Quantum Engineering of Optical Nonlinearities

Abstract

Second-order optical nonlinearities in materials are of paramount importance for optical wavelength conversion techniques, which are the basis of new high-resolution spectroscopic tools. Semiconductor technology now makes it possible to design and fabricate artificially asymmetric quantum structures in which optical nonlinearities can be calculated and optimized from first principles. Extremely large second-order susceptibilities can be obtained in these asymmetric quantum wells. Moreover, properties such as double resonance enhancement or electric field control will open the way to new devices, such as fully solid-state optical parametric oscillators.

Theory of the effective Hamiltonian for degenerate bands in an electric field

“…Now since k · p theory (Kane 1982) uses zone-centre Bloch functions as basis states, it seems reasonable to expect that the potential (1.1) would give rise to Hamiltonian matrix elements of the form eE · x nn (1.2) where x nn is a matrix element of x connecting two zone-centre Bloch functions (see equation (2.10) below). This procedure has been used by many authors, both for the construction of effective-mass Hamiltonians (Aspnes 1975, Lommer et al 1985, Zhu and Chang 1994, Khurgin 1994, Krebs and Voisin 1996, Khurgin and Voisin 1997 and for the calculation of interband optical transition rates (Khurgin (1988); Wang (1989), p 603; Weisbuch and Vinter (1991), p 58; Singh (1993), p 154; Haug and Koch (1994), p 71; Chuang (1995), p 355; Szmulowicz (1995); Fiore et al (1995); Rosencher et al (1996); Khurgin (1999)). The difficulty with this procedure is that the matrix element x nn is ill defined (Burt 1993).…”

Microscopic approach to second harmonic generation in quantum cascade lasers

“…the diagonal elements in the density matrix, and the widths of the transitions. This approach is common when nonlinear conversion is considered [3,6,39] and the concept is outlined by both Shen [40] and Boyd [41]. In the following we compare our data with the standard density matrix approach of calculating the second order susceptibility.…”

“…The Quantum Cascade Laser [1] (QCL) consisting of hundreds of coupled quantum wells is well known to exhibit strong optical nonlinearities [2,3] in particular in the infrared [4]. These nonlinearities have attracted much attention as they have proved a useful tool to achieve roomtemperature terahertz sources through difference-frequency generation [5] and they can also be used the opposite way, extending the spectral range of the QCLs to lower wavelengths through Second Harmonic (SH) generation [6,7].…”

Optical sideband generation up to room temperature with mid-infrared quantum cascade lasers

“…Even though there is an overlap of the modes, a spatial overlap between the modes and the AR is necessary to obtain frequency mixing. This is a result of inversion symmetry arguments -GaAs does not possess a large second order resonant nonlinearity unless there is an asymmetry in the electronic potential, for example when a large electric field is applied to quantum wells [19], or in asymmetric coupled quantum wells [20], as in the AR. Indeed sideband generation was not detected with a QCL with this type of waveguide.…”

“…It should be noted that if a double resonance can be achieved when all the beams are at resonance with real states, an order of magnitude increase in the susceptibility could be achieved, which would result in a much larger sideband efficiency. In this case the k-space dispersion [19] and the inclusion of the QCL state populations would need to be taken into account.…”