Intersubband-transition-induced phase matching

Abstract

We suggest the use of the refractive-index changes associated with the intersubband transitions in quantum wells for phase matching in nonlinear materials.An improvement in the conversion efficiency of mid-IR secondharmonic generation by almost 2 orders of magnitude over non-phase-matched bulk GaAs is predicted. We also show that the linear phase contributions of intersubband transitions used for resonant enhancement of secondharmonic generation must be considered, as they could limit the conversion efficiency by increasing the phase mismatch on one hand or offset the bulk's dispersion and lead to phase matching on the other.The second-harmonic generation (SHG) efficiencies of nonlinear materials are often limited by their coherence lengths, 1 and schemes for phase matching or quasi-phase matching 2 need to be employed for reasonable conversion efficiencies to be achieved.Recently it was demonstrated that the refractive index of bulk material may be selectively altered by the large refractive-index contributions associated with the intersubband transitions (ISBT's) in quantum wells. 3 ' 4 In this Letter we suggest the use of these tailorable refractive-index contributions to offset the bulk's dispersion and obtain a phase-matched material at a selected wavelength. The phase matching obtained in this manner is intrinsic and requires no external process such as quasi-phase matching or angle tuning. We examine the contribution of this technique to the conversion efficiency of mid-IR radiation in GaAs phase matched by GaAs/AlGaAs n-doped quantum wells. Both the ideal case of a bulk material embedded with quantum wells and the case that is more practical as a result of growth limitations of the TM mode in a narrow dielectric waveguide 5 are considered. We consider ISBT index contributions originating either from symmetric (two-level) wells, designed for phase matching only, or from asymmetric (threelevel) quantum wells, designed both for resonant enhancement of the SHG and for phase matching. First we examine the former, in which the source of the SHG nonlinearity is the bulk material. Introduction into bulk material of a transition whose real part of the optical susceptibility will offset the bulk's dispersion will lead to phase matching. Doped quantum wells are optimal for this purpose, because the ISBT's constitute a two-level system with a designable energy-level separation and large optical dipole elements. In the following treatment we shall limit ourselves to electron ISBT's in quantum wells, but the treatment is valid for any two-level system that may be distributed uniformly (on a wavelength scale) in a dispersive host material.The ISBT's offsetting the bulk's dispersion are unavoidably 6 accompanied by loss; hence a solution of the SHG propagation equations that takes the absorption into account 7 is necessary. Maxwell's equations for a field of w and 2w frequency components (E,, and E 2 w, respectively) reduce with the slowly varying amplitude approximation 8 towhere n,,, and n 2 a,, are the first-and sec...

Nonlinear phase matching in THz semiconductor waveguides

“…An alternative way for phase matching was suggested by Almogy and co-workers: [17]. They proposed to use a two-level system to appropriately introduce an absorption line in the nonlinear material.…”

“…If the optical transition of the two-level system is resonant at a frequency between the nonlinear interacting frequencies, the refractive index dispersion associated with this transition (via the Kramers-Kronig relation) can compensate the chromatic dispersion of the material. This configuration had been first theoretically proposed using intersubband transitions in quantum wells as a two-level system [17] and subsequently experimentally demonstrated [18].…”

“…This gives, via Kramers-Kronig relations, a negative variation of the linear susceptibility lower than 10 −5 , which is three to four orders of magnitude lower than the typical bulk dispersion that has to be compensated. A very different situation occurs for electronic intersubband transitions in III-V semiconductor compounds [17], where absorption cross sections have values between 10 −14 and 10 −15 cm 2 . This enhancement has its origin in the very high dipole matrix element, due to the optimized overlap between the wavefunctions, and the low effective mass of electrons in III-V semiconductors.…”

Second-harmonic generation in absorptive media

“…typical for ISBT's 4 ), the transition-induced phase mismatch 8 ' must be considered if the propagation length is comparable with the absorption distance. Before drawing further conclusions we must consider the limitations of our perturbative, nondepleted derivation in view of the saturable nature of nearresonant SHG.1 0 Since the effects of saturation will become significant at roughly the two-level system's saturation intensity,' the perturbative solution is limited to…”

Modelling second harmonic generation at mid-infrared frequencies in waveguide integrated Ge/SiGe quantum wells

“…Here it has to be mentioned that the PM condition in WG integrated ACQWs could be achieved by different methods, including refractive index engineering [40] and WG shape modulation [41].…”