Theory of the two-photon Franz-Keldysh effect and electric-field-induced bichromatic coherent control

Published

October 17, 2025

Author(s)

Jared Wahlstrand, John Sipe

Abstract

The effect of a constant electric field on two-photon absorption in a semiconductor is calculated using an independent-particle theory. The theoretical framework is an extension of a theory of the one-photon Franz-Keldysh effect [Wahlstrand and Sipe, Phys. Rev. B 82, 075206 (2010)]. The theory includes the effect of the constant field, including field-induced coupling between closely spaced bands, in the electronic wavefunctions and calculates optical absorption perturbatively. Numerical calculations are performed using a 14-band k ·p band structure model for GaAs. Field enabled two-photon absorption below the band gap and Franz-Keldysh oscillations are predicted for all independent tensor elements, with a generally larger effect in elements with more components parallel to the constant electric field direction. Some tensor elements that are zero in the absence of a field become nonzero in the presence of the constant electric field and depend on its sign. Notably, these elements and certain orientations of the electric and optical fields with respect to the crystal axes are linear in the electric field to lowest order and may thus survive away from band structure critical points at room temperature and/or with a non-uniform field. Electric field induced changes in the carrier injection rate due to interference between one- and two-photon absorption are also calculated. The electric field enables this bichromatic coherent control process for polarization configurations where it is normally forbidden and also modifies the spectrum of the process for configurations where it is allowed by crystal symmetry.

Citation

Physical Review B

Volume

112

Issue

15

Pub Type

Journals

Download Paper

https://doi.org/10.1103/zkp2-fjj4

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Keywords

Semiconductors, two-photon absorption, electro-optic effect, numerical calculations

Citation

Wahlstrand, J. and Sipe, J. (2025), Theory of the two-photon Franz-Keldysh effect and electric-field-induced bichromatic coherent control, Physical Review B, [online], https://doi.org/10.1103/zkp2-fjj4, https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=959084 (Accessed December 2, 2025)