406 INTERNATIONAL JOURNAL OF MICROWAVE AND OPTICAL TECHNOLOGY, VOL.12, NO.5, SEPTEMBER 2017 Fano Resonance Based on 3x3 Multimode Interference Structures for Fast and Slow Light Applications Trung-Thanh Le* * International School (VNU-IS) Vietnam National University (VNU), Hanoi, Vietnam E-mail: thanh.le@isvnu.vn Abstract- We present for the first time a new method for creating Fano resonance by using only one 3x3 multimode interference (MMI) coupler with a feedback waveguide We use the silicon waveguide for the whole design, so it is compatible with CMOS technology The device is compact and has a large tolerance fabrication In addition, many useful optical functions such as all-optical switches, filters and singlemode lasers can be realized using Fano-type transmission device The transfer matrix method (TMM) and beam propagation method (BPM) are used to optimally design the structure We show that by using the proposed structure, fast and slow light can be obtained Index Terms- Multimode interference, Fano resonance, microring resonator, Electromagnetically induced transparency (EIT), optical signal processing, signal processing, fast light and slow light I INTRODUCTION Devices based on optical microring resonators have attracted considerable attention recently, both as compact and highly sensitive sensors and for optical signal processing applications [1-3] In the literature, the coupling element in microring resonator is to use co-directional evanescent coupling between the ring and an adjacent bus waveguide The transmission spectrum of the bus waveguide with a single ring resonator will show dips around the ring resonances A single microring resonator behaves as a spectral filter and notch filter, which can be used for applications in optical communication, especially wavelength division multiplexing (WDM) The resonance line shape of a conventional microring resonator is symmetrical with respect to its resonant wavelength However, microring resonator coupled Mach Zehnder interferometers can produce a very sharp asymmetric Fano line shape that are used for improving optical switching and add-drop filtering [4, 5] It is shown that for functional devices based on onering resonator such as optical modulators and switches, it is not possible to achieve simultaneously high extinction ratio and large modulation depth [6, 7] To maximize the extinction ratio and modulation depth, we can use an asymmetric resonance such as the Fano resonance Fano resonance is a result of interference between two pathways One of the conventional way to generate a Fano resonance is by the use of a ring resonator coupled to one arm of a Mach-Zehnder interferometer, with a static bias in the other arm [810] The strong sensitivity of Fano resonance to local media brings about a high figure of merit, which promises extensive applications in optical devices such as optical switches [10] Fano resonances have long been recognized in grating diffraction and dielectric particles elastic scattering phenomena The physics of the Fano resonance is explained by an interference between a continuum and discrete state [9] The simplest realization is a one dimensional discrete array with a side coupled defect In such a system scattering waves can either bypass the defect or interact with it It has been suggested that optical Fano resonances have many applications in resonance line shape sensitive bio-sensing, optical channel switching and filtering [11, 12] Recently, optical Fano resonances have also been reported in various optical microcavities including integrated waveguide-coupled microcavities [13], prism-coupled square micropillar resonators, multimode tapered fiber coupled micro-spheres and Mach Zehnder interferometer IJMOT-2017-4-1294 © 2017 IAMOT 407 INTERNATIONAL JOURNAL OF MICROWAVE AND OPTICAL TECHNOLOGY, VOL.12, NO.5, SEPTEMBER 2017 (MZI) coupled micro-cavities [14], plasmonic waveguide structure [8, 15] In this study, we propose a new structure based on only one 3x3 multimode interference coupler based microring resonator to produce Fano resonance line shape The proposed device is analyzed and optimized using the transfer matrix method (TMM), the beam propagation method (BPM) and finite difference time domain (FDTD) method [16] A description of the theory behind the use of multimode structures to achieve the Fano effect presented in Section II Simulation results of MMI based structures for components in the device structure are covered in Section III A brief summary of the results of this research is given in Section IV II PRINCIPLE OF OPERATION Microring structures based on a 3x3 MMI coupler for optical filtering, modulating and switching applications have been proposed in the literature [1719] The aim of this study is to show that this structure can create the Fano line shape The phase and group delay of the transmissions of the structure are analysed It is shown that the fast and slow light can be induced The schematic of a microring resonator based on a 3x3 MMI coupler is shown in Fig The 3x3 MMI coupler can be described by a transfer matrix M which describes the relationships between the input and output complex amplitudes of the coupler [20] Recently, we proposed a microring resonator based on 3x3 MMI coupler for the first time [21] In order for this microring resonator to operate correctly, the width, length and access waveguide positions need to be chosen carefully It is assumed that the access waveguides are located at the positions y1 We / , y We / , y3 5We / , where WMMI , We are the width and effective width of the MMI coupler [20] The length of the MMI coupler is to be L MMI L , where L is the beat length of the MMI coupler The relationship between the output complex amplitudes b j (j=1,2,3) and the input complex amplitudes a i (i=1,2,3) of the coupler can be expressed by (1) b Ma T T where a [a1 a a ] , b [b1 b2 b3 ] and M [mij ]3x3 (i, j=1, 2, 3) z y1 y2 WMMI y3 y Fig Microring resonators based on a 3x3 MMI coupler Equation (1) can be rewritten as e j2 /3 e j2 /3 1 a1 b1 j2 /3 1 e j2 /3 a (2) b2 e e j2 /3 e j2 /3 a b3 1 where e j2 /3 e j2 /3 1 j2 /3 M 1 e j2 /3 (3) e 3 j2 /3 j2 /3 1 e e and 0 0 L MMI 9 , a [ exp(j)]b , and 3 24 e xp( L) is the transmission loss along the ring waveguide, where L 2R L MMI and (dB/cm) is the loss coefficient in the core of the optical waveguide; 0 L is the phase accumulated over the racetrack waveguide, where 0 2n eff / , and n eff is the effective refractive index In our design, we use silicon waveguide, where SiO ( n SiO =1.46) is used as the upper cladding material An upper cladding region is needed for devices using the thermo-optic effect in order to reduce loss due to metal electrodes Also, the upper cladding region is used to avoid the influence of IJMOT-2017-4-1294 © 2017 IAMOT 408 INTERNATIONAL JOURNAL OF MICROWAVE AND OPTICAL TECHNOLOGY, VOL.12, NO.5, SEPTEMBER 2017 moisture and environmental temperature [22] The parameters used in the designs are as follows: the waveguide has a standard silicon thickness of h co 220nm and access waveguide widths are Wa 0.5 m for single mode operation It is assumed that the designs are for the transverse electric (TE) polarization at a central optical wavelength 1550nm For the first order design, the TMM is used, then we use the three dimensional beam propagation method (3D-BPM) and FDTD to design finally the whole structure [2] structure Fig shows the BPM simulation results for output powers at output port 1, and at different MMI lengths when input is at port For a compact device, the width of the MMI coupler is to be WMMI 6m The simulations show that the optimized length of the MMI is to be L MMI 99.8m The insertion loss of the device at this optimized length is -0.96dB Fig.3 shows the insertion loss at different lengths The field transmitting through the 3x3 MMI coupler at the length of L MMI 99.8m is shown in Fig Fig Optical field through the 3x3 MMI coupler at optimized length when input is at port Fig Output powers at port 1, 2, at different MMI length when input at port Fig shows the simulation results for output powers at output ports 1, 2, when input signal is at port The insertion loss in this case is about -0.45dB Our simulations show that the fabrication tolerance in MMI length of 30nm causes the fluctuation in output power of 0.05 For the existing CMOS fabrication technology with fabrication error of 5nm [3], the microring resonator based on 3x3 GI MMI coupler has an extremely large tolerance fabrication The complex amplitudes at output ports and are given by m13m31e j b1 (m11 )a1 m33e j e j Fig Insertion loss at different MMI length when input at port m m (m12 13 32 )a m33e j Here we show the optimized design of 3x3 GI MMI coupler used for our proposed microring resonator IJMOT-2017-4-1294 © 2017 IAMOT (4) 409 INTERNATIONAL JOURNAL OF MICROWAVE AND OPTICAL TECHNOLOGY, VOL.12, NO.5, SEPTEMBER 2017 m 23m31e j b2 (m 21 )a1 j m33e m 23m32e j (m 22 )a m33e j T1 (5) b1 and T2 a1 b2 (6) a1 For the input signal presented at input port ( a1 ): b T3 a2 and T4 b2 a2 (7) From the above equations, the transmissions are calculated III SIMULATION DISCUSSIONS (a) Insertion loss, input port (b) Field at the optimized length, input port Fig Output powers at port 1, 2, at different MMI length when input at port As a result, the transmissions at these output ports are given by: For the input signal presented at input port ( a ): RESULTS AND Without loss of generality, we choose silicon waveguide with the width of 500nm and height of 220nm for our design The effective refractive index calculated by the FDM method is to be n eff 2.416299 for the TE polarization [20] It assumed that the loss coefficient of the silicon waveguide is 0.98 [23], the length of ring waveguide is L R 700m , the transmissions at output ports and port when input signal is at port and port are shown in Fig and Fig.7, respectively Next we investigate the effect of loss coefficients of the silicon waveguide on the transmissions The transmissions at output port when input signal is at port with different loss coefficients are shown in Fig.8 We see that the resonance wavelength of the structure is still not changed when the loss coefficient is changed These simulation result has a good agreement with theoretical analysis of microring resonator based on a 4-port device [24] In recent years, the group delay and transmission characteristics of microring resonators used for optical filters and dispersion compensators have been studied [25, 26] However, these structures provide positive group delay and mainly designed for pulse delay applications While slow and fast light generation are emerging as a very attractive research topic Various techniques have been developed to realize fast light and slow light in atomic vapors and solid-state materials [27] One application among these techniques is to control the group velocity IJMOT-2017-4-1294 © 2017 IAMOT 410 INTERNATIONAL JOURNAL OF MICROWAVE AND OPTICAL TECHNOLOGY, VOL.12, NO.5, SEPTEMBER 2017 v g of light pulses to make them propagate either very slow ( v g < c) or very fast ( v g > c or v g is negative), where c is the velocity of light In order to verify our proposed analytical theory, we use the FDTD for accurate predictions of device’s working principle Fig.10(a) shows the comparison the TMM and FDTD simulations for the 3x3 MMI based microring resonator, where a Gaussian light pulse of 15fs pulse width is launched from the input to investigate the transmission characteristics of the device The grid sizes x y 0.02nm and z 0.05nm are chosen in our simulations It is shown that the FDTD simulation has a good agreement with our theoretical analysis Fig.10(b) and (c) show the field propagation via the device and the mask design of the whole device fabricated on an silicon on insulator (SOI) platform using CMOS technology Fig Transmissions at output port and port when input signal at port Fig Transmissions at output port and port when input signal at port at different loss coefficients Fig Transmissions at output port and port when input signal at port In our recent results, we have shown a new structure by cascading microring resonators based on directional couplers for fast and slow light applications [28] Here, we show that by using only one microring resonator based on a 3x3 MMI coupler, the fast and slow light can be achieved very effectively The group delay can be positive (slow light) or negative (fast light) as shown in Fig.9 Fig Group delay of the transmissions at port and when signal at port IJMOT-2017-4-1294 © 2017 IAMOT 411 INTERNATIONAL JOURNAL OF MICROWAVE AND OPTICAL TECHNOLOGY, VOL.12, NO.5, SEPTEMBER 2017 Fano resonance profile produced by our structure has a good agreement with the conventional Fano resonance profile The shape of the proposed Fano resonance profile has a steeper slope compared with the original profile As a result, our structure can be applied to potential applications such as low power optical switching and high sensitive optical sensors (a) Transmissions by using TMM and FDTD simulations Fig 11 Comparison of Fano resonance profiles (b) FDTD simulation IV CONCLUSIONS (c) Mask design Fig 10 (a) Transmissions by using TMM and FDTD, (b) field propagation by using FDTD simulation of the microring resonator based on 3x3 MMI for input port and (c) mask design of the whole device on an SOI platform Next, we compare our analysis with the Fano resonance in the literature In general, Fano resonance profile can be expressed by the universal formula for a scattering cross section [10]: ( q)2 (8) 1 Where q is the shape parameter, is the reduced energy The proposed structure can produce the Fano profile (transmission input port 1, output port 1) compared with the Fano resonance profile for q=1 as shown in Fig 11 The simulation shows that the This paper has presented a new way of creating Fano resonance based on only one 3x3 general interference multimode interference coupler The 3x3 MMI coupler has been designed and optimized by using the TMM and BPM It is shown that the FDTD simulation of the whole device has a good agreement with the theoretical analysis Effect of loss coefficients is also analyzed Our structure can created a sharp Fano resonance and the device has a large fabrication tolerance In addition, it is shown that the fast and slow light can be achieved from our structure This property is useful for high performance optical switches, optical buffers and high sensitive optical biosensors ACKNOWLEDGEMENTS This research is funded by Vietnam National University, Hanoi (VNU) under project number QG.15.30 IJMOT-2017-4-1294 © 2017 IAMOT REFERENCES 412 INTERNATIONAL JOURNAL OF MICROWAVE AND OPTICAL TECHNOLOGY, VOL.12, NO.5, SEPTEMBER 2017 [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] D.G Rabus, Integrated Ring Resonators – The Compendium: Springer-Verlag, 2007 Trung-Thanh Le, Multimode Interference Structures for Photonic Signal Processing: Modeling and Design: Lambert Academic Publishing, Germany, ISBN 3838361199, 2010 Wim Bogaerts, Peter De Heyn, and Thomas Van Vaerenbergh, "Silicon microring resonators," Laser Photonics Review, vol 6, pp 47–73, Jan 2012 Ying Lu, Jianquan Yao, Xifu Li et al., "Tunable asymmetrical Fano resonance and bistability in a microcavity-resonator-coupled Mach-Zehnder interferometer," Optics Letters, vol 30, pp 3069-3071, Nov 2005 Linjie Zhou and Andrew W Poon, "Fano resonancebased electrically reconfigurable add-drop filters in silicon microring resonator-coupled Mach-Zehnder interferometers," Optics Letters, vol 32, pp 781-783, Apr 2007 Liron Stern, Meir Grajower, and Uriel Levy, "Fano resonances and all-optical switching in a resonantly coupled plasmonic–atomic system," Nature Communications vol 5, Sept 2014 Mikkel Heuck, Philip Trøst Kristensen, Yuriy Elesin et al., "Improved switching using Fano resonances in photonic crystal structures," Optics Letters, vol 38, pp 2466-2468, July 2013 Bing-Hua Zhang, Ling-Ling Wang, Hong-Ju Li et al., "Two kinds of double Fano resonances induced by an asymmetric MIM waveguide structure," Journal of Optics, vol 18, Apr 2016 Yi Xu and Andrey E Miroshnichenko, "Nonlinear Mach-Zehnder-Fano interferometer," Europhysics Letters, vol 97, pp 44007-, Feb 2012 Andrey E Miroshnichenko, Sergej Flach, and Yuri S Kivshar, "Fano resonances in nanoscale structures," Review Modern Physics, vol 82, pp 2257-, Aug 2010 S Darmawan, L Y M Tobing, and D H Zhang, "Experimental demonstration of coupled-resonatorinduced-transparency in silicon-on-insulator based ring-bus-ring geometry," Optics Express, vol 19, pp 17813-17819, Aug 2011 J Heebner, R Grover, and T Ibrahim, Optical Microresonators: Theory, Fabrication, and Applications: Springer, 2008 Shanhui Fan, "Sharp asymmetric line shapes in sidecoupled waveguide-cavity systems," Applied Physics Letters, vol 80, pp 908 - 910, Nov 2002 Kam Yan Hon and Andrew Poon, "Silica polygonal micropillar resonators: Fano line shapes tuning by using a Mach -Zehnder interferometer," in Proceedings of SPIE Vol 6101, Photonics West 2006, Laser Resonators and Beam Control IX, San Jose, California, USA, January 2006 Chen Zong-Qiang, Qi Ji-Wei, ChenJing et al., "Fano Resonance Based on Multimode Interference in Symmetric Plasmonic Structures and its Applications [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] in Plasmonic Nanosensors," Chinese Physics Letters, vol 30, January 2013 W.P Huang, C.L Xu, W Lui et al., "The perfectly matched layer (PML) boundary condition for the beam propagation method," IEEE Photonics Technology Letters, vol 8, pp 649 - 651, May 1996 T.T Le and L.W Cahill, "The modeling of MMI structures for signal processing applications," Integrated Optics: Devices, Materials, and Technologies XII Edited by Greiner, Christoph M.; Waechter, Christoph A Proceedings of the SPIE, vol 6896, pp 68961G-68961G-7, March 2008 T.T Le, "Design and analysis of optical filters using 3x3 multimode interference couplers based microring resonators," Journal of Sciences and Technology, Vietnam Academy of Sciences, vol 12, Dec 2009 T T Le and L.W Cahill, "Photonic Signal Processing Using MMI Coupler-Based Microring Resonators," in The 20th Annual Meeting of the IEEE Lasers and Electro-Optics Society (LEOS 2007), Lake Buena Vista, FL, USA, Oct 2007, pp 395-396 Trung-Thanh Le, Multimode Interference Structures for Photonic Signal Processing: LAP Lambert Academic Publishing, 2010 Trung-Thanh Le and Laurence Cahill, "Microresonators based on 3x3 restricted interference MMI couplers on an SOI platform," in IEEE LEOS Annual Meeting Conference Proceedings (LEOS 2009), Belek-Antalya, Turkey, Oct 2009, pp 479 480 F Liu, Q Li, and Z Zhang et al., "Optically tunable delay line in silicon microring resonator based on thermal nonlinear effect," IEEE Journal of Selected Topics in Quantum Electronics, vol 14, pp 706 - 712, May-June 2008 F Xia, L Sekaric, and Y A Vlasov, "Mode conversion losses in silicon-on-insulator photonic wire based racetrack resonators," Optics Express, vol 14, pp 3872-3886, May 2006 Yun Long and Jian Wang, "Optically-controlled extinction ratio and Q-factor tunable silicon microring resonators based on optical forces," Scientific Reports, Nature, vol 4: 5409, June 2014 Hao Shen, Jian-Ping Chen, Xin-Wan Li et al., "Group delay and dispersion analysis of compound high order microring resonator all-pass filter," Optics Communications, vol 262, pp 200–205, Dec 2006 Jingya Xie, Linjie Zhou, Zhi Zou et al., "Continuously tunable reflective-type optical delay lines using microring resonators," Optics Express, vol 22, pp 817-823, January 2014 Robert W Boyd and Daniel J Gauthier, "Controlling the Velocity of Light Pulses," Science, vol 326, p 1074, Nov 2009 Duy-Tien Le, Manh-Cuong Nguyen, and Trung-Thanh Le, "Fast and slow light enhancement using cascaded microring resonators with the Sagnac reflector," Optik - International Journal for Light and Electron Optics, vol 131, pp 292–301, Feb 2017 IJMOT-2017-4-1294 © 2017 IAMOT ... microring resonators based on directional couplers for fast and slow light applications [28] Here, we show that by using only one microring resonator based on a 3x3 MMI coupler, the fast and slow light. .. way of creating Fano resonance based on only one 3x3 general interference multimode interference coupler The 3x3 MMI coupler has been designed and optimized by using the TMM and BPM It is shown... Jose, California, USA, January 2006 Chen Zong-Qiang, Qi Ji-Wei, ChenJing et al., "Fano Resonance Based on Multimode Interference in Symmetric Plasmonic Structures and its Applications [16] [17]