Amplified total internal reflection: theory, analysis, and demonstration of existence via FDTD

Abstract

The explanation of wave behavior upon total internal reflection from a gainy medium has defied consensus for 40 years. We examine this question using both the finite-difference time-domain (FDTD) method and theoretical analyses. FDTD simulations of a localized wave impinging on a gainy half space are based directly on Maxwell's equations and make no underlying assumptions. They reveal that amplification occurs upon total internal reflection from a gainy medium; conversely, amplification does not occur for incidence below the critical angle. Excellent agreement is obtained between the FDTD results and an analytical formulation that employs a new branch cut in the complex "propagation-constant" plane.

Total internal reflection in gain medium slab

“…Often a special choice of an analytical branch of the square root function is considered. Unfortunately, this choice depends on the angle of the incidence or the thickness of the gain slab [2][3][4][5]. Therefore, even the case of a homogeneous slab, which has repeatedly been described in the literature [3,4,6,7], has not obtained unambiguous treatment until now [8,9].…”

Modification to the Fresnel formulas for amplified or attenuated internal reflection

“…we find r p = r p0 x ρ p = exp(−jΦ p ) exp(−k 0 κδ p ), (14) where the Goos-Hänchen shift for p-polarized waves is written as δ p = 2(n l /n h ) 2 cos α sin α [(n l /n h ) 4 cos 2 α sin 2 α − (n l /n h ) 2 ] −1 d s l .…”

Laser drilling of superdeep micron holes in various materials with a programmable control of laser radiation parameters

“…A Gaussian spatial distribution based on a totalfield/scattered-field (TF/SF) technique is chosen as the unidirectional input field to excite the fundamental mode of the input W1 waveguide. 19,20) The input signal is defined in the uniform background and is located at entrance port A of the waveguide structure. Next, the power flow propagating through line detectors B and D is integrated to obtain the output power.…”