1. Introduction

Optical parametric oscillation (OPO) provides easy access to specific wavelength ranges from fixed-wavelength lasers [1,2]. The quasi-phase-matching (QPM) technique, which permits the use of materials with high nonlinearity, realize efficient OPOs with low oscillation thresholds [3,4]. However, efficient QPM could introduce unwanted parasitic processes into OPO through second-harmonic generation (SHG) and sum frequency generation (SFG) from the pump and the signal (idler), and these parasitic processes lead to inefficient energy transfer and also trigger catastrophic damage. Parasitic processes can result from both higher order QPM and random QPM due to the duty ratio errors [5,6].

In pulse-operated wavelength conversion, catastrophic damage is a factor that limits both the output power and the lifetime of devices. For 1 μm-wavelength pumped OPO, significant parasitic green light resulting from SHG is usually observed [7–9], and this parasitic green light increases the risk of damage due to green-induced infrared absorption (GRIIRA) [10–12]. The damage threshold becomes much lower for pulsed operation when parasitic green light coexists [13]. The reduction of parasitic second-harmonic (SH) power is a key issue for increasing the damage threshold of an OPO device.

Intensity modulation of interacting waves during wavelength conversion is enabled by engineering QPM structures – such as phase shifters or aperiodic domains – to control the relative phase between interacting waves. Intensity modulation via a phase shifter in QPM SHG was already proposed in the 1990s [14,15] and was demonstrated in the 2000s [16,17]. A phase shifter can be made to primarily affect undesired SHG while having little effect on OPO thanks to the difference in coherence length. Suppression of χ⁽²⁾−cascaded 3ω generation was also proposed by domain control to measure the pure χ⁽³⁾ effect [18]. In this paper, we propose a special QPM structure, and we subsequently demonstrate suppression of parasitic SHG in OPO by selectively controlling the relative phase in the SHG process without degrading OPO performance.

2. Principle of parasitic-light suppression (PLS)

Here, we propose a special periodic pattern of domains, the parasitic-light suppressed (PLS) structure. The PLS structure includes π-phase shifters for the SH wave between periodically-poled-domain clusters. The phase shifters have the same length as the coherence length, lc ( = π/Δk) of SHG, where Δk is the phase mismatch between fundamental and SH waves. Therefore SH wave experiences a phase slip of π between the clusters. Compared with OPO, parasitic SHG is much more sensitive to the phase shifter because the coherence length of SHG is four times shorter than the coherence length of OPO. In this scheme, domain clusters work as phased arrays with a π phase slip.

The proposed PLS structure is depicted in Fig. 1. The arrows in the domains represent the direction of spontaneous polarization. The shaded domains are the phase shifters. This PLS structure can be represented as follows:

 

Fig. 1 Schematic of the proposed parasitic-light suppressed (PLS) structure.

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The output power of SHG and OPG in the PLS structure can be expressed as follows:

We numerically simulated the effect of PLS structures. Figure 2 shows the calculated fourth-order QPM SHG and the first-order OPG intensities for a different number of clusters (S = 1, 2, 5, 25) with a 1.064-μm pump. Here, $\tilde{C}(\Delta k)$ is transferred to $\tilde{C}(\lambda )$ by calculating Δk for the SHG and OPG processes with material dispersion [19]. In the simulation, we set S, N, R_P, Λ, and Δl to the following values:$S\times N=250$, R_P = 0.625 (or 0.375) for maximum fourth-order QPM SHG, Λ = 32 μm (corresponding to OPG), and Δl = 4 μm (corresponding to SHG). The length of a 4-μm phase shifter is the coherence length of SHG with a 1.064-μm fundamental in 1-mol% Mg-doped lithium tantalate (MgSLT) crystals at 30°C [19]. For SHG [Fig. 2(a)], the QPM SH intensity at 1.064 μm is modulated and eliminated by one phase shifter (S = 2). When the number of clusters increases, the QPM SH peaks are more separated from the fundamental wavelength. However, QPM signal intensity in OPG is slightly modulated by one phase shifter (S = 2), as shown in Fig. 2(b). With an increasing number of clusters, the QPM signal peak retains its intensity and is red-shifted due to the spacing of the phase shifters. It is notable that the total crystal length L corresponds to $S\cdot N\cdot \Lambda +(S-1)\cdot \Delta l$, and a larger cluster number S results in a longer total length increased by a factor of $(S-1)$. If the total lengths of both the periodic device and the PLS structure are identical, the PLS structure has lower efficiency than the periodic device’s efficiency due to the reduced effective length resulting from the additional phase shifter spacing. For S = 25, the broadening in the peak in Fig. 2(b) arises from only the dispersion of the material not the effect of the PLS structure.

 

Fig. 2 Calculated fourth-order SH intensity (a) and first-order signal intensity in OPG (b) with pump wavelength of 1.064 μm for different number of clusters, S = 1, 2, 5, and 25, in the PLS structure. Parameters: R_p = 0.625, Λ = 32 μm, Δl = 4 μm.

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3. Experiments and discussion

To prove this principle of parasitic light suppression, we measured SHG and OPO performance in periodic devices and PLS structures. We used 1-mol% MgSLT in device fabrication, having fascinating features such as a high damage threshold and high thermal conductivity [20]. An average period of 31.8 μm was defined for a 1.7-μm emission wavelength at room temperature. For PLS structure, 4.0-μm-long phase shifters were built between clusters with periodic domains for green suppression. The clusters with five and four periods per cluster are referred to as PLS 1 and PLS 2, respectively. The devices were fabricated using electric field poling with a patterned photoresist and liquid electrodes. The poling process was monitored with an electric current and was terminated after each pulse by integrating poling currents, where the integrated charge for each pulse was set to 0.5 μC. This multi-pulse poling process produced 2-mm-thick devices with a length of 35 mm [21].

We examined parasitic green power for single pass SHG in two periodic devices (periodic 1 and 2) and two PLS devices (PLS 1 and 2). We used a pulsed Nd:YVO₄ laser (repetition rate: 3 kHz, pulse width: 25 ns) with a beam waist of 100 μm as the pump. The measurements were performed at 30°C with an accuracy of 0.1°C. The origin of parasitic green light is SHG with a pump wavelength of 1.064 μm. We observed a strong green power of >16 mW in periodic device 2, as shown in Fig. 3. The normalized conversion efficiency, ${\eta }_{norm}^{SHG}$ ( = P_SH/P_F²) was 3.4%/W. Corresponding to the intensity of 720 kW/cm², such green power caused catastrophic damage to periodic device 2 owing to GRIIRA. The strong green power was caused by fourth-order QPM SHG because the domain length of 15.9 μm approaches four times the coherence length of ~4 μm for SHG. Even ordered QPM has been observed for an uneven or fluctuating duty ratio. Compared with lower order QPM, higher order QPM is more sensitive to duty ratio errors because m^th-order QPM has m numbers of optimum duty ratios and a relatively larger variation in the duty ratios on the scale of its coherence length.

 

Fig. 3 Comparison of parasitic green SH powers in two periodic devices and two PLS devices. Solid line: quadratic dependence of SH power.

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However, compared with the periodic devices, the two PLS devices presented lower output power. For PLS 1, the normalized conversion efficiency was 0.24%/W, and up to the maximum pump power, no damage appeared. The conversion efficiency in PLS 1 was 14 times smaller than the conversion efficiency of 3.4%/W in periodic device 2. Such a reduction in parasitic green light is attributed to the QPM SH peaks’ shift from the pump wavelength, as shown in Fig. 2(a).

The above SH response in complex QPM structures can be examined using linear diffraction methods. The SHG wavelength response and far-field diffraction pattern correspond to the Fourier transformed pattern for the QPM domain structure [22,23]. Figure 4 shows a typical measured far-field diffraction pattern from PLS 1, where chemical etching was used to make a relief grating on the original –z surface of the sample. We used a He-Ne laser (λ = 543.5 nm) with a beam diameter of 820 μm to illuminate 5~6 clusters including 4~5 phase shifters in PLS 1. In Fig. 4(a), the measured first-order far-field diffraction pattern has only a single peak, which reflects the OPG wavelength band ($lc\approx 16\mu m$). However, the measured fourth-order far-field diffraction pattern, corresponding to fourth-order QPM SHG ($lc\approx 4\mu m$) has two separate peaks, as shown in Fig. 4(b). Although the proposed PLS model is based on uniform domain structures producing a deterministic phase of SH waves, the assumption is rational if the cluster-to-cluster fluctuation of integrated phases is small enough since the distances between clusters are defined by photolithography. Nevertheless, the conversion efficiency of 1.3%/W in periodic device 1 was similar to the conversion efficiency of 1.1%/W in PLS 2. The parasitic SH power can be suppressed by decreasing domain fluctuations, and the effect of the PLS structure can be boosted by decreasing fluctuations.

 

Fig. 4 Captured far-field diffraction pattern and intensity profile at a local part of PLS 1. Clean separation of 4th order peak is observed as predicted in Fig. 2(a).

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We also examined the devices’ OPO performance in a singly resonant OPO cavity. A Nd:YVO₄ pump beam (repetition rate: 10 kHz, pulse width: 35 ns) was focused to a diameter of 200 μm, which corresponds to a confocal length of more than 124 mm. The input and output couplers with reflectances of 99.5 and 96% (wavelengths: 1.5-1.85 μm) were separated by 70 mm in a linear cavity. The radius of curvature for the input and output couplers were 100 mm, which thereby enabled a stable cavity. The 35-mm-long devices were uncoated and experienced Fresnel loss at both input and output surfaces.

All the devices exhibited stable oscillation at 30°C, with slope efficiencies around 55% as shown in Fig. 5. The parasitic green light was weaker in OPO than OPG due to efficient energy transfer from pump to signal and idler. The periodic devices showed 59.5% and 57.9% slope efficiencies while the efficiencies for the PLS devices were 53.9% and 54.1%. The maximum output powers were almost the same around 3.5 W for total output power of the signal (around 1.7 μm) and the idler (around 2.8 μm). The observed performance is comparable to previously reported results [7].

 

Fig. 5 Comparison of OPO performance in two periodic devices and two PLS devices. Solid line: linear fitting for slope efficiency.

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4. Conclusion

We demonstrate a novel concept to suppress unwanted parasitic interaction in QPM-based nonlinear wavelength conversion. The phase shifter inserted between domain clusters reduced parasitic green power. The reduction in OPO slope efficiency was less than 10% of original efficiency. We believe that this concept could help to increase the damage threshold and will be applicable to other nonlinear processes in QPM devices.