Fundamentals of Nonlinear Optics

Phase matching in hyperbolic wire media for nonlinear frequency conversion

“…The FEM simulations also provide propagation losses, and thus propagation lengths in the selected wire media for all modes. For FF and SH these are 45 μm and 23.5 μm respectively, which is substantially larger than the coherence length for GaAs which is L = 12.5 μm at FF 3.1 μm [2]. The FF pump thus propagates with reasonable losses over four coherence lengths, and since the phase matched SHG signal grows quadratically with distance we may expect a 16 time enhancement in the lossy wire medium compared to the isotropic medium.…”

“…Therefore, satisfying a phase-matching condition is of great importance to SHG processes, and is necessary for the SH waves to add in phase. For SHG, the phase-matching condition imposes the wave vector relation 2 However, phase matching is challenging to achieve because of material dispersion. A common technique for achieving phase matching is birefringent phase matching [2].…”

“…For SHG, the phase-matching condition imposes the wave vector relation 2 However, phase matching is challenging to achieve because of material dispersion. A common technique for achieving phase matching is birefringent phase matching [2]. By appropriately choosing the propagation direction in an anisotropic medium, the birefringence of the ordinary and the extraordinary wave cancels the phase mismatch due to dispersion.…”

“…However, this is not possible for optically isotropic materials, and thus cubic materials such as GaAs, which otherwise have attractive nonlinear optical properties, have been little exploited for frequency conversion applications [3]. Another important technique is quasi-phase matching (QPM) [1,2], where efficient conversion can be achieved by periodically varying the sign of the nonlinearity by poling. However, this modulation of material properties is difficult to achieve, limiting the practical utility of this approach [4].…”

“…Frequency conversion by nonlinear optical interaction is an effective means of generating electromagnetic radiation in spectral regions differing from the incident field [1,2]. Secondharmonic generation (SHG), for instance, can be used to convert incident radiation at a fundamental frequency (FF) ω into radiation at the second-harmonic (SH) frequency 2ω [1].…”