Phenomenological Single-Particle
Modeling of Reactive Transport
in Semiconductor Processing
6.3 Optical Parameter Extraction
The feature detection procedure described in Section 6.2 is sufficient for determining a thorough description of a single cavity. However, to understand the impact of the quality of the microcavity on the assembled resonator, the entire device must be considered. Through Gaussian beam analysis of an assembled resonator [187], optical parameters can be extracted in a rough approximation of a device simulation, as they are representative of possible device performance. For simplicity, a PC resonator is considered, which is shown in Fig. 6.6 together with the extraction procedure of such parameters.
The starting point of the optical parameter extraction procedure is the feature detection algorithm, first presented in Section 6.2. Having obtained the maximum cavity
opening
With the ROC having been determined, the next step is the extraction of the Gaussian beam waist size
The waist
With these parameters available, attention must now be placed on interpreting them in order to optimize the quality of the resonators. As previously indicated, to achieve a finesse above the state of the art [168], the
resonator must be able to capture the majority of the beam. Thus, the first design criterion is having an opening large enough to capture three standard deviations of the beam intensity, i.e.,
The second criterion comes from the insight that the best resonator performance is obtained from a parabolic cavity shape. Since the shapes have been functionally described via sixth-order polynomial of the form
Finally, a resonator must be as compact as possible, such that the beams become concentrated and the likelihood of spurious interactions is reduced. This is achieved through a cavity which is not only highly parabolic but which is also characterized by a sharp parabola. Alternatively, this can be interpreted through Eq. (6.2) as minimizing the ROC. Therefore, the three optimization design criteria are, in summary: