ISSN 1063�7850, Technical Physics Letters, 2011, Vol. 37, No. 7, pp. 627–630. © Pleiades Publishing, Ltd., 2011.Original Russian Text © A.M. Kurbatov, R.A. Kurbatov, 2011, published in Pis’ma v Zhurnal Tekhnicheskoі Fiziki, 2011, Vol. 37, No. 13, pp. 70–77.

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Optical components transfer to the fiber basebegun many years ago [1]. Here we’ll consider fiberpolarizers on the base of lightguides Panda [1] withrefractive index (RI) W�profile [2].

Earlier [3] we reported about 500�m W�lightguidePanda with dichroism. IN the present work it isreported about dichroism in developed by us light�guides with lengths 200 m, 1 m and 50 mm, and mostprobable dichroism physical mechanisms of thisdichroism are also described with brief description ofits calculation ways for the first two cases. Lightguideswere manufactured from 2003 to 2007 according totechnical requirement and technology developed byauthors of the present work in different Russia organi�zations having optical fiber manufacturing base.

On Fig. 1a W�lightguide Panda cross section isshown with germanosilicate core 1 having RI = n1, flu�orine reflective cladding 2 having RI = n2, quartz clad�ding 3 with RI = n3, and circle stress�applying rods 4,which are boron doped and induce the linear bire�fringence. Additional layer 5 takes place only inthird (50�mm) lightguide. In Table parameters of allthree lightguides are listed.

On Fig. 2a x� and y�modes spectral losses in 200�mlightguide are shown. On Fig. 2b, related to 1�m light�guide, curves 1 and 2 are x� and y�modes losses instraight lightguide and curves 3 and 4 are those incoiled one with 60 mm diameter (3 turns). In eachcase light with õ� and ó�polarization is by turn waslaunched by white light source. Unfortunately ousmeasurements were limited by wavelength ~1.7 μm, sowe don’t see the whole dichroism windows. In 200�mlightguide this window is right�hand to operationregion (1.55 μm), but at lower winding radius it will goleftward at the spectrum.

Consider 200�m lightguide in more details. Havingin [3] excellent agreement with experiment our bend�

ing losses models here gave us too slow growth of x�and y�modes spectral losses comparing with Fig. 2a.So we considered one more loss mechanism:microbends. We generalized microbend loss model inconvenient straight lightguides [4] to the case of bentlightguide with any RI profile and PML�layer [5].Bent lightguide RI profile is related to straight one

profile n0(x, y) as n2(x, y) = (x, y)(1 + x/R) [5] (R is

bending radius). Light in bent lightguide could bedescribed in the form of supermodes [6] having fieldsψj. One of them, ψj0 (detailed), has a form similar tofundamental mode of straight convenient two�layerlightguide and it’s microbending loss coefficient hasthe form:

(1)

n02

2γ k2 Cj2Φ Δβj( )/ Reβj0Reβj( ).

j

∑=

Fiber polarizer based on W�lightguide Panda1¶A. M. Kurbatov and R. A. Kurbatov

Department of Center for terrestrial space infrastructure objects exploiting,Kuznetsov Research Institute for Applied Mechanics, Moscow, 111123 Russia

e�mail: akurbatov54@mail.ruReceived January 11, 2011

Abstract—Three kinds of fiber W�polarizer Panda are described: with lengths 200 m, 1 m and 50 mm. In thefirst two cases dichroism is higher than 30 dB, in the third case it is higher than 15 dB. The feature of 50�mmpolarizer is the scattering layer in quartz cladding. In each case a most probable physical dichroism mecha�nisms are described.

DOI: 10.1134/S106378501107011X

Fig. 1. W�lightguide Panda cross section. 1 is the core, 2 isfluorine cladding, 3 is quartz cladding, 4 is stress rods, 5 isadditional scattering layer (absent in 200�m and 1�m light�guides).1The article was translated by the authors.

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A.M. KURBATOV, R.A. KURBATOV

Here k is vacuum wavenumber, Cj is coupling coeffi�cient of detailed and number j supermodes Cj =

⟨ψj|xψj0⟩/(⟨ψj0|ψj0⟩⟨ψj|ψj⟩)1/2, ⟨A|B⟩ = dyA*(x,

y)B(x, y) (* is complex conjugate), Δβj = Re(βj0 – βj)is propagation constants difference (synchronism) ofdetailed and number j supermodes. In Gaussianmicrobends model with correlation length we have [4]

(2)

where σ is root�mean�square of inverse microbendsradius. We applied (1) and (2) to detailed supermodeswith õ� and ó�polarization (further x� and y�modes) of200�m lightguide. Calculations with Lc ~1.5 mm gaveus good resemblance with Fig. 2a graphs.

Physically bend and microbends co�operated workcould look like the following. As the wavelength growsx� and y�modes synchronism with the rest supermodesgets better (Δβj decreases). It (and also Lñ) sets thegrowth abruptness of microbending spectral loss curve(2), i.e. dichroism window width. As for its position,due to x� and y�modes fields bending distortion [7]coefficients Cj of their coupling with the rest super�modes are increase and loss curves get leftward at thespectrum. Thus the bend here may regulate dichroismwindow position and microbends may regulate itswidth.

Let’s turn now to 1�m lightguide. In [8] W� light�guide is described with dichroism window in visiblespectrum range (with relative width 5%) which isdetermined by cutoff thresholds of fundamental x�and y�modes. Due to bend this window goes leftwardat the spectrum and gets narrower. In [9] a W� light�guide with 13% dichroism window is described in theregion 0.85 μm. Here the desired x�mode cutoffthreshold is infinite so the dichroism window shouldbe limited only from below. However as the wavelengthgrows õ�mode penetrates into quartz cladding touch�ing the coating, its spectral losses grow and the dichro�ism window is also limited from above.

So, we’ve got W� lightguide Panda which on thelength ~1 m may give dichroism ~30 dB and more dueto x� and y�modes cutoff thresholds difference [8]. Forfundamental mode cutoff normalized frequency Vcut

dx∫

Φ Δβj( ) 2π1/2

σ2Lc ΔβjLc/2( )

2–[ ],exp=

when fluorine cladding is not very thin (our case)we’ve got an approximation Vcut ≈ 0.333 + 1.859Λ1/2 +

0.078Λ – 5.035 × 10–4Λ2, where Λ ≡ ( – )/( –

). Hereof, assuming that birefringence takes placeonly in the core and fluorine cladding we’ve gotdichroism window position in straight lightguide.Bending gets it narrower basically due to x�modelosses (Fig. 2b) which are well described by our bend�ing losses models [3]. However, birefringence in thislightguide is not large enough for such kind of applica�tions (see Table), and as it is objectively enough toincrease it up to ~0.001 then one may get substantiallightguide characteristics improvement with the sameRI profile.

Unfortunately our bending loss models are ade�quate only if these losses are large before the cutoffthreshold, which is probably due to applied PML�layer model imperfections. On Fig. 2b y�mode bend�ing losses are not large even after cutoff threshold.However one may calculate y�mode losses in straightlightguide using other methods [6, 10] and togetherwith x�mode bending losses accept it as worst variantof dichroism window.

Thus, the bend is almost not replaces dichroismwindow of our lightguide (contrary to [8]). To ourpoint of view for not thin enough fluorine claddings itcould be explained assuming that fundamental modebending losses are due to its bending coupling to radi�ation modes [11]. If fo fundamental mode we roughlyhave Vcut > 2.4–2.6 then it is packed tightly enough inthe core and has a weak coupling to radiation modes,i.e. low bending losses even in cutoff regime. Other�wise situation is reverse. In our lightguide one mayassume that Vcut ≈ 2.8 for y�mode is large enough andVcut ≈ 2.2 for x�mode is small enough.

The imperfection of obtained lightguide is thenecessity to coil it without axial twist. To our point ofview it is due to the following. When modeling thebending losses we saw that they essentially depend onstress rods orientation at the bending plane becausethey have reduced RI. When bending with twist thisorientation angle changes continuously so the turnshave long enough sections with the worst orientation.In favor of this explanation speaks the fact that bend�ing losses could be substantially reduced coiling thislightguide without twist. One way to overcome thisproblem is again birefringence increasing.

Bending dichroism window reducing leads to ideaof short polarizers (~50 mm). However the experi�ments with such W�lightguides Panda sections, whereat the length 1 m dichroism was ~30 dB, gave usdichroism ~1–3 dB. So for y�mode suppression weapplied the scattering layer near the cladding boundarywith the air [12, 13] (Fig. 1). Figure 3 shows the spec�tral losses graphs in such W�lightguide having length50 mm (range 1.15 μm) both ends of which are splicedwith single�mode PM�lightguides Panda. It is seen

n32 n2

2 n12

n32

Polarizing W�lightguides Panda parameters

Parameter 200�mlightguide

1�mlightguide

50�mmlightguide

Core RI 1.465 1.4626 1.462

Fluorine cladding RI 1.451 1.4567 1.4566

Linear birefringence 4.7 × 10–4 7.5 × 10–4 7 × 10–4

Core diameter, µm 9.0 9.5 8

Fluorine cladding diameter, µm

27 22.8 19.2

Fiber diameter, µm 95 125 125

TECHNICAL PHYSICS LETTERS Vol. 37 No. 7 2011

FIBER POLARIZER BASED ON W�LIGHTGUIDE PANDA 629

−59.9

−71.9

−77.9

−83.9

−89.9

−65.9

1450 1550 20.00 1650nm/Dnm

2

1

3(a)

3.0 2.000 500dB/D RES: AVG:SENS: SMPL:NORMAL 501 (AUTO)

dB

m

REF

−100.8

−90.8

−80.8

−70.8

−60.8

−50.85.0 dB/D RES:

SENS: MID2.000 10AVG:

SMPL: 1001 (AUTO)

15001300 40.00 nm/D 1700nm

2−4−

1:2:3:4:1:3:

1550.0000 nm1300.0000 nm−66.92 dBm−71.80 dBm−250.000 nm−4.88 dBm

REF

2

4

2

33

1(b)

dB

m

Fig. 2. (a) Fundamental x� and y�modes spectral losses in lightguide having length 200 m (curves 1 and 2), and light source spec�trum (3). Vertical axis scale factor (power level) is 3 dB, horizontal axis scale factor (wavelength) is 20 nm. (b) Fundamental x�and y�modes spectral losses in straight lightguide with the length 1 m (curves 1 and 2) and in the coiled one with diameter 60 mm(curves 3 and 4). Vertical axis scale factor (power level) is 5 dB, horizontal axis scale factor (wavelength) is 40 nm.

−60.0

−85.0

−110.0930 30.0 1080 1230in Vacnm/div

nm

5.0 dB/div

dB

m

REF

TMkr (Peak)1120.2 nm−69.83 dBm

Normal (A & B)

: A : B

21

Fig. 3. Fundamental x� and y�modes spectral losses in lightguide having length 50 mm (curves 1 and 2). Vertical axis scale factor(power level) is 5 dB, horizontal axis scale factor (wavelength) is 30 nm.

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that this time dichroism is not lower than 15 dB in therange ~90 nm. Here y�mode is scattered by additionallayer into other modes decaying in the next ÐÌ�light�guide coating. This layer was manufactured by intro�ducing in it of additions (basically of ytterbium). Thelatter have their own narrow absorption bands whichare probably can’t be responsible for y�mode decayingwithin the whole dichroism window which is to ourpoint of view is determined by the scattering which isnot so sensitive to wavelength.

So, for broad�band PZ�fibers generally it is neces�sary: 1) to avoid too wide fluorine claddings which areprevent to suppress the undesirable polarizationy�mode, choosing its minimal width when x�modebending losses are acceptable; 2) to grow the birefrin�gence up to ~0.001. The rest RI profile parameters inthe case of lightguide with the length ≤1 m should bechosen from fundamental x� and y�mode cutoffthresholds calculation (setting the y�mode cutoff at~1.4–1.5 μm). In the case of long lightguides the restRI profile parameters should be chosen by fundamen�tal x� and y�modes bending losses modeling.

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