Abstract

Cavity opto-mechanics enabled radiation pressure (RP) driven oscillators shown in the past offer an all optical Radio Frequency (RF) source without the need for external electrical feedback. However these oscillators require external tapered fiber or prism coupling and non-standard fabrication processes. In this work, we present a CMOS compatible fabrication process to design high optical quality factor opto-mechanical resonators in silicon nitride. The ring resonators designed in this process demonstrate low phase noise RP driven oscillations. Using integrated grating couplers and waveguide to couple light to the micro-resonator eliminates 1/f3 and other higher order phase noise slopes at close-to-carrier frequencies present in previous demonstrations. We present an RP driven opto-mechanical oscillator (OMO) operating at 41.97MHz with a signal power of −11dBm and phase noise of −85dBc/Hz at 1kHz offset with only 1/f2 noise down to 10Hz offset from carrier.

© 2011 OSA

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References

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  1. T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: Back-action at the mesoscale,” Science 29,  321(5893), 1172–1176, (2008).
    [CrossRef]
  2. A. Cho, “Putting light’s light touch to work as optics meets mechanics,” Science 14,  5980(5893), 812–813, (2010).
    [CrossRef]
  3. M. Hossein-Zadeh, H. Rokhsari, A. Hajimiri, and K. J. Vahala, “Characterization of a radiation-pressure-driven micromechanical oscillator,” Phys. Rev. A 74, 023813 (2006).
    [CrossRef]
  4. T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94, 223902 (2005).
    [CrossRef] [PubMed]
  5. G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Rivire, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, “Near-field cavity optomechanics with nanomechanical oscillators,” Nature Phys. 5, 909–914 (2009).
    [CrossRef]
  6. Q. P. Unterreithmeier, E. M. Weig, and J. P. Kotthaus, “Universal transduction scheme for nanomechanical systems based on dielectric forces,” Nature 458, 1001–1004 (2009).
    [CrossRef] [PubMed]
  7. M. Tomes and T. Carmon, “Photonic micro-electromechanical systems vibrating at X-band (11-GHz) rates,” Phys. Rev. Lett.,  102, 113601, (2009).
    [CrossRef] [PubMed]
  8. A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, D. Seidel, and L. Maleki, “Surface acoustic wave opto-mechanical oscillator and frequency comb generator,” Opt. Lett. 36, 3338–3340 (2011).
    [CrossRef] [PubMed]
  9. M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462, 7882 (2009).
  10. G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using optical forces,” Nature 462, 633636 (2009).
    [CrossRef] [PubMed]
  11. S. Tallur, S. Sridaran, and S. A. Bhave, “Phase noise modeling of opto-mechanical oscillators,” IEEE Frequency Control Symposium (FCS 2010), Newport Beach, California, 268–272, (2010).
  12. A. Gondarenko, J. S. Levy, and M. Lipson, “High confinement micron-scale silicon nitride high Q ring resonator,” Opt. Express 17, 11366–11370 (2009).
    [CrossRef] [PubMed]
  13. S. S. Verbridge, J. M. Parpia, R. B. Reichenbach, L. M. Bellan, and H. G. Craighead, “High quality factor resonance at room temperature with nanostrings under high tensile stress,” J. Appl. Phys. 99, 124304 (2006).
    [CrossRef]
  14. H. Rokhsari, T. J. Kippenberg, T. Carmon, and K. J. Vahala, “Theoretical and experimental study of radiation pressure-induced mechanical oscillations (parametric instability) in optical microcavities,” IEEE J. Sel. Top. Quantum Electron. 12, 96–107 (2006).
    [CrossRef]
  15. Low Phase Noise Quartz Crystal Oscillator, Model FE-102A. http://www.freqelec.com/qz_osc_fe102a.html

2011 (1)

2010 (2)

A. Cho, “Putting light’s light touch to work as optics meets mechanics,” Science 14,  5980(5893), 812–813, (2010).
[CrossRef]

S. Tallur, S. Sridaran, and S. A. Bhave, “Phase noise modeling of opto-mechanical oscillators,” IEEE Frequency Control Symposium (FCS 2010), Newport Beach, California, 268–272, (2010).

2009 (6)

G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Rivire, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, “Near-field cavity optomechanics with nanomechanical oscillators,” Nature Phys. 5, 909–914 (2009).
[CrossRef]

Q. P. Unterreithmeier, E. M. Weig, and J. P. Kotthaus, “Universal transduction scheme for nanomechanical systems based on dielectric forces,” Nature 458, 1001–1004 (2009).
[CrossRef] [PubMed]

M. Tomes and T. Carmon, “Photonic micro-electromechanical systems vibrating at X-band (11-GHz) rates,” Phys. Rev. Lett.,  102, 113601, (2009).
[CrossRef] [PubMed]

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462, 7882 (2009).

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using optical forces,” Nature 462, 633636 (2009).
[CrossRef] [PubMed]

A. Gondarenko, J. S. Levy, and M. Lipson, “High confinement micron-scale silicon nitride high Q ring resonator,” Opt. Express 17, 11366–11370 (2009).
[CrossRef] [PubMed]

2008 (1)

T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: Back-action at the mesoscale,” Science 29,  321(5893), 1172–1176, (2008).
[CrossRef]

2006 (3)

S. S. Verbridge, J. M. Parpia, R. B. Reichenbach, L. M. Bellan, and H. G. Craighead, “High quality factor resonance at room temperature with nanostrings under high tensile stress,” J. Appl. Phys. 99, 124304 (2006).
[CrossRef]

H. Rokhsari, T. J. Kippenberg, T. Carmon, and K. J. Vahala, “Theoretical and experimental study of radiation pressure-induced mechanical oscillations (parametric instability) in optical microcavities,” IEEE J. Sel. Top. Quantum Electron. 12, 96–107 (2006).
[CrossRef]

M. Hossein-Zadeh, H. Rokhsari, A. Hajimiri, and K. J. Vahala, “Characterization of a radiation-pressure-driven micromechanical oscillator,” Phys. Rev. A 74, 023813 (2006).
[CrossRef]

2005 (1)

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94, 223902 (2005).
[CrossRef] [PubMed]

Anetsberger, G.

G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Rivire, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, “Near-field cavity optomechanics with nanomechanical oscillators,” Nature Phys. 5, 909–914 (2009).
[CrossRef]

Arcizet, O.

G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Rivire, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, “Near-field cavity optomechanics with nanomechanical oscillators,” Nature Phys. 5, 909–914 (2009).
[CrossRef]

Bellan, L. M.

S. S. Verbridge, J. M. Parpia, R. B. Reichenbach, L. M. Bellan, and H. G. Craighead, “High quality factor resonance at room temperature with nanostrings under high tensile stress,” J. Appl. Phys. 99, 124304 (2006).
[CrossRef]

Bhave, S. A.

S. Tallur, S. Sridaran, and S. A. Bhave, “Phase noise modeling of opto-mechanical oscillators,” IEEE Frequency Control Symposium (FCS 2010), Newport Beach, California, 268–272, (2010).

Camacho, R. M.

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462, 7882 (2009).

Carmon, T.

M. Tomes and T. Carmon, “Photonic micro-electromechanical systems vibrating at X-band (11-GHz) rates,” Phys. Rev. Lett.,  102, 113601, (2009).
[CrossRef] [PubMed]

H. Rokhsari, T. J. Kippenberg, T. Carmon, and K. J. Vahala, “Theoretical and experimental study of radiation pressure-induced mechanical oscillations (parametric instability) in optical microcavities,” IEEE J. Sel. Top. Quantum Electron. 12, 96–107 (2006).
[CrossRef]

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94, 223902 (2005).
[CrossRef] [PubMed]

Chan, J.

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462, 7882 (2009).

Chen, L.

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using optical forces,” Nature 462, 633636 (2009).
[CrossRef] [PubMed]

Cho, A.

A. Cho, “Putting light’s light touch to work as optics meets mechanics,” Science 14,  5980(5893), 812–813, (2010).
[CrossRef]

Craighead, H. G.

S. S. Verbridge, J. M. Parpia, R. B. Reichenbach, L. M. Bellan, and H. G. Craighead, “High quality factor resonance at room temperature with nanostrings under high tensile stress,” J. Appl. Phys. 99, 124304 (2006).
[CrossRef]

Eichenfield, M.

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462, 7882 (2009).

Gondarenko, A.

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using optical forces,” Nature 462, 633636 (2009).
[CrossRef] [PubMed]

A. Gondarenko, J. S. Levy, and M. Lipson, “High confinement micron-scale silicon nitride high Q ring resonator,” Opt. Express 17, 11366–11370 (2009).
[CrossRef] [PubMed]

Hajimiri, A.

M. Hossein-Zadeh, H. Rokhsari, A. Hajimiri, and K. J. Vahala, “Characterization of a radiation-pressure-driven micromechanical oscillator,” Phys. Rev. A 74, 023813 (2006).
[CrossRef]

Hossein-Zadeh, M.

M. Hossein-Zadeh, H. Rokhsari, A. Hajimiri, and K. J. Vahala, “Characterization of a radiation-pressure-driven micromechanical oscillator,” Phys. Rev. A 74, 023813 (2006).
[CrossRef]

Ilchenko, V. S.

Kippenberg, T. J.

G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Rivire, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, “Near-field cavity optomechanics with nanomechanical oscillators,” Nature Phys. 5, 909–914 (2009).
[CrossRef]

T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: Back-action at the mesoscale,” Science 29,  321(5893), 1172–1176, (2008).
[CrossRef]

H. Rokhsari, T. J. Kippenberg, T. Carmon, and K. J. Vahala, “Theoretical and experimental study of radiation pressure-induced mechanical oscillations (parametric instability) in optical microcavities,” IEEE J. Sel. Top. Quantum Electron. 12, 96–107 (2006).
[CrossRef]

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94, 223902 (2005).
[CrossRef] [PubMed]

Kotthaus, J. P.

Q. P. Unterreithmeier, E. M. Weig, and J. P. Kotthaus, “Universal transduction scheme for nanomechanical systems based on dielectric forces,” Nature 458, 1001–1004 (2009).
[CrossRef] [PubMed]

G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Rivire, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, “Near-field cavity optomechanics with nanomechanical oscillators,” Nature Phys. 5, 909–914 (2009).
[CrossRef]

Levy, J. S.

Lipson, M.

A. Gondarenko, J. S. Levy, and M. Lipson, “High confinement micron-scale silicon nitride high Q ring resonator,” Opt. Express 17, 11366–11370 (2009).
[CrossRef] [PubMed]

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using optical forces,” Nature 462, 633636 (2009).
[CrossRef] [PubMed]

Maleki, L.

Matsko, A. B.

Painter, O.

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462, 7882 (2009).

Parpia, J. M.

S. S. Verbridge, J. M. Parpia, R. B. Reichenbach, L. M. Bellan, and H. G. Craighead, “High quality factor resonance at room temperature with nanostrings under high tensile stress,” J. Appl. Phys. 99, 124304 (2006).
[CrossRef]

Reichenbach, R. B.

S. S. Verbridge, J. M. Parpia, R. B. Reichenbach, L. M. Bellan, and H. G. Craighead, “High quality factor resonance at room temperature with nanostrings under high tensile stress,” J. Appl. Phys. 99, 124304 (2006).
[CrossRef]

Rivire, R.

G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Rivire, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, “Near-field cavity optomechanics with nanomechanical oscillators,” Nature Phys. 5, 909–914 (2009).
[CrossRef]

Rokhsari, H.

H. Rokhsari, T. J. Kippenberg, T. Carmon, and K. J. Vahala, “Theoretical and experimental study of radiation pressure-induced mechanical oscillations (parametric instability) in optical microcavities,” IEEE J. Sel. Top. Quantum Electron. 12, 96–107 (2006).
[CrossRef]

M. Hossein-Zadeh, H. Rokhsari, A. Hajimiri, and K. J. Vahala, “Characterization of a radiation-pressure-driven micromechanical oscillator,” Phys. Rev. A 74, 023813 (2006).
[CrossRef]

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94, 223902 (2005).
[CrossRef] [PubMed]

Savchenkov, A. A.

Schliesser, A.

G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Rivire, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, “Near-field cavity optomechanics with nanomechanical oscillators,” Nature Phys. 5, 909–914 (2009).
[CrossRef]

Seidel, D.

Sridaran, S.

S. Tallur, S. Sridaran, and S. A. Bhave, “Phase noise modeling of opto-mechanical oscillators,” IEEE Frequency Control Symposium (FCS 2010), Newport Beach, California, 268–272, (2010).

Tallur, S.

S. Tallur, S. Sridaran, and S. A. Bhave, “Phase noise modeling of opto-mechanical oscillators,” IEEE Frequency Control Symposium (FCS 2010), Newport Beach, California, 268–272, (2010).

Tomes, M.

M. Tomes and T. Carmon, “Photonic micro-electromechanical systems vibrating at X-band (11-GHz) rates,” Phys. Rev. Lett.,  102, 113601, (2009).
[CrossRef] [PubMed]

Unterreithmeier, Q. P.

G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Rivire, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, “Near-field cavity optomechanics with nanomechanical oscillators,” Nature Phys. 5, 909–914 (2009).
[CrossRef]

Q. P. Unterreithmeier, E. M. Weig, and J. P. Kotthaus, “Universal transduction scheme for nanomechanical systems based on dielectric forces,” Nature 458, 1001–1004 (2009).
[CrossRef] [PubMed]

Vahala, K. J.

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462, 7882 (2009).

T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: Back-action at the mesoscale,” Science 29,  321(5893), 1172–1176, (2008).
[CrossRef]

M. Hossein-Zadeh, H. Rokhsari, A. Hajimiri, and K. J. Vahala, “Characterization of a radiation-pressure-driven micromechanical oscillator,” Phys. Rev. A 74, 023813 (2006).
[CrossRef]

H. Rokhsari, T. J. Kippenberg, T. Carmon, and K. J. Vahala, “Theoretical and experimental study of radiation pressure-induced mechanical oscillations (parametric instability) in optical microcavities,” IEEE J. Sel. Top. Quantum Electron. 12, 96–107 (2006).
[CrossRef]

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94, 223902 (2005).
[CrossRef] [PubMed]

Verbridge, S. S.

S. S. Verbridge, J. M. Parpia, R. B. Reichenbach, L. M. Bellan, and H. G. Craighead, “High quality factor resonance at room temperature with nanostrings under high tensile stress,” J. Appl. Phys. 99, 124304 (2006).
[CrossRef]

Weig, E. M.

G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Rivire, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, “Near-field cavity optomechanics with nanomechanical oscillators,” Nature Phys. 5, 909–914 (2009).
[CrossRef]

Q. P. Unterreithmeier, E. M. Weig, and J. P. Kotthaus, “Universal transduction scheme for nanomechanical systems based on dielectric forces,” Nature 458, 1001–1004 (2009).
[CrossRef] [PubMed]

Wiederhecker, G. S.

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using optical forces,” Nature 462, 633636 (2009).
[CrossRef] [PubMed]

Yang, L.

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94, 223902 (2005).
[CrossRef] [PubMed]

IEEE Frequency Control Symposium (FCS 2010), Newport Beach, California (1)

S. Tallur, S. Sridaran, and S. A. Bhave, “Phase noise modeling of opto-mechanical oscillators,” IEEE Frequency Control Symposium (FCS 2010), Newport Beach, California, 268–272, (2010).

IEEE J. Sel. Top. Quantum Electron. (1)

H. Rokhsari, T. J. Kippenberg, T. Carmon, and K. J. Vahala, “Theoretical and experimental study of radiation pressure-induced mechanical oscillations (parametric instability) in optical microcavities,” IEEE J. Sel. Top. Quantum Electron. 12, 96–107 (2006).
[CrossRef]

J. Appl. Phys. (1)

S. S. Verbridge, J. M. Parpia, R. B. Reichenbach, L. M. Bellan, and H. G. Craighead, “High quality factor resonance at room temperature with nanostrings under high tensile stress,” J. Appl. Phys. 99, 124304 (2006).
[CrossRef]

Nature (3)

Q. P. Unterreithmeier, E. M. Weig, and J. P. Kotthaus, “Universal transduction scheme for nanomechanical systems based on dielectric forces,” Nature 458, 1001–1004 (2009).
[CrossRef] [PubMed]

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462, 7882 (2009).

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using optical forces,” Nature 462, 633636 (2009).
[CrossRef] [PubMed]

Nature Phys. (1)

G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Rivire, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, “Near-field cavity optomechanics with nanomechanical oscillators,” Nature Phys. 5, 909–914 (2009).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. A (1)

M. Hossein-Zadeh, H. Rokhsari, A. Hajimiri, and K. J. Vahala, “Characterization of a radiation-pressure-driven micromechanical oscillator,” Phys. Rev. A 74, 023813 (2006).
[CrossRef]

Phys. Rev. Lett. (2)

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94, 223902 (2005).
[CrossRef] [PubMed]

M. Tomes and T. Carmon, “Photonic micro-electromechanical systems vibrating at X-band (11-GHz) rates,” Phys. Rev. Lett.,  102, 113601, (2009).
[CrossRef] [PubMed]

Science (2)

T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: Back-action at the mesoscale,” Science 29,  321(5893), 1172–1176, (2008).
[CrossRef]

A. Cho, “Putting light’s light touch to work as optics meets mechanics,” Science 14,  5980(5893), 812–813, (2010).
[CrossRef]

Other (1)

Low Phase Noise Quartz Crystal Oscillator, Model FE-102A. http://www.freqelec.com/qz_osc_fe102a.html

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Figures (10)

Fig. 1
Fig. 1

Simulated mode shape highlighting deformed geometries for the ring expanding and contracting. The frequency of this fundamental radial expansion mode of the ring is 39.8MHz

Fig. 2
Fig. 2

Illustration of the process flow to microfabricate grating couplers, waveguides, and opto-mechanical resonators in silicon nitride

Fig. 3
Fig. 3

(Left) Optical micrograph of the integrated device showing the ring resonator, tapered waveguide and grating couplers (top view), (Right) Scanning electron micrograph (SEM) of the ring resonator and released section of the waveguide

Fig. 4
Fig. 4

Illustration of the test setup to probe the mechanical resonance of the opto-mechanical resonator

Fig. 5
Fig. 5

Insertion loss measured for −10dBm laser input power for a high loaded Q (>300,000) optical resonance

Fig. 6
Fig. 6

Transition from subthreshold brownian noise motion to self oscillation of the mechanical mode of the ring when the laser input exceeds threshold. The laser is biased at a relative detuning (Δω/2δ) of 0.38

Fig. 7
Fig. 7

Wide frequency sweep showing various harmonics of the fundamental mode for +15dBm laser input power and relative detuning (Δω/2δ) of 0.38

Fig. 8
Fig. 8

Phase noise for OMO operating at 41.947MHz with −11.37dBm output power. The laser input power is +15dBm and it is biased at a relative detuning (Δω/2δ) of 0.38. It varies as 1/f2 below 100kHz offsets as indicated by the dotted red trend-line implying that the OMO has no flicker noise. The corner frequency for 1/f2 region is around 20kHz which agrees with the measured mechanical Q of 2,000 at 41.947MHz. The phase noise is measured with an Agilent E5052B signal source analyzer

Fig. 9
Fig. 9

Variation of RF output power (Left) and phase noise at 1kHz offset (Right) with input laser power. The relative detuning was set at 0.31

Fig. 10
Fig. 10

Extinction of oscillation waveform at output of the APD measured for various relative detuning values. As we can see, a relative detuning of 0.5 enables us to see maximum extinction of 20dB, which corresponds to extinction at resonance as in Fig. 5

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