         !" # $" % &" ’ ()" *( %(("   *!(" ’( %" +! ’"    School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332 USA atabaki@ece.gatech.edu , sivay@ece.gatech.edu , momeni@ece.gatech.edu , ehsan@ece.gatech.edu , qli6@mail.gatech.edu , soltani@ece.gatech.edu , eftekhar@ece.gatech.edu , adibi@ece.gatech.edu , A travelingwave resonator structure with interferometriccoupling scheme is shown to have the capability of supporting both overcoupled and criticallycoupled modes, simultaneously. This device is demonstrated in SOI with an integrated microheater to tune its coupling. The application of this device for nonlinear optics is discussed. With the fast increase in communications data rates and reaching the limitation of copper transmission lines, there is a grave need for integrated optical communications systems that can basically emulate the functionality of fiber optics systems. Although many integrated linear devices such as filters and delay lines have been successfully demonstrated, high power requirement for nonlinear functionalities has impeded their development significantly. Recently, resonators are employed to reduce the power constraint for onchip nonlinear applications [1]. This enhancement of efficiency comes at the price of a lower signal bandwidth. In this paper we propose and demonstrate a travelingwave resonator structure which can support both criticallycoupled (highQ) and overcoupled (lowQ) modes which significantly improves this bandwidthefficiency tradeoff which is inherent to any resonancebased device. By including a thinfilm microheater and tuning the coupling to the device, criticalcoupling is achieved for the highQ mode and the possibility of efficient pump power transfer is discussed. The modes of a simple travelingwave resonator such as a microring with singlepoint coupling (Fig. 1(a)) have almost equal intrinsic and coupled Q and consequently equal bandwidth. Red curve in Fig. 1(c) shows the transmission of a microring resonator with a diameter of 40,m, loaded Q of 11,000 and intrinsic Q of 100,000. The modes of this resonator have a bandwidth of approximately 20 GHz. In a nonlinear experiment this overcoupling leads to less enhancement of pump wave in the resonator by a factor of 2.87 compared to the criticallycoupled situation. In order to simultaneously achieve criticalcoupling for pump wavelength and desired bandwidth for the signal wavelength, a frequencysensitive coupling scheme should be employed [2, 3]. Figure 1(b) shows the structure of an interferometricallycoupled microring resonator in which the coupling is determined by the interference of wave in two arms of the interferometer (i.e., L 1 and L 2 ). In the weak coupling case ( 1 2 << κ ), where κ 2 is the power coupling coefficient at each waveguideresonator coupling point, effective coupling is calculated by ( ) ( ) [ ] ( ) 2 1 2 2 2 cos 4 κ β β κ L L eff = , where ( ) i L β is the propagation phase along the i*th arm of the interferometer. This wavelength sensitive coupling can be exploited for example for fourwavemixing application in which the pump mode should exhibits criticalcoupling and its adjacent signal and idler modes should fulfill the bandwidth requirement of the system (overcoupled regime). This can be achieved by setting the length difference in the interferometer arms to half of the resonator perimeter, i.e., ( ) 2 1 2 res L L L = or for a microring, res L L = 2 . Also, it can be shown that κ 2 and ( ) ( ) [ ] 1 2 L L β β ϕ = are uniquely defined to achieve criticalcoupling for pump wavelength and the desired bandwidth at the signal wavelength. For the example above (i.e., loaded Q of 11,000 and intrinsic Q of 100,000), κ 2 = 0.0585 and o 7 . 36 = ϕ provide the desired resonator properties and the corresponding transmission spectrum is depicted by blue curve in Fig. 1(c). Insets in Fig. 1(c) clearly show that criticalcoupling is achieved for desired modes while the bandwidth of the rest of the modes is the same as those of a singlepoint coupled resonators. The precise phase difference control between the coupling arms is critical for the operation of the device. In this work we assume that by placing thinfilm microheater on top of arm L 2 , this phase can be controlled through thermooptic effect. This microheater also enables the correction for any dispersion mismatch between the two coupling arms caused by fabrication imperfection. Figures 1(d) and 1(e) show the transmission spectra of the interferometicallycoupled microring at highQ and lowQ modes, respectively; where the temperature of the L 2 arm is increased. This temperature rise provides the required phaseshift ( ϕ ) for achieving criticalcoupling at the high Q mode. It is also observed that this temperature rise has negligible effect on the lowQ mode. 89 WA3.2 14:15 – 14:30 978-1-4244-2611-9/09/$25.00 IEEE