1. Introduction

Continuous-wave (cw) optical parametric oscillators (OPOs) in singly resonant oscillator (SRO) configuration are now firmly established as viable sources of tunable high-power coherent radiation [1], nearly two decades after their first demonstration [2]. Due to the substantially lower intensities available from cw pump lasers, resulting in lower nonlinear gain and high oscillation threshold, the development of cw OPOs in SRO design remained particularly challenging for many years. However, with the advent of quasi-phase-matched (QPM) nonlinear materials, together with advances in high-power pump sources, particularly fiber lasers, cw SROs with wide tuning range and high output power have been realized, covering spectral regions from the visible to mid-infrared [3–9]. The high optical nonlinearity together with long interaction lengths and noncritical phase-matching in QPM materials has enabled operation of cw SROs at practical pump power thresholds (watt-level) and elevated output power levels (>10 W) [6,9]. Operation of cw SROs based on QPM materials is now sufficiently robust that for the attainment of highest extracted power, limited output coupling of the resonant signal wave can be tolerated [10]. This enables substantial enhancement not only in the total (signal plus idler) output power and external efficiency, but also in the usable tuning range. At the same time, the use for signal output coupling has been shown to be imperative at increased pump powers, where the high intracavity signal intensities can lead to significant thermal loading in the nonlinear crystal, limiting conversion efficiency and degrading output power, wavelength stability and beam quality [11–13]. As such, the deployment of signal output coupling represents an important strategy to achieve optimum performance in cw SROs with regard to several important operating parameters. As in laser oscillators, the conventional technique for the attainment of output coupling in cw SROs relies on the use of different output coupler (OC) mirrors with discrete transmission values at the resonant wavelength [9]. However, this approach requires the search for different OC mirrors to obtain the optimum value of output coupling. Moreover, under different cw SRO operating conditions, such as the resonant wavelength and pumping level, the optimum value of output coupling can change, making absolute optimization of output power at all wavelengths and under all operating conditions difficult, costly, and time-consuming.

Recently, we demonstrated an alternative new approach for absolute optimization of extracted power from optical oscillators using an antiresonant ring (ARR) interferometer as an output coupler, and realized this concept for the first time in a femtosecond OPO [14]. Later, we extended this technique to traveling-wave oscillators, where we demonstrated optimum output coupling in a picosecond OPO configured in a ring resonator [15]. The ARR interferometer essentially consists of two highly reflecting mirrors and a beam-splitter (BS). For an optical input beam separated by the BS, the reflected beams from the ARR and the transmitted beams through the ARR interfere constructively and destructively, respectively. The ARR output coupling technique exploits the ability to adjust the ratio of the transmitted (T) and reflected (R) power from the BS simply by varying the angle of incidence (θ_BS) on the BS. This results in a change in the transmitted power (T_ARR) from the ARR, which can then be used as a means to vary the optical feedback into an optical oscillator incorporating the ARR.

Here we report the integration of an ARR interferometer into a cw SRO and demonstrate its use for optimization of extracted output power from the device. While we have previously demonstrated the technique in pulsed optical oscillators [14,15], where high levels of output coupling (>50%) can be readily supported, the integration of such an ARR into a cw SRO can be challenging due to the low tolerance of cw SROs to loss and output coupling (typically <5%). We demonstrate that despite the high sensitivity to loss and output coupling, the ARR offers a unique and practical approach to achieve fine, adjustable, and in situ optimization of output power from cw SROs.

2. Experimental setup

The schematic of the experimental setup is shown in Fig. 1 . The fundamental pump source is a cw Yb-fiber laser (IPG Photonics, YLR-30-1064-LP-SF), delivering up to 30 W of output power at 1064 nm in a single-frequency, linearly-polarized beam with a spatial quality factor of M²~1.01 and a nominal linewidth of 89 kHz. A Faraday isolator (FI) with an isolation of ~25 dB was used at the output end of the fiber to prevent back-reflection into the laser. To maintain stable output characteristics, we operated the pump laser at maximum output power and attenuated the power using a combination of a half-wave plate (HWP) and a polarizing beam-splitter (PBS). A second HWP was used to control the pump polarization for phase-matching in the nonlinear crystal, which is a 50-mm-long, 6.2-mm-wide, 1-mm-thick, 5% MgO-doped periodically poled LiNbO₃ (MgO:PPLN). The crystal was housed in an oven with a stability of ± 0.1°C and adjustable from room temperature to 200°C. The crystal contains five gratings with periods ranging from Λ = 29.5 μm to Λ = 31.5 μm, in steps of 0.5 μm. However, we only used the Λ = 31.5 μm grating period in this work, providing a theoretical wavelength tuning range of 1663-1944 nm for the signal and 2954-2350 nm for the idler, for the crystal temperature varying from 25°C to 200°C. A lens of focal length, f = 250 mm, was used to focus the fundamental beam to a waist radius of w_p = 63 μm (ξ~1), while the design of the SROcavity resulted in a signal beam waist radius of ws = 76 μm at the centre of the crystal (bp~bs). The OPO was configured in a standing-wave cavity, comprising two concave mirrors, M1 and M2 (r = 150 mm), one plane mirror (M3) in one arm, and an ARR interferometer formed by two plane mirrors (M4 and M5) and a BS integrated into the other arm. For the BS, we used a standard, low-cost, commercial fused silica plate available in our laboratory. The plate was 3-mm-thick with broadband coating over 0.9-2.6 μm. Such a BS could allow output coupling optimization over a broad spectral range, given the simplicity and effectiveness of the ARR technique. However, in this work we only performed the measurements at a fixed signal wavelength, using a single grating period to demonstrate the concept in a cw SRO, for the first time. All the OPO mirrors (M1-M5) were highly reflective (R>99%) for the signal (1.3-1.9 μm) and highly transmitting (T>90%) for the idler (2.2-4 μm), ensuring SRO operation. The mirrors are also highly transmitting (T>92%) for the pump. A dichroic mirror, M, was used to separate the pump from the generated idler beam. The total SRO cavity length was LSRO = 183 cm, which was the sum of the standing-wave cavity length (2Llinear = 166.8 cm) and length of the ARR interferometer (Lring = 16.2 cm).

 

Fig. 1 Schematic of the experimental setup. FI: Faraday isolator, HWP: Half-wave plate, PBS: Polarizing beam-splitter, L: Lens, M₁-M₅: Mirrors, M: Dichroic mirror, BS: Beam-splitter.

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3. Results and discussion

Initially, we performed the power scaling of the cw SRO with a conventional 5% OC mirror in place of the ARR output coupler (ARR-OC). The total SRO cavity length was 2L_linear = 2 × 91.5 cm = 183 cm, equal to that of the ARR output-coupled SRO (ARR-OC-SRO). In both configurations, we used the same focusing condition for the pump and adjusted the cavity for optimum overlap between the pump and the signal beam in the cold cavity. We operated the SRO at the center of the tuning range for the Λ = 31.5 μm grating, and generated a signal wavelength of λ_signal = 1706 nm and a corresponding idler wavelength of λ_idler = 2826 nm, maintaining the crystal temperature at 88.5°C. Figure 2(a) shows the variation of signal, idler and the total power (signal plus idler) as a function of pump power for the conventional 5% output-coupled SRO (OC-SRO). We obtained a signal power of 4.56 W and idler power of 4.09 W at a maximum pump power of 28.6 W. The total power extracted at the maximum pump power was thus 8.65 W.

 

Fig. 2 (a) Variation of signal and idler power along with the total power extracted from the OPO using conventional 5% OC as a function of input pump power, and (b) Transmission from ARR interferometer as a function of BS angle.

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In order to perform output coupling optimization using the ARR technique, we first characterized the ARR interferometer prior to integration into the cw SRO by evaluating the transmission of output signal wavelength through the ARR at different angles, θ_BS, external to the SRO cavity. We measured the input power into the ARR and the output power from the ARR at a fixed signal wavelength (1706 nm), and estimated the ARR transmission as a function of the incident angle, θ_BS, on the BS. The result is shown in Fig. 2(b), where it can be seen that with the increase in θ_BS from 20° to 40°, the transmission of the ARR increases continuously from 0.8 to 7.3%. Since the performance of cw SRO depends strongly on the cavity losses, we estimated the additional average loss due to the ARR elements. By measuring the transmitted and reflected power from the BS at different θ_BS, the total average BS loss at 1706 nm was found to be ~1.5% throughout the BS angular range, while the extra mirror (M₅) introduced an additional coating loss of ~0.5%. Therefore, with the available BS and mirror M₅, the characterization of the ARR-OC-SRO, as described below, was performed in the presence of an additional loss background of ~2%. By using a more optimum BS and mirror combination with lower insertion loss, we expect significant improvements in ARR-OC-SRO performance with regard to output power and pump threshold.

After external characterization, we integrated the ARR into the cw SRO cavity. In order to determine the optimum ARR-OC value for the signal, we varied θ_BS continuously, as we did in external characterization. We performed power scaling measurements for different angles of incidence, θ_BS, at a signal wavelength of 1706 nm (idler at 2826 nm), by recording the signal output power from the ARR-OC-SRO, and the corresponding single-pass idler power from the oscillator. At the smallest BS angle, θ_BS = 20° (T_ARR = 0.8%), a signal power of 1.5 W and the highest idler power of 4.2 W was achieved for a pump power of 28.6 W.

To study the behavior of simultaneously extracted signal and idler power with the increase in the ARR transmission, and hence to obtain the absolute value of optimum ARR-OC at different pumping levels, we optimized the cw ARR-OC-SRO for input powers of 15.9 W and 23.2 W. Figures 3(a) and 3(b) show the output coupling optimization of signal at pumppowers of 15.9 W and 23.2 W, respectively, by varying the BS angle, θ_BS. As seen in Fig. 3(a), the signal power increases from 0.54 W at θ_BS = 20° (T_ARR = 0.8%) to a maximum value of 1.22 W at θ_BS = 22° (T_ARR = 2%). Further increasing the BS angle beyond θ_BS = 22° results in the drop of signal power to 0.87 W at θ_BS = 25° (T_ARR = 2.1%), confirming 2% as the optimum ARR-OC value for the signal at 15.9 W of pump power. Measurements beyond θ_BS = 25° were not possible due to the increase in the threshold power. Similarly, at a pump power of 23.2 W, seen in Fig. 3(b), the signal power increases from 1.15 W to a maximum value of 2.28 W at θ_BS = 33° (T_ARR = 4.6%). Further increasing the BS angle results in the drop of signal power to 1.64 W at θ_BS = 40° (T_ARR = 7.3%), confirming 4.6% as the optimum ARR-OC value for the signal at 23.2 W of pump power. This clearly shows the potential of the ARR technique for in situ optimization of output power from the cw SRO (or any optical oscillator) under different operating conditions, including different pumping levels. Figure 3(c) and 3(d) show the simultaneously extracted single-pass idler power at pump powers of 15.9 W and 23.2 W, respectively, as a function of BS angle. As evident from Fig. 3(c), at a pump power of 15.9 W, the idler power decreases from 2.35 to 1.79 W for an increase in θ_BS from 20° to 25°. Similarly, at a pump power of 23.2 W, the idler power decreases gradually from 3.36 to 3.15 W for an increase in θ_BS from 20° to 32°, and has a sharp fall with further increase of θ_BS beyond the optimum angle of θ_BS = 33°, up to 40°. The decrease in the idler power with the increase in θ_BS can be attributed to the increasing output coupling loss of the resonating signal wave with increase in ARR transmission, resulting in reduced intracavity signal intensity to mix with the pump to generate the single-pass idler. Thus, the idler output power is reduced with increasing θ_BS (higher signal output coupling) for all pump powers, indicating that the idler power is not necessarily maximized at the optimum signal output coupling. Hence, the ARR also enables the possibility of exploring the idler output power as a function of output coupling as well as independently maximizing the signal and idler output power, which are difficult to study with conventional discrete output couplers.

 

Fig. 3 Optimization of signal power versus BS angle, θ_BS, at input pump power of (a) 15.9 W, and (b) 23.2 W. Optimization of simultaneously extracted single-pass idler power versus BS angle, θ_BS, at input pump power of (c) 15.9 W, and (d) 23.2 W.

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In order to compare the observed behavior of signal and idler power in Figs. 3(a)-3(d) with theory, we also performed calculations to obtain the variation of extracted signal power, and the corresponding idler power, as a function of signal output coupling. We performed the calculations for a conventional cw OC-SRO deploying a partially transmitting mirror, while considering a fixed background cavity loss of 2%, a pump depletion of 70%, a Gaussian pump beam profile, and assuming no thermal effects [16–18]. The results are shown in Fig. 4(a) and 4(b) for a fixed pump power of 15.9 W and 23.2 W, respectively. As evident, at pump power of 15.9 W and 23.2 W, the optimum output coupling for the signal is attained at 3.6% and 4.8%, respectively, and the corresponding idler power decreases with increase in output coupling. The maximum idler power is obtained at the minimum signal output coupling value for both the pumping levels, as also observed in Fig. 3(c) and 3(d).

 

Fig. 4 Theoretically calculated optimization curves for signal and idler power as a function of output coupling at input pump power of (a) 15.9 W, and (b) 23.2 W.

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It is also evident from theoretical curves, Fig. 4(a) and 4(b), that with increase in pump power, the output coupling optimization curve for signal is broadened, which is also observed in Fig. 3(a) and 3(b). The theoretical variation of signal and idler power as a function of output coupling in Fig. 4 are thus in good agreement with the experimental results shown in Fig. 3, confirming that the ARR behaves in the same way as a conventional output coupler. To obtain a clearer picture, we calculated the signal output power optimization curve at a low pump power of 5 W and a high pump power of 28.6 W, with the results shown in Fig. 5 . As seen, at high pump power the range of optimum output coupling values is significantly broader than at the low pump power, where the attainment of optimum output coupling is critical.

 

Fig. 5 Theoretically calculated optimization curves for signal power as a function of output coupling at low pump power of 5 W and high pump power of 28.6 W.

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Figure 6 (a) shows the corresponding pump depletion for the cw ARR-OC-SRO at a fixed pump power of 23.2 W, for different BS angle. As seen, pump depletion decreases gradually from 56.6% to 51% for an increase in θ_BS from 20° to 32°, and has a sharp fall with further increase of θ_BS beyond the optimum angle (θ_BS = 33°) of signal power extraction. It has been observed that the pump depletion follows a similar behavior to the variation of idler power as a function of BS angle, and thus signal output coupling, as seen in Fig. 3(d).

 

Fig. 6 (a) Pump depletion as a function of BS angle, θ_BS, at input pump power of 23.2 W. (b) Signal and corresponding idler along with total output power scaling at BS angle, θ_BS = 33°.

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At the ARR-OC value of 4.6%, the power scaling of the ARR-OC-SRO is shown in Fig. 6(b), depicting the variation of signal power, the corresponding idler power, and the total output power as a function of input pump power. The maximum signal and idler power achieved is 2.81 W and 3.88 W, respectively, corresponding to a maximum achieved total output power (signal plus idler) of 6.69 W, representing a total extraction efficiency of 23.4%. The signal and idler power vary linearly up to the maximum pump power of 28.6 W. The variation of the total output power as a function of pump power also confirms the linear dependence. It is to be noted here that although no sign of saturation in the output power for higher pump power has been observed at the ARR-OC value of 4.6% (θ_BS = 33°), we have also not observed any evidence of saturation at lower output coupling values (smaller BS angles). This is attributed mainly to the background loss present at all the BS angles.

Figure 7(a) shows the signal power extracted from the cw ARR-OC-SRO at the optimum output coupling value versus pump power. Each data point represents the maximum signal power at a given pump power, obtained by measuring the extracted signal power as a function of BS angle, while keeping the pump power fixed. As seen, the optimum signal power increases almost linearly, reaching 2.81 W for a maximum input power of 28.6 W. The inset of Fig. 7(a) shows the theoretical power scaling of the signal for a conventional cw OC-SRO, calculated at the corresponding theoretical optimum output coupling values [16–18]. As can be seen, the theoretical power scaling shows the same behavior as the experimental variation of Fig. 7(a). We also measured the extracted idler power as a function of pump power at minimum signal output coupling values corresponding to maximum idler power, for different pumping levels, as shown in Fig. 7(b). The output coupling for the signal, at which the idler power is maximum, always corresponds to the lowest value (T_ARR = 0.8%) at θ_BS = 20° for all pump powers. The maximum idler power achieved is 4.2 W for a pump power of 28.6 W. The curve depicts the linear dependence of idler power on the input pump power. The calculated theoretical power scaling for the maximum idler [16–18] under minimum signal output coupling is also shown in the inset of Fig. 7(b), confirming a linear behavior similar to the experimental variation in Fig. 7(b).

 

Fig. 7 (a) Signal power scaling at optimum signal output coupling values. (b) Idler power scaling at minimum signal output coupling values. Inset: Corresponding theoretical plots.

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We also recorded the cw ARR-OC-SRO threshold pump power for different values of ARR-OC, with the results shown in Fig. 8 . By increasing the output coupling from 0.8% to 7.3%, the threshold pump power for the ARR-OC-SRO rises from 12.3 to 22.1 W, with the corresponding intracavity power estimated to decrease from 187 to 28 W at the maximum pump power of 28.6 W.

 

Fig. 8 The cw SRO threshold power as a function of signal output coupling with the ARR. Inset: far-field energy distribution of extracted signal with optimum ARR-OC value of 4.6% at 23.2 W of input pump power.

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The lower output power obtained from the optimal ARR-OC-SRO at 23.2 W of pump power as compared to that with the conventional non-optimal 5% OC-SRO (see Fig. 2(a)) is attributed to the extra insertion loss induced by the un-optimized BS and mirror coatings used in the present experiment, as noted previously. Although, the maximum output power from optimal ARR-OC-SRO has not been achieved, a background loss is present for all BS angles, indicating θ_BS = 33° (T_ARR = 4.6%) as the optimum angle for maximum output power extraction. The optimum ARR-OC value of 4.6% together in the presence of the background insertion loss associated with the ARR results in reduced intracavity signal power, leading to a lower maximum signal power extraction (see Fig. 6(b)) than with the 5% conventional output coupler (see Fig. 2(a)), and without any saturation in power scaling (see Fig. 6(b)). The loss due to the ARR is also evident from the comparison of threshold power for the cw 5% OC-SRO and that for the 4.6% ARR-OC-SRO, which are measured to be 15.1 W and 18.3 W, respectively. By using a BS and mirrors with improved coatings, the absolute highest signal power can be extracted at optimum ARR-OC value. Further, with reduced insertion loss, we can expect similar output power and pump power threshold for the ARR-OC-SRO to that in the conventional OC-SRO of the same output coupling.

We also recorded the far-field energy distribution of the output signal from the cw ARR-OC-SRO with θ_BS = 33° at 23.2 W of pump power, as shown in inset of Fig. 8. Using a f = 100 mm focal length lens and a scanning beam profiler, the quality factor of the signal beam was measured to be M_x²~1.9 and M_y²~1.9, confirming TEM₀₀ spatial mode. We have not observed any degradation in output beam quality due to the integration of the ARR into the cw SRO. We do not expect any change in the beam quality with other ARR-OC values, as we have not observed any thermal effects at lowest as well as highest output coupling values.

4. Conclusions

In conclusion, we have demonstrated, for the first time to our knowledge, a versatile technique based on the use of an ARR interferometer for continuous fine adjustment of output coupling and in situ optimization of the output power in cw SROs. With fine adjustment of the ARR transmission, optimum output coupling value for signal and idler can be attained at different input pumping levels. The experimental results have also been shown to be in good agreement with the theoretical modeling. By deploying a custom-made BS and a mirror with improved coatings, resulting in lower insertion loss, the same maximum signal output power is expected from the cw ARR-OC-SRO as with a conventional cw OC-SRO of the same optimum output coupling. The technique is wavelength-independent, and so can be used over an extended spectral range with a single ARR setup. With advances in QPM materials, together with the available broadband-coated beam-splitters, the present set up can be further deployed over a wide wavelength range using fanned or multiple grating structures in combination with temperature tuning, indicating the potential use of this technique for widely tunable OPOs. This proof-of-principle demonstration also opens up new possibilities for other applications of the technique in cw optical oscillators in general, for example in the implementation of coupled cavities or cavity dumping, as first suggested in the context of lasers nearly four decades ago [19–22].