Amplified total internal reflection: theory, analysis, and demonstration of existence via FDTD.
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.
1Department of Electrical and Computer Engineering, University of Wisconsin, Madison, WI 53706, USA.
Keely J
KJ
Willis
John B
JB
Schneider
Susan C
SC
Hagness
D000669:Amplifiers, Electronic; D003198:Computer Simulation; D020342:Finite Element Analysis; D008027:Light; D008962:Models, Theoretical; D012031:Refractometry / Q000379:methods*; D012542:Scattering, Radiation