Calculation of the coupling coefficient for trapezoidal gratings using the ray optics technique

기하광학 방법을 이용한 사다리꼴 회절격자의 결합계수 계산

Using the ray optics technique, we derive the analytic expressions of TE mode coupling coefficient for five-layer distributed feedback (DFB) structure devices. We compare the coupling coefficient calculated by the ray optics technique with those calulated by the extended additional layer method (EALM) which may be a most accurate method of calculating the coupling coefficient. The difference between the results of the ray optics technique and those of the EALM is small for most cases of grating depth and forms being practically made. In the case of rectangular gratings, the difference increases as the duty cycle of graing deviates from 0.5. In the case of the trapezoidal grating, the difference increases as the ratio of the top to the period of grating deviates from 0.5 and as the length of the top becomes longer than that of the base. The difference of theree-layer DFB structures is smaller than that of five-layer DFB structures.