Im𝑛, where Im𝑛 value is the reason of absorption. Frequency domain finite difference method (FDFDM) is implemented for scalar wave equation [8] within this configuration.

This method is of the same simplicity for any weak-guiding profile. Moreover, realistic smoothed-index profiles require even sparser grid than piecewise profile. Also, configurations 2 and 3 at Fig. 2 illustrate other geometries of absorbing (black) regions. For attenuation simulation, configurations 1 and 2 yield the same results, while configuration 3 leads to the same result as the widespread perfect match layer (PML) method [9]. The latter was specially developed for absorbing simulation, eliminating the light reflection from boundaries of black region of configuration 3 at Fig. 2. However, implemented below complex index method for absorbing region allows doing all of this in considerably simpler and less artificial manner, being much closer to the practical fibre with absorbing coating. Indeed, for absorbing simulating by PML method, one has to replace the coordinate derivatives within the absorbing region in the

manner 𝜕 𝜕𝑥⁄ → [1 + 𝑖𝜎𝑥(𝑥)]−1 𝜕 𝜕𝑥⁄ , 𝜕 𝜕𝑦⁄ → [1 + 𝑖𝜎𝑦(𝑦)]−1

𝜕 𝜕𝑦⁄ , which obviously complicates

the consideration (𝜎𝑥,𝑦 are the dependences of artificial absorbing within PML region of the

form of rectangular black region of configuration 3 at Fig. 2). One more advantage of complex index method is the same simplicity for arbitrary form of absorbing region (not only shown at Fig. 2). For further description, configuration 1 is chosen with black absorbing layer of width 𝑑 = 10 μm.

During simulation, the value Im𝑛 should be increased, leading, firstly, to calculated loss growth. It should be done until this growth stops. Typically, these desired Im𝑛 values appeared within the range (2.5 − 5.0) × 10−3 for below simulations. This is some kind of disadvantage of complex index method (one more similarity with PML-method), but it does not lead to conceptual or technical complications. However, one should avoid of further too large Im𝑛 increasing, because loss becomes decrease due to the fact that field penetrates into absorbing region at the distances order of grid step, so this could not be treated as the approximation of differential equation. Also, the real part of refractive index Re𝑛 of absorbing region is chosen to

Fig. 2. Left configuration 1 shows the complete

simulation rectangular region of dimensions 𝑳𝒙 × 𝑳𝒚.

Configuration 1 contains the following: fibre cross

section, which is the core, two depressed claddings,

silica cladding, and boron-doped stress-applying parts

(SAP), surrounded by thin silica layers, and

absorbing complex-index region (the black ring).

Right configurations 2 and 3 illustrate the alternative

geometries for (black) absorbing region.

provide the value Re2𝑛 − Im2𝑛 of real part of absorbing region dielectric constant equal to that of neighbouring silica (white regions at Fig. 2). This is done for reflections eliminating from the boundaries of absorbing region, similar to PML-method. Alternatively, for this purpose, one may set Im𝑛(𝑥, 𝑦) = Im𝑛(𝑟) = Im𝑛0[(𝑟 − 𝜌𝑐𝑙) 𝑑⁄ ]2, similar to Ref. [10] (and again, similar to PML-method in its most widespread version with 𝜎𝑥(𝑥)~[(𝑥 − 𝜌𝑐𝑙) 𝑑⁄ ]2,

𝜎𝑦(𝑦)~[(𝑦 − 𝜌𝑐𝑙) 𝑑⁄ ]2), where 𝑟 = √𝑥2 + 𝑦2 is the radial polar coordinate, 𝜌𝑐𝑙 is the silica

cladding radius (or the inner radius of absorbing region). Nevertheless, for below simulation, it was set Im𝑛 = 𝑐𝑜𝑛𝑠𝑡.

Further, for bend loss simulation, apart from complex index region, a modification is used for refractive index profile 𝑛𝑏𝑒𝑛𝑡(𝑥, 𝑦) of bent fibre, using the result from Ref. [11], so it is related to profile 𝑛𝑠𝑡𝑟(𝑥, 𝑦) of straight fibre as

𝑛𝑏𝑒𝑛𝑡(𝑥, 𝑦) ≈ 𝑛𝑠𝑡𝑟(𝑥, 𝑦)[1 + 𝑥𝑏𝑒𝑛𝑑 (1.325𝑅)⁄ ] = 𝑛𝑠𝑡𝑟(𝑥, 𝑦)[1 + (𝑥 cos 𝜃 − 𝑦 sin 𝜃) (1.325𝑅)⁄ ]. (1)

Coefficient 1.325 is the elastooptical correction factor [12], and the angle 𝜃 is illustrated by Fig. 3. For bend loss simulation, the averaging over 𝜃 is implemented within 𝜃 = 0-900 with step 2.50.

Consider the method of searching of necessary solutions for scalar Helmholtz equation [10]:

[𝜕2 𝜕𝑥2 + 𝜕2 𝜕𝑦2 +⁄ 𝜕2 𝜕𝑧2 +⁄⁄ 𝑘2𝑛2(𝑥, 𝑦)]𝐸(𝑥, 𝑦, 𝑧) = 0 (2) where 𝐸(𝑥, 𝑦, 𝑧) is the electric field, 𝑛(𝑥, 𝑦) is the refractive index profile. Light propagation in this case could be described by supermode method proposed in Ref. [13] for DC-fibres, while the term “supermode” itself is introduced in Ref. [14] and implemented in Ref. [15] for MC- and DC-fibres. Supermode is the eigenmode of the whole fibre cross section (Fig. 2). In this case one may set 𝐸(𝑥, 𝑦, 𝑧) = 𝜓(𝑥, 𝑦)exp(𝑖𝛽𝑧), because index profile does not depend on 𝑧, so Eq. (2) may be rewritten as [𝜕2 𝜕𝑥2 + 𝜕2 𝜕𝑦2 +⁄⁄ 𝑘2𝑛2(𝑥, 𝑦)]𝜓(𝑥, 𝑦) = 𝛽2𝜓(𝑥, 𝑦) (3)

Here 𝛽 is supermode propagating constant. Values of 𝛽 and 𝜓(𝑥, 𝑦) of any supermode could be found from Eq. (3), being discretised by FDFDM and yielding the following algebraic eigenvalue problem [8]:

𝑎(𝜓𝑖−1,𝑗 + 𝜓𝑖+1,𝑗) + 𝑏(𝜓𝑖,𝑗−1 + 𝜓𝑖,𝑗+1) + 𝑐𝑖,𝑗𝜓𝑖,𝑗 = 𝛽2𝜓𝑖,𝑗. (4)

Fig. 3. Illustration of bent fibre. 𝑹 is bending radius, 𝜽 is the

angle of SAP orientation relative to bending plane, 𝒙 and 𝒚

are the fibre anisotropy axes, 𝒙𝒃𝒆𝒏𝒅 and 𝒚𝒃𝒆𝒏𝒅 are the axes

parallel and perpendicular to bending plane.

Here 𝑎 ≡ ∆𝑥−2, 𝑏 ≡ ∆𝑦−2, 𝑐𝑖,𝑗 ≡ 𝑘2𝑛2(𝑥𝑖 , 𝑦𝑗) − 2𝑎 − 2𝑏. Also, 𝑥𝑖 ≡ −𝐿𝑥 + (𝑖 − 1)∆𝑥 and

𝑦𝑗 ≡ −𝐿𝑦 + (𝑗 − 1)∆𝑦 are grid points coordinates, ∆𝑥 ≡ 2𝐿𝑥 (𝑁𝑥 − 1)⁄ and ∆𝑦 ≡

2𝐿𝑦 (𝑁𝑦 − 1)⁄ are the discretisation steps along 𝑥- and 𝑦-axis, 𝑖 = 1,2, … 𝑁𝑥, 𝑗 = 1,2, … 𝑁𝑦.

In Ref. [13-15], only azimuthally symmetric supermodes 𝐻𝐸1,𝑚 are treated with

𝜓(𝑥, 𝑦) = 𝜓(𝑟) for the case 𝑛(𝑥, 𝑦) = 𝑛(𝑟) (isotropic and straight fibres). They are excited by Gaussian input beam, the same at all wavelengths. This method could be generalized for supermodes 𝐻𝐸𝑙,𝑚 with any 𝑙 > 1. However, this again could be done only for profiles of the kind 𝑛(𝑟), so Panda-type profile (Fig. 2) is not the case (for both straight and bent fibre), likewise the bent fibre with isotropic profile.

In Ref. [16], a procedure is described for bend loss and modal filtering calculations in DC-fibres. This procedure searches only two selected supermodes (SSM) at each wavelength, allowing omitting the rest plenty of supermodes, and it does not require the initial concretising or further searching of the numbers of these two SSM. Bend loss is characterised by first selected supermode (SSM-I) and modal filtering is characterised by second selected supermode (SSM-II). SSM-I and SSM-II have the parameters and field distributions close to those for modes HE11 and HE21 of equivalent MC-fibre with the same core parameters. The equivalent MC-fibre for double-DC fibre is illustrated by left part of Fig. 4.

The fields of modes HE11 and HE21 of equivalent MC-fibre are the input beams for SSM-I and SSM-II at each wavelength, and their propagation parameters are the initial approximations of SSM-I and SSM-II parameters for both straight and bent double-DC fibre.

Similarly, one may introduce equivalent DC-fibre (right part of Fig. 4). Its own SSM-I and SSM-II could be even more accurate initial approximations for SSM-I and SSM-II of double-DC fibre, being calculated, in turn, using the modes HE11 and HE21 of equivalent MC-fibre. However, lots of calculations show that equivalent MC-fibre is enough for direct simulations of double-DC fibre.

One more notification should be done. In Ref. [5] (and at Fig. 10 below), a practical double DC-profile is presented, which has slightly reduced core refractive index by the amount 5×10-4 with respect to silica due to unavoidable technological Fluorine penetration from DC. This effect is taken into account for below simulations results, although, still allowing treating such profile as approximately pure-silica core profile 4 from Fig. 1. This is because the difference of simulation results is small comparing to completely pure silica core double-DC profile.

2.1 First selected supermode of double-DC fibre and bend loss Solving the eigenvalue problem (4) for 𝐻𝐸11 mode of equivalent (straight) MC-fibre

without absorption, one yields its real β11-eigenvalue as the initial approximation of complex β-eigenvalue for SSM-I of double-DC fibre with absorption (straight or bent). Two β-eigenvalues are calculated in the vicinity of β11 for eigenvalue problem (4) with absorption. SSM-I is searched among these complex supermodes by maximizing the overlap integral of their fields with the field of 𝐻𝐸11 mode. The value larger than 0.4 is enough for this integral, otherwise, the procedure is repeated for larger number of complex supermodes in the vicinity of β11 till SSM-I is found. Further, the grid could be done thicker, so SSM-I in this case could be found starting from already found parameters of SSM-I for sparser grid.

Fig. 4. Double-DC profile (black solid line). Left figure

illustrates the equivalent MC-profile (dashed grey line),

right figure illustrates the equivalent DC-profile (dashed

grey line).

Left part of Fig. 5 illustrates the real part of SSM-I field at 1.55 μm in double-DC fibre (profile parameters are listed in Table 1 below). Inset 2 illustrates the field oscillations in silica cladding for straight fibre (leakage loss); inset 3 illustrates the field distortion due to the fibre bending (bend loss). The difference between the intensities of SSM-I and the mode HE11 of equivalent MC-fibre could be seen only in logarithmic scale (right part of Fig. 5).

Fig. 5. Left figure: Graph of the real part of SSM-I field (1). Insets 2 and 3 illustrate this field in silica cladding for straight and bent fibre, respectively. Right figure: logarithmic graph of intensity of SSM-I (black solid line) and of HE11 mode of equivalent MC-fibre (grey dash-dotted line), plotted for straight fibres.

How bend loss depends on bend diameter? Fig. 6 illustrates some graphs of bend loss at 1.55 μm.

Graph 1 is for isotropic double-DC fibre. Up to 40-mm bend diameter, loss is only several times larger than in straight fibre (the dashed horizontal asymptote for graph 1). This is because the radiation caustic is fixed at the boundary of DC-2 with silica cladding 𝑥𝑐 = 𝜏2 (𝜏2 is the radius of DC-2), when the bend radius is larger than so called critical bending radius 𝑅𝑐𝑟 estimated below by Eq. (5). This is shown at left part of Fig. 7 for black profile. In this case, looking at the inset 3 of Fig. 5, loss increasing due to field distortion on the right is noticeably counter-balanced by loss decreasing due the field distortion on the left. This slow loss dependence on 2𝑅 due to fixed caustic position is of the same nature than similar slow dependence in DC-fibre from Ref. [17]. This, in particular, means that for winding such fibre into the coil of diameter larger than 100 mm, bend loss is not a problem.

Fig. 6. Graph 1 is the bending loss of isotropic double-DC

fibre, graph 2 is the same for Panda fibre with SAP

surrounded by silica layers, graph 3 is the bend loss of

equivalent DC-fibre. Dashed horizontal lines are the

asymptotes for graph 1 and 2, corresponding to leakage

losses in straight isotropic and Panda fibres.

Fig. 7. Left figure: solid lines are profiles of bent fibre

with radius 𝐑 < 𝐑𝐜𝐫 (𝐑 = 5 mm, grey profile) and 𝐑 > 𝐑𝐜𝐫

(𝐑 = 15 mm, black profile), horizontal dashed line is

effective index 𝐧𝐞𝐟𝐟 of SSM-I, crossing the profiles at the

points of radiation caustic with coordinate 𝐱𝐜. Right

figure: thick grey line is the bent fibre profile, dashed

black line within the core is the effective index of SSM-I

of equivalent DC-fibre (right part of Fig. 4), black dash-

dotted lines are the indices of whispering gallery modes

propagating within the DC-2.

For bend radius 𝑅 < 𝑅𝑐𝑟, the caustic penetrates into DC-2 (𝑥𝑐 < 𝜏2), so its coordinate 𝑥𝑐

becomes dependent on R (as it always occurs, for example, in MC-fibres), leading to sharper bend loss growth at Fig. 6. For bend diameters 2𝑅𝑐𝑟 < 20 mm, graph 1 tends to another asymptote (dash grey line 3 at Fig. 6), which is the bend loss of equivalent DC-fibre (lower inset of Fig. 6). Another phenomenon for 𝑅 < 𝑅𝑐𝑟 is the resonances with whispering gallery modes (right part of Fig. 7) leading to peaks at graph 1 (Fig. 6), similar to peaks of bend loss described in Ref. [18] for realistic MC-fibre with raised-index coating.

The critical bend radius 𝑅𝑐𝑟 for caustic penetration into DC-2 could be estimated similar to Ref. [17] in the following manner:

2𝑅𝑐𝑟 ≈ 4𝑘2𝜌2𝑛0

2𝜏2[(1.1428𝑉 − 0.996)2 − 𝑉2 (1 + Ʌ)⁄ ] (5)

where 𝑉 = 𝑘𝜌√𝑛02 − 𝑛1

2, Ʌ = (𝑛02 − 𝑛1

2) (𝑛02 − 𝑛2

2)⁄ . These estimations are derived from condition for propagation constant of mode HE11 of equivalent MC-fibre 𝛽 = 𝑘𝑛0(1 + 𝜏2 𝑅𝑐𝑟⁄ ), which is obvious from left part of Fig. 7, where 𝑘 is the vacuum wavenumber, 𝜌 is the core radius, 𝑛0 is the silica index, 𝑛1,2 are DC-1 and DC-2 indices. In our case, this yields Rcr = 9 mm, which is in good agreement with graph 1 at Fig. 6. Similar behaviour of bend loss occurs for profiles 1 (Ʌ = ∞) and 2 at Fig. 1.

Fig. 6 also presents the graph 2 of bending loss for double-DC profile at the presence of SAP surrounded by 1.0-μm silica layers. We also assume that SAP index is equal to the index of DC-2. Graph 2 is similar to graph 1, but at higher level. However, peaks are smoothed because graph 2 is averaged over angle 𝜃 (see Fig. 3), so for each 𝜃 one has the individual system of whispering gallery modes.

2.2 Second selected supermode of double-DC fibre and modal filtering efficiency Parameters of SSM-II are calculated in the same manner as SSM-I ones, using 𝐻𝐸21

mode field and its β21-eigenvalue of equivalent (straight) MC-fibre without absorption as the initial approximation. Fig. 8 illustrates the graph of real part of SSM-II field for isotropic double-DC fibre at 1.55 μm.

Also, the field 2 is presented of HE21 mode of equivalent MC-fibre. Note that SSM-II field is small in silica cladding. One may conclude that this should result in small attenuation coefficient (non-effective modal filtering). However, the latter is determined by the efficiency of light penetration into absorbing coating, not into silica cladding. And this is determined not only by the field amplitude near the coating but also by the rays incident angle on it, which is large enough (large oscillations frequency of the field in silica cladding) to compensate the weak light penetration into silica cladding.

What is the spectral behaviour of attenuation coefficient of SSM-II? The basic feature of SSM-II of straight isotropic double-DC fibre is its degeneracy into even and odd modes with the

Fig. 8. Graph of the real part of SSM-II radial field

distribution (solid black line), and of the input HE21

mode radial field distribution of equivalent MC-fibre

(grey dashed line).

same propagation parameters and loss. Contour graphs of these modes fields are illustrated by the insets at low right corners of both parts of Fig. 9, and the losses for both of them are illustrated by grey dash-dotted curves (the same for both parts of Fig. 9).

Fig. 9. Left figure: leakage loss of odd SSM-II of straight isotropic (grey dash-dotted) and Panda (black solid)

fibres, contour graph at low right corner illustrates the field of odd SSM-II. Right figure: the same for even

SSM-II.

However, for Panda fibre with SAP (Fig. 2), this degeneracy is no more the case, so two supermodes with different parameters could be called as SSM-II. Their spectral loss graphs are illustrated by black solid lines at both parts of Fig. 9. Thus, measuring the fibre cutoff, one should yield the approximate result 1.23 μm, according to solid graph at the left part of Fig. 9. Below it is seen that the experimental cutoff is close to this value (1.25 μm).

3. Experimental characteristics of double-DC fibre Left part of Fig. 10 illustrates refractive index profiles 1-3 in different parts of fibre

preform made by SPCVD-method [2]. These are the realistic cases of profile 4 at Fig. 1. In Ref. [5], isotropic 200-μm diameter fibre is described drawn from the end of the preform with profile 3 at Fig. 10, while 125-μm diameter fibre from the same end of the preform did not transmit the light for wavelengths larger than 1.25 μm. Thus, careful simulation is needed for such index profile. From Fig. 10 it is seen, that profile noticeably varies along the preform. Profile 1 at Fig. 10 is the most bending resistant, but it has the largest cutoff. Consequently, according to simulation, it is impossible to draw the fibre from the whole preform which could be simultaneously single mode and bend resistant everywhere along its length. However, this is possible for two profile pairs 1-2 and 2-3, so preform was divided in two equal parts.

Fig. 10 also shows the photo of PM-fibre cross section, drawn from the half of preform

with profiles 1-2, unlike the fibre from Ref. [5]. Geometrical parameters of drawn PM-fibre are listed in Table 1. As for SAP, they have the form between Panda and bow-tie (near the core it is closer to Panda) [19]. Standard optical characteristics of drawn Hi-Bi fibre were measured (see Table 2).

Fig. 10. Left figure: profiles at the

beginning (1), midpoint (2), and at the

end (3) of preform. These graphs are

for index difference n(r) – n0, where

n(r) is refractive index profile, n0 is

silica index. Right figure: photo of fibre

cross section drawn from the half of

preform with profiles 1 and 2. Here 4 is

the core, 5 and 6 are DC-1 and DC-2, 7

is silica cladding, 8 are boron-doped

SAP.

Table 1 Double-DC fibre geometric parameters

Parameter Value

Fibre diameter (μm) 90 Core diameter (μm) 8.8 DC-1 diameter (μm) 17 DC-2 diameter (μm) 57 MFD (calculated value), μm 7.3

Table 2 Double-DC fibre experimentally measured basic optical parameters

Parameter Value

Cutoff wavelength, μm 1.25 Insertion loss, dB/km 2.4 h-parameter, 1/m 7.1∙10-6

Linear birefringence 3.9∙10-4

Polarisation maintaining ability of the fibre of length L is usually characterised by so

called h-parameter [20]. The measured value h = 7.1×10-6 1/m is several times lower than the value from conventional range h = (2-5)×10-5 1/m. Birefringence B was measured by usual method of spectral observation of polarization modes beating, leading to result B = 3.9×10-4, which is modest enough for providing the measured small h-parameter only by itself. Since there was no dichroism, probably, the tight confinement of HE11 mode within the core is one more reason of small h-parameter.

As for measured insertion loss, it is higher than according to above simulation of leakage loss.

However, it has completely technological nature. For example, preform contained too much water, which is illustrated by Fig. 11 for fibre sections 1 m (graph 1) and 1100 m (graph 2). Non-waveguiding nature of this loss could be seen at Fig. 12, showing three output spectra for 1.5-m fibre section (even here a small water peak 4 is seen!). Spectrum 1 corresponds to straight fibre, spectra 2-3 correspond to the fibre with one and ten loops with 10-mm diameter. If the insertion loss was due to the light tunnelling into silica cladding, the fibre was extremely sensitive to bending with such a diameter. However, from Fig. 12 it is clear that there is no bending loss at 1.55 μm even for ten 10-mm diameter loops. This agrees with calculated graph 2 at Fig. 6.

Fig. 11. Output spectra for 1-m fibre

(graph 1) and for 1100 m (graph 2).

Also, this experiment is the method of cutoff measurement, which is the wavelength at

Fig. 12 where graphs 1-3 meet each other (near 1.25 μm). This is again in agreement with theory predicted the value 1.23 μm (black solid graph at the left part of Fig. 9). Thus, other theoretical predictions (such as high modal filtering at 1.55 μm) could be treated as reasonable, although not verified experimentally. Note that small difference of graphs 1 and 2 for one 10-mm loop could be explained by the fact that the field of high order mode (SSM-II) penetrates into cladding weaker than for MC-fibre (Fig. 8), so it is distorted by the bend weaker, requiring ten 10-mm loops for cutoff accurate measurement.

4. Profile with double depressed claddings and fluorine doped core Method of further radiation hardening of fibre assumes the core doping with fluorine,

similar to DC [4, 21]. In Ref. [4, 21] such modification is described for profiles 3 and 1 at Fig. 1. For double-DC profile this modification is the profile at Fig. 13.

One may say that, strictly speaking, profiles from Fig. 10 are the types of the one from Fig. 13. However, this Fluorine-core profile has the core refractive index reduced by the values larger than 3×10-4, which could not be provided by Fluorine spontaneous penetration, but only due to controllable purposive Fluorine doping. According to experimental data from Ref. [21], this especially improves the characteristics for radiation doses over 100 krad. In this case, according to simulation, waveguiding characteristics still may be excellent, similar to pure silica core fibre, although MFD will be larger (up to 10-11 μm). This is due to required larger core diameter.

5. Conclusion A new polarisation maintaining pure silica core fibre is described based on double

depressed-clad profile. This construction provides improved optical parameters (wide MFD values range, high bending resistance, low h-parameter value). Also, careful and strict mathematical simulation, verified by bend loss and cutoff measurements, predicts the effective modal filtering and even the opportunity for broad-band dichroism. This is the new type of fibre for high-accuracy fibre optic gyro for space applications.

6. Acknowledgments

Fig. 12. Output spectra for 1.5-m fibre.

Graph 1 is for straight fibre, graph 2 is

for fibre with one loop having ~10-mm

diameter, graph 3 is for fibre with ten

such loops. Arrow 4 shows the water

peak.

Fig. 13. Double-DC profile with fluorine doped core

(modification of profile 4 from Fig. 1).

Authors would like to thank Golant K. M. for double-DC preform manufacturing.

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