Design, fabrication and testing of high performance fiber optic depolarizer

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1 Design, fabrication and testing of high erformance fiber otic deolarizer Jagannath Naak *a, Pradee Kumar a, Himansu Shekhar Pattanaik b, S. Sarath Chandra b a Research Center Imarat, Vignana Kancha, Hderabad, AP, INDIA 569; b lectro Otical Instruments Research Academ, Hderabad, AP, INDIA 569 ABSTRACT Fiber otic deolarizers both Lot te and non-conventional one made from single section of a Hi-Bi fiber have been fabricated and tested. ffect of critical design arameters like azimuth of the inut olarization, source sectral width, and length of the olarization maintaining fiber on the correlation between the two orthogonal eigen modes are analzed. These arameters are crucial for reduction of residual degree of olarization resulting miniaturization of the device. Performance results for both tes of deolarizers have been comared. It has been shown with recision control of design arameters it is ossible to obtain low value of DOP and R even with small length of the PM fiber. Residual degree of olarization of <% and etinction ratio of. db are measured with diminution of length u to 5cm for non conventional whereas 6cm is required for Lot deolarizer. Kewords: Degree of Polarization (DOP), tinction Ratio (R), Polarization Maintaining (PM) fiber, Device Under Test (DUT), High Birefringent (Hi-Bi) fiber. INTRODUCTION Fiber otic deolarizers are ver attractive devices used in interferometric fiber otic sensors in general and FOG in articular. Deolarization of light is essential in devices where reduction of olarization couling noise is a ke issue. Usuall the commercial available fiber otic deolarizers are fabricated based on Lot condition, where two birefringent fibers with their fast and slow aes aligned at 45 with each other and maintain a length ratio of :. Polarization aes alignment and length ratio, between two fibers are imortant arameters that determines the erformance of a fiber otic deolarizer based on Lot condition. Basic requirement of deolarization of a highl olarized light is a birefringent medium but nevertheless it deends on the source characteristics such as source sectral width, length of the birefringent medium over which light is allowed to travel, fiber grou dela difference between the two olarization modes and inut conditions. The olarization disersion rather than birefringence is essential to calculate degree of olarization 3. The differential grou velocities associated with the olarization modes of the Hi-Bi lead to the deolarization of the broadband source 4. Deolarization effect in the birefringent fiber to some etent can be observed with an source for which the grou dela difference eceeds the coherence time of the source 5. In this aer we have designed, fabricated, and tested high erformance deolarizers and comared Lot and non-conventional one. Section gives the mathematical formalism to calculate DOP at the outut of the fiber and accordingl design arameters are otimized. Section 3 describes fabrication and testing of the deolarizer. The variation of DOP with azimuth of inut olarization and length of the PM fiber are observed. Simulation results and eerimental results are discussed in Section 4.. THORTICAL ANALSIS The configuration for the deolarizer of Lot te and non-conventional te are shown in Fig and Fig where linearl birefringent Hi-Bi fibers are considered. The two eigen olarization modes of the Hi-Bi fiber are ecited b launching olarized light at an angle of θ with resect to fast (or slow) aes. But hsical erturbations, coule ower between the olarization modes that leads to non zero residual olarizations 5. *naak_jagannath@rediffmail.com; hone ; fa

2 Here it is assumed that there is no mode couling between the olarization modes. Inside the fiber roagation constants of olarization modes are functions of the inut light frequenc ω.. Non-conventional deolarizer X in The inut light incident to the deolarizer is linearl olarized and is given as follows. ρ ( t) ( t) Cos ( θ ) ( θ ) in in e t e in Sin iω t ( ) L c θ Fig. L d (a) Deolarized light PM Fiber where the time varing inut light is eressed as a comle analtic signal 6 given b e ( t ) ν ( ω) i ω t e dω * ( t) e ( t ) e (c) The otical source considered has sectral intensit ν ( ω ) and center frequenc ω. Where L c is coherence length of the source and L d is the deolarization length, which is defined as the length over which the two olarization modes inside the fiber loses correlation and still interfere uon recombination. L c λ λ The roagation in the fiber is given b the transfer matri iβ L e iβ L e where β and β are the roagation constants of the two eigen modes of the fiber. Following few mathematical stes the outut time varing electric field is given b o i( ωt β L) ( t) Cos( θ ) ν ( ω ) e dω (3) For a broad band source eanding β( ω) ' ( ω ) β + ( ω ω ) β + Λ in Talor s series β (4) β and ' dβ β Where, β ( ω ) Considering onl u to first order o i ω t βl t Cos θ e e t dω ω ( ) ' ( ) ( ) ( β L) Similarl, o i ( ) ( ) ( ω ) t β L ' t Sin θ e e( t β L) Degree of olarization is defined as the fraction of the intensit of light olarized ( ol ) is determined from coherenc matri 6 J of the outut light (b) () (5) (6) I to the total intensit ( I ) tot and

3 o o o o + o o J. (7) o o o o Where + signifies Hermitian transose. Degree of olarization is given b 6 I 4 det ol J DOP I ( tot ) (8) det J Sin ( )( θ S S ) 4 (9) Where, S ν ( ω) dω () ( L) ν ( ω) Cos( ω ω ) δτ L dω S g () d β δτ g, β β β dω Parameter S can be shown equivalent to incident light ower S Tr. in + in and arameter S deends on light source sectral distribution, fiber grou dela difference, and fiber length. Using eq n (9), (), and () the final eression for DOP is DOP [ ( ) Sin ( θ )] ( θ ) γ ( L) (3) quation () ields DOP at the outut of the single section of the Hi-Bi fiber. Where ( ) () ( z ) γ L defines S the mutual correlation function between the two eigen olarization modes and takes minimum value for equall slit owers between two olarization modes. Absolute value of the correlation function γ is a function of light source characteristics and incident conditions. With light incident at 45 to the fast and slow aes, degree of olarization solel deends on γ and aroaches zero, when absolute value of mutual correlation function tends to zero. The reliance of DOP on the above mentioned factors establishes the design arameters. So critical design arameters are azimuth of the electric vector of the inut light, fiber length, and coherence time of the source.. Lot deolarizer S The degree of olarization for the Lot deolarizer is obtained as DOP ( θ ) Cos ( θ ) γ ( L ) + Sin ( θ ) + γ ( L ) + [ γ ( L ) X in θ L { L Fig Deolarized light

4 [ ] ( L + L ) γ ( L L )] Cos β L + γ ( L + L ) + γ ( L L ) γ Sinθ Cos θ γ ( L )[ γ ( L + L ) γ ( L L )] Cos β L ) where β β ( ω ) β ( ) (4) ω The Lot deolarizer is obtained with two ieces of Hi-Bi fibers with their birefringent aes aligned at 45 and length ratio of : is maintained between L and L for minimal necessit. With this condition satisfied the outut degree of olarization becomes indeendent of the azimuth of the inut olarization( θ ). From equation (4) for an azimuth of the inut olarization to get DOP zero at the outut it requires L γ L, γ ( L + L ) and γ ( L L ) ( γ ( )), ( ( )) The degree of coherence γ ( L) for for Gaussian source is given as 3 δωδτ g L γ ( L) e (5) ln where δω is sectral width of the source and δτ is the differential grou dela of the fiber. Deolarization length is given as L d ln δω δτ g g Fabrication setu 3. FABRICATION The fabrication setu comrises a semi automatic active alignment sstem having four degrees of freedom (,,z, θ), slicing machine, broadband sources, olarizer, lightwave olarization analzer (Agilent 859C) and etinction ratio meter(pm 3). The fiber used for eeriment is a olarization maintaining fiber having large birefringence (B) given 4 b 4. ; beat length (L b ) is 3.7mm at 55 nm and differential grou dela δτ g is.6ns/km. Deolarizers of both te are fabricated with high birefringent fiber. The critical factor is the angular orientation with resect to the slow and fast ais of the high birefringent fiber, at which light is incident to the fiber. The figure deicts the eerimental setu used. It consists of broadband source, in our case, which is suerluminescent diode (SLD), recision alignment sstem, and light wave olarization analzer (LPA) used for characterization of the deolarizer. The olarized broadband sources used for the eeriment are SLDs with central wavelengths( λ ) nm and nm and sectral widths( λ) 36.9 nm and nm resectivel. Sectrums of both SLDs are eamined on sectrum analzer, which were almost Guassian. Fig 3 illustrates the eerimental setu used for non-conventional deolarizer. With the hel of alignment sstem light is couled to the fiber with recision rotation. The length of the PM fiber used for the eeriment is m, which is ver large comared to the deolarization length L d, observed with both the sources used. So for a good aroimation mutual correlation function is taken to be zero. The outut is allowed to fall on the detector of the light wave olarization analzer and degree of olarization at the outut of the fiber is observed with the LPA. The DOP at the outut of the deolarizer is constantl monitored for various inut azimuths. The curve is lotted between DOP and azimuth of the inut light. The minimum DOP was observed at azimuth of 45. In the nd eeriment we have used the same setu but different lengths of fibers. With this eeriment we have shown with a broadband source, if there is a recision control of azimuth of the inut light (equal ecitation of both olarization modes) with a small section of high birefringent fiber we can get a ver low DOP. The reeatabilit of the DOP values is also observed. Fig 4 ortras the eerimental setu for Lot deolarizer. The eeriment is similar to the nd art of the above one. For comarison of non-conventional te and Lot te, length of both ieces of PM fiber was cutback eriodicall but length ratio of : between them is maintained. The eeriment was erformed with both broadband sources and DOP at the outut is lettered.

5 X L Broadband olarized source Z Fig 3 erimental setu to measure DOP of non-conventional deolarizer. X L L Light wave olarization analzer (LPA) Broadband Z olarized source Source igtail 45 slicing Fig 4 erimental setu to measure DOP of Lot deolarizer. Light wave olarization analzer (LPA) 4. RSULTS The results obtained for non-conventional deolarizer are shown below. Theoretical and eerimental findings are differentiated b solid line and stared dots resectivel. Fig 5 describes effect of length of the fiber on the DOP for the two broadband sources 36.9 nm and nm. Fig 6 shows variation of DOP with azimuth of the inut light. There is good correlation between theoretical and eerimental values. The minimum DOP observed is at azimuth of 45. Fig 7 illustrates effect of source sectral width on erformance of the deolarizer with arametric variation of length. 5 eriment 5 eriment 4 4 L. Degree of olarization (%) 3 Degree of olarization (%) Fig 5 Variation of DOP with length of non-conventional deolarizer (a) sectral width 36.9 nm (b) sectral width 49.45nm 9 8 eriments 9 8 Degree of olarization (%) Degree of Polarization (%) L Azimuth of the inut light (deg.) Fig 6 Variation of DOP with azimuth of the inut light for source of sectral width 36.9 nm Source Sectral Width (nm) -8 Fig 7 Variation of DOP with sectral width of the source.

6 The simulation and eerimental results for Lot deolarizer are shown in Fig 8, which deicts variation of DOP with length of the fiber used. In all the eeriments carried out, the results are in well agreement with theor. 5 eriment 5 eriment 4 4 Degree of olarization (%) 3 Degree of olarization (%) Fig 8 Variation of DOP with length of Lot deolarizer (a) sectral width 36.9 nm (b) sectral width 49.45nm 5. CONCLUSION The erformance of the fiber otic deolarizer both for non conventional and Lot deolarizer with various critical arameters is investigated. The residual DOP <% is achieved with PM fiber 5cm for non conventional deolarizer and 6cm for Lot te with the broad band olarized source. For larger linewidth (49.45nm ), for PM fiber length of 5cm we obtained DOP of.5%, where as for lower line width (36.9nm), for the same length we obtained DOP of %. The residual value ma be attributed to olarization mode couling between the two eigen modes. For ractical alications non-conventional deolarizer is more suitable as almost same DOP is obtained for smaller size of the device in comarison to the Lot deolarizer. Being small in size it facilitates miniaturization and can be easil incororated in devices such as fiber otic interferometric sensors where olarization control is a ke issue. But limitation with this deolarizer is, the inut light to be linearl olarized. RFRNCS. Low drift fiber gro using a suerluminescent diode: K. Bohm, P. Martin, K. Petermann, lectron Letters, Vol. 7, 35 (98).. Degree of olarization in Lot Deolarizer: W. K. Burns, I/OSA Journal of Lightwave Technolog, Vol. LT-, No. 3, 475 (983). 3. Degree of olarization in anisotroic single mode otical fibers: J. I. Sakai, S. Machida, and T. Kimura, I Journal of Quantum lectronics, Vol. Q-8, No. 4, 488 (98) 4. Polarization mode disersion in single mode fibers: S. C. Rashleigh and R. Ulrich, Otics Letters, Vol. 3, 6 (978) 5. Deolarization in a single mode fiber: W. K. Burns, R. P. Moeller, Chin-Lin Chen, I/OSA Journal of Lightwave Technolog, Vol. LT-, No., 44 (983). 6. M. Born and. Wolf, Princiles of Otics, Cambridge Universit, 6 th edition