Second-harmonic generation in absorptive media

Abstract

The solution of the coupled-wave equations for second-harmonic generation in a near-resonant three-level system is extended to include absorption.It is shown, within second-order perturbation theory, that double resonance is the optimal conversion condition, despite absorption enhancement.We extend the solution numerically, using nonperturbative susceptibilities derived within the rotating-wave approximation, to saturating intensities and discuss the modifications to the perturbative conclusions as well as the regimes of validity for the various approximations.The propagation equations for second-harmonic generation (SHG) are typically 1 presented for transparent materials with nondispersive SHG coefficients. Because any nonlinear-optical material may be viewed as a summation of discrete level systems, the transparency assumption is a priori unjustified. Whereas all optical transitions contribute to the absorption, only the asymmetrical ones contribute to SH;G. Furthermore, in a three-level system the SHG is inversely proportional to the product of the detuning of the first and the second harmonics, whereas the absorption of each harmonic is inversely proportional to the respective detuning squared. Hence the ratio of the SHG to the dominating absorption is, at best, unchanged with detuning from resonance.Recently, 2 -6 following the advent of quantum-well systems with tailored intersubband transition (ISBT) energies, there has been heightened interest in resonant nonlinearities. Several calculations and assumptions have been made 5`8 regarding the optimal detunings and the maximal attainable conversion efficiency, but the conclusions vary. We use SHG coefficients derived from second-order perturbation theory to solve the coupled-wave equations in the nondepleted approximation. The results show that double resonance is the optimal conversion condition but that near-resonance saturation limits the use of second-order perturbation theory to small conversion efficiencies. This justifies the neglect of depletion of the first harmonic in the perturbative regime but calls for a nonperturbative solution that extends the treatment to higher intensities. For large detunings, on the other hand, saturation is avoided, the conversion distance decreases with increasing intensity, and the absorption may be neglected. The approximate solution is then extended numerically 5`7 to include the effects of depletion, dispersion, absorption, and saturation. The modifications of the perturbative nondepleted conclusions are examined, and it is shown that some detuning is preferable, in some circumstances, at high intensities but that high conversion efficiencies are obtainable on resonance, despite saturation.To examine SHG in a three-level system, in which the first harmonic is close to the ground-to-firststate (cool) and first-to-second-state (C012) transition frequencies and the second harmonic is close to the ground-to-second-state transition frequency (o02), we write the relevant resonantly enhanced first-and second-order suscepti...

Photonic Crystals

“…These experiments were interpreted using the formalism of cavity polaritons (Savvidis 2001), and the configuration where the phase-matching was optimised was given the name of 'magic angle configuration'. However, the phase-matching phenomenon described by the authors is actually similar to a phenomenon which had previously been reported in another experiment, where the absorption in a quantum well had been used for controlling the index function (Almogy 1994). While there may not be any 'magic' involved in this phenomenon, it nonetheless finds its place among other phase matching phenomena (Baas 2004;Eastham 2003;Whittaker 2001).…”

Efficient three‐wave mixing via intersubband transitions in a semiconductor quantum well

“…Alternatively, they also reported an experimental observation of resonantly enhanced slow-light four-wave mixing in such cold Rb atomic media [16]. For three-level system, efficient second-harmonic generation in absorptive media was studied by Almogy and Yariv [20].…”