Measurement of phases and amplitudes of AWG by fitting interference intensities

We measured the phases and amplitudes of an arrayed waveguide grating (AWG) by fitting interference intensities via a frequency domain method. The intensities were recorded as a function of the laser frequency in an interferometer containing the AWG. We fit the theoretical intensity profile to the recorded data via the Monte-Carlo method after filtering out the low-frequency noise. The phases and amplitudes are the parameters in the fitting process, and hence, the values are determined from the final fit. The variations in the measured phase values with the change in the initial condition of the Monte-Carlo process were less than $0.1^circ $ . The variations in the measured amplitude values were negligible. In order to verify our measurement, we calculated the transmission spectrum of the AWG using the measured phases and amplitudes and compared it with a directly measured spectrum. The calculated and measured spectrums are in good agreement with each other.