We report an investigation on angle-cut beta barium borate (BBO) whispering gallery mode (WGM) resonators operating in the ultra violet (UV) wavelength range. A quality (Q) factor of 1.5 × 108 has been demonstrated at 370 nm. New upper bounds for the absorption coefficients of BBO are obtained from the Q factor measurements. Moreover, polarization rotations of WGMs in the angle-cut birefringent resonators are observed and investigated. To the best of our knowledge, this is not only the first reported demonstration of an angle-cut WGM resonator but also the first reported high Q WGM resonator in the UV region.
©2012 Optical Society of America
An optical whispering gallery mode (WGM) resonator confines light along the circumference of a circular dielectric material by continuous total internal reflection. WGM resonators feature ultra-high quality (Q) factors and small mode volumes in the entire transparency range of the material that they are made from [1–3]. Mechanical polishing techniques offer a way for high Q factors in WGM resonators from crystalline material [3,4]. Combined with their intriguing material properties and compact size, crystalline WGM resonators have drawn strong interests in various applications especially nonlinear optics. For example, efficient second harmonic frequency generation was studied in nonlinear crystalline WGM resonators utilizing different phase matching techniques. So far, these studies were performed in the visible, infrared and terahertz regions. The first demonstration of second harmonic generation (SHG) in WGM resonators was from linearly poled lithium niobate via quasi-phase matching . SHG and optical parametric oscillations using non-critical phase matching were observed in MgO doped lithium niobate WGM resonators [6,7]. Generation of harmonics and parametric oscillations were also demonstrated in radially poled lithium niobate resonators [8,9]. The symmetry axis of the resonators has been exclusively chosen to coincide with the optic axis of the crystal (often referred to as a z-cut resonator).
More recently, a strong interest has arisen in extending high Q WGM resonators to the ultra violet (UV) region . So far, only lithium niobate and lithium tantalate have been used for second-order nonlinear optics in WGM resonators [5–11]. These crystal materials are not suited in the UV range due to strong photorefractivity and poor UV transparency. There exist, however, several other crystals such as beta barium borate (BBO)  that are transparent in UV and have relatively high nonlinear coefficients. BBO is an attractive material to be investigated in WGM resonator systems for nonlinear optics applications in UV. Motivated by exploring various types of phase matching conditions for nonlinear processes, we also studied resonators made of uniaxial crystals where the optic axis is titled with respect to the resonator symmetry axis (we will refer to it as angle-cut WGM resonators).
This paper reports the first demonstration of a WGM resonator made from angle-cut BBO crystals . We show that not only WGMs with high Q factors still exist in angle-cut BBO resonators, but also high Q factors are achievable from near infrared to UV. These measurements yield new upper bounds for the absorption coefficients of BBO. Moreover, we present characterization of the polarization properties of WGMs in the angle-cut crystalline resonators. The results are non-intuitive and interesting, and will lead to further study of WGMs in angle-cut birefringent medium.
2. Experimental setup
To fabricate a BBO resonator, we first identify the optic axis of the crystal substrate by sending a visible linearly polarized beam of light through it and detecting the incident angle where the birefringence disappears. The substrate is then cut into disks. The edge of the disk is polished into a spheroid shape with optical grade smoothness . We have fabricated a number of BBO WGM resonators with 33 ± 3° and 57 ± 3° angles between the crystal optic axis and the symmetry axis normal to the disk plane, as well as the z-cut resonators.
The experimental setup for studying the BBO resonators is illustrated in Fig. 1 . A number of laser sources were used including a UV laser at 370 nm. The laser can be scanned over one free spectral range (FSR) of the WGMs and the scanning frequency is calibrated by sending a small fraction of the beam to a Fabry-Pérot cavity. The major fraction of the beam is sent to the WGM setup and focused on the back side of a sapphire prism. This prism provides for evanescent coupling with the BBO resonator. A piezo actuator is used to control the coupling gap. The inset in Fig. 1 shows a photograph of the resonator where the blue line indicates the crystal axis. The light couples in and out of the resonator via the prism and the reflected beam is thereafter collimated and guided into a photodetector.
3. Q factor measurements
The strong birefringence of the BBO crystal combined with an angle-cut resonator geometry gives rise to interesting questions regarding the existence of high Q modes and the mode polarization properties in the WGM resonator. Concerning the first question, we measured the Q factors of the resonator modes in the under-coupled condition with various lasers at 370 nm in UV, 980 nm in NIR, and 1560 nm in IR. These lasers have the short-term linewidths of 1 MHz, 300 kHz, and 5 kHz respectively, according to the laser manufacture’s specifications. Figure 2 shows an example of the WGM spectrum at 370 nm. It was obtained from a 33° cut disk with a diameter of 2.7 mm. A Lorentzian fit of the central resonance line gives a linewidth (full width half maximum) of Δf = 5.6 MHz, corresponding to a Q = f/Δf = 1.5 × 108.
The measured Q factors at 370, 980 and 1560 nm are tabulated in Table 1 . Recall that the Q factor in an under-coupled resonator of mm size is dominated by either the material absorption or surface scattering loss . It is clear from the table that the wavelength dependence of the measured Q factors does not scale as a typical Rayleigh scattering loss. This suggests that surface scattering is not the dominant loss limiting the Q over the wavelength range measured. Since the measured resonance linewidths are all larger than the expected linewidths of the lasers, we can assume the measured Q factors are limited by the internal material absorption loss. The absorption limited Q factor for a WGM is given by Qabs = 2πn0/(λαint), where n0 is the refractive index and αint is the absorption coefficient. The inferred absorption coefficients for BBO crystals are presented in Table 1. These coefficients are one order of magnitude lower than those reported in literature  and, therefore, yield a set of new upper bounds.
4. Polarization rotation
In a birefringent crystal, one expects to see an ordinary ray and an extraordinary ray, and the corresponding modes associated with them. This is indeed the case for z-cut WGM resonators where the TM modes are ordinarily and TE modes are extraordinarily polarized. Since the usual TE and TM polarization directions of a WGM resonator change with respect to the optic axis in an angle-cut crystal as light travels along the resonator, the actual mode polarizations in such resonators can become complicated. To study the polarization properties, we first investigate the polarization orientations of the high Q modes by monitoring the maximum and minimum excitation with varying input polarization at 1557 nm. Using a linear polarizer and a half-wave plate, we can probe the resonator excitation with linear input polarization at a variable angle of 2θ, where θ is the rotation angle of the wave plate with respect to the resonator plane (horizontal plane). The input polarization angle and other related geometries are illustrated in Fig. 3(a) ; the initial input polarization set by the polarizer is in the horizontal direction. To ensure that the input polarization remains linear, the birefringent sapphire prism in Fig. 1 was replaced by an isotropic SF11 prism.
Figure 3(b) shows a set of the observed mode spectra at various input polarization angles for a 33° cut disk. In particular, we notice that all modes are either maximally excited or minimized at the same input polarization angles. In other words, only one polarized family of WGMs is observed in the angle-cut BBO resonator. To account for possible differences in optimal coupling conditions for different polarization states, we have varied the coupling parameters such as coupling gap and light incident angle. Only one polarization was observed in all cases. This is in sharp contrast to z-cut resonators, where we easily find both ordinary and extraordinary polarized WGM families. To see the dependence of the excitation on the input polarization, we focus on one of the modes (between the two dashed lines in Fig. 3(b)). The coupling efficiency, i.e. the resonance dip contrast, vs. the input beam polarization angle is plotted in Fig. 3(c). It follows a cosine squared function, strongly suggesting a linear polarization projection coupling according to the Malus’s law. In other words, the excited WGM inside the resonator is linearly polarized as well. The optimal polarization orientation for the input beam in this case is 2θ0 = 54°. Since this orientation does not correspond to any of the typical TE (2θ0 = 90°) or TM (2θ0 = 0°) modes, the polarization of the WGM mode is not trivial and likely rotates along the circumference of the disk.
The polarization rotation inside the resonator can be mapped by performing the same measurements along the disk circumference at various coupling position. The coupling position is parameterized by the angle β between the projection of the optic axis and the prism-resonator interface, as illustrated in Fig. 3(a). We place the resonator on a rotation stage that allows us to change the coupling position readily at a set of points along the circumference. 2θ0 is determined at each β. The resulting plot of 2θ0 vs. β is shown in Fig. 4 . Obviously, the polarization rotates from TM orientation for the optical axis being aligned with the coupling interface to a maximum angle for the projection of the optic axis being perpendicular to the coupling interface.
5. Nature of the WGM polarization state
BBO crystals have a large birefringence; the relative birefringence (no-ne)/no is larger than 6%. By measuring the FSR of the observed WGM, we can determine the effective index of refraction neff, and therefore learn about the nature of the average polarization of the mode. We carefully measured the FSRs by employing laser modulation such that the investigated mode overlaps with its own sidebands span across the FSR. The FSR determined this way has a precision better than 2 MHz out of about 30 GHz. The diameter of the resonator is carefully measured with a calibrated precision micrometer under a microscope. The measurement error is 4 µm out of the diameters about 2 mm. By comparing the measured FSRs with the calculated ones of different radial modes, we found an index value neff = 1.645(0.003) for the 33° cut resonator. This index of refraction value matches well with the known ordinary ray index no = 1.646 calculated from the Sellmeier equation . The calculated extraordinary index is ne = 1.531. We can conclude from the index measurements that the only observed mode propagates along the entire resonator circumference as the ordinary ray. Similar results were found in all other 33° and 54° cut resonators.
The polarization of the ordinary WGM must always be in the plane perpendicular to the optic axis, and at the same time, in the plane perpendicular to propagation direction of the light. From these two planes, we can derive the relationship of the WGM polarization angle ψ of the ordinary ray polarization direction as a function of the crystal cut angle γ and resonator position β: tan(ψ) = tan(γ)sin(β). The theoretically calculated WGM polarization angle ψ for the ordinary ray polarization in the resonator is plotted in Fig. 4 together with the measured optimal coupling angle 2θ0 of the incident light. The measured polarization angle 2θ0 follows the change of the ordinary ray polarization direction in the crystal resonator around the circumference in a similar functional dependence: it is horizontally polarized at β = 0° or 180° when the optic axis is in the plane parallel to the prism coupling surface; and it reaches a maximum angle when the optical axis is in the plane perpendicular to the prism coupling surface.
The exact transformation from a linear polarization of the incident light to the polarization inside the resonator is not trivial. Experimentally we observed a coupling behavior of linearly polarized light following Malus’s law at all coupling positions β. Thus, it is justified to assume linear polarization inside the disk. We can then write tan(ψ) = c tan(2θ0), where c is a constant coefficient describing the linear polarization change from the input polarization to the WGM polarization. The function fits well the measured 2θ0, yielding c = 0.54, as shown in Fig. 4.
In contrast with z-cut cases, we have not been able to find the second, orthogonally polarized family of WGMs in the angle-cut BBO resonators. We attribute this to the inhibited reflection phenomenon . It is well known that when an ordinary or extraordinary polarized beam impinges on the inner surface of a birefringent crystal, each reflection in general produces two rays, again ordinary and extraordinary polarized. For nearly-grazing incidence at the inner surface of negative crystals, the ordinary-to-extraordinary reflection may be inhibited, and the energy is then redistributed to the ordinary polarization . Though the polarization state of light in a WGM resonator is more complicated and may not be completely treated using the ray theory, the double reflection and inhibited reflection mechanism may be responsible for the lack of the second polarization mode and for the polarization rotation discussed above. A quantitative analysis of this phenomenon is out of the scope of this report and will be a subject of further investigation.
In conclusion, we have fabricated for the first time a WGM resonator from BBO crystals. We demonstrated the first ultra-high Q WGMs in the UV wavelength range and in an angle-cut resonator made of a strongly birefringent crystal. New upper bounds of the material absorption coefficients of BBO at three different wavelengths are established. Furthermore, polarization properties of WGMs in an angle-cut BBO resonator have been experimentally investigated. There exists only one polarization mode of ordinary ray in the angle-cut BBO resonators and its polarization precession is observed. This work lays a foundation for further investigation of WGM properties of non-z cut birefringent resonators and their role as sensor and nonlinear optics applications.
This work was performed at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with NASA. We acknowledge discussions with Doctor Harald Schwefel and Florian Sedlmeir. G. Lin acknowledges support from the NASA Postdoctoral Program, administered by Oak Ridge Associated Universities (ORAU). J. Fürst acknowledges financial support from the Max Planck Society.
References and links
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