[OPTICAL REVIEW Vol. 13, No. 4 (2006) 249-253]
© 2006 The Optical Society of Japan

Determinant of Wave Operator as a Measure for Resonance and Bound States in One-Dimensional Potential Scattering System

Itsuki BANNO*, Daisuke KANEKO and Kazumi FUJIMA

Interdisciplinary Graduate School of Medicine and Engineering, University of Yamanashi, 4-3-11 Takeda, Kofu 400-8511, Japan

(Received November 15, 2005; Accepted March 3, 2006)

The determinant of the wave operator or its transposed operator (source operator) works as a measure for resonance and bound states in one-dimensional potential scattering system. This fact is based on an identity proved here: the determinant of the wave or source operator equals to the transmission coefficient, which represents the field amplitude in the forward side of the scatterer. Utilizing this measure, resonance and bound states in one-dimensional system are properly assigned without solving wave equation. In future, local enhancement of optical near-field in three-dimensional system, i.e., local plasmon resonance will be treated, generalizing the present method.

Key words: resonance, wave operator, bound state, potential scattering, scattering theory

*E-mail address: banno@es.yamanashi.ac.jp