Field localization and enhancement of phase-locked second- and third-order harmonic generation in absorbing semiconductor cavities

Abstract

We predict and experimentally observe the enhancement by three orders of magnitude of phase mismatched second and third harmonic generation in a GaAs cavity at 650 and 433 nm, respectively, well above the absorption edge. Phase locking between the pump and the harmonics changes the effective dispersion of the medium and inhibits absorption. Despite hostile conditions the harmonics resonate inside the cavity and become amplified leading to relatively large conversion efficiencies. Field localization thus plays a pivotal role despite the presence of absorption, and ushers in a new class of semiconductor-based devices in the visible and uv ranges.Since it was discovered by Franken in the 1960s, second harmonic ͑SH͒ generation has been one of the most studied phenomena in nonlinear optics ͓1͔. To date most efforts have been directed at improving the efficiency of the process by developing new materials with high effective nonlinear coefficients, accompanied by phase and group velocity matching ͓2-10͔. Consequently, most studies have been concerned with maximizing conversion efficiencies, generally achievable at or very near phase matching ͑PM͒ conditions, ensuring maximum energy transfer from the fundamental beam to the harmonics. A special effort was focused toward engineering new artificial materials capable of compensating material dispersion, for example, using quasiphase matching techniques ͓11,12͔ or structured materials ͓13͔. Outside of PM conditions, which generally coincide with low conversion efficiencies ͓3͔, the only relevant processes that have been investigated are cascaded parametric processes that can produce phase-modulation of the fundamental beam ͓14͔, pulse breaking ͓15͔ or nonlinear diffraction ͓16͔. This has caused other possible working conditions to remain largely unexplored. A relevant feature is that in all these previous studies the nonlinear material was assumed to be transparent for both fundamental and harmonics beams, since conventional wisdom holds that an absorptive material will reabsorb any generated harmonic signal.More recently, an effort was initiated to systematically study the behavior of SH and third harmonic ͑TH͒ fields in transparent and opaque materials under conditions of phase mismatch ͓17-19͔. Briefly, when a pump pulse crosses an interface between a linear and a nonlinear medium there are always three generated SH ͑and/or TH͒ components. One component is generated backward into the free space, due the presence of the interface, and the remaining components are forward moving. These components may be understood on the basis of the mathematical solution of the homogeneous and inhomogeneous wave equations at the SH frequency ͓4͔. Continuity of the tangential components of all the fields at the boundary leads to generation of the two forwardpropagating components that interfere in the vicinity of the entry surface and give rise to Maker fringes ͓2,20͔ and to energy exchange between the fundamentals and SH and/or TH beams. It turns out that while the homogeneous component tr...

Enhanced second-harmonic generation from resonant GaAs gratings

“…We assume a TE-polarized pump field at 1064nm incident at a 10° angle to exploit the bulk quadratic susceptibility of GaAs, χ (2) =10pm/V, and we consider a TE-polarized SH field generated at 532nm. This typical experimental setup is described in reference [5].…”

Phase locked harmonic localization and enhancement in an absorbing semiconductor cavity

“…Recently, an effort was initiated to more systematically study the dynamics of second and third harmonic generation in transparent and opaque materials under conditions of phase mismatch [8][9][10][11] . The dynamic of the phase locking (PL) mechanism is deeply related with the harmonic generation theory.…”

Second harmonic generation (SHG) from resonant GaAs gratings

“…We find large enhancement of conversion efficiency when the pump field excites the guided mode resonances (GMRs) [1] of the grating. Under these circumstances the spectrum near the pump wavelength displays sharp resonances characterized by dramatic enhancements of local fields and favorable conditions for second harmonic generation, even in regimes of strong linear absorption at the SH wavelength thanks to the phase-locked (PL) component of the SH [2). In particular, in a GaAs grating pumped at 1064nm, we predict SH conversion efficiencies approximately five orders of magnitude larger than conversion rates achievable in either bulk or etalon structures of the same materials [3).…”