Thermal tunability of photonic bandgaps in liquid crystal filled polymer photonic crystal fiber

Optical Fiber Technology 29 (2016) 95–99

Contents lists available at ScienceDirect

Optical Fiber Technology www.elsevier.com/locate/yofte

Regular Articles

Thermal tunability of photonic bandgaps in liquid crystal filled polymer photonic crystal fiber Doudou Wang a,⇑, Guoxiang Chen b, Lili Wang c a

College of Science, Xi’an University of Science and Technology, Xi’an 710054, China College of Science, Xi’an Shiyou University, Xi’an 710065, China c State Key Laboratory of Transient Optics and Photonics, Xi’an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi’an 710119, China b

a r t i c l e

i n f o

Article history: Received 19 April 2015 Revised 8 January 2016 Accepted 3 April 2016 Available online 16 April 2016 Keywords: Polymer photonic crystal fiber Liquid crystal Photonic bandgap Finite element method

a b s t r a c t A highly tunable bandgap-guiding polymer photonic crystal fiber is designed by infiltrating the cladding air holes with liquid crystal 5CB. Structural parameter dependence and thermal tunability of the photonic bandgaps, mode properties and confinement losses of the designed fiber are investigated. Bandgaps red shift as the temperature goes up. Average thermal tuning sensitivity of 30.9 nm/°C and 20.6 nm/°C is achieved around room temperature for the first and second photonic bandgap, respectively. Our results provide theoretical references for applications of polymer photonic crystal fiber in sensing and tunable fiber-optic devices. Ó 2016 Elsevier Inc. All rights reserved.

1. Introduction Photonic crystal fibers (PCFs), with a periodic microstructure of air holes running along the axial direction in the cladding, have received particular interest due to their novel structure and properties [1]. The presence of the microstructured air holes around the fiber core allows more degrees of freedom in design than conventional fiber design [2–4]. Furthermore, an index guiding PCF can be converted to a photonic bandgap (PBG) guiding PCF by filling the cladding air holes with high-index materials, such as high-index fluids or Liquid Crystals (LCs), which was firstly demonstrated in Ref. [5]. The attractive properties of nematic LCs, i.e. high thermal, electrical and magnetic tunability, make them more suitable for filling material of tunable devices. LC-PCF based tunable fiber devices, such as threshold switching, tunable birefringence controller and tunable filter, were reported in [6,7] and references therein. The effects of LC alignment on bandgap formation and polarization dependent guiding were theoretically investigated by Sun et al. [8] and Ren et al. [9], respectively. However, most work to date concentrates on LC filled silica PCFs. In recent years, polymer photonic crystal fibers (pPCFs) [10] have attracted much attention on account of the lower processing temperature, variety of processing methods and polymer materials compared with silica PCFs. Yuan et al. demonstrated for the first ⇑ Corresponding author. E-mail address: [email protected] (D. Wang). http://dx.doi.org/10.1016/j.yofte.2016.04.004 1068-5200/Ó 2016 Elsevier Inc. All rights reserved.

time the photonic bandgap effect and the thermal tunability of bandgaps in pPCFs filled with two kinds of nematic LCs, E7 (T c = 58 °C) and MDA-00-1444 (T c = 98.5 °C), respectively [11]. However, the insertion losses were higher than those of LC filled silica PCFs as their designed LC pPCFs has only three rings of air holes. Hu et al. analyzed thermal influence on the bandgap properties of silica PCF filled with LC of 5CB type [12]. But material dispersion of 5CB was neglected, which could cause discrepancy with experiments, especially at short wavelength region. In this paper, a thermally tunable bandgap guiding pPCF is designed by infiltrating the cladding air holes with 5CB (4-cyano4-n-pentylbiphenyl), which has lower clearing temperature (T c = 35.3 °C) and larger temperature gradient of the ordinary refractive index (dn0 =dT) at room temperature compared with E7 and MDA-00-1444 [11]. Structural dependence and thermal tunability of the PBGs, mode properties and confinement loss of the designed LC-filled pPCF (LC-pPCF) are studied by using the powerful full-vector finite element method (FEM) [13]. 2. LC-pPCF design 2.1. Fiber structure design Cross-section of the designed LC-pPCF is shown in Fig. 1. We construct the fiber cladding by arranging circular holes (with hole diameter d) in triangular lattice pattern (with lattice constant K) in the background of Polymethyl methacrylate (PMMA). The cladding

96

D. Wang et al. / Optical Fiber Technology 29 (2016) 95–99

The commercial LC of 5CB type, well-known for its simple structure, is selected as the filling material of our designed LC-pPCF due to its nematic property (within 22.0–35.3 °C), low T c and large dn0 =dT around room temperature [23]. Besides, the wavelengthand temperature-dependent refractive indices for the 5CB have been widely studied, providing us both reliable experimental data and theoretical models [14–16]. The variation of refractive indices with temperature for 5CB is shown in Fig. 2. The wavelength- and temperature-dependence of refractive indices can be expressed by the extended Cauchy equation [15], which can be extrapolated to infrared [16]:

no=e ðT; kÞ ¼ Ao=e ðTÞ þ

Fig. 1. Cross section of the LC-pPCF.

holes are infiltrated with LC of 5CB type. As 5CB has higher refractive indices [14–16] (no ¼ 1:5361, ne ¼ 1:7124 at 589 nm, 25.4 °C) than PMMA (n = 1.49), the effective index of fiber cladding is higher than that of the core area. Propagation mechanism of the designed LC-pPCF fiber is based on PBG effect. However, pPCF without LC filling guides light with improved total internal reflection (TIR) effect, abbreviated as TIR-pPCF. Several factors should be considered to design the suitable fiber structural parameters. Firstly, hole diameter to pitch ratio (d=K) should be less than 0.45 in order to obtain endlessly single-mode behavior for the unfilled TIR-PCF [17]. Secondly, position of the effective PBG should be in consistent with the low loss window of core material [10,11]. Structural parameter dependence of the PBG position and its scaling property will be discussed in Section 3.1. Thirdly, more than three rings of cladding holes filled with high-index material are necessary for better mode confinement, especially for the low refractive index contrast solid core photonic bandgap fibers [18]. Six rings of cladding holes are necessary to obtain confinement loss less than 0.01 dB/m for the designed LCpPCF (see Section 3.4). In our previous papers, a series of theoretical and experimental investigations have been carried out for the fabrication and application of pPCFs [19–21]. Both high-index solid filled [20] and highindex liquid [21] filled pPCFs with 13 rings of air holes arranged in triangular lattice have been fabricated by the extrusion-stretching techniques as reported in Ref. [22]. The relatively simple architecture of the designed LC-pPCF in this paper will be fabricated by the same method in our consequent researches.

Bo=e ðTÞ k

2

þ

C o=e ðTÞ

ð1Þ

k4

where Ao=e , Bo=e , and C o=e are the Cauchy coefficients of 5CB. These parameters used in the simulation are taken from Ref. [15]. For convenience, they are listed in Table 1. Experimental results of Yuan et al. [11] and Alkeskjold et al. [24] show that the director of LC filled in the cladding holes PCF is parallel to the fiber axis when temperature is below T c without external electric (or magnetic) static field across the fiber. Dielectric tensor of the nematic LC takes the form eLC ¼ diagðn2o ; n2o ; n2e Þ. The ordinary indices no of LC predominantly determine the spectral features, and the x- and y-polarized fundamental modes are degenerate [8,9]. This kind of LC alignment can theoretically be exhibited under the influence of the appropriate homeotropic anchoring conditions. 3. Results and discussion A systematic investigation of the PBGs and guided modes properties of the designed LC-pPCF is carried out by using the commercially available FEM solver COMSOL. In this simulation, the dielectric properties of LC are directly included through the extended Cauchy equation [15]. 3.1. Structural parameter dependence of PBGs PBGs of infinitely cladding structure (periodic triangular lattice of LC inclusions in a background of PMMA) are calculated and presented in Fig. 3 at T = 25.1 °C. For certain structural parameters, areas between the corresponding boundary lines represent PBGs. There exist two effective PBGs as the green shading regions shown. The horizontal core line corresponds to refractive index of PMMA. Fig. 3(a) shows PBGs for cladding structure with fixed d=K ¼ 0:44

1.8 ne

2.2. Refractive indices of LC Thermally tunable PCFs (devices) utilize the thermal-induced refractive index change of nematic LCs. Thermal tunability of the LC-PCF is mainly determined by the dn0 =dT of the LC [11]. Tuning sensitivity is increasing with temperature approaching the clearing temperature of LC, due to an increasing temperature gradient of no . For thermally tunable LC-PCFs with resistive or optical pumpinduced heating, it is desirable to have a high tuning sensitivity at approximately room temperature in order to decrease the power consumption and ease handling and packaging [6].

n

1.7

1.6 no

1.5 10

15

20

25

30

35

T(°C) Fig. 2. Temperature dependent refractive indices of 5CB at 589 nm [14].

40

97

D. Wang et al. / Optical Fiber Technology 29 (2016) 95–99 Table 1 Fitting parameters of the extended Cauchy model for 5CB [15]. Temperature T/°C

no

ne

Ao 25.1 29.9 32.6 34.8 36.1

1.679 1.670 1.658 1.643 1.572

46 30 66 04 09

1.50

2

Bo/lm 0.004 0.004 0.004 0.003 0.002

82 62 40 80 10

1st PBG Upper boundary

Re(neff)

1.49 2nd PBG

Lower boundary

0.1

0.2

0.3

0.4

0.5

/ 1.50

(b) Re(neff)

1.49 Core line

1.48

d=4 m, d=4 m, d=4 m,

=8 m =9 m =10 m

1.47 0.1

0.2

0.3

0.4

0.5

/

(c)

Re(neff)

1.49

Core line

1.48 =9 m, d=3 m =9 m, d=4 m =9 m, d=5 m

0.1

0.2

0.002 0.002 0.002 0.002 0.001

73 57 48 17 61

1.518 1.520 1.523 1.530 1.572

66 12 69 28 09

Be/lm2

Ce/lm4

0.001 0.001 0.001 0.001 0.002

0.001 0.001 0.001 0.001 0.001

63 58 74 83 10

14 21 25 35 61

0.3

PBGs of infinite cladding structure (K ¼ 9 lm, d=K ¼ 0:44) at different temperatures are shown in Fig. 4. The green shading area indicates the bandgap at 34.8 °C. It can be seen that increment of the temperature (from 25.1 °C to 34.8 °C) red-shifts and widens the bandgaps, which becomes more significant as temperature reaches the T c (35.3 °C) of 5CB. Red shift of the bandgap is due to the positive temperature gradient of the ordinary refractive index (dn0 =dT > 0) and thus an increasing index contrast between the PMMA and the LC as temperature reaching T c . Increasing of the bandgap width implies that the upper boundary experiences a larger shift than the lower boundary. These conclusions are in consistent with experimental results in [11]. Average thermal tuning sensitivities, about 51.5 nm/°C and 27.8 nm/°C, are obtained at the long-wavelength bandgap edge for the first and the second PBG, respectively. 3.3. Guided mode properties of the designed LC-pPCF

1.50

1.47

Ae

3.2. Thermal tunability of PBGs

d/ =0.44, d=3 m d d/ d =0.44, d=4 m d/ d =0.44, d=5 m

1.47

Co/lm

red-shifts the position of PBGs. Cladding structure with d=K around 0.44 has the maximum bandgap width. Therefore, it is possible to move the PBGs to certain wavelengths, such the low loss window of core material (PMMA) [11] by carefully tailoring the structural parameters of the fiber.

(a) Core line

1.48

4

0.4

0.5

/ Fig. 3. Variation of PBGs with different structural parameters at 25.1 °C. The vertical axis is effective index neff, and the horizontal axis is normalized wavelength k/K.

(LC filling fraction about 18%). We find that the first PBGs and the second PBGs for different hole diameters d center at normalized wavelength k/K around 0.26 and 0.14, respectively. PBGs can be transposed to certain wavelengths by scaling the structure. From Fig. 3(b), we notice that for cladding structure with fixed hole diameters d, position of the PBGs is approximately unchanged with lattice constant K, considering that scaling of the horizontal axis is normalized by K. This conclusion evidences that the bandgap formation is based on antiresonances of the individual LC inclusions. Fig. 3(c) shows PBGs for cladding structure with fixed lattice constant K and different hole diameter d. We can clearly see that increment of the hole diameters d (LC filling fraction) drastically

Dispersion curves (thick black lines) of the fundamental modes and mode profiles at 34.8 °C are shown in Fig. 4. The lower panels (i), (ii) and (iii) show power flow of the fundamental mode at the short-wavelength edge, central wavelength and long-wavelength edge of the second bandgap of the LC-pPCF, respectively. It can be seen from Fig. 4(ii) that most energy of the guided mode is concentrated in the fiber core around the central wavelength of the PBG due to the photonic bandgap effects. The mode’s effective index is neff = 1.488324 + i2.209856  1010. The imaginary part of effective index is proportional to the confinement loss (see Section 3.4), which here is 0.008 dB/m. The mode field spreads to the cladding area as wavelength approaching the band edges. Fig. 4(iv) shows power flow of the fundamental mode of the unfilled TIRpPCF. The wavelength of the guided mode in panel (iv) and panel (ii) are identical. By comparing panel Fig. 4(ii) and Fig. 4(iv), it can be seen clearly that the mode fields of LC-pPCF and TIR-pPCF with the same structural parameters are different, which is due to their different propagation mechanism. For the pPCF devices, the main origin of the insertion loss is the splicing loss due to the mismatch of physical parameters and modes effective areas of the aligned fibers, which is difficult to establish exactly [6,11,25]. However, the fundamental modes of the designed LC-pPCF with wavelengths around the center of the PBG are well confined as shown in Fig. 4(ii), which have approximate Gaussian mode profiles in the core area. The TIR-pPCF with the same structural parameters is endlessly single-mode and well confined as shown in Fig. 4(iv). Around the central wavelength of the PBG, it is possible to estimate the splicing loss of the aligned LC-pPCF and TIR-pPCF in terms of the power transmission

98

D. Wang et al. / Optical Fiber Technology 29 (2016) 95–99

1.495

Re(neff)

1.490

Core line

1.485 (

)

(

)

( )

T=25.1 ° C T=29.9 ° C T=32.6 ° C T=34.8 ° C

1.480

1.475 0.1

0.2

0.3

0.4

0.5

/

Fig. 4. PBGs at different temperatures, dispersion curves (thick black lines) of the fundamental modes and mode profiles at the short-wavelength edge (i), central wavelength (ii) and long-wavelength edge (iii) of the second PBG for the LC-pPCF at 34.8 °C, and (iv) is for the unfilled TIR-pPCF at a wavelength the same with that in panel (ii).

coefficient as described in [17]. The calculated power transmission coefficient is about 90% and 99% at the central wavelength of the first and second PBG, respectively. It is difficult to estimate the splicing loss near the PBG edges by using the power transmission coefficient, as the mode profile of LCpPCF deviates from the Gaussian shape. We found that the fraction of core confined energy of the fundamental mode against wavelength could provide a qualitative estimation of the fiber’s transmission spectrum and splicing loss of the aligned LC-pPCF and pffiffiffi TIR-pPCF. Fig. 5 shows fraction of core (with radius of K= 3) confined energy at different temperatures. It can be seen that fraction of core confined energy in both the first and the second PBGs shows thermal tunability in consistent with the thermal tunability of PBGs. Thus thermal tunability of the fiber’s transmission

100 T=25.1°C T=29.9°C T=32.6°C T=34.8°C

Power in core ( )

80

60

40

20

/ Fig. 5. Fraction of core confined energy as a function of normalized wavelength at different temperatures.

spectrum could be predicted by the thermal tunability of the PBGs or core confined energy fraction. 3.4. Confinement loss of the designed LC-pPCF For realistic PCFs, the fundamental modes are inherently leaky as a result of the finite number of air-hole rings in the cladding region. So the confinement loss occurs inevitably. Theoretical investigations about the dependence of confinement losses on wavelength and fiber structural parameters (hole size, hole diameter to pitch ratio, and the number of rings of holes) for both the TIR-PCF [26] and the high-index material filled PBG-PCF [18], reveal that the mode confinement loss (corresponding to the imaginary part of neff) decreases with the addition of more cladding hole rings, while the dispersion curve (corresponding to the real part of neff) and the position of the confinement loss minimum (depending on the scattering properties of LC cylinders) are unchanged in the meanwhile. The confinement loss can be deduced from the complex effective index neff [13]:

CL ¼ 8:686

2p Imðneff Þ k

ð2Þ

in decibels per meter, where Im stands for the imaginary part. Confinement losses of the fundamental mode at different temperatures are shown in Fig. 6. It can be seen that the confinement loss becomes minimum around the center of PBGs and increases as approaching the band edges. The second PBG provides lower confinement loss than the first PBG, but with narrower transmission window. This trend is coincides with that of the silica-based LCPCF [9]. Thermal tunability of the confinement loss is consistent with that of the core confined energy fraction. From 25.1 °C to 34.8 °C, the average tuning sensitivities corresponding to the position of the confinement loss minimum (peaks of the transmission spectra) in the first and the second PBG are about 30.9 nm/°C and 20.6 nm/°C, respectively. The lower T c and larger dno =dT of

D. Wang et al. / Optical Fiber Technology 29 (2016) 95–99

References

103

Confinement loss (dB/m)

99

102 101 100 10-1

T=25.1°C T=29.9°C T=32.6°C T=34.8°C

10-2 10-3

/ Fig. 6. Confinement losses of the fundamental mode as a function of normalized wavelength at different temperatures.

5CB around room temperature give rise to relatively higher tuning sensitivities of the designed LC-pPCF, compared with that reported in Refs. [5,7,11,12].

4. Conclusion A highly tunable bandgap-guiding pPCF is designed by infiltrating the cladding air holes with a nematic LC of 5CB type. Structural dependence of the PBGs is studied in detail. Thermal tuning sensitivity of the PBGs and confinement losses of the designed LC-pPCF are investigated theoretically. PBGs shift toward a longer wavelength as temperature increased due to the positive dno =dT of 5CB. From 25.1 °C to 34.8 °C, average thermal tuning sensitivity of 30.9 nm/°C and 20.6 nm/°C is achieved for the first and the second PBG, respectively. Fundamental modes of the designed LCpPCF are well confined around the central wavelength of the PBGs, which will lead to high power transmission coefficient and low splicing loss between the aligned LC-pPCF and TIR-pPCF. Our results can provide theoretical references for applications of pPCF in sensing and tunable fiber-optic devices. Acknowledgements The authors would like to acknowledge the Natural Science Basic Research Plan in Shaanxi Province of China (Program Nos. 2014JQ8335, 2014JQ6206), China Postdoctoral Science Foundation (No. 2015M582766XB) and the National Natural Science Foundation of China (Grant No. 11504292) for providing financial support for this research.

[1] P.S.J. Russell, Photonic-crystal fibers, J. Lightwave Technol. 24 (2006) 4729– 4749. [2] T.A. Birks, J.C. Knight, P.S.J. Russell, Endlessly single-mode photonic crystal fiber, Opt. Lett. 22 (1997) 961–963. [3] N.A. Mortensen, M.D. Nielsen, J.R. Folkenberg, A. Petersson, H.R. Simonsen, Improved large-mode-area endlessly single-mode photonic crystal fibers, Opt. Lett. 28 (2003) 393–395. [4] M.S. Habib, M.S. Rana, M. Moniruzzaman, M.S. Ali, N. Ahmed, Highly birefringent broadband-dispersion-compensating photonic crystal fibre over the E + S + C + L + U wavelength bands, Opt. Fiber Technol. 20 (2014) 527–532. [5] T.T. Larsen, A. Bjarklev, D.S. Hermann, J. Broeng, Optical devices based on liquid crystal photonic bandgap fibres, Opt. Express 11 (2003) 2589–2596. [6] T.T. Alkeskjold, J. Lægsgaard, A. Bjarklev, D.S. Hermann, J. Broeng, J. Li, S. Gauza, S.T. Wu, Highly tunable large-core single-mode liquid-crystal photonic bandgap fiber, Appl. Opt. 45 (2006) 2261–2264. [7] D. Noordegraaf, L. Scolari, J. Lægsgaard, T.T. Alkeskjold, G. Tartarini, E. Borelli, P. Bassi, J. Li, S.T. Wu, Avoided-crossing-based liquid-crystal photonic-bandgap notch filter, Opt. Lett. 33 (2008) 986–988. [8] J. Sun, C.C. Chan, Effect of liquid crystal alignment on bandgap formation in photonic bandgap fibers, Opt. Lett. 32 (2007) 1989–1991. [9] G.B. Ren, P. Shum, J.J. Hu, X. Xu, Y.D. Gong, Polarization-dependent bandgap splitting and mode guiding in liquid crystal photonic bandgap fibers, J. Lightwave Technol. 26 (2008) 3650–3659. [10] A. Argyros, Microstructured polymer optical fibers, J. Lightwave Technol. 27 (2009) 1571–1579. [11] W. Yuan, L. Wei, T.T. Alkeskjold, A. Bjarklev, O. Bang, Thermal tunability of photonic bandgaps in liquid crystal infiltrated microstructured polymer optical fibers, Opt. Express 17 (2009) 19356–19364. [12] J.J. Hu, P. Shum, G.B. Ren, X. Yu, G.H. Wang, C. Lu, S. Ertman, T.R. Wolinski, Investigation of thermal influence on the bandgap properties of liquid-crystal photonic crystal fibers, Opt. Commun. 281 (2008) 4339–4342. [13] K. Saitoh, M. Koshiba, Leakage loss and group velocity dispersion in air-core photonic bandgap fibers, Opt. Express 11 (2003) 3100–3109. [14] J. Li, S.T. Wu, Self-consistency of Vuks equations for liquid-crystal refractive indices, J. Appl. Phys. 96 (2004) 6253–6258. [15] J. Li, S.T. Wu, Extended Cauchy equations for the refractive indices of liquid crystals, J. Appl. Phys. 95 (2004) 896–901. [16] J. Li, S.T. Wu, Infrared refractive indices of liquid crystals, J. Appl. Phys. 97 (2005). 073501-1–073501-5. [17] N.A. Mortensen, Effective area of photonic crystal fibers, Opt. Express 10 (2002) 341–348. [18] T.P. White, R.C. McPhedran, C. Martijn, N.M. Litchinitser, B.J. Eggleton, Resonance and scattering in microstructured optical fibers, Opt. Lett. 27 (2002) 1977–1979. [19] D.D. Wang, L.L. Wang, Design of Topas microstructured fiber with ultraflattened chromatic dispersion and high birefringence, Opt. Commun. 284 (2011) 5568–5571. [20] D.P. Kong, L.L. Wang, Ultrahigh-resolution fiber-optic image guides derived from Microstructured polymer optical fiber preforms, Opt. Lett. 34 (2009) 2435–2437. [21] J. Wang, L.L. Wang, Liquid-filled microstructured polymer fibers as monolithic liquid-core array fibers, Appl. Opt. 48 (2009) 881–885. [22] J. Wang, X.H. Yang, L.L. Wang, Fabrication and experimental observation of monolithic multi-air-core fiber array for image transmission, Opt. Express 16 (2008) 7703–7708. [23] W.H. De Jeu, Physical Properties of Liquid Crystalline Materials, Gordon and Breach Science Publishers, New York, 1980. [24] T.T. Alkeskjold, J. Lægsgaard, A. Bjarklev, D.S. Hermann, J. Anawati, J. Broeng, J. Li, S.T. Wu, All-optical modulation in dye-doped nematic liquid crystal photonic bandgap fibers, Opt. Express 12 (2004) 5857–5871. [25] V. Parmar, R. Bhatnagar, P. Kapur, Optimized butt coupling between single mode fiber and hollow-core photonic crystal fiber, Opt. Fiber Technol. 19 (2013) 490–494. [26] T.P. White, R.C. McPhedran, C.M. de Sterke, L.C. Botten, M.J. Steel, Confinement losses in microstructured optical fibers, Opt. Lett. 26 (2001) 1660–1662.