## Abstract

Continuous-wave (cw) optical parametric oscillators (OPOs) are ideally suited for applications, for example high-resolution spectroscopy, that need coherent sources combining narrow-linewidth emission with good wavelength tunability. Here, we demonstrate for the first time cw OPOs based on a millimeter-sized whispering gallery resonator (WGR) made of cadmium silicon phosphide (CdSiP_{2}). By employing a compact laser diode at 1.57-μm wavelength for pumping, a cw OPO with wavelength tunability from 2.3 μm to 5.1 μm is realized based on such a resonator. The oscillation thresholds are in the milliwatt range. The maximum total power conversion efficiency reaches more than 15%. The intrinsic quality factor at 1.57 μm is determined to be 3.5 × 10^{6}. This work suggests that CdSiP_{2} is a very promising alternative for constructing mid-infrared parametric devices.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

## 1. Introduction

The mid-infrared (mid-IR) spectral region contains strong characteristic vibrational transitions of many important molecules as well as atmospheric transmission windows, which makes it interesting for spectroscopic applications, such as chemical and biomolecular sensing, security and industrial process control [1–4]. Continuous wave (cw) optical parametric oscillators (OPOs) are now well recognized as powerful and viable solid-state laser sources of single-frequency radiation, providing access to the mid-IR spectral region with wide wavelength tunability from a single device [5–7]. Such sources are therefore very valuable for mid-IR high-resolution spectroscopy.

The great majority of cw OPOs at present is established based on conventional mirror-based optical cavities/resonators using oxide non-centrosymmetric crystals such as lithium niobate (LiNbO_{3}), potassium titanyl phosphate (KTP) and their respective isomorphs [7]. Such configurations are indeed very useful. However, their spectral coverage is limited to ˂ 5 μm due to the onset of multi-phonon absorption in oxide crystals. Besides, in order to achieve a wide wavelength tunability, different sets of reflecting elements are usually required in mirror-based cavities [8]. To extend the OPO tuning wavelength efficiently far into the mid-IR, now non-oxide nonlinear optical crystals raise a lot of attention because they are capable of providing transparency beyond 5-10 μm as well as high nonlinear optical coefficients [9,10]. However, in contrast to OPOs in the pulsed regime, the reported accessible wavelength range of mirror-based cw OPOs is still limited to 4.7 µm, even employing non-oxide crystals including silver gallium sulfide (AgGaS_{2}) and orientation-patterned gallium arsenide (OP-GaAs) [9–12].

Enabled by the pioneering work from the Jet Propulsion Lab [13], a new OPO configuration based on whispering gallery resonators (WGRs) was firstly demonstrated by Fürst *et al.* some years ago [14]. In such resonators, the light is guided by total internal reflection in a spheroidally-shaped nonlinear-optical crystal. These monolithic devices do not require any reflective or anti-reflection coating, and they are easily miniaturized down to sub-millimeter diameters [15,16]. Furthermore, due to their high quality factors and low oscillation thresholds, they can be pumped by compact laser diodes. Despite they are intrinsically triply-resonant, *i.e.* all three interacting waves are simultaneously circulating in the cavity, controllable mode-hop-free tuning of the output wavelengths over MHz-wide resonances is possible [17,18]. Benefiting from these unique advantages, most recently, the first cw OPO generating mid-IR light up to wavelengths beyond 8 μm was realized employing a WGR made of silver gallium selenide (AgGaSe_{2}) [19]. This progress is indeed impressive, but the obtained OPO output power is still limited to values below 1 mW due to the low thermal conductivity of AgGaSe_{2}, which leads to thermally induced mode distortions and optical power dissipation inside the resonator [19,20]. Furthermore, a so far unresolved shortcoming of the technology is that such devices were not able to cover the so-called point of degeneracy [19].

Cadmium silicon phosphide (CdSiP_{2}) is a newly developed nonlinear optical non-oxide crystal providing a thermal conductivity (13.6 W/mK) that is more than ten times larger than that of AgGaSe_{2} (1.0 W/mK) [9,10,21]. This property, along with a high nonlinear figure of merit (*d*^{2}/*n*^{3} = 250 pm^{2}/V^{2} for CdSiP_{2} to be compared with about 60 pm^{2}/V^{2} for AgGaSe_{2}) and a relatively broad transparency range (1-6.5 μm), make CdSiP_{2} a promising candidate for constructing mid-IR OPOs [21]. However, up to now, only mirror-based OPOs in the pulsed regime have been realized by employing such crystals [21]. In this work, we present, to the best of our knowledge for the first time, a cw OPO based on a millimeter-sized WGR made of CdSiP_{2}. For pumping with 1.57-μm light from a compact laser diode, milliwatt-threshold optical parametric oscillation with wavelength tunability covering the 2-5 μm spectral range is demonstrated, including the point of degeneracy. The total output power of generated light is determined to be > 4 mW, which is much larger than the one using AgGaSe_{2} WGRs [19].

## 2. Fundamentals

#### 2.1 Wavelength tuning

An OPO based on a WGR is sketched in Fig. 1(a). Cw pump light with the power *P*_{p} at the wavelength λ_{p} is coupled into the resonator. If *P*_{p} exceeds a threshold value *P*_{th}, signal and idler light are generated at the wavelengths λ_{s,i} due to second-order optical nonlinearity. These two waves are coupled out of the resonator with the powers *P*_{s,i} together with the residual pump light having the power ${P}_{\text{p}}^{\text{*}}$.The wavelengths of the interacting light fields are related by

*m*

_{j}denote the number of field maxima of the interacting light waves along their circular path in the rotational symmetric resonator. The indices

*j*=

*p*,

*s*,

*i*here and hereafter represent the pump, signal, and idler waves, respectively. A spatially varying optical nonlinearity during one roundtrip is taken into account by the number

*M*. For a constant value we have

*M*= 0, whereas

*M*= ± 2 for WGRs made of crystals with $\overline{4}$ symmetry such as

*c*-cut CdSiP

_{2}[22].

In order to simulate the wavelength tunability of a WGR OPO based on *c*-cut CdSiP_{2}, we combine Eqs. (1) and (2) with the single-frequency condition [15], the Sellmeier equation of CdSiP_{2} and the relation for its thermal expansion [23]. Furthermore, we take into account that the effective refractive index depends on the resonator geometry and on the transverse mode structure of the interacting waves [24]. The latter is described by the mode numbers *p*_{j} (zeros in polar direction) and *q*_{j} (extrema in radial direction).

Figure 1(b) shows different wavelength-tuning branches of an OPO based on a millimeter-sized WGR made of CdSiP_{2}, assuming *p*_{j} = 0. From this simulation, it is clear that the output wavelengths can be tuned over a large spectral range (from 2 μm to 6 μm) by adjusting the temperature of the WGR and by varying *q*_{p}.

#### 2.2 Oscillation threshold and conversion efficiency

The resonator loss is a crucial parameter for the conversion efficiencies of WGR-based OPOs. We can distinguish between internal loss (absorption and scattering) proportional to the coefficient *α*_{int} and coupling loss proportional to the coefficient *α*_{c}. The first is given by the cavity itself, the second can be varied, *e.g*. by changing the distance between the coupler and resonator. The ratio *r* = *α*_{c}/*α*_{int} defines three coupling regimes: undercoupling (*r* < 1), critical coupling (*r* = 1), and overcoupling (*r* > 1). The loaded quality factor is a function of the coupling ratio. It can be written as *Q* = *Q*_{int}/(1 + *r*) with the intrinsic quality factor *Q*_{int} [15]. For strong undercoupling (*r* << 1) the intrinsic loss is the major contribution to the quality factor (*Q*_{int}), while it can be neglected for strong overcoupling (*r* >> 1).

Optical parametric oscillation occurs, if *P*_{p} > *P*_{th}. Then, we have to consider three interacting waves and consequently three ratios *r*_{p,s,i} and three quality factors *Q*_{p,s,i}. At pump powers below the oscillation threshold only the pump wave is propagating in the resonator. The coupling efficiency *K* = 1 - ${P}_{\text{p}}^{\text{*}}/{P}_{\text{p}}$ = 4*r*_{p}/(1 + *r*_{p})^{2} [25] has a maximum at *r*_{p} = 1, *i.e.* at critical coupling. The pump threshold is given by [15,25]

*r*

_{p}= 1) whereas the generated waves are undercoupled (

*r*

_{s,i}<< 1). This will maximize the coupling efficiency for the pump and simultaneously minimize the losses for signal and idler.

At pump powers above *P*_{th}, there is an additional loss for the pump light since energy is converted to the signal and idler waves due to the second-order nonlinearity. Hence, the coupling efficiency for the pump light and also the conversion efficiency depend on how much the pump power exceeds the threshold value. For the latter, we find [15]

*N*=

*P*

_{p}/

*P*

_{th}representing the pump power normalized to the oscillation threshold. The maximum conversion efficiency

*N*= 4. Equation (5) shows that overcoupling for all waves (

*r*

_{j}> 1) is favorable for reaching high conversion efficiencies,

*i.e.*intrinsic losses by absorption and scattering should be as small as possible.

As a numerical example, assuming that the coupling ratios for the interacting waves are equal, the theoretical maximum total conversion efficiency is calculated to be ${\eta}^{max}={\eta}_{s}^{max}+{\eta}_{i}^{max}$ = 25% for critical coupling (*r*_{j} = *r* = 1).

## 3. Experimental Methods

The starting materials for preparation of WGR is a 1-mm-thick CdSiP_{2} wafer (*c*-cut) grown by BAE Systems, Inc. A femtosecond laser at wavelength of 388 nm is employed, first, for drilling out a millimeter-diameter cylindrical preform from the raw wafer, and then, for shaping the rim of the rotating disk after gluing it onto a tapered brass post to achieve spheroidal geometry and to define the WGR dimensions. By employing a CNC-controlled *x*-*y*-axis movement stage, the ratio between two local curvature radii *R* (disk radius) and *ρ* (rim radius) can be tailored to be close to the optimal value given by *ρ*/*R* = 1 - (*n*_{wgr}/*n*_{prism})^{2} for establishing efficient optical coupling [26]. Here, *n*_{wgr} and *n*_{prism} represent the refractive indices of the WGR material and the prism, respectively. The symmetry axis of this spheroidal WGR is carefully aligned with the optic axis of the crystal during the machining. The inset in Fig. 2 is a photograph of the manufactured CdSiP_{2} WGR with a disk and rim radii of approximately 0.75 and 0.17 mm, respectively, to coincide the dimension for simulation in Section 2.1. Subsequent surface smoothening to further improve the quality factor of the WGR is conducted by fine polishing with diamond paste (grain size of 0.05 µm for final fine polishing).

The experimental setup for the basic characterization of the CdSiP_{2} WGR-based cw OPO is sketched in Fig. 2. A 1.57-μm *e*-polarized light beam provided by a fiber-coupled distributed feedback (DFB) laser diode is coupled into the resonator (*n*_{wgr} ≈3.0522 at 1.57 μm [23]) via evanescent-field coupling employing a silicon prism (*n*_{prism} ≈3.4742 at 1.57 μm [27]). Up to 20 GHz variations of the pump frequency can be introduced by changing the laser driving current. We use a fiber optic splitter to guide a small fraction of the incident light into a Fabry-Pérot interferometer (FPI) with a free spectral range of 1.5 GHz, acting as a standard frequency ruler for determining the frequency detuning. In parallel, the remaining large portion of the polarized incident light is focused onto the base of the coupling silicon prism via a gradient-index (GRIN) lens, which is positioned at an adjustable distance from the fiber output end. The resonator and the coupling prism are both placed on a rotational mount with a piezo translator, allowing for nanometer-scale adjustment of the distance between prism base and WGR. This mount is then placed in a housing with a temperature stabilization on a millikelvin scale, enabling wavelength tuning of the cw WGR OPOs. By increasing the power of the *e*-polarized pump light, *o*-polarized signal and idler waves at the respective wavelengths are generated when the oscillation threshold is reached. The generated waves together with the residual pump light are coupled out of the resonator via the prism and then separated by dichroic filters for the respective transmission and output power measurements. A Fourier-transform infrared (FTIR) spectrometer and a high-resolution optical spectrum analyzer are employed to investigate the wavelength tunability.

## 4. Results and discussion

#### 4.1 Linear optical characterization

By employing the experimental setup sketched in Fig. 2 and a low pump power of *P*_{p} < 1 mW, the intrinsic quality factor of the manufactured CdSiP_{2} WGR is determined to be approximately *Q*_{int} = 3.5 × 10^{6} (narrowest linewidth ∆ν = 55 MHz) at 1.57 μm after fine polishing. This value is in fact limited only by the internal material loss, considering the absorption coefficient (0.04 cm^{−1} at 1.57 μm) of CdSiP_{2} crystals grown by the same manufacturer [28]. When the resonator touches the prism base, the quality factor is approximately *Q* = 2.2 × 10^{6}, which gives us a maximum *r _{p}* value of only 0.6 according to the relation of

*Q*=

*Q*

_{int}/(1 +

*r*

_{p}) introduced in Section 2.2. Thus, the internal material loss is always higher than the coupling loss in our experiments,

*i.e. α*

_{int}>

*α*

_{c}, and the critical coupling and overcoupling are unreachable with such high material absorption.

Thermally-induced pump mode distortion is not noticeable until we increase the in-coupled pump power up to 40 mW. This advantage stems from the relatively high thermal conductivity of CdSiP_{2} with respect to that of AgGaSe_{2}. In the latter case, only 3-mW in-coupled pump power already initiates such phenomenon. The spectral mode profiles are almost independent of the laser frequency scan direction, being a further indication of negligible thermo-optical effects [16,20].

#### 4.2 OPO conversion efficiency

The output power measurements are conducted when the resonator rim and prism base are in contact. By doing so, one can achieve the highest OPO conversion efficiency as discussed in Section 2.2, even though with relatively high pump threshold [25]. When the pump power *P*_{p} overcomes the oscillation threshold of *P*_{th} = 6.1 mW, nonzero output powers of *P*_{s} and *P*_{i} are observed, as shown in Fig. 3(a). The output wavelengths are measured to be λ_{s} = 2.29 μm and λ_{i} = 4.99 μm by employing a FTIR spectrometer, as shown in Fig. 3(b), confirming a valid OPO process that fulfills the energy conservation of Eq. (1). By further increasing the pump power, signal and idler output powers grow to 2.92 mW and 1.32 mW, respectively. The maximum signal power achieved in this work is more than 3 times higher than that of the AgGaSe_{2} WGR OPOs, which also validates our expectation of how the difference in thermal conductivities of CdSiP_{2} and AgGaSe_{2} would influence the signal/idler output powers [19,20]. The maximum power conversion efficiencies for signal and idler waves are determined to be ${\eta}_{s}^{max}$ = 11% and ${\eta}_{i}^{max}$ = 5%, respectively. With these two values and the *r*_{p} = 0.6, the coupling ratios *r*_{s} = 0.75 and *r*_{i} = 0.74 for signal and idler waves can be therefore obtained according to Eq. (5). As we can see, coupling ratios for all three interacting waves in CdSiP_{2} WGR are all lower than 1, resulting in conversion efficiencies that are lower than the theoretical expectation as desired in Section 2.2 for critical coupling.

In order to improve the performance further, the transparency of the CdSiP_{2} crystals has to be improved, allowing for large *r*_{j} values. An alternative is to minimize the WGR disk radius *R* and thus to lower the internal round trip absorption loss. And by doing so, moreover, even stronger nonlinear interaction in WGRs can be expected according to the power scaling law of ${\left|\sigma \right|}^{2}\propto {R}^{-1.8}$, where *σ* is the mode overlap integral [16].

The theoretical dependences of *η*_{s} and *η*_{i} are plotted as solid lines in Fig. 3(a) according to Eq. (4). The curves are in fairly good agreement with the experimental data, and the conversion efficiencies reach maximum values at a saturation pump power of approximately 24.5 mW, which is as expected about 4 times that of the pump threshold, *i.e. N* = *P*_{p}/*P*_{th} ≈4 [15]. This result also further verifies the reasonability of our measurements and calibrations. Furthermore, we were able to minimize the oscillation threshold down to ˂ 2 mW by adjusting the prism-resonator distance, *i.e.* by varying the *r*_{j} values according to Eq. (3).

#### 4.3 Wavelength tunability

To study the wavelength tuning behavior of WGR-based cw OPOs, stable cw operation is essential. Considering this, we use a ZnSe window to reflect a portion of the generated signal light onto a photodiode, which is used to stabilize the pump laser via a servo-loop (PID control) onto the side-of-fringe of the resonance of the signal light. This ensures that the pump laser frequency tracks the cavity resonance and meanwhile the power of the generated signal/idler light is constant [29]. With such an actively stabilized laser locking solution and by adjusting the temperature of the WGR from 25 to 100°C, the signal and idler wavelengths of every observed parametric process are recorded by the FTIR spectrometer, covering the whole spectral range starting from 2.29 to 5.13 μm, including the processes close to the point of degeneracy (close to 3.14 μm), as shown in Fig. 4(a). By doing so, 50- and 200-nm-wide tunabilities are provided respectively by signal and idler waves with the processes away from the point of degeneracy, while 290- (signal) and 370-nm-wide (idler) tunablities are achieved near the point of degeneracy. Comparing Fig. 1(b) with Fig. 4(a), it becomes evident that the shapes of the experimentally determined wavelength-tuning branches are in fairly good agreement with the simulations, although no OPO process with idler wavelengths > 6 μm is observed in experiments. The wavelength tunability obtained in this work fill up nicely the spectral gap between the 0.6-3 μm and 4-8 μm left by previously reported WGR-based cw OPOs made of oxide and non-oxide nonlinear optical crystals [15,19,30]. Besides, this is in general the first experimental demonstration of a CdSiP_{2} OPO source operating in the cw domain [21]. A high-resolution optical spectrum analyzer is employed to further investigate the continuity of the wavelength tunability. Figure 4(b) shows the result, corresponding to the small area in Fig. 4(a). The experimental data (●) are recorded every 0.2-0.3 K, showing a near-continuous wavelength tuning behavior from 2291.2 to 2288.4 nm, underlining the great potential of such a device for spectroscopic analysis.

## 5. Conclusion

We have demonstrated the first WGR-based cw OPO made of CdSiP_{2}. By using a compact diode laser at 1.57 μm as the pump source, a monolithic mid-IR laser with continuously tunable wavelengths ranging from 2.29 to 5.13 μm is realized, emitting total output powers up to 4 mW. This work shows that non-oxide crystals such as CdSiP_{2} are promising candidates for constructing miniaturized parametric devices operating in the mid-IR. Some other promising non-oxide crystals, such as orientation-patterned gallium phosphide (OP-GaP) and OP-GaAs, may allow to produce > 100 mW mid-IR light at > 10 μm wavelength due to their even higher thermal conductivities and wider transparency with respect to CdSiP_{2}.

## Funding

German Federal Ministry of Education and Research (funding program Photonics Research Germany, 13N13648).

## Acknowledgments

The authors thank C. S. Werner, S. J. Herr, and R. Wolf for fruitful discussions. Y. Jia is supported by a fellowship from Alexander von Humboldt Foundation.

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