$N$-channel comb filtering and lasing in $\mathcal{PT}$-symmetric superstructures

A comb spectrum generating device based on Bragg grating superstructures with gain and loss is suggested in this paper. It includes a comprehensive analysis of the device formulation, generation and manipulation of the comb spectrum with a number of degrees of freedom such as duty cycle, sampling period and gain-loss parameter. For applications such as RF traversal filters and tunable multi-wavelength laser sources, the reflected intensities of the comb resulting from the superstructures should have uniform intensities, and this is guaranteed by optimizing the physical length of the device, gain and loss in the unbroken $\mathcal{PT}$-symmetric regime. Alternatively, it can be accomplished by reducing the duty cycle ratio of the superstructure to extremely small values in the broken $\mathcal{PT}$-symmetric regime. Such a customization will degrade the reflectivity of the conventional grating superstructures, while it gives rise to narrow spectral lines with high reflectivity in the proposed system. Remarkably, combs with an inverted envelope are generated for larger values of gain and loss.