1. Introduction

Already in the early days of nonlinear optics, the idea came up to place the nonlinear optical crystal for frequency conversion inside a laser cavity, rather than focusing a laser beam into the crystal [1]. Inside the laser cavity, a much higher electric field strength is achievable than with the outcoupled laser beam, which leads to a boosted light-matter interaction, especially attractive for continuous wave (cw) operating systems. In 1965, as a first experimental realization, Smith and collaborators demonstrated cw second-harmonic generation (cw-SHG), by means of a lithium niobate (LN) crystal, which was placed inside the laser cavity (intracavity) of a Nd:YAG laser [2]. As a straightforward development, researchers simplified this two-crystal approach by integrating laser-activity and nonlinear polarizability in one dual-purpose crystal, also called self-frequency-doubling (SFD) crystal [3, 4]. Phase matching can be ensured by the birefringence of the SFD crystal. It should be noted, that the development of SFD crystals is still a very active academic field [5]. Within the last decades, neodymium and magnesium oxide codoped lithium niobate (Nd:MgO:LN) turned out to be an outstanding SFD crystal, as this material combines the excellent lasing properties of the Nd-ion with the nonlinear optical properties of LN. Furthermore, birefringence of LN allows for non-critically phase matched SHG of the ordinarily (o) polarized laser line. Evidently, intracavity and self-pumped frequency conversion is not restricted to harmonic generation. However, it took about one decade more until the first demonstration of an intracavity cw-optical parametric oscillation (cw-OPO) was realized, using a titanium-sapphire crystal as the laser active medium and a KTiOPO₄ (KTP) crystal as the nonlinear optical crystal [6]. Later, periodically-poled Yb-doped LN was used to demonstrate the first self-pumped cw-OPO based on one dual-purpose crystal [7]. Here, we demonstrate a self-pumped cw-OPO which follows the trend of ultimate integration: The system presented here combines laser-activity, quasi-phase-matched parametric gain and broadband cavity mirrors in a mm-sized monolithic device. Instead of a conventional mirror-based cavity, we use a whispering-gallery-mode micro-resonator (WGR), a class of resonators, which has proven to be an excellent platform for cw three wave mixing [8]. The strongly confined whispering-gallery modes (WGMs), the ultra-high quality factors (Q-factor) and the intrinsic triple resonance give rise to an extremely low oscillation threshold [9,10]. Recently, we introduced a novel class of WGRs, combining laser-activity and χ⁽²⁾-nonlinearity in a single WGR, and demonstrated SFD in a WGR made of Nd:MgO:LN [11]. Phase matching was provided by the birefringence of LN and the geometric dispersion of the WGMs. Now, we present self-pumped cw-OPO in a mm-sized monolithic WGR made from Nd:MgO:LN. Here, two major difficulties come into play: (1) Birefringence cannot provide phase matching for a self-OPO, such that quasi-phase-matching (QPM) techniques are essential. (2) In contrast to SHG, an OPO exhibits an oscillation threshold, which needs to be overcome. Despite of these difficulties, we achieved self-OPO in a WGR, representing a highly integrated, monolithic, and multi-functional device.

2. Theoretical considerations

In order to avoid confusion, we need to distinguish the light which pumps the laser process from the light which pumps the OPO process. In the following, the former is called excitation light and the latter is called pump (p) light. An OPO is induced at the pump light frequency ν_p, and generates two light waves with the frequencies ν_s and ν_i, where ν_p = ν_s + ν_i. The latter ones are called signal (s) and idler (i) waves, respectively. An optical WGM can be characterized by its integer mode numbers p, q, and m [8]. The mode numbers p and q describe the transverse electric field distribution, with p zeros in the polar direction and q maxima in the radial direction. The azimuthal mode number m quantifies the number of oscillations along one round-trip. Phase matching in a WGR is fulfilled when

Birefringent phase matching (i.e. M = 0) cannot satisfy Eq. (1) for the given ν_p. Thus, QPM is indispensable to realize a self-OPO in a WGR made of Nd:MgO:LN. In this report, we choose a QPM structure with 262 radially oriented inverted domain lines, i.e. with M = 262. With a major radius R of the WGR of 1 mm, this refers to a periodicity Λ of 24 μm. Within a certain range, the choice of the number of domain lines is arbitrary. A different periodicity results in shifted tuning curves, such that any output wavelength within the transparency range of the host crystal can be chosen at will, by designing the QPM structure accordingly. Figure 1 illustrates the simulated tuning curves of a type 0 (eee) OPO with a QPM structure of 262 radial domain lines. A weak off centering of the QPM structure provides additional M values around 262 [10]. The simulations consider material and modal dispersion as they are based on the dispersion relation of spheroidal WGRs [14] and the Sellmeier equation of MgO:LN [15]. It is known, that the tuning behavior of WGR-based OPOs depends on the transverse mode numbers of the interacting WGMs, i.e. p_p,s,i and q_p,s,i. In Figure 1, near fundamental tuning curves are presented. All solid lines refer to M = 262. The tuning curve for a fundamental pump, signal, and idler WGM (i.e. p_p,s,i = 0 and q_p,s,i = 1), is illustrated by the solid green line in Fig. 1. This process provides a signal wavelength of about 1.8 μm at room temperature. A non-fundamental pump mode with q_p = 2 yields a signal wavelength of about 1.5 μm. A non-zero p_s,i brings the signal and idler wavelengths closer to the point of degeneracy. The effect of a slight variation of M is illustrated for the fundamental interaction by the dashed and the dotted lines.

 

Fig. 1 Tuning curves for OPOs, pumped at 1084 nm wavelength in a WGR made from MgO:LN with 262 radial domain lines. The major radius R and the minor radius r are 1 mm and 0.25 mm, respectively. The transversal mode numbers p and q of pump, signal, and idler WGMs have a strong influence onto the tuning behavior of a WGR-based OPO. The dotted lines refer to M = 261, the solid ones to M = 262, and the dashed lines to M = 263.

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3. Resonator fabrication and experimental setup

As the starting material we choose a 0.4-mol%-Nd and 5.1-mol%-MgO-codoped LN z-cut wafer. The wafer thickness is 250 μm. The QPM structure is generated by calligraphic electric field poling [16,17], before shaping of the resonator. For this purpose, chromium is deposited onto the +z-face of the crystal, in order to ensure a good electrical contact to the crystal surface. By moving a negatively charged metal tip over the −z-face of the crystal, the spontaneous polarization of the crystal flips its sign along the trajectory of the tip. The original approach [16] was improved by a constant current control, which keeps the electric current flowing through the crystal during poling at a constant value [17]. This improved technique yields superior poling results, even in congruently melting LN, as presented in Figs. 2 (a) and 2 (b). The Nd-doping of the crystal had no notable influence on the poling result. Domain-writing was done at elevated temperatures of about 150 °C, which reduces the anisotropic poling behavior along the crystallographic x- and y-axes. After the poling process, the chromium is removed and domain selective etching with potassium hydroxide (KOH) reveals the generated domain pattern. Subsequently, a preform is cut out of the poled wafer material by means of a femtosecond (fs) laser emitting at 388 nm with a 2 kHz repetition rate, and about 300 mW average output power, see Fig. 2 (c). Here, it is essential, that the symmetry center of the preform coincides with the center of the QPM structure, as elucidated in [10]. After shaping of the WGR on a lathe, again with fs-laser pulses, the WGR is polished by hand providing a Q-factor of 5.7 × 10⁷ at 1040 nm wavelength. We consider this as a lower-limit estimate for the Q-factor at the lasing wavelength, because 1040 nm is even closer to the nearest Nd-resonance than the actual lasing wavelength. By means of a Fourier transform infrared (FTIR) spectrometer, we verified, that the Nd-doping causes no measurable absorption in the mid-infrared range. According to [18] we expect a similar Q-factor for the signal light as measured for the pump light and about one order of magnitude less for the idler light. Figure 2 (d) shows the experimental setup for the optical experiments. Excitation light from a cw-emitting titanium-sapphire laser at 813 nm wavelength is focused to the base of the coupling prism. At this wavelength the Q-factor is about 10⁵ due to the strong absorption of the Nd-ions, such that the excitation light does not need to be tuned to a narrow-band WGM [11]. The excitation light is e-polarized, which leads to strong e-polarized lasing, which is the prerequisite for a self-OPO [11]. Generated laser, signal, and idler light are analyzed by power detectors and a grating spectrometer. All experiments are performed at room temperature.

 

Fig. 2 (a) Quasi-phase-matching structure after domain selective etching under dark field illumination. Domain walls appear as bright lines. The dotted circle marks the anticipated shape of the WGR. The solid circle refer to the trajectories of the fs-laser for cutting out the WGR preform. The central cross serves as a spatial reference mark. (b) Magnification of the marked square in part (a). (c) Work flow of the WGR fabrication. (d) Experimental setup. Dichroic mirrors (DM) and a beam splitter (BS) steer the light beams to the power detectors and the spectrometer. (e) Photograph of the WGR on a brass post with coupling prism.

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4. Results and discussion

Below an excitation pump power of 53 mW, e-polarized lasing around 1084 nm and SFD into the green spectral range occurs. The generation of coherent green light via SFD is discussed in a previous study [11]. Interestingly, blue light emission is observable with the naked eye when having some mW of outcoupled laser light. The emission is independent of the presence of a self-OPO. A grating spectrometer for the visible spectral range reveals a wavelength of about 465 nm, which can be attributed to sum-frequency generation of the excitation light and the internally generated laser light. This assumption is supported by the finding, that a change of the excitation wavelength changes the wavelength of the blue light, whereas the wavelength of the SFD light stays unchanged. At a coupled excitation power of 53 mW, we observe a self-OPO. The excitation power at the prism base is about 0.23 W which corresponds to a coupling efficiency of about 23 %. A higher coupling efficiency can be achieved by bringing the coupling prism closer to the WGR. However, this can overcouple the pump, signal and idler wave, which in turn increases the OPO threshold and is detrimental for a low-threshold OPO [8]. The outcoupled power of the internal laser oscillation P_lasing is about 5.0 mW. Considering bidirectional lasing, we find an internal laser efficiency of 19 %. In this configuration, the measured power of signal and idler light P_s+i reaches a value of 107 μW. When coupling 56.4 mW of excitation light to a different WGM, while having 0.36 W at the prism base, P_s+i reached values exceeding 1.2 mW, while having about 6 mW of P_lasing. This refers to 20 % conversion efficiency. As we have very limited information about the interacting modes, we cannot properly compare the measured efficiency with theoretical expectations. However, the measured conversion efficiency is comparable with those efficiencies, observed in other WGR-based OPOs [8]. Figure 3 presents the signal and idler wavelengths of all observed OPO processes. As the grating spectrometer could not measure above 2.55 μm, we deduced the idler wavelengths from their signal wavelengths. As described in the theory part above, the flexibility in the output wavelengths comes from the interaction of WGMs with different transverse mode numbers. Some OPO processes show coincidence with the simulated ones in Fig. 1: The second OPO process in Fig. 3 matches with a p_p = 0, p_s,i = 1, q_p,s,i = 1 interaction. The third process in Fig. 3 is likely to be caused by an interaction of fundamental pump, signal, and idler WGMs. The fifth process shows coincidence with a q_p = 2 OPO process. The first and the fourth processes might come from higher p_s,i mode numbers or from an interaction with a M ≠ 262 contribution.

 

Fig. 3 Normalized spectra of all observed self-OPO processes. The numbers indicate signal and idler wavelength pairs. The values above the spectrometer cut-off wavelength of 2.55 μm are calculated values.

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Obviously, the flexibility of the pump mode numbers p_p, q_p, and m_p provides a high flexibility in the OPO output wavelengths, as different pump WGMs lead to different OPO processes. Deterministic tuning of the signal and idler wavelength by changing the temperature is yet not feasible, as mode hops and an undesired change of the transversal pump mode numbers can lead to a different OPO process. This uncertainty makes it also not yet feasible to properly record the output versus the excitation power, as a changed excitation power results in a different WGR temperature, which spectrally shifts the WGMs and can lead to mode hops of the pump mode. In case controlled and deterministic wavelength tuning is required, our analysis shows that the number of possible laser modes needs to be reduced by appropriate mode selection techniques. Suitable morphology-engineering of the resonator [19] as well as the introduction of a spatially inhomogeneous gain- [20] or loss-profile [21,22] reduces the range of possible p_p and q_p mode numbers, whereas a smaller WGR with an increased free-spectral range leads to a reduced variation of the m_p mode number.

5. Conclusion

In conclusion, we demonstrate that lasing and quasi-phase-matched OPO can be integrated in a single monolithic mm-sized WGR. Our study shows that laser modes with low transverse mode numbers are of major importance for a self-OPO. Quasi-phase-matching can be designed at will, such that any emission wavelength within the transparency range of the host material comes into reach of self-pumped frequency conversion in a WGR. A further prospect is also to replace the titanium-sapphire laser for pumping by a cheap laser diode, as it was demonstrated for SFD in a micro-resonator of similar size [11]. The required excitation powers are achievable with low-cost laser diodes, such that the concept presented here bears great potential for a cheap and highly wavelength-tunable coherent light source, which is of utmost importance for cost sensitive applications outside of research laboratories.