An exact and compact formula for the optical intersubband response of finite-barrier quantum wells, wires and dots

The optical response of quantum wells, wires and dots is frequently modelled without including continuum states. This is reasonable in a low-energy regime but fails to capture phenomena such as bound-to-continuum transitions. We show that, in fact, the full optical intersubband response of quantum confined structures can be expressed in an exceedingly simple exact formula for arbitrary barrier height, confinement dimension, and optical frequency. We illustrate the consequences of transitions reaching the continuum for several representative cases, including asymmetric quantum wells. Moreover, we derive a simple modification that may be added to bound-states-only simulation in order to include the continuum. For the asymmetric quantum well, both linear and second-order nonlinear response is obtained. Finally, excellent agreement with measured bound-to-continuum absorption in narrow quantum wells is demonstrated.