# A Micro-Processor-Based Feedback Stabilization Scheme for High-Q, Non-Linear Silicon Resonators
## 3 Results and Discussion  
### \(\pi\)-Phase Shifted Grating Response  
Figure 6a shows the measured transmission spectrum of the \(\pi\)-phase shifted grating device, with a low injection power to avoid non-linear effects. The inset shows an enlargement of the resonance mode, with a Q-factor of \(\approx\)40 k. Figure 6b shows near-infrared (NIR) camera images of the light scattered vertically from the grating filter and access waveguides, where light is injected from the left hand side of the images. These images were taken before fabrication of the metal heater elements. (I) is the out of band transmission, showing scattering along the waveguide length; (II) is the in-band rejection showing little light transmitted from the input to the output waveguide; and (III) is the on-resonance transmission mode showing clear localization to the centre of the grating device. Figure 7a presents the measured transmission spectra of the device as a function of input power, along with the simulated spectra from Figure 4. The onset of the thermal non-linear behaviour is clear at around 0.09 mW of power on-chip. Figure 7b shows the tuning effect of the on-chip thermal heating element. By increasing the the power dissipated on the heater the global spectrum of the device can be shifted to longer wavelengths, whilst still retaining the non-linear thermal resonance shift as a function of injected optical power. Figure 5: Schematic of the feedback control scheme for the micro-resonator device. The micro-processor stores the transfer matrix method (TMM) model of the device and calculates an error signal based on the measured transmitted power and injection power, taking the on-resonance position as a working point. Figure 6: (**a**) Measured transmission spectrum of a \(\pi\)-phase shifted grating with a length of 200 μm; (**b**) near-infrared (NIR) images of vertically scattered light from the grating and access waveguides, corresponding to spectral positions detailed in (**a**). For the stabilization experiments, the device is operated at its maximum resonance position for an injection power of 0.6 mW. In order to demonstrate that the device remains in this optimal condition, a measure of the resonant enhancement is required. Here, the bistable switching of the cavity [7], was chosen as a convenient demonstration. Figure 8a shows the measured hysteresis curve for the resonator with an injection wavelength set at the optimal working point. At point (1) the laser wavelength is on the red side of the resonance line and at a low value of transmission. Increasing the injection power to point (2) increases the power trapped in the resonator, red-shifting the resonance line towards the injection wavelength setting the device to the high transmission state. The trapped optical power maintains this high transmission state as a function of reducing power through point (3). At this point the power is insufficient to cause a red shift alignment of the resonant line with the injection wavelength and the resonator returns to point (4) where its cavity resonance line is blue detuned from the laser wavelength and the device is in the low transmission state. The temporal bistable switching operation used to monitor the device operation was achieved by using a signal generator to apply a direct modulation to the tunable laser output power. The laser was set at an average power on-chip of 0.6 mW with a modulation amplitude of 0.09 mW. In addition, to allow positive and negative detuning via the thermal heating element, the device is operated with an initial bias on the heater. All the results below were taken at an initial operating wavelength of  
Figure 8: (**a**) Measured transmitted power of the grating device as a function of injected power showing hysteresis effects. The laser wavelength was set on the red side of the cold cavity resonance peak; (**b**) Input modulation signal and micro-resonator response for thermal bistability operation.