Photonic circuits for laser stabilization with integrated ultra-high Q and Brillouin laser resonators

B. Brillouin laser stabilization

The stabilized laser experimental setup is shown in Fig. 2(a). The nonlinear Brillouin and ultra-low loss resonators are housed inside passive enclosures to minimize environmental fluctuations, e.g., air flow in the laboratory, and each is mounted on independent temperature-controlled fiber-coupling stages (see the supplementary material, Sec. I, for details). Each chip is mounted on a separate coupling stage in a separate enclosure, with its own coupling fibers and temperature stabilization. The SBS laser output power is 6 ± 1 dBm measured into the fiber (∼9 dBm on-chip output optical power and 3 ± 1 dB fiber-to-chip coupling loss) and then passes through an erbium-doped fiber amplifier (EDFA), EOM, AOM, and 90/10 splitter for power amplification and laser frequency stabilization. The SBS laser output in the fiber is amplified with an EDFA to a power level of ∼18 dBm. Taking into account the approximate insertion losses of the EOM (5 dB) and AOM (6 dB), the stabilized laser output power after a 90/10 splitter is ∼7 dBm (see the supplementary material, Sec. I, for the optical powers and insertion losses in the PDH lock). The free-running Brillouin S1 emission is generated by PDH locking the pump laser to the SBS resonator. The on-chip pump power is maintained at 42 ± 2.2 mW such that S1 operates just below its clamping point. The Brillouin S1 emission is then modulated using an AOM driven by a voltage-controlled oscillator (VCO) and PDH locked to the reference cavity, with an on-chip power of −10 dBm and a lock loop bandwidth of ∼20 kHz. An unbalanced fiber Mach–Zehnder interferometer (MZI) with a 1.026 MHz FSR is used as an optical frequency discriminator (OFD) to measure the frequency noise above ∼1 kHz offset from the carrier.41,6641. S. Gundavarapu, G. M. Brodnik, M. Puckett, T. Huffman, D. Bose, R. Behunin, J. Wu, T. Qiu, C. Pinho, N. Chauhan, J. Nohava, P. T. Rakich, K. D. Nelson, M. Salit, and D. J. Blumenthal, “Sub-hertz fundamental linewidth photonic integrated Brillouin laser,” Nat. Photonics 13 (2018). https://doi.org/10.1038/s41566-018-0313-266. J. Li, H. Lee, T. Chen, and K. J. Vahala, “Characterization of a high coherence, Brillouin microcavity laser on silicon,” Opt. Express 20, 020170 (2012). https://doi.org/10.1364/oe.20.020170 For frequency noise below ∼1 kHz frequency offset from carrier, we heterodyne the stabilized S1 with a reference Rock™ single frequency fiber laser that is PDH locked to a Stable Laser Systems™ ultra-low-expansion (ULE) high-finesse cavity. The reference laser has a Hz-level linewidth output at 1550 nm wavelength, with a frequency drift of ∼0.1 Hz/s and frequency stability of ∼10−15 at 1 s averaging time. We refer to this reference laser as the stable reference laser (SRL) and the frequency noise measurement using this laser as the SRL frequency noise measurement. The stabilized Brillouin S1 is photomixed with the SRL output to produce a heterodyne signal that carries the Brillouin laser’s frequency noise combined with the noise of the VCO-driven AOM. The resulting heterodyne signal, an ∼100 MHz beatnote, is characterized using a Keysight 53230A frequency counter (FC) with a frequency noise floor below 10−3 Hz2/Hz. The combination of the SRL frequency stability below a 1 kHz offset and the frequency noise floor of the frequency counter below 10−3 Hz2/Hz enables accurate measurement of both the free-running and stabilized Brillouin laser emission at frequencies below 1 kHz. The OFD and SRL frequency noise measurements and the impact of VCO and AOM are discussed in detail in the supplementary material, Sec. III. The laser frequency noise measurements are shown in Fig. 2(b) yielding the free-running and stabilized Brillouin laser fundamental linewidths of 0.72 and 1.6 Hz, respectively. The frequency noise spectra are plotted in Fig. 2(b) with 60 and 120 Hz tones removed. Figure S3(c) in the supplementary shows the original frequency noise spectra with the 60 and 120 Hz tones. The increase in high-frequency noise is due to added phase noise from the VCO that in turn drives the AOM (see the supplementary material, Sec. I, for more discussion on the VCO-added phase noise).The integral linewidths are calculated from the frequency noise spectrum for the free-running and stabilized Brillouin laser. A factor of 10 decrease is measured in the stabilized linewidth over the free-running linewidth, at 292 Hz and 3.24 kHz, respectively (see the supplementary material, Sec. II, for the integral linewidth calculation). The increase in the high-frequency noise in the AOM-modulated S1 output is due to the Brillouin laser fundamental linewidth being lower than that of the AOM and its VCO. The stabilized S1 frequency noise is close to the resonator-intrinsic TRN limit for frequencies from 80 Hz to 10 kHz, as shown in Fig. 2(b). The overlapping ADEV shown in Fig. 3(a) is calculated from the time trace of heterodyne frequency recorded by the frequency counter, which for the stabilized Brillouin laser reaches a minimum of 4.9 × 10−13 at 8 ms averaging time. While the 1/π integral linewidth of 292 Hz for the stabilized laser does not take an averaging time into account, the measured ADEV at 8 ms does, and therefore, correlates the linewidth contributions at 8 ms to the integral linewidth before the linewidth becomes drift dominated. The TRN sets a lower limit for the stabilized ADEV at averaging times up to around 5 ms, while, outside this range, other noise sources dominate the ADEV. The random walk frequency noise (drift), estimated to be 10 kHz/s over the time scale of several seconds, dominates the linewidth at ADEV averaging times longer than 10 ms [right-hand upward purple-dashed curve in Fig. 3(a)]. As shown in Fig. 3(b), the Fourier transform of the SRL and the Brillouin laser heterodyne beatnote yields linewidths of 330 Hz for the stabilized and 2.93 kHz for the free-running Brillouin laser. These values are in good agreement with our calculated integral linewidths from the frequency noise spectrum.1818. D. G. Matei, T. Legero, S. Häfner, C. Grebing, R. Weyrich, W. Zhang, L. Sonderhouse, J. M. Robinson, J. Ye, F. Riehle, and U. Sterr, “1.5 μm lasers with sub-10 mHz linewidth,” Phys. Rev. Lett. 118, 263202 (2017). https://doi.org/10.1103/physrevlett.118.263202 The heterodyne beatnote frequency recorded by the counter over a 1-second period [Fig. 3(c)] shows the improvement in laser frequency fluctuation when the Brillouin laser is cavity stabilized over the free-running laser.

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