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Acción de Grupos sobre Conjuntos

Parte II. Acción de Grupos y Aplicaciones

15. Acción de Grupos sobre Conjuntos

Two ultrahigh-Q, single-crystal CaF2WGM resonators were fabricated. Resonator 1 was fabricated

with a UV-grade fluorite from Edmund Optics and had a larger radius of curvature as compared to resonator 2, made with an excimer-grade fluorite from Corning. A Nd:YAG laser with 5 kHz linewidth manufactured by Lightwave Electronics was used to excite WGMs at the wavelength of 1064 nm. The diameters of the resonators were determined from the FSR, measured as a spacing

between multiple Raman lines observed at 1102 nm, and the value of the refractive index of CaF2

at this wavelength,n= 1.4283. The cavities are shown in Fig. 5.11. The spectra of the resonators contain an abundance of modes with the average spacing of 25 MHz for both polarizations. The laser

Figure 5.11: Fluorite resonators. WGM localization areas are highlighted with the white brackets on the left. Shadow photographs of the highlighted regions are on the right. Diameters are 5.52 mm for resonator 1 and 5.21 mm for resonator 2.

frequency was locked to a selected cavity mode using a simplified Pound-Drever-Hall technique. A signal generator was used to provide the excitation for the resonant phase modulator. This signal was also used to synchronize the lock-in amplifier SR844, which operated as a frequency mixer and servo. This technique made it possible to maintain a fixed optical power in the cavity mode.

Alignment of the angle-polished fiber couplers, similar to those presented in [25], mounted onto the three-axis piezo positioning stages provided input and output coupling efficiencies of up to 80%. The light that was scattered backwards by the cavity mode was branched into the arm of a 90/10 fiber coupler. The setup schematically shown in Fig. 5.12 was used to measure the power and spectral properties of both forward and backward beams with help of a Yokogawa AQ6319 optical spectrum analyzer and a Thorlabs detector “DET10C”. A WGM was excited with approximately 50µW of optical power in a measurement conducted with the first cavity. The spectrum of light from the coupler B (Fig. 5.13) revealed the presence of a Stokes line offset by 34.9 GHz and a weak Stokes

Figure 5.12: Experimental setup diagram. Laser is locked to a cavity mode; the optical power in the fiber can be monitored in forward and backward directions.

line offset by 17.5 GHz. The intensity of the Stokes line at 34.9 GHz was 13.9 dB weaker than the pump. Neither stimulated Raman scattering (SRS) nor four-wave mixing (FWM) oscillations were observed in this measurement. The difference of intensities of the pump and the Stokes line at 34.9 GHz decreased to 9.4 dB when the pump optical power was further increased. Two groups of SRS lines appeared around 1101.8–1102.3 nm and 1142.4–1142.9 nm with this increase of power. The peak level of the Raman lasing lines were -16.2 dB for the 1st Stokes and -11.9 dB for the 2nd Stokes with respect to the pump. A set of similar measurements was made with the second cavity.

Figure 5.13: (Left) Optical spectrum around the laser line for resonator 1 obtained from coupler B. The pump power is 50µW. The gap between coupler B and the cavity was increased, which explains lower power at the spectrum analyzer. The two Stokes lines have frequencies red-shifted by 17.465 GHz for the weak Stokes and by 17.465×2 = 34.93 GHz for the strong Stokes line. The width of each line is limited by the optical spectrum analyzer resolution of 0.012 nm. (Right) Backward signal from coupler C for resonator 2. Stokes offset is 18 GHz for the first and 17.5 GHz for the second relative to the first.

This time the pump power was lower, and no Stokes line around 35 GHz was observed. However, we carried out simultaneous measurements of the forward and backward optical spectrum using couplers B and C (see Fig. 5.12). Typical spectra are shown on Fig. 5.14. From this spectrum we

see that the intensity of the backscattered Stokes line exceeds the backscattered pump light. The asymmetry of the spectra may be explained by the residual power leakage between inputs 2 and 1 of the 90/10 coupler, increasing the backward signal at the pump wavelength. The excited WGM had

Figure 5.14: Typical optical spectra from couplers B and C, representing forward and backward signals. Stokes offset is 17.7 GHz.

a coupling efficiency of 70%, loaded Q factor of 4×109, and an intrinsic Q of around 1.4×1010. The spectrum of the light exiting the resonator in the backward direction is shown in Fig. 5.13 (right). Optical pump power was reduced to 2.9µW, below which the first Stokes line was still present but weak. Above this power the intensity of the Stokes line jumps by around 10 dB and grows quickly until it reaches the levels presented in Fig. 5.13 (right). Hence, the threshold of the process was estimated to be around 3µW for the mode with loaded Q of 4×109. At pump power well above

10µW Raman lasing was observed, the spectrum of which is shown on Fig. 5.15. A modulation of the SRS intensity similar to the spectrum of the Stokes line observed near the pump is visible.

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