Topological aspects of electromagnetic wave propagation in one-dimensional photonic crystal

Abstract

The adiabatic following has been widely employed for achieving near-complete population transfer in a ‘two-level’ quantum mechanical system. The theoretical basis could be adopted in any equivalent system exhibiting special unitary (2) or SU (2) symmetry. We have drawn an analogy of population transfer dynamics of a quantum two-level system with that of light propagation in classical “one-dimensional photonic crystals” (1D-PC), which are commonly known as distributed-Bragg-reflectors (DBRs). We show that there exists a one-to-one correspondence between the coupled wave equations of a 1D PC with the time-dependent Schrodinger equation of a quantum mechanical two-level system of spin-1/2 particles in a homogeneous magnetic field. In 1D-PCs, the incident beam state |i⟩ and reflected beam state |r⟩ are equivalent to the ground state |g⟩ and excited state |e⟩ of a two-level system. The propagation length (z) inside the 1D-PC is analogous to the time (t) coordinate while the coupling strength (κ) and the phase-mismatch (∆K) between the interacting waves represent the parameters equivalent to Rabi frequency and detuning respectively. With this analogy, we employed the idea of rapid adiabatic passage (RAP) which is a well-known technique in a two-level atomic system for realizing 100% power transfer from the incident beam to the reflected beam for a broad spectral band. We designed and explored the propagation of light in a chirped photonic crystal (CPC) in which adiabatic constraints are completely satisfied and we found that the reflection spectrum of the configuration exhibits substantial broadening of the photonic bandgap (PBG) as well as suppression of sharp reflection peaks in the transmission band. When a thin plasmon active metal is placed adjacent to the CPC configuration, the backscattered phase undergoes multiple π phase jumps which enable the excitation of multiple optical Tamm (OT) modes. All the OT modes are separated in the spectral domain and their strong confinement results in a reduced group velocity up to 0.17 times the velocity of light, thus allowing to trap a broad spectrum with lifetime ≥ 2.8ps. In a separate study, we have focused on utilizing the topological features of the 1D-PC for carrying out beam wavefront shaping. The light transmitted through 1D-PC acquires a ‘quantized’ geometric phase (0 or π) which is also known as Zak phase. This gives rise to the structuring of optical beams over a broad spectral bandwidth via suitably designing the 1D-PC structure. In the last section of the work, we explore a 1D PC-based optical system that obeys non-Hermitian dynamics and we show that each photonic bandgap of an all-dielectric 1D-PC hosts at least two exceptional points in its eigenvalue spectrum. By introducing suitable apodization in the PC, the geometry supports multiple exceptional points which distinguishes the PT-symmetric region from the region where PT-symmetry is broken. The interaction of eigenvalues around the exceptional points provides a deeper knowledge of the electromagnetic-wave propagation dynamics.