Giant gain enhancement in photonic crystals with a degenerate band edge

Giant Gain Enhancement in Photonic Crystals with a Degenerate Band Edge Mohamed A. K. Othman 1 , Farshad Yazdi 1 , Alex Figotin 2 and Filippo Capolino 1 Department of Electrical Engineering and Computer Science, University of California, Irvine, Irvine, CA,.92697 USA Department of Mathematics, University of California, Irvine, Irvine, CA, 92697 USA arXiv:1411.0657v3 [physics.optics] 8 Dec. 2015 {mothman, fyazdi, afigotin, f.capolino}@uci.edu We propose a new approach leading to giant gain enhancement. It is based on unconventional slow wave resonance associated to a degenerate band edge (DBE) in the dispersion diagram for a special class of photonic crystals supporting two modes at each frequency. We show that the gain enhancement in a Fabry-Perot cavity (FPC) when operating at the DBE is several orders of magnitude stronger when compared to a cavity of the same length made of a standard photonic crystal with a regular band edge (RBE). The giant gain condition is explained by a significant increase in the photon lifetime and in the local density of states. We have demonstrated the existence of DBE operated special cavities that provide for superior gain conditions for solid-state lasers, quantum cascade lasers, traveling wave tubes, and distributed solid state amplifiers. We also report the possibility to achieve low-threshold lasing in FPC with DBE compared to RBE-based lasers. I. INTRODUCTION Light confinement using either mirrors or Bragg reflectors provides for high quality (Q)-factor in Fabry-Perot cavity (FPC) resonators and enhanced optical field intensity. Such cavities are commonly used for laser applications and spectroscopy. An important class of high Q-factor structures is formed by slow-wave resonators based on the regular band edge (RBE) of the wavenumber-frequency dispersion diagram relative to photonic crystals, whose simplest architecture is a periodic stack of dielectric layers, with one dimensional periodicity [1–3]. More elaborate designs of nanocavities adopted Silicon heterostructures [4], liquid crystals [5] technologies and demonstrated improved Q-factor compared to previously reported designs. The use of photonic crystals resulted in enhanced amplification properties for low-threshold lasing [2,6], enhanced directional- wave propagation through magneto-optical effects [7–9], nonlinear optics [10] and quantum processing [11]. Pursuing better performing photonic crystal cavities is essential to further advancement of photonic technology [12–15], and photonic integrated circuits [16–18] in particular. These advancement established a basis for a novel class of solar cell architecture with enhanced absorption [19–21], and other thin film applications [22], along with superior atomic interaction with strongly localized photons [23], and unconventional spontaneous emission dynamics [24,25]. Slow light in photonic crystals is yet another fundamental utility that can tailor the electromagnetic response and achieve superior performance through dispersion engineering [26–28]. Figotin and Vitebsky in [29–33], proposed FPC resonators made of unconventional photonic crystals composed by anisotropic dielectric layers. Those FPC resonators exhibit sharper transmission peaks, higher Q-factors, and better general performance in a vicinity of the photonic band edge frequency compare to conventional photonic crystal FPCs of the same size made of isotropic layers. The related field enhancement properties in those unconventional structures can be attributed to the degenerate band edge (DBE) conditions. This special DBE condition produces some four electromagnetic modes (EM) at the DBE frequency; that phenomenon does not occur in regular photonic crystals, i.e., conventional photonic crystals exhibiting an RBE providing a single EM mode operation. Consequently, it is important to acknowledge that the resonance characteristics in DBE cavities studied in this paper are fundamentally different from those in standard band-gap cavities [2,3,34,35]. Significant differences between DBE and RBE based FPCs are highlighted in Sec. II. The principal result of this paper that the DBE condition based on resonance properties discussed in [29–33] lead to giant power gain when an active