1 Introduction

High-power, coherent, dual-wavelength light sources are of significant interest for many scientific and technological applications such as spectroscopy, frequency metrology, differential absorption lidar, and nonlinear frequency conversion [1–5]. In particular, the ability to produce two closely spaced tunable wavelengths is important for the generation of THz radiation [3–5]. Optical parametric oscillators (OPOs) are recognized as one of the most versatile and viable sources of tunable coherent radiation from the ultraviolet to mid-infrared [6, 7]. However, the generation of two independent and arbitrarily tunable signal and idler wavelengths from a single device is constrained by energy conservation and phase-matching conditions. Moreover, in a conventional OPO, the closest signal and idler wavelength pair can be generated only near degeneracy, but in practice this is challenging due to instabilities associated with double resonance. In earlier reports, various schemes based on dual-crystal parametric amplification, double-pass in a single crystal and pump-enhanced OPO have been demonstrated to achieve dual-wavelength generation [3–5]. However, in these configurations, the effects of pump beam quality degradation on conversion efficiency, thermal effects, and damage to the nonlinear crystal can be limitations. Alternatively, one may achieve two arbitrarily tunable signal (idler) wavelength pairs by using the outputs from two independent and identical OPOs. While this may be a viable approach in pulsed OPOs, in continuous-wave (cw) regime the technique can be prohibitive because of the extremely low parametric gain, requiring very high input pump powers to each OPO for the generation of sufficiently high external cw powers for subsequent experiments such as difference-frequency-mixing for THz generation. Recently, to overcome these limitations, we developed a dual-wavelength cw OPO incorporating two nonlinear crystals, generating signal (idler) pairs with high intracavity (extracavity) power using a single pump laser of moderate power, and demonstrated signal frequency separation down to 0.55 THz. In this scheme, the minimum wavelength separation is limited by the parametric gain overlap of the nonlinear crystals [8]. Here we report an alternative architecture for a two-crystal cw OPO that avoids coherent coupling between the two resonant waves in close proximity, thus permitting the generation of signal (idler) wavelength pairs with indefinitely close separation. The technique is based on the use of an anti-resonant ring (ARR) interferometer to couple two cw OPO cavities. It also similarly offers high cw intracavity powers using a single moderate power pump laser, which makes the technique efficient and practical for intracavity cw frequency mixing and cw THz generation.

The ARR interferometer is a well-known two-port optical element that was introduced a century ago [9] and has been suggested for many applications in the context of lasers [10, 11]. In recent years, we have also shown the potential of the ARR interferometer for a number of applications in OPOs [12–15]. The ARR consists of a beam-splitter (BS) and two high-reflecting mirrors, M′ and M″, as depicted in Fig. 1. In different configurations, we have demonstrated its use as an in situ optimum output coupler [12–14], as in Fig. 1a, and as a mode-locking element in combination with an electro-optic modulator (EOM) [15], as in Fig. 1b. Figure 1c shows the use of an ARR to couple two OPO cavities, thus providing high intracavity powers for both resonant wavelengths in the same direction, inside the ARR. Recently, we reported such an approach in femtosecond OPOs [16].

Fig. 1
figure 1

Schemes for using the ARR interferometer for applications in OPOs. a Variable output coupler, b mode-locker, c cavity coupler. The directions of the counter-propagating beams are shown

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Here we report the use of the ARR interferometer for dual-wavelength generation in cw OPOs, for the first time, providing two distinct signal (idler) wavelength pairs that can be independently and arbitrarily tuned to indefinitely close separation, through degeneracy, and beyond. We use the particular geometry of the ARR interferometer shown in Fig. 1c. Using two cw singly resonant OPOs connected with a common ARR interferometer, we generate signal waves with frequency separation of 0.8 THz, limited by measurement and show their overlap at 951 nm. The architecture provides high intracavity power at both signal waves within the ARR, while avoiding coupling between the two circulating fields.

2 Experimental setup

The configuration of ARR-coupled cw OPO is shown in Fig. 2. The experiment uses a single pump source, a 10 W cw green laser at 532 nm [17]. The pump radiation is divided into two beams (P1 and P2) using a combination of a half-wave plate (H1) and a polarizing beam-splitter (PBS), and the two beams then separately pump two OPOs (OPO-1 and OPO-2). The half-wave plates, H2 and H3, are used to control the pump polarization for phase-matching in the two nonlinear crystals, X1 and X2. The crystals are identical 30-mm-long MgO:sPPLT, each with a single grating period of Λ = 7.97 μm [18]. They are housed in separate ovens, whose temperature can be controlled from room temperature to 200 °C with a stability of ±0.1 °C. Using two identical lenses, L1 and L2 (f = 150 mm), we focused the pump beams to waist radii, w p1 ~ w p2 ~ 31 μm, at the center of X1 and X2. OPO-1 is configured in a standing-wave cavity comprising two concave mirrors, M1 and M2, with an ARR in the folded arm. Considering the higher pump threshold of a four-mirror x-cavity due to the use of an additional mirror, we have chosen a three-mirror v-cavity configuration for our OPO. The ARR consists of a BS and two plane mirrors, M3 and M4. OPO-2 is also configured in standing-wave v-cavity, identical to OPO-1, using two concave mirrors, M5 and M6, and shares the same ARR incorporated in the folded arm. However, unlike OPO-1, in order to integrate the ARR into OPO-2, we used three additional plane mirrors, M7–9, in the folded arm. All mirrors were highly reflecting for the signal (R > 99.7 % @ 840–1,020 nm) and transmitting for the pump (T > 98 % @ 532 nm) and idler (T > 97 % @ 1,100–1,400 nm), thus ensuring single-pass pumping and singly resonant signal oscillation in both OPOs. The total cavity length of OPO-1 is L OPO-1 = 106.6 cm, which is the sum of the standing-wave cavity length (2L linear-1 = 2 × 45.5 cm) and the length of the ARR (L ring = 15.6 cm), while for OPO-2, it is L OPO-2 = 2L linear-2 + L ring = 112.6 + 15.6 = 128.2 cm. The free spectral range (FSR) of OPO-1 and OPO-2 has been calculated to be 281 and 234 MHz, respectively. The BS is a UV-fused silica plate (12.5 mm diameter, 3 mm thick) with broadband coating over 700–1,100 nm, available in our laboratory. The half-inch diameter broadband BS used to construct the ARR in our experiment is shown in the inset of Fig. 3. In order to couple the two OPOs, using the ARR, while avoiding any perturbation in one due to the other, we arranged the incident angle (θ BS) on the BS for near-zero output coupling. In OPO-2, mirrors M8,9 were used to adjust the near-zero output coupling through the ARR. Thus, the ARR behaves as two interlaced, but independent mirrors, highly reflecting at signal wavelength for both OPOs.

Fig. 2
figure 2

Experimental setup of the ARR-coupled cw OPO. H 1–3 Half-wave plates, PBS polarizing beam-splitter, P 1 , P 2 pump beams, L 1–2 lens, M 1–9 cavity mirrors, X 1–2 MgO:sPPLT crystals, M dichroic mirrors, BS beam-splitter, λ 1s , λ 2s dual signal wavelengths leaked through M3, I 1–2 idler beams

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Fig. 3
figure 3

Transmission of the ARR interferometer as a function of BS angle. Inset Half-inch diameter broadband BS used for ARR

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3 Results and discussion

To determine near-zero output coupling angle for the BS, we initially characterized the ARR externally. As the 1st surface of BS faces OPO-1 and 2nd surface faces OPO-2, we performed the characterization consecutively in both directions, as perceived by the signal beams from the two OPOs. We measured the input power to the ARR and the output power from the ARR at different angles, θ BS, and calculated the transmission of the ARR, T ARR, at a fixed signal wavelength of 951 nm. Figure 3 shows the ARR transmission as a function of θ BS for both BS surfaces. With the 1st surface, the transmission remains minimum (T ARR = 0.3 %) at smaller angles of 5° < θ BS < 15°. With further increase of θ BS beyond 15°, T ARR increases to 3.3 % at θ BS = 35°. The transmission of the ARR with input from the 2nd surface at large angles (θ BS > 25º) is qualitatively the same as that with input from the 1st surface. However, in this case, the minimum transmission was measured to be 0.7 % for angles 5° < θ BS < 15°. The difference in the ARR transmission is attributed to the broadband coating only on the 2nd surface of the BS. Thus, we fixed θ BS = 12° for minimum transmission through both surfaces and incorporated the ARR inside OPO-1 and OPO-2.

It is interesting to note that for some applications, it would be required to insert a nonlinear crystal within the ARR, which may result in a change in the ARR transmission as a function of BS angles. In such cases, to obtain the near-zero output coupling, the external characterization of the ARR together with the nonlinear crystal would be helpful. The ARR, in addition, is inherently stable, as both the counter-propagating beams are affected in the same way, from any mechanical or temperature perturbations.

We optimized OPO-1 and OPO-2 to achieve equal idler powers of >1 W, while pumping simultaneously with pump power of 4.3 and 5.7 W, respectively. In order to demonstrate versatile tuning capabilities of the ARR-coupled cw OPO, we systematically temperature tuned each OPO and recorded the spectrum of the signal leaking through the ARR mirror (M3), where high-power, dual-wavelength operation is expected. OPO-1 is temperature tuned from T 1 = 110 down to 90 °C, while OPO-2 is tuned from T 2 = 90 up to 110 °C. The results are shown in Fig. 4. As evident, this systematic variation of the temperature enables smooth and continuous tuning of the resonant signal wavelengths with a frequency difference from 6.6 THz, indefinitely down, until they completely overlap and tune through degeneracy, up to 7 THz. At T 1 = 102 °C (λ 1s = 949.9 nm) and T 2 = 98 °C (λ 2s = 952.5 nm), the difference between the resonant signal frequencies is as low as 0.8 THz, limited by the measurement. The frequency difference is further reduced by decreasing T 1 toward 101 °C and increasing T 2 toward 100 °C, finally leading to two identical resonant signal wavelengths at 951 nm (T 1 = 101 °C, T 2 = 100 °C) oscillating independently in each OPO. The 1 °C difference in crystal temperatures to generate the same signal wavelength is mainly due to the small difference in design and calibration of the two ovens. Further decrease in T 1 and increase in T 2 lead to the crossover of the resonant wavelengths from the two OPOs, confirming arbitrary tuning enabled by the ARR coupling. As seen, the frequency difference between the resonant waves then increases from 1.8 THz (T 1 = 98 °C, T 2 = 102 °C) to 7 THz (T 1 = 90 °C, T 2 = 110 °C).

Fig. 4
figure 4

Signal spectra from the ARR-coupled dual-wavelength OPO at independently tunable crystal temperatures, T 1 and T 2

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Maintaining the crystal temperatures at T 1 = 101 °C and T 2 = 100 °C, we observed the spectrum of the resonant signal waves at degeneracy, where both OPOs generate the same signal wavelength (λ 1s = λ 2s = 951 nm), leaked through the same ARR mirror (M3), using a confocal Fabry–Perot interferometer (FSR = 1 GHz, finesse = 400). The results are shown in Fig. 5. By blocking P2 and operating OPO-1 at a pump power of 4.3 W, we recorded the typical fringe pattern of the transmitted signal, confirming single-frequency operation of OPO-1 with an instantaneous linewidth of ~20 MHz. Similarly, by blocking P1 and operating OPO-2 pumped at 5.7 W of pump power, we confirmed single-frequency operation of OPO-2 with a linewidth of ~20 MHz. We further recorded the instantaneous transmission spectrum of both waves together, using the same Fabry–Perot interferometer, and measured the frequency separation of ~220 MHz between the two signal waves relative to each other, as shown in Fig. 5. In order to confirm the isolation provided by the ARR at degeneracy, we measured the output power during simultaneous and individual operation of the OPOs. We did not observed any change in the output idler power from the OPOs. Also, the threshold pump power remains the same. Therefore, this confirms that there is no signal seeding from one OPO to the other. Another method to verify independent operation of both OPOs is to monitor the signal from mirrors M2 and M6. However, we were not able to do so, due to the presence of idler wavelength in the output, even after using a highly reflecting mirror to filter out the idler wave. Further, we calculated the combined FSR of the ARR-coupled OPO cavity to be 127 MHz. The measured 220 MHz spacing between the two waves inside the ARR is not equal to the multiple of the combined FSR of the ARR-coupled OPO cavity, confirming that it is the relative frequency separation between the two independently oscillating signal waves.

Fig. 5
figure 5

Fabry–Perot transmission spectra of the dual signal wavelengths

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It is interesting to note that when we misalign one of the OPOs minutely, the threshold and output idler power of the other OPO is observed to decrease and increase, respectively, by small values. We calculated the spectral acceptance bandwidth for our crystal at 951 nm to be 0.35 THz. The misalignment may result in the signal beam from one OPO to perturb the other and act as a seed beam, when operating near the same wavelength. Thus, it also opens up the possibility of using one OPO as a seed source to another with broad spectral acceptance bandwidths of crystal, when the ARR is not aligned for near-zero output coupling.

To show power scalability of the system, we measured the idler output power as a function of input pump power for both OPOs when oscillating simultaneously, keeping T 1 = 101 °C and T 2 = 100 °C. The results are shown in Fig. 6. For OPO-1, the idler power increases linearly up to 4.5 W of pump power, while for OPO-2, it is linear up to 5 W of pump, beyond which there is slight evidence of saturation. We achieved a maximum idler power of 1.6 W from OPO-1 for a pump power of 6.3 W, while OPO-2 is close to threshold using the remaining 3.7 W of pump. Similarly, 1.4 W of idler is generated from OPO-2 for 7 W of pump power, with OPO-1 operating near threshold at a pump power of 3 W. Further increasing the pump power to one OPO makes the other OPO unstable until it finally ceases operation. OPO-1 and OPO-2 have an operation threshold power of 2.8 and 3.2 W, respectively. We also performed power scaling for both OPOs in the short v-cavity configuration by placing high-reflecting mirrors (at signal) in place of the ARR. Each OPO without the ARR was configured with a cavity length of 63 cm. Both OPOs without ARR showed similar performance, providing maximum idler power of ~2.3 W for a pump power of ~10 W with an operation threshold of ~1.4 W. The inset of Fig. 6 shows the power scaling results for OPO-2 without the ARR. As evident, OPO-1 with the ARR incorporated shows similar output power as that of the OPO without ARR. The increase in threshold power, and lower output power from OPO-2 as compared to OPO-1, when ARR is incorporated, at same pump power, is attributed to the longer cavity length and additional mirrors (M7–9) used in OPO-2. Further, the increase in threshold power for both OPOs with the ARR incorporated, as compared to that of without ARR, is attributed to the additional losses due to the ARR elements, which can be further reduced.

Fig. 6
figure 6

Idler output power from OPO-1 and OPO-2 versus pump power, with both OPOs in simultaneous operation. Inset Power scaling of OPO-2 without the ARR

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4 Conclusions

In conclusion, we have demonstrated an ARR-coupled dual-wavelength cw OPO with signal (idler) wavelength pairs, which can be independently and arbitrarily tuned through degeneracy and beyond. We have demonstrated frequency separation from 7 THz down to ~220 MHz at identical signal wavelengths, although there is no limit to the minimum attainable wavelength separation, even to exact degeneracy. Both circulating signal waves provide high intracavity power and narrow linewidth, which are important factors for applications in the cw regime, making the technique attractive for efficient intracavity generation of widely tunable terahertz radiation, as well as other potential applications. At the same time, the independent and arbitrarily tunable idler waves at watt-level output power can be similarly used for the generation tunable terahertz radiation at practical efficiencies using extracavity schemes. The technique can also be extended to other spectral regions and operating timescales.