Layered optomagnonic structures: Time Floquet scattering-matrix approach

Abstract

A fully dynamic theoretical approach to layered optomagnonic structures, based on a time-Floquet scattering-matrix method, is developed. Its applicability is demonstrated on a simple design of a dual photonic-magnonic cavity, formed by sandwiching a magnetic garnet thin film between two dielectric Bragg mirrors, subject to continuous excitation of a perpendicular standing spin wave. Some remarkable phenomena, including nonlinear photon-magnon interaction effects and enhanced inelastic light scattering in the strong-coupling regime, fulfilling a triple-resonance condition, are analyzed and the limitations of the quasi-static adiabatic approximation are established.

High-efficiency triple-resonant inelastic light scattering in planar optomagnonic cavities

“…The structure in this geometry, with the magnetic field parallel to the surface and also perpendicular to the propagation direction, remains invariant under reflection with respect to the plane of incidence. Consequently, contrary to the Faraday configuration studied in our previous work [18][19][20], the transverse magnetic (TM) and transverse electric (TE) polarization modes, i.e. modes with the electric field oscillating in and normal to the plane of incidence, respectively, are eigenmodes of the system.…”

“…The solutions of the Maxwell equations for the dynamic structure under consideration are Floquet modes T=2π/Ω, where by F we denote electric field, electric displacement, magnetic field, and magnetic induction, while ω is the Floquet quasi-frequency, similarly to the Floquet quasi-momentum (or else the Bloch wave vector) when there is spatial periodicity [28,29]. Seeking Floquet modes in the form of plane waves with given q y and expanding all time-periodic quantities into truncated Fourier series in the basis of complex exponential functions n t exp i W ( ), n N N N , 1 , , = --+ ¼ , leads to an eigenvalue-eigenvector equation, which has 4(2N+1) physically acceptable solutions [19]. We characterize them by the following indices: s=+(−) that denotes waves propagating or decaying in the positive (negative) z direction, p=1, 2 that indicates the two eigen-polarizations, and ν=−N,−N+1, L, N which labels the different eigenmodes.…”

“…We characterize them by the following indices: s=+(−) that denotes waves propagating or decaying in the positive (negative) z direction, p=1, 2 that indicates the two eigen-polarizations, and ν=−N,−N+1, L, N which labels the different eigenmodes. These eigenmodes are polychromatic waves, each composed of 2N+1 monochromatic components of angular frequency ω − nΩ, n=−N, −N+1, K, N [19]. We note that, in a static homogeneous medium, the corresponding eigenmodes of the electromagnetic (EM) field are monochromatic waves characterized by the indices s, p, and n.…”

“…However, since light is guided inside Bi:YIG, the introduction of realistic dissipative losses would result in significant decrease of the efficiency. To this end, optomagnonic cavities formed in a magnetic dielectric film bounded by two mirrors [17][18][19], or in a defect layer in a dual photonic-magnonic periodic layered structure [20], have also been investigated. However, the studies reported so far refer to the Faraday configuration, with out-of-plane magnetized films, where it is challenging to obtain two optical resonances in the required close proximity to each other.…”

“…In section 2 we describe the statically magnetized structure and discuss its optical response. In section 3 we summarize our recently developed fully dynamic time-Floquet method for layered optomagnonic structures [19] and in section 4 we present details of our attained numerical results. The last section concludes the article.…”