JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 26, NO. 6, MARCH 15, 2008 663 Tunable Photonic Crystal Fiber Couplers With a Thermo-Responsive Liquid Crystal Resonator Kunimasa Saitoh, Member, IEEE, Member, OSA, Nikolaos J. Florous, Member, IEEE, Member, OSA, Shailendra K. Varshney, Member, IEEE, Member, OSA, and Masanori Koshiba, Fellow, IEEE Abstract—We theoretically address the thermo-optical response of multicore photonic crystal fiber (PCF) couplers infiltrated with nematic liquid crystals (LCs). The proposed PCF coupler consists of two identical cores separated by a third one which acts as a liquid crystal resonator. With an appropriate choice of the design param- eters associated with the liquid crystal core, phase matching at a single wavelength can be achieved, thus enabling thermo-tunable narrow-band resonant directional coupling between the input and the output cores. The verification of the proposed coupler design is ensured through an accurate PCF analysis based on finite ele- ment and beam propagation methods. The enhanced thermo-op- tical properties of LC-based PCF couplers are highly attractive for photo-thermal sensing applications. Index Terms—Bandpass filter, finite-element method (FEM), holey fiber, liquid crystal (LC), microstructured optical fiber, photonic crystal fiber (PCF), resonant coupling, thermal sensors. I. INTRODUCTION P HOTONIC crystal fibers (PCFs) [1], a new class of optical cables, have revealed many interesting features success- fully applied to the telecommunication as well as to the sensing industries because they can provide unprecedented degrees of freedom in tailoring their modal and coupling properties. A typ- ical PCF consists of pure silica with a periodic distribution of air holes in the cladding. In PCFs, light can be guided either by the effective index mechanism related to the total internal reflection (TIR) [2], or through light confinement by the photonic band gap (PBG) effect [3]. Although PCFs are usually formed by a central defect region surrounded by multiple air holes with the same diameter in a regular triangular lattice, the manufacturing technology of PCF such as multiple-capillary drawing method [4] can readily realize multicore PCFs as well. The use of multicore PCFs for realizing fiber couplers has re- cently been investigated both experimentally [5]–[7] as well as theoretically [8]–[11]. The operation of PCF couplers typically involves energy transfer over a certain coupling length between two distinct fiber cores coupled by proximity interaction. Modes in closely separated individual cores are phase matched over a certain frequency region which ultimately defines the filter’s bandwidth. When the two fiber cores are the same, such filters Manuscript received September 12, 2007; revised November 01, 2007. K. Saitoh, S. Varshney, and M. Koshiba are with the Graduate School of In- formation Science and Technology, Hokkaido University, Sapporo 060-0814, Japan (e-mail: ksaitoh@ist.hokudai.ac.jp). N. J. Florous is with the Optoelectronics Division, PerkinElmer Japan Co., Ltd., Yokohama 220-0004, Japan. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JLT.2007.915276 are also known as symmetric directional couplers. As the modes in identical fiber cores are degenerated, symmetric directional couplers exhibit large operational bandwidths. When the two cores are not identical, and their modal dispersion relations are matched at a single frequency, such filters are called asymmetric directional couplers. Thus designed asymmetric directional cou- plers exhibit narrow-band filtering characteristics [12]–[14]. When designing a tunable narrow-band fiber filter a chal- lenging issue is how to achieve a given filtering profile with great controllability over a predefined wavelength range. De- vices based solely on proximity coupling are thus limited as there are few degrees of freedom in the design space. In this respect, a promising alternative strategy for realizing tunable narrow band-pass fiber filters is the phenomenon of resonant tunneling [15]–[17]. According to this approach, instead of bringing two fiber cores to interact directly via proximity coupling, one separates them instead, so that proximity effect become negligible. To induce interaction between the cores, one places a resonator in between identical fiber cores. The resonator is designed in such a way as to be phase-matched at a single frequency with the two cores. Narrow bandwidth energy transfer between identical cores is thus achieved via excitation of a resonator state, while a required filtering profiled can be obtained via the resonator specifications. Moreover, if we introduce an externally tunable resonator in the fiber, a tunable narrow-band fiber filter can be designed. Perhaps among the most interesting materials for filling the PCF air-holes for realizing tunable devices are liquid crystals (LCs), since they open up a wide range of new possibilities for tuning the properties of light propagation, due to the fact that these are materials with high optical anisotropy strongly de- pendent on external temperature and electric field. Other mate- rial platforms may also include highly thermo-responsive chem- ical platforms [18]. As it was recently demonstrated [19]–[28], when PCFs are being infiltrated with LCs, they can demonstrate very promising properties over a wide range of applications, such as variable optical attenuators, tunable filters, switches, flu- idic sensors, and other devices applied to sensing and optical transmission systems. An essential study however on how to ra- tionally design PCF-based narrow-band filters with enhanced thermo-optically tunable characteristics mainly for sensing ap- plications remains an open scientific task up to nowadays. Taking all the above circumstances into account, we devote the present investigation to describe a new family of a com- pact PCF couplers based on the thermo-optical effect of the molecular orientation of the LC. By using versatile numerical algorithms based on the finite-element method (FEM) [29] and beam propagation method (BPM) [30], we show that three-core 0733-8724/$25.00 © 2008 IEEE