1. Introduction

The ${\chi }^{(2)}$ nonlinear photonic crystal (NPC), namely the two-dimensional (2D) periodically poled nonlinear optical crystal has attracted great interest since first introduced by Berger [1].

Usually it can supply several reciprocal vectors to ensure the quasi-phase-matching (QPM) requirements in nonlinear optical interactions following either a collinear or noncollinear geometry, therefore the key advantage of such materials lies in the fact that it can provide multiple-beam or multiple-frequency generation through concurrent QPM processes. Recently, concurrent QPM parametric downconversion (PDC) processes have been paid great attention since it brings the fundamental concerns in the mutual coherence between multiple PDC processes which can further be adopted to engineer multiple parametric beams and new types of photonic path-entanglement. Liu and Kung [2] first studied the coherent effect in concurrent PDC processes and prove that in some specific optical parametric amplification (OPA) process, the parametric gain can be competitive with one-dimensional structure through simultaneous utilizing several reciprocal vectors. Afterwards, multiple-beam PDC processes were demonstrated experimentally among which the common-signal or common-idler case was specified [3–5]. The angular detuning of such process was also observed [3–5]. Meanwhile in quantum optics, people have utilized such concurrent processes to engineer path-entanglement at single photon level in a compact and post-selection free way [6–9].

In this paper, the concurrent dual-PDC processes in a two-dimensional (2D) hexagonal periodically poled lithium tantalate (HexPLT) crystal is investigated. We made quantitive measurements on the conversion efficiency of dual-PDC processes under different spatial configurations, demonstrating the coherent enhancement when two PDC processes share a common-parametric beam. The spectrum and emitting angle properties of both degenerate and non-degenerate dual-PDC processes are studied by tuning the working temperature, during which a beamlike parametric output is obtained. Our results can further stimulate the design for the generation of multiple parametric beams and also shed light on the engineering of compact and high-quality beamlike entangled photon pairs based on concurrent QPM PDC processes.

2. Experimental setup

The experimental configuration is shown in Fig. 1. The 532 nm pump with a 20 ps pulse width, 1 nm linewidth and 10 Hz repetition rate is generated from a high energy picosecond Nd:YAG laser. The maximum pulse energy is 33 mJ. The pump beam is focused by a 350mm-focal-length lens to an elliptical cross-section, with 1/e²-radii of 115 $\mu m$ and 125 $\mu m$ in the lateral and vertical directions, respectively. In the 2D HexPLT, the pump beam is converted into the signal and idler beams ensured by a pair of reciprocal vectors under a symmetric QPM PDC configurations. After passing through the crystal, the pump beam is eliminated by a high reflection mirror and further suppressed by a narrowband interference filter centered at the parametric beam generated by the PDC process. A sensitive CCD camera is placed on the back focal plane of a 50mm-focal-length lens to capture spectrum images of the generated beams.

 

Fig. 1 Experimental setup used for optical parametric downconversion processes in 2D HexPLT. F_1, 700 nm high pass filter; HWP, half wave plate; PBS, polarization beam splitter; M, mirror; S, pinhole; L, lens; F₂, 532 nm HR, 1064 nm HT; F₃, narrowband filter centered at 1064 nm for the degenerate dual-PDC processes. The inset is a micrograph of the 2D HexPLT.

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3. Degenerate dual-PDC processes

The 2D HexPLT sample used in our experiment is fabricated by electric field poling technology [10,11]. The dimensions of the wafer is $15mm(x)\times 8mm(y)\times 0.5mm(z)$. The inset in Fig. 1 shows a micrograph of the etched domain structure with the structure parameter $a=7.507\mu m$, the duty cycle $r/a\approx 28\%$ (r is the radius of round domain-inverted areas). To ensure higher conversion efficiency, the maximum nonlinear coefficient d₃₃ is hired which leads to the type-0 nonlinear process $e\to e+e$. For the desired frequencies we design the domain structure to satisfy two concurrent type-0 processes, in which both energy and momentum conservation laws should be satisfied, as shown by Eq. (1).

In this experiment, the pump beam propagates along $\widehat{x}$-axis and its polarization direction is along the $\widehat{z}$-axis of the crystal. By simply tuning the temperature, different QPM configurations can be observed. Figures 2(a) and 2(b) illustrate the coherent and incoherent dual-PDC configurations, respectively. At 153.8°C, the dual-PDC processes share a common 1064 nm beam, resulting twin noncollinear 1064 nm parametric beams aside the pump by $\pm {2.2}^o$ as shown in Fig. 2(a). The inset is the captured spatial photograph. The incoherent dual-PDC processes happen when the temperature is tuned away from 153.8°C. At 176°C specific incoherent dual-PDC processes are observed. In this case, the signal and idler 1064 nm parametric beams are collinear but both slightly tilted to the pump as shown in Fig. 2(b) with an intersection angle of $\pm {1.1}^o$. The spatial distribution is captured by a sensitive CCD. In this case, the parametric beam exhibits a well-defined beamlike profile.

 

Fig. 2 (a) At 153.8°C, the dual-PDC processes share a common parametric beam paralleled to $\widehat{x}$-axis, meanwhile the other parametric beam slightly tilts to the pump at $\pm {2.2}^o$. The above is the spatial distribution shot by a CCD camera placed at the focal plane of a 50mm convex Lens. (b) At 176°C, the degenerate 1064 nm parametric beams are collinear, both slightly tilted to the pump at $\pm {1.1}^o$. The RLVs ${\overrightarrow{G}}_{1,0}$ and ${\overrightarrow{G}}_{0,1}$ can be expressed as ${\overrightarrow{G}}_{0,1}={\overrightarrow{G}}_{1,0}=4\pi /(\sqrt{3}a)$ (oriented $\pm {30}^o$ with respect to $\widehat{x}$-axis).

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We examined the output energy for coherent and incoherent dual-PDC processes. At 153.8°C, the coherent dual-PDC processes are observed with a linewidth of 11 nm (FWHM)and a pump threshold of ~0.5 GW/cm². At 176°C, a much higher intensity of the pump is required to produce the twin beamlike 1064 nm beams. The output energy of multiple 1064 nm parametric beams is recorded in Fig. 3(a) under different temperatures. The output energy reaches the highest value of $8.3\mu J$ when the temperature increases to around 153.8°C, corresponding to a conversion efficiency of 13% (loss of mirror’s reflection has been takeninto account). When the temperature is tuned away from 153.8°C, the parametric energy slowly decreases. At 176°C, the conversion efficiency was obtained to be nearly 0.14%.

 

Fig. 3 (a) The output energy of multiple parametric beams after two optical IF filters centered at 1064 nm as the temperature is varied. The largest conversion efficiency is observed near 153.8°C. (b) The emitting angle of the parametric beams versus the temperature.

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These results provide a solid evidence for the coherent enhancement of dual-PDC processes when they share a common parametric beam. The common-beam supplies as the cross-seeding for the dual-PDC processes and gain a coherent exchange among them, which effectually ensures a higher parametric gain for both signal and idler beams. The external angles of 1064 nm parametric beams are also recorded in Fig. 3(b), showing an interesting evolution of spatial form of parametric 1064 nm beams, which exhibits either beamlike two-port output (at 176°C), three-port output (at 153.8°C), or even four-port output (at 150°C).

Here it is worth noticed that if we remove the 1064 nm IF filter, when the temperature is increasing above 153.8°C, the nondegenerate dual-PDC processes is observed instead. The dual-PDC processes share the common-idler collinearly with the pump, while the dual signal beams emit noncollinearly with the pump. In this situation, the two PDC processes are also coherent, thus yielding a high efficiency compared with the incoherent degenerate process at the same temperature. This is considered as another evidence for the coherent enhancement. When the temperature is set around 176°C (Fig. 2(b)), the 1064 beams are weak and can hardly be captured when utilizing a narrowband 1064 nm IF before the CCD camera. But, when after removing the 1064 nm IF, spectrum analysis indicates that under this temperature there exists strong dual-PDC processes of $532nm\to 971nm+1176nm$. This process achieves a much higher conversion efficiency of 8% than the degenerate case (0.14%).

4. Nondegenerate dual-PDC processes

We designed another 2D HexPLT sample for examining the nondegenerate dual-PDC processes. The HexPLT used in this experiment has a structure parameter $a=9.950\mu m$. Again ${\overrightarrow{G}}_{0,1}$ and ${\overrightarrow{G}}_{1,0}$ are involved in the dual-PDC processes, ensuring a pair of $532nm(e)\to 680nm(e)+2444nm(e)$ taking place simultaneously. Theoretically, the QPM geometry is designed to be common-idler and common-signal configuration at 117°C and 175°C, respectively. At 180°C, the signal and idler beams are designed to be collinear but both noncollinear with the pump, namely a specific incoherent dual-PDC configuration. The experiment setup is similar with the degenerate case except that a long wave pass filter with a cut off wavelength at 650 nm is employed to eliminate the pump beam after the HexPLT.

Experimentally we found that the dual-PDC processes with the common-idler are dominant as shown in Fig. 4(a). The spatial distribution is recorded in the inset. When tuning the temperature, we recorded the spectra of the noncollinear signal beams as shown in Fig. 4(b). From 110°C to 200°C, the signal wavelength changes from 686 nm to 677 nm, corresponding the idler within 2370 nm and 2484 nm, while the external angle of signal beams is almost a fixed value of $\pm {2.41}^o$. These results consist well with the theoretical design of $\pm {2.25}^o$. When the pump energy is 70 $\mu J$ (we find the pump energy affects the output spectrum), the FWHM linewidth of the signal is 2.1 nm during the varying of temperature, meanwhile the corresponding linewidth of the idler is calculated to be 27.1 nm for $532nm\to 680nm+2444nm$ at 168°C.

 

Fig. 4 (a) The common-idler configuration of dual-PDC processes utilizing the RLVs ${\overrightarrow{G}}_{0,1}$ and ${\overrightarrow{G}}_{1,0}$, the right hand is the spatial distribution after the long wave pass filter when the temperature reaches 150°C. (b) Temperature dependence of signal and idler wavelengths. The signal wavelength is recorded by a UV-Vis spectrometer. The corresponding idler wavelength is obtained by the conservation law of energy.

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As mentioned before, dual-PDC processes’ gain benefits from the coherent enhancement effects, caused by either sharing the common-signal or common-idler. But the common-signal case corresponds to a larger noncollinear angle between the pump and idler beams, thus a shorter spatial walk-off length, therefore the parametric gain will be lower compared with the common-idler case. This will be more evident when the signal and idler frequencies are far from degenerate. Actually, we observed a similar phenomenon in the situation of degenerate dual-PDC processes as introduced in section 3.

5. Conclusion

In conclusion, we examined the concurrent dual-PDC processes in a two-dimensional hexagonal poled lithium tantalate (2D HexPLT) crystal. The conversion efficiency is measured to be enhanced when the two PDC processes share an identical parametric beam. The coherent enhancement between PDC processes is convinced. We also study the spectrum and emitting angle properties of both degenerate and non-degenerate dual-PDC processes by tuning the working temperature, during which a beamlike parametric output is obtained. These results will stimulate the design for high-gain coherent generation of multiple parametric beams and also paves a way for the design of compact path-entanglement based on concurrent QPM spontaneous PDC processes. In spontaneous parametric regime, due to the low pump power, the parametric gain is low and the signal or idler beam is at the single photon level. In this case, the spatial form of parametric beams will be different [7] with the stimulated regime in this work.