Complex transmission eigenvalues for spherically stratified media

We investigate the existence of complex transmission eigenvalues for spherically stratified media in R2 and R3. In R2 with the index of refraction being constant, we show that there exists an infinite number of complex eigenvalues. In R3 and constant index of refraction, we show that if the index of refraction is an integer there are no complex eigenvalues, whereas if the index of refraction is a rational number, complex eigenvalues can exist. Under appropriate assumptions we also show that complex eigenvalues can exist for a spherically stratified variable index of refraction. (paper)