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We studied a flexible design for directional quasi-phase-matching (DQPM) in AlGaAs waveguide resonators, which can be exploited for implementing optical frequency combs (OFCs) in cavity-enhanced second-harmonic generation. A TE-polarized electromagnetic pump field, guided in a curved path laying, e.g., in the (001) crystal plane, undergoes a spatial modulation of the nonlinear coupling constant, depending on the field polarization direction with respect to the crystal axes. This directional dependence has been experimentally observed in GaAs and AlGaAs microdisk whispering-gallery-mode resonators. DQPM can also be implemented in curve-shaped waveguides, for single-pass frequency mixing, or, as we proposed, in modular resonant configurations, by combining a sequence of arc- and S-shaped segments in a closed loop.
We numerically investigated the power threshold for the onset of quadratic OFCs in AlGaAs suspended-waveguide resonators with directional quasi-phase-matched second harmonic generation [Par17]. We also numerically simulated the spectral dynamics of frequency comb generation by solving the infinite-dimensional map for the field envelopes centred around the fundamental and second harmonic frequencies.
Fig.1: Pump power threshold (circles) versus resonator length, for different values of internal losses and two power transmission coefficients: θ = 0.02 (a) and θ = 0.04 (b).
Figure 1 shows the calculated pump power threshold as a function of the resonator length for different values of internal losses and transmission coefficients θ. We assumed global internal losses of 0.5, 1, and 2 dB/cm, which are close to losses experimentally observed in AlGaAs resonators. In the absence of internal losses, the OPO threshold would decrease monotonically with increasing round-trip path. Conversely, finite internal losses lead to an optimal round-trip length. For 0.5 dB/cm of internal losses and θ=0.04 (Q = 5.4 × 105 ), the lowest pump power threshold is around 4 μW, with an optimal round-trip length of 3.3 mm, dropping down to 2 μW for θ = 0.02 and L = 1.8 mm (Q = 5.6 × 105).
Fig.2: Stationary temporal patterns (c) and corresponding spectra for FF (d) and SH (e).
Figure 2 shows examples of the resulting intracavity comb generation, obtained for a resonant structure with a length of 1.8 mm, 1 dB/cm of linear losses, and coupling coefficient θ1 = θ2 = 0.02, pumped by 1 mW of infrared power. After a transient regime the temporal patterns in Fig. 2(c) at the fundamental (FF) and second harmonic (SH) reach a steady state, i.e., they maintain the same shape over thousands of round-trip time, except for a small drift in the frame of reference moving at the group velocity of the fundamental frequency.
A first example of suspended “snaky” AlGaAs waveguide, shown in Fig. 3, has been realized and characterized in collaboration with the Laboratoire Matériaux et Phénomènes Quantiques, of the Université Paris Diderot, in France [Mor17]. The role of DQPM in the snake waveguide has been tested by comparing the efficiency of SHG in the “snake” waveguide with the efficiency of mode-matched SHG in a straight waveguide. Figure 4 shows the SHG efficiency spectra. The thick black curve is the experimental SHG efficiency for a straight 1-mm-length nanowire oriented along the 〈110〉 direction. The thick red curve is the experimental SHG efficiency spectrum of a snake-shaped nanowire with the same cross-section and average orientation, and length ≈1.46 mm. It systematically reveals two distinct QPM spectral features around the wavelengths λ1 = 1591 nm and λ2 = 1596 nm, which are in excellent agreement with the calculated QPM condition Δk = k2ω − 2kω = ± 2π∕Λ = ± 2∕R. The measured peak SHG efficiency is 1.2% W−1 for the snake nanowire and 2.7% W−1 for the straight nanowire, respectively.
Fig.3: Sample of suspended AlGaAs nanowires used for directionally phase matched SHG.
Fig.4: Experimental and calculated SHG efficiency curve with a modal-phase-matched straight waveguide (black lines) and snake-shaped waveguide (red lines).
[Par17] M. Parisi, N. Morais, I. Ricciardi, S. Mosca, T. Hansson, S. Wabnitz, G. Leo, and M. De Rosa, J. Opt. Soc. Am. B 34, 1842 (2017).
[Mor17] N. Morais, I. Roland, M. Ravaro, W. Hease, A. Lemaître, C. Gomez, S. Wabnitz, M. De Rosa, I. Favero, and G. Leo, Opt. Lett. 42, 4287 (2017).
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