Distributed Feedback Laser Based on Tunable Photonic Hypercrystal

Abstract

In this work, we investigate the generation of light in a distributed feedback (DFB) laser composed of periodically arranged layers of hyperbolic medium and active material forming a 1D photonic hypercrystal (PHC). The scope of our study covers the analysis of laser action in the presence of different types of dispersion that are achievable in a hyperbolic medium. Using the example of a PHC structure consisting of graphene-based hyperbolic medium, we demonstrate the possibility of controlling laser action by tuning effective dispersion. Our analysis reveals the possibility of obtaining a single-frequency generation with high side-mode suppression and controllable wavelength of operation. Moreover, we present a new mechanism for the modulation of laser amplitude arising from voltage-controllable dispersion of hyperbolic medium.

Spatial Dispersion in Hypercrystal Distributed Feedback Lasing

“…In the case of the PHC with HMM based on dielectric layer thickness t ZnO = 5 nm, due to dielectric character of dispersion, all observed generation spectra are similar to behavior of a conventional DFB laser with small gain/loss- and dominant index-modulation [ 25 , 40 ]. Moreover, it can be observed that generation properties predicted with the local EMT approach are very consistent with the nonlocal response for both light polarizations, compare Figure 4 a,b and Figure 4 c,d.…”

“…It is worth noting that the vector of field amplitudes describes all modes, i.e., backward and forward propagating waves with TE (with field components ) and TM (with field components ) polarizations, that exists in the medium. More detailed description of presented approach may be found in our previous research [ 15 , 16 , 25 ]. Finally, by assuming appropriate conditions for adjacent layers/media, it is possible to formulate a relationship between amplitudes at the input c in and output side c out of a single layer where is the transfer matrix of the layer, is the thickness of the considered layer, while is eigenvector matrix of output layer/medium.…”

“…Along with Kogelnik’s model [ 40 ], the laser action in our analysis is understood as a result of oscillations arising from a reflection at the gain medium/air interface and further energy accumulation via scattering from counter-propagating waves inside the structure. Thus, the laser threshold is considered as nonzero output under no external incident radiation and assumed reflection conditions [ 25 ]. By combining Equations (13) and (14), (16) as well as assuming that the structure ends with gain medium on both sides, see Figure 2 a, it is possible to obtain an expression for threshold generation in such a structure [ 40 ] where is Fresnel transmission amplitude coefficient for the gain medium-air interfaces.…”

“…Along with our previous research [ 25 ], amplitude gain coefficient, which is used for calculation of generation thresholds, is expressed in the following form: where is complex permittivity of the gain medium, while the Bragg wavelength of a PHC laser is defined as follows where is the size of the PHC’s unit cell, see Figure 2 a, and , are refractive indices of hyperbolic and the gain media, respectively.…”

“…Photonic hypercrystals (PHCs) are a novel class of metamaterials combining properties of photonic crystals and hyperbolic media [ 20 ] and revealing interesting properties, such as difractionless imaging [ 21 ], optical bistability [ 22 ], cloaking [ 23 ], or tunable broadband unidirectional absorption [ 24 ]. Recently, it has also been demonstrated that tunable lasing with voltage-controllable single mode generation is also possible in this class of structure [ 25 ].…”