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Finite-difference time-domain simulation of thermal noise in open cavities

A numerical model based on the finite-difference time-domain FDTD method is developed to simulate thermal noise in open cavities owing to output coupling. The absorbing boundary of the FDTD grid is treated as a blackbody, whose thermal radiation penetrates the cavity in the grid. The calculated amount of thermal noise in a one-dimensional dielectric cavity recovers the standard result of the quantum Langevin equation in the Markovian regime. Our FDTD simulation also demonstrates that in the non-Markovian regime the buildup of the intracavity noise field depends on the ratio of the cavity photon lifetime to the coherence time of thermal radiation. The advantage of our numerical method is that the thermal noise is introduced in the time domain without prior knowledge of cavity modes. I. INTRODUCTION The finite-difference time-domain FDTD method 1 has been extensively used in solving Maxwell’s equations for dynamic electromagnetic EM fields. The absorbing boundary condition based on the perfectly matched layer PML 2 allows the simulation of open systems, e.g., leaky optical cavities, in any dimension. The incorporation of auxiliary differential equations, such as the rate equations for atomic populations 3 and the Maxwell-Bloch equations for the density of states of atoms 4‐6, has lead to comprehensive studies of light-matter interactions. Although the FDTD method has become a powerful tool in computational electrodynamics, it is applied mostly to classical or semiclassical problems. Recently, quantum fluctuations due to the spontaneous emission of atoms were introduced to the FDTD simulation of microcavity lasers 7. The light field in an open cavity also experiences quantum fluctuation because of its coupling to external reservoirs. In this paper, we model the quantum noise for the cavity field as a classical noise and incorporate it into the FDTD algorithm. There are two dissipation mechanisms for the cavity field: i Intracavity absorption and ii output coupling. In the