We propose the use of a prism with nonlinear optical properties to improve the prism-coupling method. The principle is based on the inscription of an adapted waveguide inside this prism by beam self-trapping to enhance the coupling efficiency and stability. The experimental demonstration is realized with a prism diced from a LiNbO3 wafer to couple light into a resonator.
© 2015 Optical Society of America
Since the seminal paper of Tien and Ulrich , prism coupling has been a very successful coupling method. It was the natural choice to couple light with waveguides, plasmons, or high-Q resonators when butt coupling was not feasible [1–4]. Later on, a new method involving side-polished or fused-fiber taper was proposed to couple with various devices from whispering gallery-mode resonators to photonics crystal waveguides with the benefit of optical fiber compatibility [5–8]. In the prism-coupling method, the total internal reflexion (TIR) upon the internal face of a prism is used to produce an evanescent field that can be coupled to an external device. A proper adjustment of the angle of incidence enables to fine tune the propagation constant and insure the phase matching. For best coupling, the incident-beam size should be as close as possible to the guided mode or resonance field supported by the external device. To satisfy this criterion, light is usually focused upon the coupling surface. However, focusing too much eventually leads to the coupling of neighbor modes with close propagating constants. Consequently, in the prism-coupling method, a compromise has to be found leading to an awkward method. In the tapered fiber method, a standard optical fiber is pulled when heated by a gas-burner or an electric heater. The waist of the fiber is then adiabatically reduced along the fiber. As the guided mode propagates, it reaches the smallest diameter region (typically 1 µm) where the light is guided in a silica core surrounded by air. Due to the small core diameter, the evanescent field extends in air, and thus can be coupled. Unfortunately, this method suffers from the inherent fragility of the device. All the more, a good control of the fusion-pulling process is needed to reach the proper propagating constant, consequently this method is less flexible compared to the prism coupling .
In this paper, we propose an alternative method combining the flexibility of the prism-coupling and the advantages of guided propagation. We use a prism-coupling set-up that involves a prism made of a nonlinear material. The prism-coupling configuration enables to fine tune the phase matching at low power. At high power, the light beam induces its own waveguide thanks to the optical nonlinearity and is thus self-confined. It then travels guided, that is a typical feature of the tapered fiber coupling method. As the beam goes through TIR, it is coupled to a silica micro-sphere resonator. The reflected beam at the output of the prism is also self-guided and a resonance is observed.
An isosceles prism is diced from a z-cut stoichiometric LiNbO3 0.5 mm thick wafer. This crystal features a photorefractive effect that is strong enough to obtain self-guided beam in cw regime with good 2-D stability . The optically induced waveguide were proven to last longer than a month . In order to obtain the self-focusing and the inferred waveguides, we need a focusing nonlinearity, that can be obtained either by applying a high voltage along the crystal c-axis or by slightly raising the crystal temperature to exploit the pyroelectric effect . Note that even though the writing process has to be done with visible wavelengths, this method was proven to be compatible with fiber coupling for infrared wavelengths . Since LiNbO3 refractive index is about np = 2.2, the two equal angles of the isosceles prism are chosen to be 37.4° to match the refractive index of the silica microsphere nres ≃ 1.45. The microspheres were obtained by fusion of a standard optical fiber using a programmable fusion splicer. Their diameter is typically 135µm.
The optical set-up is described in Fig. 1(a). The polarized beam of a tunable laser with a 650-660nm wavelength range (Newfocus Velocity 6305) is coupled into a Polarization Maintaining Fiber (PMF) in order to get spatial filtering and a convenient control of the polarization. The output of the fiber is imaged at the input face of the prism with two lenses (L2-L3) and a diaphragm D1 enables fine tuning of the beam waist at the prism input. The input beam is imaged thanks to the reflection on the prism input face through L4 on a CCD camera. The launched beam profile can thus be monitored. The transmitted light propagates inside the prism and is subject to TIR on the opposite face where the coupling with the micro-resonator occurs. The relative position between the resonator and the prism is controlled by a 3-axis stage. After reflection upon the coupling area, the reflected beam reaches the ouput face of the prism and is imaged on a second CCD camera thanks to lens L5. To achieve light coupling in the silica-glass microsphere, the prism is tilted so the incident beam on the coupling surface has an incident angle θ. This angle fullfil the phase matching condition nP sinθ = nres. The method flexibility comes from the ability to tune that angle. We obtain the optimum coupling angle in two steps. First we search for the proper angle that lights up the micro-resonator at binocular sight. Then the beam is focused with L3 at the TIR point to optimize the coupling surface area, and we search for resonances. Once the proper angle is found, we pull back L3 to focus on the prism input with the desired beam width for the nonlinear regime. The self-trapped beam is obtained thanks to the photorefractive effect that will be discussed in the following paragraph.
In the linear regime, the light diffracts freely in the crystal as shown schematically in Fig. 1(b). In the non-linear regime, we slightly increase the temperature of the LiNbO3 crystal. A pyroelectric internal electric field ΔEpy appears and decreases the refractive index all over the crystal because of the Pockels effect. However, at the input of the crystal, the focused beam generates free electrons because of the photoelectric effect. Those optically generated free carriers drifts along the c-axis because of the pyroelectric field and recombine on deep centers. The resulting space-charge field E partially screens ΔEpy. In the area where the field is screened, the refractive index is less affected which results in a localized high refractive index that eventually traps the light beam (see Fig. 1(c)). Because the space-charge field E results from recombinations on deep-centers, the resulting waveguide lasts even if the heater and the light are turned off.
In our set-up, a Peltier element is placed under the crystal to control its temperature as depicted in Fig. 1(a). In LiNbO3 crystals, a moderate temperature increase ΔT = 20°C leads to an internal electric field as high as ΔEpy = 47kV/cm [11, 13]. Note that for strong-coupling efficiency, the beam profile should be as similar as possible to the microsphere mode size to maximize the overlap between the evanescent part of the field. However, for whispering-gallery modes (WGM), a weak-coupling regime is usually preferred to keep the Q-factor high. Analytic calculations show that WGMs are present in our laser tuning range with a mode FWHM around 5µm . As a trade-off between self-trapping and coupling efficiencies, we choose an input beam of 22 µm FWHM that is typical for self-focussing experiment in LiNbO3 as depicted in Fig. 2(a). In Fig. 2(b), the beam observed at the output face is reported in the linear regime as witnessed by the large size of the diffracted beam. To reach the nonlinear regime, the pyroelectric effect is triggered with a temperature increase of the LiNbO3 sample of ΔT = 33°C and the light power is raised to 190 µW. In about an hour, the beam is self-focused thanks to the photorefractive effect. In Fig. 2(c), the crystal final output beam is shown, a clear confinement is seen. It has a 14.3 µm FWHM along the vertical axis (c-axis) and 16.2 µm along the horizontal one.
From , it is well known that photorefractive spatial solitons can induces single mode or multimode waveguide depending on writing parameters. To determine this feature dynamically during the waveguide inscription, we follow a similar technique to reference  based on the observation of mode beating at the output of the structure. In the present case, we take advantage on the slow response of the medium which allow to sweep the laser wavelength from time to time in order to check the waveguide properties of the inscribed waveguide. If higher modes are excited, a distinct optical beating is observed. Figure 3(a) shows two images of the output of the prism for two wavelengths separated by Δλ = 0.24nm, the upper profile shows a slight broadening on the left. When the laser wavelength is swept, the optical beating periodically changes from the upper image to the lower one which is a signature of the multimode character of the waveguide. If the writing process exceeds an hour, no more spatial deformation is observed while sweeping the wavelength. A singlemode waveguide is thus inscribed in the prism. This waveguide has the proper characteristics to guide light with the right trajectory and the adapted mode profile to couple efficiently to the resonator. It takes advantage of the unique properties of self-alignment and confinement provided by trapped beams. Note that the waveguide refractive index contrast is only of the order of 10−4, the slight induced phase mismatch with the WGM can be compensated by a laser wavelength shift of few tens of picometers.
The output camera is then replaced with a photodiode and the laser frequency is swept over 4nm. In Fig. 2(b), we compare the detected output signal obtained with three different setups. In the setup (α), the beam is focused on the input face of the prism. As a result, a diffracted beam with a large width is coupled to the resonator. The setup (β) is a standard prism coupling setup. The beam is focused upon the coupling face of the prism to increase the coupling efficiency. Note that the beam at the input face is thus wider with a curved face front. Finally, in the setup (γ), the beam is focused at the input face of the prism and propagates within the prism as a self-focused beam and couples to the resonator. As illustrated in Fig. 2(b), the poor overlap between the diffracted beam (α) and the WGM results in a very inefficient coupling. In this case, WGM resonances can barely be discriminated from the mode-hops of the tunable laser. Better mode coupling is obtained with focused (β) and self-focused beams (γ). The two measurements show the same free spectral range (FSR) meaning that the same mode family is observed. As a result, we know that the same phase matching condition occurs for standard prism coupling and self-focused beam coupling. The two first deepest resonances are separated by ΔλFSR = 0.65nm that is in good agreement with the calculated one ΔλFSR,th = 0.69nm. We also report a slight improvement in coupling efficiency since a better contrast with respect to the laser mode hops is observed. One explanation could be that the standard prism coupling method is more sensitive to spatial distortions from the perfectible polished input face since the input beam is wider.
The following characterizations are performed with the self-focused beam technique. In order to isolate one resonance, the laser is periodically swept over few tens of GHz as depicted in the inset of Fig. 4(a). The coupling transmission is normalized to the transmission measurement without resonator. The small peaks close to the main resonances are artifacts from this normalization. Note that from the large resonances measured on the spectrum, we can deduce that the loaded Q-factors are quite low (≪ 109). It could be due to the use of a standard fiber splicer to produce the resonator instead of a micro-torch, leading to atmospheric water adsorption  and high coupling losses. The resonators resonances were measured at λ = 1.55 µm using the fiber taper and cavity-ringdown method, the intrinsic Q-factor are in the 106−107 range . According to Gorodetsky et al. , the Q-factor is mostly determined by scattering losses and scales with λ3 which considerably broaden the resonances in the visible range as in our experiment. Those strong scattering losses can be observed when the coupling face is imaged on a camera as shown by the picture Fig. 4(b). However more investigation should be done before drawing further conclusions. For example, cavity-ringdown measurement could be implemented for visible wavelengths in order to discriminate the coupling from the intrinsic
To conclude, the concept of light coupling with a nonlinear prism has been presented. Beam self-trapping is exploited to induce an optimized waveguide inside a prism to perform light coupling. This original configuration gathers both the flexibility of the prism coupling and the benefits from the waveguide confinement. The experimental demonstration is realized with a photorefractive LiNbO3 prism to couple light in a resonator. Our original configuration is compared to the standard prism coupling technique. Both methods offer flexibility of the coupling by tuning the incidence angle of the injected beam. The mode selectivity of the nonlinear prism is characterized. Enhanced stability compared to the fiber-taper method is obtained thanks to the mode profile and self-alignment properties of self-focused beams. Improvements of the method and its selectivity are foreseen by optimization of the self-trapped beam shape through a better control of the dynamic of the nonlinear effect. Fiber pigtailing of such an optimized prism coupler would bring the advantages of both the standard prism coupling and the tapered fiber coupling methods. The concept can be extended to other photosensitive materials such as photopolymers to fabricate permanent sturdy coupling. Future experiments are foreseen including the use of CaF2 or MgF2 resonators  and the study of the coupling losses with cavity ring-down measurement.
We are grateful for financial support by Agence National de la Recherche for project ORA ( ANR 2010 BLAN-0312) and the Région Franche Comté. This work was realized in the framework of the French Labex Action (contract No. ANR-11-LABX-0001-01) and was partly supported by the RENATECH network and its FEMTO-ST technological facility. Kien Phan Huy thanks Thibaut Sylvestre for his technical help on the injection, and Y. Chembo’s team for fruitful interactions.
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