1. Introduction

Optical whispering gallery mode (WGM) resonators are useful for multiple fundamental and practical applications. On one hand, they offer a unique combination of high quality factors and small mode volumes leading to enhancement of efficiency of various nonlinear processes [1]. On the other hand, the resonators are monolithic solid state structures recognized for relative ease of integration into optical circuits allowing for fabrication of robust microdevices [2, 3].

The Quality (Q-) factor and finesse of these resonators are ultimately determined by the optical properties of the host material. To avoid undesirable effects related to latent impurities, many applications of WGM resonators in science and technology place strict demands upon the material quality [4]. On the other hand, the strong dependence of the resonators Q on material purity provides a useful tool for probing dopants of the material [5]. In this study we use a WGM resonator made out of nominally pure UV-grade calcium fluoride (CaF₂) crystal to study residual dopants of the material. The interaction process between the pump laser, the resonant modes, and the ionic impurities trapped within the resonator result in the emission of light that is of longer, as well as shorter, wavelength compared to the pump. The upconversion process is explored as a mechanism for achieving efficient laser cooling [6] of the solid state resonator.

The laser action from WGM resonators fabricated from rare earth doped solids has been extensively studied. Moreover, the first observations of WGMs in optics can be attributed to solid state WGM lasers. Laser action was studied in Sm:CaF₂ crystalline resonators [7]. Microsecond-long transient laser operation has been observed in [8] with a several millimeter ruby ring at room temperature. Transient oscillation was attributed to pulsed laser excitation of WGMs with Qs of 10⁸ − 10⁹. The size of the resonator was in the millimeter range.

A WGM laser based on neodymium-doped silica microspheres with 200 nW pump power threshold was realized [9] with microspheres of radius a ∼ 25–50 μm. Neodymium ions were pumped with a ∼ 810 nm diode laser on the ⁴I_9/2 − ⁴F_5/2 transition. The laser action occurred at transition ⁴F_3/2 − ⁴I_11/2 in the 1.061.09 μm range. Similar experiments with neodymium-doped microresonators were reported more recently [10–12]. A green up-conversion laser was demonstrated at room temperature in a 120 μm diameter microsphere fabricated of Er³⁺ doped ZBLAN [13–15]. Lasing occurred around 540 nm with a 801 nm pump. The lasing threshold was 30μW of absorbed pump power.

Optically clean crystals always contain trace amounts of extrinsic dopants. The dopant concentration usually does not exceed several parts per million, which is negligible for majority of applications. However, in crystalline WGM resonators with finesse exceeding a million [4] over a broad wavelength range, the small impurity concentration becomes important [16]. In the current study we show that laser action similar to that mentioned above can be realized in a microresonator made of a nominally pure material [17], but with a concentration of the active centers several thousand times smaller than the intentionally doped materials. We pumped a nominally pure CaF₂ WGM resonator at 795 nm and observed emission at both IR (1.03–1.09 μm) and green wavelengths, which confirms the common hypothesis that the pure material does indeed contain traces of Nd³⁺ and Er³⁺ ions.

The crystal structure of CaF₂ consists of F⁻ ions located along the corners of a cubic grid, with Ca²⁺ ions located in every-other cube. It is energetically favorable for some number of triply ionized rare earth impurities such as Nd³⁺, Yb³⁺, Tm³⁺, and Er³⁺ to replace Ca²⁺ centers in the stoichiometric crystal [18]. The resultant net positive charge per unit cell is compensated by a localized re-arrangement of nearby F⁻ ions leading to cell deformation. This picture suggests that a crystal with some density of impurities exhibits different optical profiles compared to an ideal crystal. In our experiment we confirm this point observing stimulated Raman scattering at a wavelength not specific for the ideal crystal.

This paper is organized as follows. In Sec. 2.1 the experimental setup is described. The experimental results pertaining to observation of IR as well as green light generation in a WGM resonator made out of nominally pure calcium fluoride are presented in Sec. 2.2. Modification of the Raman scattering in the resonator is discussed in Sec. 2.3. The data are analyzed in Sec. 3. Possible applications of crystalline WGM resonators doped with small concentration of rare earth ions are discussed in Sec. 4. Sec. 5 concludes the paper.

2. Experiment

2.1. Experimental setup

We fabricated a truncated spheroidal crystalline CaF₂ WGM resonator and pumped it with 795 nm light from a distributed feedback (DFB) semiconductor laser that was self-injection locked [19] to a selected WGM. The self-injection locking resulted from the resonant Rayleigh scattering occurring within the resonator due to surface as well as volumetric imperfections [20]. The light from the laser was sent in and retrieved out of the resonator using glass coupling prisms. The light exiting the output prism was collimated and coupled into a multi-mode optical fiber (optical pipe) to be further analyzed by an optical spectrum analyzer. The spheroidal resonator with 4.1 mm and 1 mm semi-axes was fabricated out of a 〈1, 1, 1〉-cut UV-grade CaF₂ optical window [17] by mechanical polishing. This arrangement is depicted in Fig. 1.

 

Fig. 1 Experimental setup. Laser light is coupled to the WGM resonator through a glass prism. The backscattered light injection locks the laser to the selected mode of the resonator, and keeps the laser in lock through the experiment. A second (output) prism is used to collect light transmitted through the resonator. The entire experimental platform including laser and the resonator, was thermally stabilized.

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The coupling prisms were equally spaced with the resonator surface to maximize transmission of the light. The DFB laser operating slightly above and far above threshold emitted 30 mW and 85 mW of light respectively. Approximately 70% of light entered the resonator through the first prism and 70% of light exiting the resonator was collected to the optical pipe. The transmission peaks on the output side corresponded to 50% of the input side DC power level. The spectrum of transmitted light was measured using an optical spectrum analyzer (OSA). We used the ANDO AQ6315 OSA, with a linear scanning range of 670 nm–1700 nm.

The optical Q-factor of the resonator was measured with ring down spectroscopy [21]. A fast sawtooth modulation (10 kHz) was applied to the laser current. As the result the laser frequency was modulated with 100 MHz span. The sweep time of the pumping light through the resonator mode was less than 0.3 μs (the higher Q-factor of the mode, the less the time). Measuring the decay time of the transmitted through the resonator light we are able to measure the loaded quality factor of the resonator modes. The transmitted light was sent to a photodiode (Thorlabs DET10A, responsivity 0.5 A/W and 1 ns rise time) to measure the ring down signal. If signal is fit with exponential decay ∼ exp(−t/T), where t is time and T is ring-down time constant, the quality factor of the resonator is given by Q = 2πcT/λ, where c is the speed of light in the vacuum and λ = 795 nm is the resonant wavelength.

We studied Q-factors of different mode families, fundamental (longitudinal) and higher-order transverse. The far field intensity pattern of the fundamental mode has a single lobe, while the pattern of higher order transverse mode has two lobes (see [2] for a description of whispering gallery mode nomenclature and [22] for an alternative treatment). The resonator fundamental mode was overloaded with the prism couplers. The ring-down time associated with the modes was T = 0.6μs, which corresponds to the loaded Q-factor approaching 1.4 × 10⁹.

A non-exponential decay was observed (Fig. 2) with less loaded higher-order modes, indicating that there were two time constants, T₁ = 2.7 μs and T₂ = 9 μs, associated with the ring down. The faster decay time, T₁, is observed when more light is confined in the mode. The slower decay time, T₂, is apparent when the circulating power in the mode is less than some threshold value. This behavior is consistent with the onset of nonlinear loss mechanisms within the resonator when it is optically pumped beyond the threshold power value of the nonlinear process that results in additional loss of the pump light. In the low-power regime, the resonator loaded Q-factor was 6.4 × 10⁹; in the high power regime the Q factor was 2 × 10¹⁰. The measured quality factor of the transverse modes is at the same order as the quality factors routinely observed at different wavelengths in WGM resonators fabricated from calcium fluoride [4,16]. The difference in the coupling strength results from the specific shape of the resonator as well as from the possible damage of the resonator surface in the proximity of its equatorial part that can occur due to unintentional contact with the coupling prisms.

 

Fig. 2 Resonator ring down measurement to determine Q-factor. The red dots represent the measured data, the solid blue line is an exponential decay fit to the low-Q (high intensity) regime, and the dashed blue line is an exponential decay fit to the high-Q (low power) regime.

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2.2. Generation of IR and green light

We observed generation of both IR and green light by operating the DFB laser close to threshold (approximately 20 mW of light coupled to the mode) and pumping a high-Q transverse mode. Our OSA cannot be used to characterize the wavelength of the green light, so we were able to register the generation only through visual observation.

Figure 3 shows a representative OSA scan of the IR emission lines. IR emission peaks at 1035 nm, 1045 nm, 1064 nm, and 1092 nm were observed. A green glow of the resonator is shown in Fig. 4. The laser was tuned to excite several other transverse WGM’s. All of the observed transverse modes produced similar results to what was described above: a green-glow along the resonator edge and well defined peaks in the IR. We did not study the coherence properties of the IR light, however, high contrast and narrow linewidth of the generated harmonics points out at the stimulated nature of the observed emission.

 

Fig. 3 High-resolution detail of the emission spectrum in 1025–1100 nm wavelength range. Emission peaks at 1035 nm, 1045 nm, 1063 nm, and 1092 nm are evident. The inset shows the details of the 1063 nm line takes with smaller pump power. Since the resonator has a very dense spectrum, but the number of emission lines is limited, we expect that we observe a coherent IR emission (lasing) from the resonator.

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Fig. 4 Observation of frequency upconversion in the resonator. Light input at 795 nm ultimately produces a distinct green emission. Scratches along the resonator surfaces, prominent at 1:00, 5:00, 7:00, 8:00, and 11:00, facilitate viewing of the green light.

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When the output power of the DFB laser was increased, the level of the IR emission peaks did not change, nor did the visually-assessed brightness of the green glow. Below the threshold current of the DFB laser, self-injection locking did not take place as the noise of spontaneous emission in the laser limited the amplitude build up within the WGM resonator. In this case, the IR lines were not detected by the OSA, and the green glow was reduced to a transient flicker. Optically induced thermal oscillations within the WGM resonator likely drove the resonant frequency in and out of coincidence with the fixed frequency laser emission limiting resolution of the emission lines.

2.3. Nonlinear scattering

Optical pumping the fundamental mode sequence of the WGM resonator revealed different emission spectra compared to what was observed while pumping higher order transverse modes. The emission spectra included Raman lines consistent with previous studies of CaF₂ WGM resonators [23]. However, neither IR spectral features in the 1000–1100 nm wavelength range nor any green light was observed. The primary reason for the difference is much lower Q-factor of the fundamental mode family. Generation of the green light is especially prone to a quality factor decrease, since the generation threshold is inversely proportional to the product $Q_{795nm}^2{Q}_{530nm}$, as shown below. A decreasing Q-factor makes this process less favorable compared to Raman scattering with its threshold inversely proportional to $Q_{795nm}^2$. The threshold for generation of the IR light depends on Q_795nmQ_1μm and it is not entirely clear why the IR light is not observed when the lower-Q fundamental mode sequence is pumped.

Possible explanations for the difference in the emission pattern include spatial inhomogeneities in the distribution of the impurities as well as parametric nature of the green light generation. The parametric process h̄ω_795nm + h̄ω_795nm → h̄ω_535nm + h̄ω_1550nm would result in green light generation. Since the nonlinear process requires phase matching, pumping higher order modes could be more preferable compared with pumping of the fundamental modes. However, we did not observe any emission at or around 1550 nm, which shows that the green light emission does not result from the parametric frequency conversion.

We observed Raman scattering from two phonon families at intermediate output power (45–60 mW in the mode) [24]. An OSA scan of the pump and the Raman lines is shown in Fig. 5. Five Stokes lines associated with the 320 cm⁻¹ Raman transition of CaF₂ are evident. A second Raman line, 1400 cm⁻¹ detuned from the carrier is simultaneously observed. We consider the presence of this line as the evidence of deformation of the crystalline lattice due to presence of extrinsic impurities. It was noted in [25] that ideal CaF₂ crystal has only one IR active Raman line (O_h symmetry of the crystal and the triatomic unit cell should have only one Raman-active mode, F_2g [26]). The other lines observed in the Raman spectrum originate from extrinsic or intrinsic impurities of the material. Examples of Raman spectra of heavily doped calcium fluoride can be found in [27].

 

Fig. 5 Multi-phonon Raman scattering spectrum. Five Raman Stokes lines corresponding to phonon energy of 320 cm⁻¹ are evident, and a single Stokes line corresponding to phonon energy of 1400 cm⁻¹.

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The evidence for parametric four wave mixing between the carrier and the first Stokes line was observed when the laser was set to its maximum output power (85 mW). Fig. 6 depicts an example of this observation. In this process two orders of Stokes Raman lines are generated from the optical pump. Four wave mixing process results in oscillation producing two frequency harmonics located between the pump and the first order Raman lines: h̄ω_pump + h̄ω_Raman → h̄(ω_pump − Δω) + h̄(ω_Raman + Δω). The value of frequency detuning, Δω ≃ 1.4 THz, results from phase matching conditions unique for the particular resonator. The higher order Stokes sidebands as well as other possible process are not realized because the particular resonator does not have modes to support them [28, 29]. On the other hand, the correspondence of frequency detuning to an integer number of FSR shows that four wave mixing occurs within the same mode family.

 

Fig. 6 Emission spectrum of the resonator with a fundamental WGM pumped. Line a is the carrier, line b is the first Stokes component. The second Stokes component is not labeled. Lines c and d are the result of four wave mixing between the carrier a and the first Stokes component b. This process does not result from impurities of the resonator host material. The frequency detuning, Δω ≃ 1.4 THz, is an integer number of the free spectral range (FSR) of the resonator, corresponding to 175 FSR.

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3. Analysis

The quantitative measurement of the IR lines in the WGM resonator (Fig. 3) is indicative of excitation and fluorescence of trapped impurities within the nominally pure UV-grade CaF₂ crystal. Experiments performed on CaF₂ windows using high peak power pulse lasers and arc sources have measured the spectra of rare earth impurities trapped in the crystal [30]. The spectrum of CaF₂ :Nd³⁺ includes an absorption feature (the 2F_7/2−2F_5/2 transition (Fig. 7)) centered at 795 nm, the laser pump wavelength. This excitation relaxes through emission of 1034 nm light, and 1045 nm light [18] which corresponds to the observations reported in this paper. Other reports of CaF₂ :Nd³⁺ show broad emission lines at 1090 nm and 1063 nm, and that reduced concentrations of impurities shift the line centers and narrow the line widths. Therefore, in accordance with our measurements, the nominally pure material contains Nd³⁺ ions.

 

Fig. 7 Energy level diagram of (a) Nd³⁺ and (b) Er³⁺ ions (not to scale). When the pump laser excites Nd³⁺ ions, light at 1035, 1045, 1090, and 1064 nm is produced. All emissions are co-resonant with the WGM resonances (as evidenced by the groups of peaks in Fig. 3. Resonant excitation of Er³⁺ ions through a two-photon absorption process results in green light generation. The 795 nm pump is up converted to 530 nm.

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Fluorescence studies of CaF₂ doped with Er³⁺ ions give a clue to the mechanism behind the qualitatively observed green glow of the resonator. Two-photon absorption of the pump light takes place, exciting Er³⁺ ions [13–15]. The Er³⁺ ion decays back to the ground state by emitting 530, 550, or 670 nm photons. Associated with each line is a corresponding non radiative decay. The 530 nm emission is energetically preferred since the phonon produced in that particular non radiative decay process is of lower energy than the phonon required to produce 550 or 670 nm emission. The 1550 nm emission of Er³⁺ ions was not observed. This emission could be quenched due to interaction with Nd³⁺.

It is common for CaF₂ crystals to contain some amount of rare-earth impurity ions, such as Er³⁺ and Nd³⁺ [31–33], but he residual amount of the impurities is usually much lower in UV-grade crystals. However, even a small concentration of the impurities leads to a large number of ions interacting with a single mode of the resonator. The mode volume of our resonator is approximately 𝒱 ∼ 10⁻⁶ cm³. One part per billion (ppb) concentration of the ions corresponds to 10¹³ cm⁻³ spatial density of the particles. This means that light confined in the mode interacts with 10⁷ ions if the concentration is 1 ppb. This is more than enough to sustain lasing in the mode [9]. On the other hand, such a concentration is too tiny to be detected by any other means, including optical spectroscopy. WGM-based spectroscopy improves the sensitivity of the measurements of latent impurities in a nominally pure crystal by several orders of magnitude.

4. Possible applications

The presence of multi-species impurities that interact with high-Q WGM’s can be applied to address a number of practical applications and simplify otherwise complicated and costly experiments. For example, the two photon absorption process along with anti-Stokes emission of green light could be used towards laser cooling of solids [6]; the interaction of the resonator modes with the ion emission could be used to study the Purcell effect and related processes in quantum electrodynamics.

We propose to use WGM resonators to improve the quality of optical cooling. The basic process of cooling can be understood as follows. The laser light interacts with homogeneously broadened two-level system having broad ground and excited level manifolds. Due to a strong particle interaction the excitation of any part of each manifold transfers to the excitation of the whole manifold in a very short period of time. Therefore, if the two level system is pumped at a frequency that corresponds to the frequency splitting between the top edge of the ground state manifold and bottom edge of the excited state manifold, the two level system fluoresces at a higher frequency, approximately equal to the frequency difference between the ground and the excited manifold. Such an anti-Stokes scattering of the pump radiation is possible only if a part of vibrational energy of the host material is removed. Each act of fluorescence takes from the host an amount of energy equal to h̄(f_e − f_p), where f_e − f_p is the difference between carrier frequencies of the pumping and scattered light. The total power removed from the sample is

Since the first observation of laser cooling in solids by doping fluorinated glass with ytterbium (see [6] for review), researchers have explored the use of various glass and crystal materials, and a variety of dopant species. Two strategies have been previously adopted to enhance the cooling efficiency by enhancing the absorbed radiation through a multi-passing of the applied light: intra-cavity, and extra-cavity techniques. In the extra-cavity approach, the sample is placed inside a cavity external to the laser source, where light is reflected back and forth with multi-passing through the sample. In the intra-cavity technique, the sample is placed inside the laser cavity, itself. While both techniques offer the possibility of enhancing the cooling efficiency, they both suffer from deficiencies that severely limit their usefulness. In the first case, the approach requires dielectric mirrors that absorb a fraction of the laser light might with each pass, resulting in a local heating and, thereby, increasing the overall heat load on the cooling medium. Also, the reflective coating allows leakage of the fluorescence, as the coating is not perfectly reflecting.

The intra-cavity approach eliminates the shortcomings of the external mirrors, but introduces other deficiencies. These include introducing the need for an additional tunable gain medium and added optical components. Also, in the diode-pumped solid-state laser system used in that approach, the conversion of laser diode pump radiation to tunable intra-cavity radiation represents a significant impact on the overall power budget.

We propose a technique that utilizes doped WGM resonators with high optical quality factor as a novel approach to the problem of increased cooling efficiency in light refrigerators. Unlike conventional resonators and delay lines that utilize dielectric mirrors, WGM resonators use the effect of total internal reflection to confine light. We have demonstrated in this paper that the residual losses introduced by the imperfectness of reflection in crystalline WGM resonators can be as small as 10⁻⁵ cm⁻¹, well below the absorption of cooling materials quoted above. The amount of pump radiation sent into the resonator, as well as the efficient number of cycles that the radiation makes in the resonator can be regulated by various efficient coupling techniques developed for WGM resonators. Hence, the effect of total internal reflection seems to be ideal for improving optical cooling efficiency. The advantages brought about by this technique include (i) efficient cooling with small laser power, (ii) small size of the cooling medium, (iii) large confinement of active photons, (iv) elimination of dielectric mirrors, (v) compatibility with all active materials and needed wavelengths.

5. Conclusion

We have experimentally demonstrated optical scattering as well as lasing from a whispering gallery mode resonator fabricated with nominally pure single crystal calcium fluoride. We argue that the observed emission is due to the presence of trace impurities of of rare earth ions in the resonator host material. The data presented in this report strongly support the assertion that a small number of Nd³⁺ and ions interacting with the resonator modes produce spectral emission at 1036, 1045, 1064, and 1092 nm. The assertion that there is a small amount of Er³⁺ ions in the crystal requires further study. The narrow linewidth of the emission lines compared to a typical fluorescence signal suggests lasing. Two particular examples of future studies include visible range spectroscopy, characterizing the lasing threshold of the impurities, and measuring the coherence of the emission lines. The measurement demonstrates potential usefulness of the resonator enhanced spectroscopy for quality control of optical materials.