1. Introduction

Integrated sources of entangled photon pairs are a primary necessity for quantum optics applications, and in particular in the telecom band, where they would constitute building blocks of quantum information and communication protocols. Spontaneous parametric down-conversion (SPDC) is currently the most widely used process to generate such quantum photon pairs. Up to now, room-temperature intracavity SPDC has been reported in diode lasers with pump degeneracy around 970 nm [1], while entanglement has been demonstrated in light emitting diodes only at cryogenic temperature [2]. Therefore, today the fabrication of an electrically-pumped SPDC quantum photon source operating at room temperature in the telecom range constitutes a high-potential and challenging goal.

In this context the AlGaAs platform provides great benefits in terms of: 1) large second order nonlinearity; 2) low losses; and 3) mature fabrication technology. However, since AlGaAs is neither birefringent nor ferroelectric, phase matching (PM) is not trivial and requires ad hoc schemes to compensate for the material dispersion. Among the most promising PM techniques, like modal phase matching MPM [1] and quasi-phase matching (QPM) [3], form birefringence phase matching (FBPM) [4] relies on optical heterostructures where thin aluminum oxide (AlOx) layers are intertwined with AlGaAs layers.

While three-wave mixing (TWM) experiments around 1.55 μm have been thoroughly investigated in Bragg-Reflector Waveguides (BRWs), e.g. second harmonic generation (SHG) [5], sum frequency generation (SFG) [6], and difference frequency generation (DFG) [7], the performance of FBPM has only been assessed via SHG [8,9]. In [9], by using a waveguide designed for degenerate SPDC at 1.55 μm, we demonstrated SHG results that are encouraging towards an integrated source in the telecom range. This motivated us to accurately characterize the off-degeneracy dispersion and conversion efficiencies, as well as the tunability of such device.

In this paper we report on FBPM nearly-degenerate type-I TWM around 1.55 μm, namely SFG and DFG, in the same AlGaAs/AlOx waveguide of [9], and we compare our results to recently published figures obtained in BRWs. In the following, after a quick description of the waveguide, we present propagation losses measurements in Section 2, while we devote Section 3 and 4 to SFG and DFG studies, respectively. Finally, Section 5 contains the conclusion and a few perspectives.

2. Design and linear characterization

Our samples were grown by molecular beam epitaxy on (001) GaAs, with the following vertical layout: 1 μm Al_0.8Ga_0.2As / 4 × (37.5 nm Al_0.98Ga_0.02As / 166 nm Al_0.8Ga_0.2As) / 8 × (37.5 nm Al_0.98Ga_0.02As / 166 nm Al_0.25Ga_0.75As) / 4 × (37.5 nm Al_0.98Ga_0.02As / 166 nm Al_0.8Ga_0.2As) / 30 nm GaAs (cap layer). They were then processed into 500 μm long, ~4 μm wide and ~3.7 μm deep wet-etched ridge waveguides, with the subsequent selective oxidation of Al_0.98Ga_0.02As layers. While the related modeling and fabrication have already been detailed in [9], let us just recall here that this design mainly aims at optimizing the oxidation kinetics with respect to [8], via the adoption of Al_0.98Ga_0.02As layers of equal thickness.

Since optical losses play a major role in all guided-wave PM schemes proposed so far in the AlGaAs platform, we have performed systematic measurements to assess their wavelength dependence in our device. Their results are showed in Fig. 1 . For wavelengths above 1.1 μm (TE modes around 1.55 μm in our PM scheme) Fabry-Perot fringes measurements [10] show that propagation losses are quite low (α_TE = 1.60 ± 0.14 cm⁻¹ at 1.58 μm) and decay following an inverse power law (Rayleigh-like scattering). On the other hand, for wavelengths below 1.1 μm (TM modes around 775 nm), transmission measurements reveal that propagation losses are much higher (α_TM = 151 ± 12 cm⁻¹ at 775 nm) and their decay follows an exponential curve (Urbach’s tail absorption). The transition between these two regimes takes place at a photon energy corresponding to about 65% of Al_0.25Ga_0.75As gap energy (the waveguide core material) [9].

 

Fig. 1 Propagation losses vs. wavelength, fitted by the decaying exponential exp[-λ/76.2] (the inverse-power law λ^-1.6) for short (long) wavelengths, respectively.

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This level of pump losses is currently the limiting factor of our TWM experiments.

3. SFG experiment

In our type-I SFG experiment, two TE-polarized pumps (P1, P2) at wavelengths (λ_P1, λ_P2) around 1.55 μm are mixed to generate a TM-polarized sum frequency (SF) photon at wavelength λ_SF, so that 1/λ_SF = 1/λ_P1 + 1/λ_P2.

Two external-cavity diode lasers (ECDLs) were used to perform the SFG experiment. Their TE-polarized beams were combined with a 50/50 beam-splitter (BS) and collinearly injected into the waveguide through a × 60, 0.85 NA microscope objective. Wavelengths were monitored by using the second output port of the BS and an optical spectrum analyzer. The SF signal was collected at the output facet with a similar microscope objective, focused on a silicon photodiode and detected with a lock-in amplifier.

The spectrum shown in Fig. 2a was obtained by monitoring the SF power with λ_P1 = 1543.0 nm kept constant while scanning λ_P2. The internal powers of the two pumps were also kept constant, and estimated at P_P1 = 1.37 mW and P_P2 = 194 μW from the values measured with a power-meter placed before the input objective, by taking into account the objective transmission, the facet reflectivity and the overlap integral between the laser beam and the guided modes. The experimental data (dots) show a smooth PM resonance modulated by high frequency fringes. According to [11], the high frequency factor stems from interference of the P2 beam upon multiple reflections on the waveguide facets, while the envelope is well fitted by a Lorentzian and deviates from the ideal sinc curve due to optical propagation losses of the generated field [12].

 

Fig. 2 a) SF power vs. P2 wavelength: experimental data (dots), theoretical fit (thin line) after [11], and extracted single-pass PM curve (thick line). b) Single-pass SF power at PM vs. P1 power.

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Figure 2b shows the single-pass SF power at PM as a function of the power of P1, while the power of P2 was kept constant (P_P2 = 194 μW). The linear dependency matches the theoretical predictions. Moreover, from the slope of the linear fit, we calculate a conversion efficiency of 2.7%W⁻¹, which corresponds to a normalized conversion efficiency of 1080%W⁻¹cm⁻². This result is very close to the one reported in [9] for SHG (i.e. degenerate SFG) on the same waveguide, which is consistent with the fact that the SFG was measured near degeneracy.

From the FWHM of Fig. 2a, we readily extract the SF losses at 773.3 nm: α_TM = 200 cm⁻¹, in fair agreement with the independent estimate reported in Section 2.

If we compare the above results to [6], we see that even if our losses are 40 times larger (200 cm⁻¹ vs. 5 cm⁻¹), our nonlinear efficiency is about 3 times higher (1080%W⁻¹cm⁻² vs. 298%W⁻¹cm⁻²). This consideration suggests that our approach would hugely benefit from even small loss reductions, and it motivates our current effort to further investigate the origin of such losses.

4. DFG experiment

In order to determine the experimental tuning curve of our TWM process and estimate its parametric gain, we have performed a DFG experiment. The DFG process involves the interaction of a pump mode (P) at wavelength λ_P with a seed (S) at wavelength λ_S, generating a difference frequency (DF) field at wavelength λ_DF. Note that the seed is also amplified by the parametric gain. In this case, the energy conservation reads: 1/λ_DF = 1/λ_P - 1/λ_S.

Figure 3 shows a sketch of the experimental setup: the pump is provided by a TE-polarized CW Ti:Sapphire laser around 775 nm. The first half-wave plate followed by the TEpolarizer sets the pump power without changing the laser current, whereas the second half-wave plate rotates the polarization from TE to TM, accordingly to our type-I PM scheme. The TE seed is provided by a fibered ECDL tunable between 1490 and 1600 nm; its output can be amplified with an Er⁺-doped fiber amplifier (EDFA) to perform the parametric gain measurement. Pump and seed beams are combined and collinearly aligned with a 50/50 BS, then they are chopped and coupled in (and out of) the guiding ridge through two × 40, 0.65 NA microscope objectives. At the waveguide output, we either monitor the coupling of the guided modes with a camera, or we send them through a spectrometer. At its exit port, the TE signal is filtered with a polarizer and focused on an InGaAs photodiode, whose photocurrent is sent to an adjustable pre-amplifier and a lock-in.

 

Fig. 3 Schematic DFG setup: FI, Faraday Isolator; FPC, fiber polarization controller; M, mirror; FM, flip mirror; L, lens; λ/2, half-wave plate; BS, beam splitter; PD, photodiode; C, chopper.

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Figure 4a reports a typical DFG spectrum for a pump wavelength set at degeneracy (λ_P = 773.2 nm). The seed corresponds to the peak at 1559.0 nm, while the DF signal is at 1534.0 nm. The seed wavelength was chosen so to optimize the visibility of the DF peak, which otherwise would have been masked by the non-uniform background of EDFA amplified stimulated emission. The peak located at 1546.4 nm is unambiguously attributed to the second order of the TM-polarized pump diffracted by the grating of the spectrometer. Our DFG study consisted of the acquisition of a few spectra of this type, for different wavelengths and/or powers of the injected beams.

 

Fig. 4 a) Normalized power spectral density measured at the waveguide output facet. The DF (seed) peak appears at 1534.0 nm (1559.0 nm). The central peak at 1546.4 nm is the residual 2nd-order diffraction of the pump. b) External DF-to-seed power ratio vs. external pump power: measured values and linear fit.

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Let us recall that, in the un-depleted pump regime, the parametric gain at PM is G ≈(gL)² [12], and it can be expressed as G ≈P_DF/P_S close to degeneracy [13]. In our case, G can be directly obtained as the ratio $P_{DF}^{ext}/P_S^{ext}$ of the DF and S peak values provided by each spectrum, because the output coupling is simultaneously optimized for both fields.

In Fig. 4b we show $P_{DF}^{ext}/P_S^{ext}$at PM versus the external pump power_{$P_P^{ext}$}, for λ_S = 1559.0 nm, λ_P = 773.2 nm (corresponding to the degeneracy point) and fixed seed power. The linear fit confirms that G is proportional to the pump power. It should be noted that both the pump and seed beams are injected into the waveguide with the same microscope objective, thus DFG optimization results from a compromise between the optimal coupling at λ_P and λ_S. Since we cannot accurately estimate the in-coupled pump power, the slope of the fit provides us directly with an “external” DFG efficiency ${\eta }^{ext}=P_{DF}^{ext}/L^2{P}_P^{ext}{P}_S^{ext}=9.7{\text{\%W}}^{\text{-1}}{\text{cm}}^{\text{-2}}$. Such external efficiency, which underestimates the more common internal efficiency, is two orders of magnitude higher than the external efficiency reported in [7] for CW type-II DFG. This is due to an inherently larger nonlinear overlap integral in our FBPM waveguide, stemming from the exploitation of fundamental modes instead of Bragg modes.

In Fig. 5a we report a few spectra obtained at slightly different pump wavelengths by optimizing the DF peak amplitude via an adjustment of λ_S, all at constant power. The corresponding triplets (λ_S, λ_DF, λ_P) fulfill energy conservation at PM and are also reported in Fig. 5b, where experimental data are in good agreement with the simulated tuning curve (dashed line). Due to the strong dispersion arising from the proximity to the bandgap, small shifts of λ_P from degeneracy require a large DF/seed wavelength separation to fulfill the PM condition. Indeed, Fig. 5b shows that a pump detuning as small as 5.2 nm allows to cover a broad wavelength range (570 nm), which constitutes a remarkable benefit from a practical standpoint (e.g. for a largely tunable integrated source in the near-IR).

 

Fig. 5 a) Normalized DF spectra for three different seed wavelengths (the seed peaks are slightly clipped due to the lock-in finite dynamic range). b) Tuning curve: experimental data (dots) and theoretical prediction (dashes-dots).

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Please note that the dotted lines surrounding the tuning curve represent the numerically calculated FWHM of the DFG phase-matching curve, which widens near degeneracy.

5. Conclusion

In this paper we investigated nearly-degenerate CW three-wave mixing in FBPM selectively oxidized AlGaAs waveguides. The combined study of SFG and DFG allowed their full characterization in terms of tunability and parametric gain. We demonstrated a huge tunability of 570 nm and high off-degeneracy conversion efficiencies: η = 1080%W⁻¹cm⁻² for SFG (internal value), and η^ext = 9.7%W⁻¹cm⁻² for DFG (external value). These results compare favorably with the current state of the art and confirm that FBPM in AlGaAs waveguides is a competitive technique towards an SPDC-based integrated telecom source. While oxidation induced optical losses still constitute a bottleneck, the present work allowed us to fully reveal their spectral dependence, thus providing a solid starting point for their minimization.