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Efficient third harmonic generation in photonic nanowires

Neil G. R. Broderick, Max A. Lohe, Timothy Lee, Afshar V. Shaaram, Tanya M. Monro

Published Jan 1, 2013• 0 citations
OpenAlex

Abstract

In a photonic nanowire the strong optical confinement allows for the phase matching of nonlinear interactions that would not normally be phase matched, while the large longitudinal component of the electric field serves to further enhance the effective nonlinearity. Thus such waveguides are good choices for studying nonlinear effects such as third harmonic generation. In this paper we analyse third harmonic generation analytically and present the criteria for optimal harmonic generation. In addition we analyse the inverse process of 1/3 harmonic generation and show that efficient parametric amplifiers can be made which would be a high brightness source of entangled photons for producing GHZ states.

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In a photonic nanowire the strong optical confinement allows for the phase matching of nonlinear interactions that would not normally be phase matched, while the large longitudinal component of the electric field serves to further enhance the effective nonlinearity. Thus such waveguides are good choices for studying nonlinear effects such as third harmonic generation. In this paper we analyse third harmonic generation analytically and present the criteria for optimal harmonic generation. In addition we analyse the inverse process of 1/3 harmonic generation and show that efficient parametric amplifiers can be made which would be a high brightness source of entangled photons for producing GHZ states.
The effect of the quantum properties of light on nonlinear processes has been well studied theoretically. It has been shown that the efficiency of n-photon nonlinear processes in many cases scales as the normalized n-th order correlation function. For light with high intensity correlation function, the efficiency of the n-th harmonic generation will be considerably higher than for coherent light. The experimental observation of this effect remained difficult until recently, because of the absence of bright sources with strong and fast intensity fluctuations. For the experimental demonstration of statistical effects in optical harmonic generation we use as a pump the radiation of high-gain parametric down conversion. Such light shows quantum properties (e.g. quadrature or two-mode squeezing) and has large number of photons in one mode. The normalized n-th order correlation function for this light is (2n - 1)!!, which makes it more attractive for nonlinear processes than both coherent and thermal light. For the generation of optical harmonics we used broadband parametric down conversion around frequency-degeneracy (1600 nm) produced in 1cm BBO crystal from Ti:Sapphire laser (800 nm, 1.6ps, 5kHz, 3W mean intensity). Due to spectral filtering and post-selection technique we could vary the statistics of light from coherent to super-bunched, which allowed us to demonstrate the efficiency enhancement for second-, third-, and fourth-harmonic generation. The obtained experimental results show a good agreement with the theory.
Parametric up- and down-conversion require phase matching between the generating and generated wavelengths, introducing strict requirements on the refractive index dispersion of materials used for this nonlinear processes. Optical microfibers can exploit the different modal overlap with core and cladding materials to phase match different modes at the required wavelengths. Intermodal phase-matching has been successfully exploited in optical microfibres to generate second- and third-harmonics, both in straight waveguides and related resonators. The simultaneous generation of guided higher harmonics also allowed to exploit other nonlinear effects like four wave mixing to generate light at short wavelengths in the UV part of the spectrum. Parametric down-conversion allows to generate entangled photons, but with efficiencies significantly smaller than their up-conversion processes because of their reliance of spontaneous photons generation from vacuum. The use of more complex architectures, based on multiple coupled waveguides, allows to achieve a quasi-phase matching condition, thus a sizeable improvement on the overall conversion efficiency.
All-fiber systems for third harmonic generation are of great interest because they can be used for the inverse process, namely, the generation of entangled photon triplets. Usually, chromatic dispersion prevents phase matching between the incident and generated radiation when they are both guided in an LP01-like mode. Here, we present a hybrid photonic crystal fiber that has been designed for phase matched third harmonic generation from 1596 to 532 nm in single-lobed modes. The third harmonic radiation is guided by an all-solid bandgap microstructure, while the pump frequency is confined by conventional total internal reflection. The fiber is also suitable for the generation of photon triplet states.
Ridges waveguides carved in bulk nonlinear crystals such as LiNbO 3 [1] or KTiOPO 4 (KTP) [2] are a good alternative to reach a strong confinement of electromagnetic waves with large second-order or third-order non-linearity. We report here on our most recent experiments where we show the possibility to shape the birefringence phase-matching (BPM) conditions for direct Third-Harmonic Generation (THG: ω + ω + ω → 3ω) in micrometric KTP ridge waveguides by acting on their transverse dimensions. This study is the preliminary step for designing quantum optical experiments based on Triple Photons Generation (TPG: 3ω → ω + ω + ω) that is the reverse process of THG, thus exhibiting the same BPM conditions.
The third-harmonic generation (THG) in GaAs∕AlGaAs\mathrm{GaAs}∕\mathrm{AlGaAs}GaAs∕AlGaAs cylindrical parabolic quantum wires with an applied static-electric field is studied in detail. An analytic formula for the THG susceptibility in the model is obtained by a compact density matrix approach and an iterative procedure. Finally, the calculated results show the parabolic confinement potential and the applied electric field have great influence on the THG susceptibilities in the system. Another important point is that the maximum THG susceptibility over ${10}^{\ensuremath{-}9}\phantom{\rule{0.3em}{0ex}}{\mathrm{m}}^{2}∕{\mathrm{V}}^{2}$ can be obtained by optimizing the parabolic confinement potential and the applied electric field, which is over ten orders of magnitude greater than in bulk GaAs. The contributors to the very giant three-order nonlinear include the very large dipole transition matrixes and the triple resonant condition.