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Group Birefringence Measurement in Photonic Liquid Crystal Fibers by Use of Narrowband Light Sources

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Group Birefringence Measurement in Photonic Liquid Crystal Fibers by Use of Narrowband Light Sources Vol. 116 (2009) ACTA PHYSICA POLONICA A No. 3 Optical and Acoustical Methods in Science and Technology Group Birefringence Measurement in Photonic Liquid Crystal Fibers by Use of Narrowband Light Sources D. Budaszewski¤ and A.W. Domański Faculty of Physics, Warsaw University of Technology Koszykowa 75, 00-662 Warsaw, Poland In the paper we present the results of investigating the effective group birefringence of photonic crystal fiber, partially infiltrated with 6CHBT liquid crystal mixture, which is a chemical abbreviation for 4-(trans-4-n- -hexylcyclohexyl)isothiocyanatobenzene. We also introduce a novel method of group birefringence measurement based on phenomenon of depolarization of partially coherent light in birefringent media. We use Mueller–Stokes matrix formalism extended by additional depolarization matrix, which gives us possibility to calculate degree of polarization fluctuations of the light propagating in the liquid-crystal infiltrated microstructured optical fibres. We conducted the research for green and red semiconductor laser diodes. The results may contribute in construction of tunable photonic liquid crystal fibers depolarizer. Additionally, we have controlled birefringence of the photonic liquid crystal fibers by external electric field. These research may lead to designing a new type of fiber optic depolarizer based on photonic liquid crystal fibers. PACS numbers: 42.79.Kr, 42.25.Bs 1. Introduction Over the last two decades there is a great interest in novel combination of photonic crystal fibers (PCF) and liquid crystal (LC) mixtures, also known as photonic liq- uid crystal fibers (PLCF) [1]. Such structures (Fig. 1) possesses a new uncommon properties, like polarization tuning of light propagating inside the structure. Fig. 2. Phenomenon of depolarization of partially co- herent light in birefringent medium. L — length of wave package, l — length of birefringent medium, ¢n — bire- fringence of the medium. The best way to describe degree of polarization changes Fig. 1. PCF partially infiltrated with LC mixture forming a PLCF. of light guided through birefringent medium is the Mueller–Stokes matrix formalism. We have extended it In general, state and degree of the light polarization by additional matrix, which characterizes depolarization depend on birefringence of the medium. The PLCFs may properties of the medium [2]. 2 3 2 3 be highly birefringent and may change their parameters out S0 1 0 0 0 dependent on external parameters such as temperature, 6 out 7 6 7 6 S 7 6 0 PC 0 0 7 electric and optical fields. 6 1 7 = 6 7 4 out 5 4 5 In general, partially coherent light is being depolarized S2 0 0 PC 0 out by birefringent medium. Both orthogonal components of S3 0 0 0 PC wave package may have different phase and group veloci- 2 3 2 3 in ties, which may result in changes of the state and degree m11 m12 m13 m14 S0 6 7 6 in 7 of polarization (SOP and DOP) (Fig. 2). 6 m21 m22 m23 m24 7 6 S1 7 £ 6 7 6 in 7 ; (1) 4 m31 m32 m33 m34 5 4 S2 5 in m41 m42 m43 m44 S3 in out ¤ corresponding author; e-mail: [email protected] where [Sx ] and [Sx ] are parameters of the input and output Stokes vectors, respectively, mij are elements of (285) 286 D. Budaszewski, A.W. Domański 2. Depolarization in photonic crystal fibers Birefringence in optical fibers is characterized by its beat length LB: 2¼ ¸ LB = = ; (6) j¯x ¡ ¯yj B where ¯x, ¯y are propagation constants of both ortho- gonal polarization modes, ¸ means central wavelength of the light source, and B is phase modal birefringence of the fiber. LB is beat length of the fiber after which the state of polarization is being reconstructed. The formu- lae for DOP diminishing in birefingent fibers are similar to the anisotropic crystal configuration [4, 5]: Fig. 3. Blazephotonic PM-1550-01 fiber structure. q 2 PL = 1 ¡ [1 ¡ exp (¡2´L)] sin 2θ; where the Mueller matrix of the medium and PC are elements ¸L of a depolarization matrix. DOP may be directly calcu- ´L = (7) ¢LLB lated from the elements of the Stokes vector, which can and be measured by using a quarter-wave plate and an ana- q 2 lyzer PG = 1 ¡ [1 ¡ exp (¡2´G)] sin 2θ; where p I S2 + S2 + S2 µ ¶2 DOP = polarized = 1 2 3 ; (2) ¸L ´G = : (8) Itotal S0 ¢LL 2 3 2 3 B S0 I¡;0± + I¡;90± In birefringent media, like PLCF two values of light ve- 6 7 6 7 ± ± locities can be distinguished: phase velocity defined as 6 S1 7 6 I¡;0 ¡ I¡;90 7 ! d! [S] = 6 7 = 6 7 ; (3) vp = , and group velocity defined as vg = , where ! 4 S 5 4 2I ± ¡ I ± ¡ I ± 5 k dk 2 ¡;45 ¡;0 ¡;90 is the frequency of light, and k is the wave number. The S3 2I¸=4;45± ¡ I¡;0± ¡ I¡;90± value of phase birefringence B, which depends on the where first subscript defines lack or presence of the difference between orthogonal polarization modes phase quarter-wave plate, and second subscript defines the velocities vpx and vpy , is different from group birefrin- azimuth of the analyzer. gence value G, which depends on the difference between During the propagation through a birefringent medium group velocities of the polarization modes vgx and vgy : the length shift is increasing and the degree of polariza- c c B(¸) = nx(¸) ¡ ny(¸) = ¡ ; (9) tion diminishes according to the formulae [3]: vpx (¸) vpy (¸) DOP = PG c c v G(¸) = Nx(¸) ¡ Ny(¸) = ¡ ; (10) à à !! vgx (¸) vgy (¸) u µ ¶2 u ¢nl where n and n are wavelength dependent refractive in- = t1 ¡ 1 ¡ exp ¡2 sin2(2θ); (4) x y ¢LG dices for polarization modes, while Nx and Ny are the group refractive indices, which can be calculated from DOP = PL dn s N = n ¡ ¸ : (11) µ µ ¶¶ d¸ ¢nl = 1 ¡ 1 ¡ exp ¡2 sin2(2θ); (5) Thus the phase birefringence can be defined as: ¢LL j¯ ¡ ¯ j B = jn ¡ n j = x y (12) where l and ¢n are medium length and birefringence, x y k respectively, ¢L is a coherence length of light with and the group birefringence can be obtained from G;L h i Gaussian or Lorentzian spectral distribution, E0x, E0y B(¸) 2 d are the electric field components amplitudes of the light, dB ¸ ¸ G = B ¡ ¸ = ¡ ; (13) θ is the azimuth between polarization plane and birefrin- d¸ 2¼ d¸ gence axis of the medium. where ¯x and ¯y are the propagation constants of two or- When the azimuth θ is of 45± the degree of polarization thogonal polarization modes. If the phase birefringence reaches its minimum value. Depending on birefringence, remains a constant value in broad range of wavelengths path length of the medium and coherence length light (as it does for standard polarization maintaining fibers) beam may be totally depolarized at the output of the it is equal to group birefringence (G = B) [6]. medium. 3. Experimental setup By measuring DOP we are able to calculate absolute The main aim of the research was to deal with group values of group birefringence of investigated PLCF. birefringence fluctuation measurement of the PLCF by Group Birefringence Measurement in Photonic Liquid Crystal Fibers . 287 use of novel method based on depolarization of partially temporal coherent light phenomenon. A commercially available polarization maintaining photonic crystal fiber (type Blazephotonic HB-1550-01) fabricated by CrystalFibre has been partially infiltrated with liquid crystal mixture 6CHBT and put under inves- tigation in described experiment. The fiber has a silica glass core and the light is index-guided due to higher index of refraction in the core than in partially holey cladding. The fiber structure is shown in Fig. 3 and its parameters are presented in Table I. TABLE I Blazephotonic PM-1550-01 fiber parameters. Blazephotonic Parameters PM-1550-01 large hole diameter (D)[¹m] 4.5 small hole diameter (d)[¹m] 2.2 fibre diameter [¹m] 125 The experimental setup for measuring group birefrin- gence of the PCF is shown in Fig. 4. Fig. 5. Spectrograms of two light sources used in the experiment: (a) green LD, (b) red LD. The parameters of the light beams are shown at spectrograms. pared it with the values obtained from our depolarization method. As shown at Table II the values stand in good agreement. TABLE II Comparison of values of coherence length for both light sources used in the experiment obtained by two methods. Fig. 4. Experimental setup for measuring DOP fluctu- ations in PCF. Green LD Red LD ¸2 1 ¸2 1 ¸2 1 ¢LL = ¢LL = = ¢LL = = The partially coherent light beam from laser diode ¢¸ ¼ ¢¸ ¼ ¢¸ ¼ 0:714 £ 10¡3 m 0:839 £ 10¡3 m (LD) with Lorentzian spectrum was split by beam split- ter and directed into two separate paths. In the path A depolarization ¢LL = ¢LL = the DOP of the light beam was measured after passing based method 0:662 £ 10¡3 m 1:171 £ 10¡3 m through the lithium niobate anisotropic crystal with well known birefringence and path length. To calculate DOP of the narrow-band light sources used in the experiment In the path B the group birefringence of the 1 m long we used classical method of measuring four intensities of PCF was calculated. Partially coherent light beam was light with different configurations of analyzer and quar- coupled into PCF, and the DOP at the output was mea- ter wave plate (Eq. (3)). According to Eq. (5) we are sured by use of high precision Stokes polarimeter THOR- able to calculate the coherence length of the light beams LABS PAX-5710. used in the setup From Eq.
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