Abstract

The linewidth of regenerative oscillators is enhanced by amplitude–phase coupling of the oscillator field [Phys. Rev. 160, 290 (1967)]. In laser oscillators, this effect is well known for its impact on semiconductor laser performance. Here, this coupling is studied in Brillouin lasers. Because their gain is parametric, the coupling and linewidth enhancement are shown to originate from phase mismatch. The theory is confirmed by measurement of linewidth in a microcavity Brillouin laser, and enhancements as large as $50 \times$ are measured. The results show that pump wavelength and device temperature should be carefully selected and controlled to minimize linewidth. More generally, this work provides a new perspective on the linewidth enhancement effect.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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Y.-H. Lai, M.-G. Suh, Y.-K. Lu, B. Shen, Q.-F. Yang, H. Wang, J. Li, S. H. Lee, K. Y. Yang, and K. Vahala, Nat. Photonics 14, 345 (2020).
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2019 (1)

S. Gundavarapu, G. M. Brodnik, M. Puckett, T. Huffman, D. Bose, R. Behunin, J. Wu, T. Qiu, C. Pinho, and N. Chauhan, Nat. Photonics 13, 60 (2019).
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2018 (3)

N. T. Otterstrom, R. O. Behunin, E. A. Kittlaus, Z. Wang, and P. T. Rakich, Science 360, 1113 (2018).
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K. Y. Yang, D. Y. Oh, S. H. Lee, Q. F. Yang, X. Yi, B. Shen, H. Wang, and K. J. Vahala, Nat. Photonics 12, 297 (2018).
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R. O. Behunin, N. T. Otterstrom, P. T. Rakich, S. Gundavarapu, and D. J. Blumenthal, Phys. Rev. A 98, 023832 (2018).
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2017 (2)

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J. Li, M.-G. Suh, and K. Vahala, Optica 4, 346 (2017).
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2015 (2)

2014 (2)

J. Li, X. Yi, H. Lee, S. A. Diddams, and K. J. Vahala, Science 345, 309 (2014).
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J. Li, H. Lee, and K. J. Vahala, Opt. Lett. 39, 287 (2014).
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2013 (2)

2012 (2)

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2011 (2)

2009 (2)

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2003 (1)

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2000 (2)

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1992 (1)

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1983 (3)

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1982 (2)

1967 (2)

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S. Gundavarapu, G. M. Brodnik, M. Puckett, T. Huffman, D. Bose, R. Behunin, J. Wu, T. Qiu, C. Pinho, and N. Chauhan, Nat. Photonics 13, 60 (2019).
[Crossref]

R. O. Behunin, N. T. Otterstrom, P. T. Rakich, S. Gundavarapu, and D. J. Blumenthal, Phys. Rev. A 98, 023832 (2018).
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C. Harder, K. Vahala, and A. Yariv, Appl. Phys. Lett. 42, 328 (1983).
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I. Henning and J. Collins, Electron. Lett. 19, 927 (1983).
[Crossref]

Henry, C.

C. Henry, IEEE J. Quantum Electron. 18, 259 (1982).
[Crossref]

Hile, S.

Huffman, T.

S. Gundavarapu, G. M. Brodnik, M. Puckett, T. Huffman, D. Bose, R. Behunin, J. Wu, T. Qiu, C. Pinho, and N. Chauhan, Nat. Photonics 13, 60 (2019).
[Crossref]

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H. Lee, T. Chen, J. Li, K. Y. Yang, S. Jeon, O. Painter, and K. J. Vahala, Nat. Photonics 6, 369 (2012).
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H. Ludvigsen, M. Tossavainen, and M. Kaivola, Opt. Commun. 155, 180 (1998).
[Crossref]

Kippenberg, T. J.

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, Phys. Rev. Lett. 91, 043902 (2003).
[Crossref]

Kittlaus, E. A.

N. T. Otterstrom, R. O. Behunin, E. A. Kittlaus, Z. Wang, and P. T. Rakich, Science 360, 1113 (2018).
[Crossref]

Kuppens, S.

M. Van Exter, S. Kuppens, and J. Woerdman, IEEE J. Quantum Electron. 28, 580 (1992).
[Crossref]

Lai, Y.-H.

H. Wang, Y.-H. Lai, Z. Yuan, M.-G. Suh, and K. Vahala, Nat. Commun. 11, 1610 (2020).
[Crossref]

Y.-H. Lai, M.-G. Suh, Y.-K. Lu, B. Shen, Q.-F. Yang, H. Wang, J. Li, S. H. Lee, K. Y. Yang, and K. Vahala, Nat. Photonics 14, 345 (2020).
[Crossref]

Lax, M.

M. Lax, Phys. Rev. 157, 213 (1967).
[Crossref]

M. Lax, Phys. Rev. 160, 290 (1967).
[Crossref]

Lee, H.

W. Loh, A. A. Green, F. N. Baynes, D. C. Cole, F. J. Quinlan, H. Lee, K. J. Vahala, S. B. Papp, and S. A. Diddams, Optica 2, 225 (2015).
[Crossref]

J. Li, H. Lee, and K. J. Vahala, Opt. Lett. 39, 287 (2014).
[Crossref]

J. Li, X. Yi, H. Lee, S. A. Diddams, and K. J. Vahala, Science 345, 309 (2014).
[Crossref]

J. Li, H. Lee, and K. J. Vahala, Nat. Commun. 4, 2097 (2013).
[Crossref]

J. Li, H. Lee, T. Chen, and K. J. Vahala, Opt. Express 20, 20170 (2012).
[Crossref]

H. Lee, T. Chen, J. Li, K. Y. Yang, S. Jeon, O. Painter, and K. J. Vahala, Nat. Photonics 6, 369 (2012).
[Crossref]

Lee, S. H.

Y.-H. Lai, M.-G. Suh, Y.-K. Lu, B. Shen, Q.-F. Yang, H. Wang, J. Li, S. H. Lee, K. Y. Yang, and K. Vahala, Nat. Photonics 14, 345 (2020).
[Crossref]

K. Y. Yang, D. Y. Oh, S. H. Lee, Q. F. Yang, X. Yi, B. Shen, H. Wang, and K. J. Vahala, Nat. Photonics 12, 297 (2018).
[Crossref]

Li, E.

Li, J.

Y.-H. Lai, M.-G. Suh, Y.-K. Lu, B. Shen, Q.-F. Yang, H. Wang, J. Li, S. H. Lee, K. Y. Yang, and K. Vahala, Nat. Photonics 14, 345 (2020).
[Crossref]

J. Li, M.-G. Suh, and K. Vahala, Optica 4, 346 (2017).
[Crossref]

J. Li, X. Yi, H. Lee, S. A. Diddams, and K. J. Vahala, Science 345, 309 (2014).
[Crossref]

J. Li, H. Lee, and K. J. Vahala, Opt. Lett. 39, 287 (2014).
[Crossref]

J. Li, H. Lee, and K. J. Vahala, Nat. Commun. 4, 2097 (2013).
[Crossref]

J. Li, H. Lee, T. Chen, and K. J. Vahala, Opt. Express 20, 20170 (2012).
[Crossref]

H. Lee, T. Chen, J. Li, K. Y. Yang, S. Jeon, O. Painter, and K. J. Vahala, Nat. Photonics 6, 369 (2012).
[Crossref]

Loh, W.

Lu, Y.-K.

Y.-H. Lai, M.-G. Suh, Y.-K. Lu, B. Shen, Q.-F. Yang, H. Wang, J. Li, S. H. Lee, K. Y. Yang, and K. Vahala, Nat. Photonics 14, 345 (2020).
[Crossref]

Ludvigsen, H.

H. Ludvigsen, M. Tossavainen, and M. Kaivola, Opt. Commun. 155, 180 (1998).
[Crossref]

Luther-Davies, B.

Madden, S. J.

Maleki, L.

I. S. Grudinin, A. B. Matsko, and L. Maleki, Phys. Rev. Lett. 102, 043902 (2009).
[Crossref]

Margalit, S.

K. Vahala, L. C. Chiu, S. Margalit, and A. Yariv, Appl. Phys. Lett. 42, 631 (1983).
[Crossref]

Matsko, A. B.

I. S. Grudinin, A. B. Matsko, and L. Maleki, Phys. Rev. Lett. 102, 043902 (2009).
[Crossref]

Mcfarlane, H.

Oh, D. Y.

K. Y. Yang, D. Y. Oh, S. H. Lee, Q. F. Yang, X. Yi, B. Shen, H. Wang, and K. J. Vahala, Nat. Photonics 12, 297 (2018).
[Crossref]

Otterstrom, N. T.

N. T. Otterstrom, R. O. Behunin, E. A. Kittlaus, Z. Wang, and P. T. Rakich, Science 360, 1113 (2018).
[Crossref]

R. O. Behunin, N. T. Otterstrom, P. T. Rakich, S. Gundavarapu, and D. J. Blumenthal, Phys. Rev. A 98, 023832 (2018).
[Crossref]

Painter, O.

H. Lee, T. Chen, J. Li, K. Y. Yang, S. Jeon, O. Painter, and K. J. Vahala, Nat. Photonics 6, 369 (2012).
[Crossref]

M. Cai, O. Painter, and K. J. Vahala, Phys. Rev. Lett. 85, 74 (2000).
[Crossref]

Painter, O. J.

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, Phys. Rev. Lett. 91, 043902 (2003).
[Crossref]

Pant, R.

Papp, S. B.

Pinho, C.

S. Gundavarapu, G. M. Brodnik, M. Puckett, T. Huffman, D. Bose, R. Behunin, J. Wu, T. Qiu, C. Pinho, and N. Chauhan, Nat. Photonics 13, 60 (2019).
[Crossref]

Poulton, C. G.

Puckett, M.

S. Gundavarapu, G. M. Brodnik, M. Puckett, T. Huffman, D. Bose, R. Behunin, J. Wu, T. Qiu, C. Pinho, and N. Chauhan, Nat. Photonics 13, 60 (2019).
[Crossref]

Qiu, T.

S. Gundavarapu, G. M. Brodnik, M. Puckett, T. Huffman, D. Bose, R. Behunin, J. Wu, T. Qiu, C. Pinho, and N. Chauhan, Nat. Photonics 13, 60 (2019).
[Crossref]

Quinlan, F. J.

Rakich, P. T.

N. T. Otterstrom, R. O. Behunin, E. A. Kittlaus, Z. Wang, and P. T. Rakich, Science 360, 1113 (2018).
[Crossref]

R. O. Behunin, N. T. Otterstrom, P. T. Rakich, S. Gundavarapu, and D. J. Blumenthal, Phys. Rev. A 98, 023832 (2018).
[Crossref]

Randoux, S.

A. Debut, S. Randoux, and J. Zemmouri, Phys. Rev. A 62, 023803 (2000).
[Crossref]

Schawlow, A. L.

A. L. Schawlow and C. H. Townes, Phys. Rev. 112, 1940 (1958).
[Crossref]

Shaw, H.

Shen, B.

Y.-H. Lai, M.-G. Suh, Y.-K. Lu, B. Shen, Q.-F. Yang, H. Wang, J. Li, S. H. Lee, K. Y. Yang, and K. Vahala, Nat. Photonics 14, 345 (2020).
[Crossref]

K. Y. Yang, D. Y. Oh, S. H. Lee, Q. F. Yang, X. Yi, B. Shen, H. Wang, and K. J. Vahala, Nat. Photonics 12, 297 (2018).
[Crossref]

Shen, Y. R.

Y. R. Shen and N. Bloembergen, Phys. Rev. 137, A1787 (1965).
[Crossref]

Spillane, S. M.

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, Phys. Rev. Lett. 91, 043902 (2003).
[Crossref]

Stokes, L.

Suh, M.-G.

H. Wang, Y.-H. Lai, Z. Yuan, M.-G. Suh, and K. Vahala, Nat. Commun. 11, 1610 (2020).
[Crossref]

Y.-H. Lai, M.-G. Suh, Y.-K. Lu, B. Shen, Q.-F. Yang, H. Wang, J. Li, S. H. Lee, K. Y. Yang, and K. Vahala, Nat. Photonics 14, 345 (2020).
[Crossref]

J. Li, M.-G. Suh, and K. Vahala, Optica 4, 346 (2017).
[Crossref]

M.-G. Suh, Q.-F. Yang, and K. J. Vahala, Phys. Rev. Lett. 119, 143901 (2017).
[Crossref]

X. Yi, Q.-F. Yang, K. Y. Yang, M.-G. Suh, and K. Vahala, Optica 2, 1078 (2015).
[Crossref]

Thevenaz, L.

Tomes, M.

M. Tomes and T. Carmon, Phys. Rev. Lett. 102, 113601 (2009).
[Crossref]

Tossavainen, M.

H. Ludvigsen, M. Tossavainen, and M. Kaivola, Opt. Commun. 155, 180 (1998).
[Crossref]

Townes, C. H.

A. L. Schawlow and C. H. Townes, Phys. Rev. 112, 1940 (1958).
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Supplementary Material (1)

NameDescription
» Supplement 1       theoretical calculation and supplement experiment data

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Figures (3)

Fig. 1.
Fig. 1. SBL phase mismatch illustration and experimental setup. (a) Brillouin gain process in the frequency domain. Purple (brown) curve refers to the pump (Stokes) cavity mode at frequency ${\omega _{\rm P}}$ (${\omega _{\rm S}}$). Blue curve refers to the SBL laser signal at frequency ${\omega _{\rm L}}$. Orange and red curves correspond to gain (${\rm g}$) spectrum and refractive index ($\Delta {\rm n}$), respectively. Brillouin shift frequency ($\Omega$), gain spectrum linewidth ($\Gamma$), and cavity linewidth ($\gamma$) are also indicated. Frequency detunings $\delta \omega$ and $\delta \Omega$ are defined in the text. (b) Experimental setup for $\alpha$ and linewidth measurement. An external cavity diode laser (ECDL) (Newport, TLB-6728) near 1550 nm passes through an erbium-doped fiber amplifier (EDFA) and is coupled to the microcavity (a silica wedge resonator [8]) using a tapered fiber [31,32]. Its frequency is Pound–Drever–Hall locked (not shown) to the center of the cavity resonance. Pump power is controlled using an acousto-optic modulator (AOM) as an attenuator in combination with a feedback loop (not shown). The resonator diameter is around 7.1 mm, corresponding to an FSR of 10.8 GHz, which is selected to closely match the Brillouin shift frequency in silica at 1550 nm. The resonator chip temperature is actively stabilized to $26.5000 \pm 0.0005^\circ {\rm C}$ using a temperature controller. The SBL emission propagates in the opposite direction of the pumping due to the phase-matching condition. The emission is coupled to a series of measurement instruments through a circulator. An optical spectrum analyzer (OSA) is used to record the laser and pump spectra as well as to measure SBL power. Pump and SBL signals are mixed on a fast photodetector (PD) (Thorlabs, DXM30AF) to measure their frequency difference. Another PD monitors the pumping power. An interferometer is used to measure the laser frequency noise. Therein, the laser signal is sent into an AOM that is split into frequency-shifted (first order) and unshifted (zeroth order) signals. The latter is delayed in a 1-km-long fiber, and then the two signals are mixed on a PD (Newport, 1811-FC). The delay sets up a frequency-to-amplitude discriminator with a discrimination gain that is proportional to the amount of interferometer delay. To measure the frequency noise spectral density, the detected current is measured using an electrical phase noise analyzer (PNA), and the spectrum is fit to obtain the two-sided spectral density of the SBL laser (Section 2 of Supplement 1).
Fig. 2.
Fig. 2. Brillouin gain phase mismatch and $\alpha$ factor. (a) Beating frequency between the pump laser and the SBL is plotted as a function of SBL power. Linear fitting is applied to eliminate the influence of the Kerr effect and $\alpha$ factor backaction, and the $y$-axis intercept is plotted as $\Delta \omega$ in (b). Blue, red, and yellow traces correspond to measurements at 1545 nm, 1538 nm, and 1532 nm, respectively. (b) The extrapolated beating frequency (squares) and FSR (triangles) are plotted versus wavelength. The calculated $\alpha$ factor (red circles) is plotted versus wavelength using Eq. (2). The Brillouin gain center occurs at around 1548 nm, where ${\rm FSR} = \Delta \omega$. (c) Total (${Q_{\rm T}}$), intrinsic (${Q_0}$), and external (${Q_{{\rm ex}}}$) quality factors are plotted versus wavelength. The values are measured in the same transverse mode family.
Fig. 3.
Fig. 3. SBL frequency noise enhancement. Measured SBL frequency noise ${S_{\rm F}}$ (blue), theoretical ${S_{\rm F}}$ [Eq. (3)] prediction (green) with $\alpha$ obtained from Fig. 2(b), and non-enhanced ${S_0}$ formula ($\alpha = 0$) [13] prediction (yellow); all are plotted versus pump wavelength normalized to 1 mW output power. Error bars on the ${S_{\rm F}}$ noise correspond to the error in determining slope (see inset). Error bars on the Eq. (3) prediction mainly arise from $\Delta \omega$ and ${\rm Q}$ measurement errors. Variations of the $\alpha = 0$ prediction mainly arise from ${Q_{{\rm ex}}}$ differences. Inset: SBL frequency noise ${S_{\rm w}}$ is plotted versus the reciprocal of SBL output power. A linear fitting is applied to determine ${S_{\rm F}}$ from the slope, and then plotted in the main panel. Blue, red, and yellow data correspond to measurements at 1545 nm, 1538 nm, and 1532 nm, respectively.

Equations (3)

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Δ ν S B L = Δ ν 0 ( 1 + α 2 ) ,
α = 2 δ Ω Γ = 2 δ ω γ .
Δ ν 0 = ( Γ γ + Γ ) 2 ω L 3 n t h 4 π Q T Q e x P S B L ,