Discussion

TOWARDS MILLI-HERTZ LASER FREQUENCY NOISE ON A CHIP

8.5 Discussion

We have demonstrated sub-10 mHz· Hz/Hz fundamental frequency noise levels using a chip-based Brillouin laser. The low noise level results from a combination of the high-𝑄 resonator with increased operational power through non-cascading operation. The frequency noise level was too low to measure using conventional optical discrimination methods, and cross-correlation was applied to this technique to obtain a sensitivity boost as large as 15 dB.

Several other strategies might be employed to achieve further noise level improve- ments. For example, increasing laser power ultimately leads to under-coupling of the pump mode to the resonator caused by back action from the lasing mode. This, in turn, decreases differential efficiency and laser power. To isolate this loading back action, a single-cascading scheme can be used (Fig. 8.4a), which would block the cascade at the second order (instead of first order). In this configuration, pump loading would remain constant. A calculation showing the potential improvement is provided in Fig. 8.4b, and a demonstration of this scheme using the same resonator as in the text is shown in Fig. 8.4c. At yet higher laser powers, parametric oscilla- tion due to the Kerr effect within the transverse mode families could limit operation.

Power

Frequency SBL Pump

Cascade thresholdSBL

Brillouin shift FSR

Power (dBm)

0 -20 -40 20 a

c

Wavelength (nm) 1538.8 1539.0

Pump StokesCascade b

Output power (mW)

Pump power (mW)

00 1 2 3 4

0.05 0.1

1538.9 1539.1 Cascading

blocked

cascadingNon- Single- cascading

5

Figure 8.4: Proposed single-cascading Brillouin laser pumping scheme. (a) Spectral diagram for single-cascading Brillouin laser operation. Markers below the modes indicate their transverse mode families. (b) Calculated output laser power versus pump power for non-cascading (green) and single-cascading (orange) pumping schemes, assuming constant external coupling to resonator modes from the tapered fiber. Dashed gray line shows the output power of the first Stokes mode in the single-cascading pumping scheme, which is clamped at the lasing threshold when the first-order cascaded mode start to lase. (c) Measured optical spectrum traces showing single-cascading SBL action. Blue and red traces are the forward and backward output power from the resonator, showing the pump, Stokes, and cascade modes, and second-order cascade lasing is not observed.

However, it should be possible to inhibit this oscillation through dispersion engineer- ing [31] or possible operation in the normal dispersion regime. Finally, operation with reduced amplitude-phase coupling is also important for minimization of the Brillouin laser linewidth [29].

Overall, the results presented here demonstrate the potential for silica-based high-𝑄 laser platforms to achieve extremely narrow fundamental laser linewidths. Even while the noise at low offset frequencies remains high, these noise sources can be suppressed in applications such as the Sagnac gyroscope that rely upon relative noise of co-lasing waves. Likewise, applications that are sensitive to only short-term frequency noise can benefit from these improvements.

References

[1] Grudinin, I. S., Matsko, A. B. & Maleki, L. Brillouin lasing with a CaF₂ whispering gallery mode resonator. Physical Review Letters 102, 043902 (2009).

[2] Tomes, M. & Carmon, T. Photonic micro-electromechanical systems vibrating

at X-band (11-GHz) rates. Physical Review Letters102, 113601 (2009).

[3] Pant, R. et al. On-chip stimulated Brillouin scattering. Optics Express 19, 8285–8290 (2011).

[4] Lee, H. et al. Chemically etched ultrahigh-Q wedge-resonator on a silicon chip. Nature Photonics6, 369–373 (2012).

[5] Shen, Y. R. & Bloembergen, N. Theory of stimulated Brillouin and Raman scattering. Physical Review137, A1787–A1805 (1965).

[6] Li, J., Lee, H., Chen, T. & Vahala, K. J. Characterization of a high coher- ence, Brillouin microcavity laser on silicon.Optics Express20, 20170–20180 (2012).

[7] Suh, M.-G., Yang, Q.-F. & Vahala, K. J. Phonon-limited-linewidth of Brillouin lasers at cryogenic temperatures.Physical Review Letters119, 143901 (2017).

[8] Schawlow, A. L. & Townes, C. H. Infrared and optical masers. Physical Review112, 1940 (1958).

[9] Debut, A., Randoux, S. & Zemmouri, J. Linewidth narrowing in Brillouin lasers: Theoretical analysis. Physical Review A62, 023803 (2000).

[10] Gorodetsky, M. L. & Grudinin, I. S. Fundamental thermal fluctuations in microspheres. Journal of the Optical Society of America B 21, 697–705 (2004).

[11] Matsko, A. B., Savchenkov, A. A., Yu, N. & Maleki, L. Whispering-gallery- mode resonators as frequency references. I. fundamental limitations. Journal of the Optical Society of America B24, 1324–1335 (2007).

[12] Loh, W.et al. Dual-microcavity narrow-linewidth Brillouin laser. Optica 2, 225–232 (2015).

[13] Li, J., Lee, H. & Vahala, K. J. Microwave synthesizer using an on-chip Brillouin oscillator. Nature Commun.4, 2097 (2013).

[14] Li, J., Yi, X., Lee, H., Diddams, S. A. & Vahala, K. J. Electro-optical frequency division and stable microwave synthesis. Science345, 309–313 (2014).

[15] Li, J., Suh, M.-G. & Vahala, K. Microresonator Brillouin gyroscope. Optica 4, 346–348 (2017).

[16] Gundavarapu, S.et al. Sub-hertz fundamental linewidth photonic integrated Brillouin laser. Nature Photonics13, 60–67 (2019).

[17] Lai, Y.-H.et al. Earth rotation measured by a chip-scale ring laser gyroscope.

Nature Photonics14, 345–349 (2020).

[18] Otterstrom, N. T., Behunin, R. O., Kittlaus, E. A., Wang, Z. & Rakich, P. T. A silicon Brillouin laser. Science360, 1113–1116 (2018).

[19] Yang, K. Y.et al. Bridging ultrahigh-Q devices and photonic circuits. Nature Photonics12, 297–302 (2018).

[20] Van Exter, M., Kuppens, S. & Woerdman, J. Excess phase noise in self- heterodyne detection. IEEE Journal of Quantum Electronics 28, 580–584 (1992).

[21] Ludvigsen, H., Tossavainen, M. & Kaivola, M. Laser linewidth measurements using self-homodyne detection with short delay.Optics Communications155, 180–186 (1998).

[22] Jin, W.et al. Hertz-linewidth semiconductor lasers using CMOS-ready ultra- high-Q microresonators. Nature Photonics(2021).

[23] Behunin, R. O., Otterstrom, N. T., Rakich, P. T., Gundavarapu, S. & Blumen- thal, D. J. Fundamental noise dynamics in cascaded-order Brillouin lasers.

Physical Review A98, 023832 (2018).

[24] Puckett, M., Bose, D., Nelson, K. & Blumenthal, D. J. Higher order cascaded SBS suppression using gratings in a photonic integrated ring resonator laser.

In CLEO: Science and Innovations, SM4O–1 (Optical Society of America, 2019).

[25] Wu, L.et al. Greater than one billion Q-factor for on-chip microresonators.

Optics Letters45, 5129–5131 (2020).

[26] Yi, X., Yang, Q.-F., Yang, K. Y., Suh, M.-G. & Vahala, K. Soliton frequency comb at microwave rates in a high-Q silica microresonator. Optica2, 1078–

1085 (2015).

[27] Walls, W. F. Cross-correlation phase noise measurements. InProceedings of the 1992 IEEE Frequency Control Symposium, 257–261 (IEEE, 1992).

[28] Xie, X. et al. Photonic microwave signals with zeptosecond-level absolute timing noise. Nature Photonics11, 44–47 (2017).

[29] Yuan, Z., Wang, H., Wu, L., Gao, M. & Vahala, K. Linewidth enhancement factor in a microcavity Brillouin laser. Optica7, 1150–1153 (2020).

[30] Kondratiev, N. & Gorodetsky, M. Thermorefractive noise in whispering gallery mode microresonators: Analytical results and numerical simulation. Physical Letters A382, 2265–2268 (2018).

[31] Yang, K. Y.et al. Broadband dispersion-engineered microresonator on a chip.

Nature Photonics10, 316–320 (2016).

C h a p t e r 9

LINEWIDTH ENHANCEMENT FACTOR IN A MICROCAVITY