Abstract

Precise knowledge of an optical device’s frequency response is crucial for it to be useful in most applications. Traditional methods for determining the frequency response of an optical system (e.g. optical cavity or waveguide modulator) usually rely on calibrated broadband photo-detectors or complicated RF mixdown operations. As the bandwidths of these devices continue to increase, there is a growing need for a characterization method that does not have bandwidth limitations, or require a previously calibrated device. We demonstrate a new calibration technique on an optical system (consisting of an optical cavity and a high-speed waveguide modulator) that is free from limitations imposed by detector bandwidth, and does not require a calibrated photo-detector or modulator. We use a low-frequency (DC) photo-detector to monitor the cavity’s optical response as a function of modulation frequency, which is also used to determine the modulator’s frequency response. Knowledge of the frequency-dependent modulation depth allows us to more precisely determine the cavity’s characteristics (free spectral range and linewidth). The precision and repeatability of our technique is demonstrated by measuring the different resonant frequencies of orthogonal polarization cavity modes caused by the presence of a non-linear crystal. Once the modulator has been characterized using this simple method, the frequency response of any passive optical element can be determined to a fine resolution (e.g. kilohertz) over several gigahertz.

© 2017 Optical Society of America

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Corrections

13 January 2017: A correction was made to Eqs. (1)–(24).

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    [Crossref]
  2. C. Gamache, M. Têtu, C. Latrasse, N. Cyr, M. A. Duguay, and B. Villeneuve, “An optical frequency scale in exact multiples of 100 GHz for standardization of multifrequency communications,” IEEE Photonics Technol. Lett. 8(2), 290–292 (1996).
    [Crossref]
  3. Z. Bay and G. G. Luther, “Locking a laser frequency to the time standard,” Appl. Phys. Lett. 13(9), 303–304 (1968).
    [Crossref]
  4. H. Haitjema, P. H. J. Schellekens, and S. F. C. L. Wetzels, “Calibration of displacement sensors up to 300 μm with nanometre accuracy and direct traceability to a primary standard of length,” Metrologia 37(1), 25–33 (2000).
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  5. J. R. Lawall, “Fabry-Perot metrology for displacements up to 50 mm,” J. Opt. Soc. Am. A 22(12), 2786–2798 (2005).
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    [Crossref] [PubMed]
  7. M. Pysher, Y. Miwa, R. Shahrokhshahi, R. Bloomer, and O. Pfister, “Parallel generation of quadripartite cluster entanglement in the optical frequency comb,” Phys. Rev. Lett. 107, 030505 (2011).
    [Crossref] [PubMed]
  8. M. Chen, N. C. Menicucci, and O. Pfister, “Experimental realization of multipartite entanglement of 60 modes of a quantum optical frequency comb,” Phys. Rev. Lett. 112, 120505 (2014).
    [Crossref] [PubMed]
  9. R. Medeiros de Araújo, J. Roslund, Y. Cai, G. Ferrini, C. Fabre, and N. Treps, “Full characterization of a highly multimode entangled state embedded in an optical frequency comb using pulse shaping,” Phys. Rev. A 89, 053828 (2014).
    [Crossref]
  10. R. Williamson and C. Terpstra, “Precise free spectral range measurement of telecom etalons,” Proc. SPIE 5180, 274–282 (2004).
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  11. S. Gee, S. Ozharar, F. Quinlan, and P. J. Delfyett, “High-precision measurement of free spectral range of etalon,” Electron. Lett. 42(12), 715–716 (2006).
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  12. S. K. Korotky, A. H. Gnauck, B. L. Kasper, J. C. Campbell, J. J. Veselka, J. R. Talman, and A. R. McCormick, “8-Gbit/s transmission experiment over 68 km of optical fiber using a Ti: LiNbO3 external modulator,” IEEE J. Lightwave Technol. LT-5(10), 1505–1509 (1987).
    [Crossref]
  13. T. Okiyama, H. Nishimoto, I. Yokota, and T. Touge, “Evaluation of 4-Gbit/s optical fiber transmission distance with direct and external modulation,” IEEE J. Lightwave Technol. 6(11), 1686–1692 (1988).
    [Crossref]
  14. E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron.,  6(1), 69–82 (2000).
    [Crossref]
  15. I. Kobayashi and M. Koyama, “Measurement of optical fiber transfer functions based upon the swept-frequency technique for baseband signals,” Trans. IECE Jpn. E59(4), 11–12 (1976).
  16. T. Ito, S. Machida, T. Izawa, T. Miyashita, and A. Kawana, “Optical-transmission experiment at 400 Mb/s using a single-mode fibre,” Trans. IECE Jpn. E59(1), 19–20 (1976).
  17. N. Uehara and K. Ueda, “Accurate measurement of ultralow loss in a high-finesse Fabry-Perot interferometer using the frequency response functions,” Appl. Phys. B 61(1), 9–15 (1995).
    [Crossref]
  18. P. J. Manson, “High precision free spectral range measurement using a phase modulated laser beam,” Rev. Sci. Instrum. 70(10), 3834–3839 (1999).
    [Crossref]
  19. I. Ozdur, S. Ozharar, F. Quinlan, S. Gee, and P. J. Delfyett, “Modified Pound-Drever-Hall scheme for high-precision free spectral range measurement of Fabry-Perot etalon,” Electron. Lett. 44(15), 927–928 (2008).
    [Crossref]
  20. D. Mandridis, I. Ozdur, M. Bagnell, and P. J. Delfyett, “Free spectral range measurement of a fiberized Fabry-Perot etalon with sub-Hz accuracy,” Opt. Express 18(11), 11264–11269 (2010).
    [Crossref] [PubMed]
  21. M. Aketagawa, S. Kimura, T. Yashiki, H. Iwata, T. Q. Banh, and K. Hirata, “Measurement of a free spectral range of a Fabry-Perot cavity using frequency modulation and null method under off-resonance conditions,” Meas. Sci. Technol. 22, 025302 (2011).
    [Crossref]
  22. T. S. Tan, R. L. Jungerman, and S. S. Elliott, “Optical receiver and modulator frequency response measurement with a Nd:YAG ring laser heterodyne technique,” IEEE Trans. Microw. Theory Techn. 37(8), 1217–1222 (1989).
    [Crossref]
  23. R. T. Hawkins, M. D. Jones, S. H. Pepper, and J. H. Goll, “Comparison of fast photodetector response measurement by optical heterodyne and pulse response techniques,” IEEE J. Lightwave Technol. 9(10), 1289–1294 (1991).
    [Crossref]
  24. A. K. M. Lam, M. Fairburn, and N. A. F. Jaeger, “Wide-band electrooptic intensity modulator frequency response measurement using an optical heterodyne down-conversion technique,” IEEE Trans. Microw. Theory Technnol. 54(1), 240–246 (2006).
    [Crossref]
  25. A. A. Chtcherbakov, R. J. Kisch, J. D. Bull, and N. A. F. Jaeger, “Optical heterodyne method for amplitude and phase response mmeasurement for ultrawideband electrooptic modulators,” IEEE Photonics Technol. Lett. 19(1), 18–20 (2007).
    [Crossref]
  26. S. Uehara, “Calibration of optical modulator frequency response with application to signal level control,” Appl. Opt. 17(1), 68–71 (1978).
    [Crossref] [PubMed]
  27. C. R. Locke, D. Stuart, E. N. Ivanov, and A. N. Luiten, “A simple technique for accurate and complete characterisation of a Fabry-Perot cavity,” Opt. Express 17(24), 21935–21943 (2009).
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  29. P. Skeath, C. H. Bulmer, S. C. Hiser, and W. K. Burns, “Novel electrostatic mechanism in the thermal instability of z-cut LiNbO3 interferometers,” Appl. Phys. Lett. 49(19), 1221–1223 (1986).
    [Crossref]
  30. R. L. Jungerman, C. Johnsen, D. J. McQuate, K. Salomaa, M. P. Zurakowski, R. C. Bray, G. Conrad, D. Cropper, and P. Hernday, “High-speed optical modulator for application in instrumentation,” IEEE J. Lightwave Technol. 8(9), 1363–1370 (1990).
    [Crossref]
  31. R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31(2), 97–105 (1983).
    [Crossref]
  32. G. J. Edwards and M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16(4), 373–375 (1984).
    [Crossref]

2014 (2)

M. Chen, N. C. Menicucci, and O. Pfister, “Experimental realization of multipartite entanglement of 60 modes of a quantum optical frequency comb,” Phys. Rev. Lett. 112, 120505 (2014).
[Crossref] [PubMed]

R. Medeiros de Araújo, J. Roslund, Y. Cai, G. Ferrini, C. Fabre, and N. Treps, “Full characterization of a highly multimode entangled state embedded in an optical frequency comb using pulse shaping,” Phys. Rev. A 89, 053828 (2014).
[Crossref]

2011 (2)

M. Pysher, Y. Miwa, R. Shahrokhshahi, R. Bloomer, and O. Pfister, “Parallel generation of quadripartite cluster entanglement in the optical frequency comb,” Phys. Rev. Lett. 107, 030505 (2011).
[Crossref] [PubMed]

M. Aketagawa, S. Kimura, T. Yashiki, H. Iwata, T. Q. Banh, and K. Hirata, “Measurement of a free spectral range of a Fabry-Perot cavity using frequency modulation and null method under off-resonance conditions,” Meas. Sci. Technol. 22, 025302 (2011).
[Crossref]

2010 (1)

2009 (1)

2008 (1)

I. Ozdur, S. Ozharar, F. Quinlan, S. Gee, and P. J. Delfyett, “Modified Pound-Drever-Hall scheme for high-precision free spectral range measurement of Fabry-Perot etalon,” Electron. Lett. 44(15), 927–928 (2008).
[Crossref]

2007 (2)

R. J. Senior, G. N. Milford, J. Janousek, A. E. Dunlop, K. Wagner, H-A. Bachor, T. C. Ralph, E. H. Huntington, and C. C. Harb, “Observation of a comb of optical squeezing over many gigahertz of bandwidth,” Opt. Express 15(9), 5310–5317 (2007).
[Crossref] [PubMed]

A. A. Chtcherbakov, R. J. Kisch, J. D. Bull, and N. A. F. Jaeger, “Optical heterodyne method for amplitude and phase response mmeasurement for ultrawideband electrooptic modulators,” IEEE Photonics Technol. Lett. 19(1), 18–20 (2007).
[Crossref]

2006 (2)

A. K. M. Lam, M. Fairburn, and N. A. F. Jaeger, “Wide-band electrooptic intensity modulator frequency response measurement using an optical heterodyne down-conversion technique,” IEEE Trans. Microw. Theory Technnol. 54(1), 240–246 (2006).
[Crossref]

S. Gee, S. Ozharar, F. Quinlan, and P. J. Delfyett, “High-precision measurement of free spectral range of etalon,” Electron. Lett. 42(12), 715–716 (2006).
[Crossref]

2005 (1)

2004 (1)

R. Williamson and C. Terpstra, “Precise free spectral range measurement of telecom etalons,” Proc. SPIE 5180, 274–282 (2004).
[Crossref]

2000 (2)

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron.,  6(1), 69–82 (2000).
[Crossref]

H. Haitjema, P. H. J. Schellekens, and S. F. C. L. Wetzels, “Calibration of displacement sensors up to 300 μm with nanometre accuracy and direct traceability to a primary standard of length,” Metrologia 37(1), 25–33 (2000).
[Crossref]

1999 (1)

P. J. Manson, “High precision free spectral range measurement using a phase modulated laser beam,” Rev. Sci. Instrum. 70(10), 3834–3839 (1999).
[Crossref]

1996 (1)

C. Gamache, M. Têtu, C. Latrasse, N. Cyr, M. A. Duguay, and B. Villeneuve, “An optical frequency scale in exact multiples of 100 GHz for standardization of multifrequency communications,” IEEE Photonics Technol. Lett. 8(2), 290–292 (1996).
[Crossref]

1995 (1)

N. Uehara and K. Ueda, “Accurate measurement of ultralow loss in a high-finesse Fabry-Perot interferometer using the frequency response functions,” Appl. Phys. B 61(1), 9–15 (1995).
[Crossref]

1991 (1)

R. T. Hawkins, M. D. Jones, S. H. Pepper, and J. H. Goll, “Comparison of fast photodetector response measurement by optical heterodyne and pulse response techniques,” IEEE J. Lightwave Technol. 9(10), 1289–1294 (1991).
[Crossref]

1990 (1)

R. L. Jungerman, C. Johnsen, D. J. McQuate, K. Salomaa, M. P. Zurakowski, R. C. Bray, G. Conrad, D. Cropper, and P. Hernday, “High-speed optical modulator for application in instrumentation,” IEEE J. Lightwave Technol. 8(9), 1363–1370 (1990).
[Crossref]

1989 (2)

A. G. Adam, A. J. Merer, D. M. Steunenberg, M. C. L. Gerry, and I. Ozier, “A precise calibration system for high-resolution visible-laser spectroscopy,” Rev. Sci. Instrum. 60(6), 1003–1007 (1989).
[Crossref]

T. S. Tan, R. L. Jungerman, and S. S. Elliott, “Optical receiver and modulator frequency response measurement with a Nd:YAG ring laser heterodyne technique,” IEEE Trans. Microw. Theory Techn. 37(8), 1217–1222 (1989).
[Crossref]

1988 (1)

T. Okiyama, H. Nishimoto, I. Yokota, and T. Touge, “Evaluation of 4-Gbit/s optical fiber transmission distance with direct and external modulation,” IEEE J. Lightwave Technol. 6(11), 1686–1692 (1988).
[Crossref]

1987 (1)

S. K. Korotky, A. H. Gnauck, B. L. Kasper, J. C. Campbell, J. J. Veselka, J. R. Talman, and A. R. McCormick, “8-Gbit/s transmission experiment over 68 km of optical fiber using a Ti: LiNbO3 external modulator,” IEEE J. Lightwave Technol. LT-5(10), 1505–1509 (1987).
[Crossref]

1986 (1)

P. Skeath, C. H. Bulmer, S. C. Hiser, and W. K. Burns, “Novel electrostatic mechanism in the thermal instability of z-cut LiNbO3 interferometers,” Appl. Phys. Lett. 49(19), 1221–1223 (1986).
[Crossref]

1984 (1)

G. J. Edwards and M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16(4), 373–375 (1984).
[Crossref]

1983 (1)

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31(2), 97–105 (1983).
[Crossref]

1978 (1)

1976 (2)

I. Kobayashi and M. Koyama, “Measurement of optical fiber transfer functions based upon the swept-frequency technique for baseband signals,” Trans. IECE Jpn. E59(4), 11–12 (1976).

T. Ito, S. Machida, T. Izawa, T. Miyashita, and A. Kawana, “Optical-transmission experiment at 400 Mb/s using a single-mode fibre,” Trans. IECE Jpn. E59(1), 19–20 (1976).

1968 (1)

Z. Bay and G. G. Luther, “Locking a laser frequency to the time standard,” Appl. Phys. Lett. 13(9), 303–304 (1968).
[Crossref]

Adam, A. G.

A. G. Adam, A. J. Merer, D. M. Steunenberg, M. C. L. Gerry, and I. Ozier, “A precise calibration system for high-resolution visible-laser spectroscopy,” Rev. Sci. Instrum. 60(6), 1003–1007 (1989).
[Crossref]

Aketagawa, M.

M. Aketagawa, S. Kimura, T. Yashiki, H. Iwata, T. Q. Banh, and K. Hirata, “Measurement of a free spectral range of a Fabry-Perot cavity using frequency modulation and null method under off-resonance conditions,” Meas. Sci. Technol. 22, 025302 (2011).
[Crossref]

Attanasio, D. V.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron.,  6(1), 69–82 (2000).
[Crossref]

Bachor, H-A.

Bagnell, M.

Banh, T. Q.

M. Aketagawa, S. Kimura, T. Yashiki, H. Iwata, T. Q. Banh, and K. Hirata, “Measurement of a free spectral range of a Fabry-Perot cavity using frequency modulation and null method under off-resonance conditions,” Meas. Sci. Technol. 22, 025302 (2011).
[Crossref]

Bay, Z.

Z. Bay and G. G. Luther, “Locking a laser frequency to the time standard,” Appl. Phys. Lett. 13(9), 303–304 (1968).
[Crossref]

Bloomer, R.

M. Pysher, Y. Miwa, R. Shahrokhshahi, R. Bloomer, and O. Pfister, “Parallel generation of quadripartite cluster entanglement in the optical frequency comb,” Phys. Rev. Lett. 107, 030505 (2011).
[Crossref] [PubMed]

Bossi, D. E.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron.,  6(1), 69–82 (2000).
[Crossref]

Bray, R. C.

R. L. Jungerman, C. Johnsen, D. J. McQuate, K. Salomaa, M. P. Zurakowski, R. C. Bray, G. Conrad, D. Cropper, and P. Hernday, “High-speed optical modulator for application in instrumentation,” IEEE J. Lightwave Technol. 8(9), 1363–1370 (1990).
[Crossref]

Bull, J. D.

A. A. Chtcherbakov, R. J. Kisch, J. D. Bull, and N. A. F. Jaeger, “Optical heterodyne method for amplitude and phase response mmeasurement for ultrawideband electrooptic modulators,” IEEE Photonics Technol. Lett. 19(1), 18–20 (2007).
[Crossref]

Bulmer, C. H.

P. Skeath, C. H. Bulmer, S. C. Hiser, and W. K. Burns, “Novel electrostatic mechanism in the thermal instability of z-cut LiNbO3 interferometers,” Appl. Phys. Lett. 49(19), 1221–1223 (1986).
[Crossref]

Burns, W. K.

P. Skeath, C. H. Bulmer, S. C. Hiser, and W. K. Burns, “Novel electrostatic mechanism in the thermal instability of z-cut LiNbO3 interferometers,” Appl. Phys. Lett. 49(19), 1221–1223 (1986).
[Crossref]

Cai, Y.

R. Medeiros de Araújo, J. Roslund, Y. Cai, G. Ferrini, C. Fabre, and N. Treps, “Full characterization of a highly multimode entangled state embedded in an optical frequency comb using pulse shaping,” Phys. Rev. A 89, 053828 (2014).
[Crossref]

Campbell, J. C.

S. K. Korotky, A. H. Gnauck, B. L. Kasper, J. C. Campbell, J. J. Veselka, J. R. Talman, and A. R. McCormick, “8-Gbit/s transmission experiment over 68 km of optical fiber using a Ti: LiNbO3 external modulator,” IEEE J. Lightwave Technol. LT-5(10), 1505–1509 (1987).
[Crossref]

Chen, M.

M. Chen, N. C. Menicucci, and O. Pfister, “Experimental realization of multipartite entanglement of 60 modes of a quantum optical frequency comb,” Phys. Rev. Lett. 112, 120505 (2014).
[Crossref] [PubMed]

Chtcherbakov, A. A.

A. A. Chtcherbakov, R. J. Kisch, J. D. Bull, and N. A. F. Jaeger, “Optical heterodyne method for amplitude and phase response mmeasurement for ultrawideband electrooptic modulators,” IEEE Photonics Technol. Lett. 19(1), 18–20 (2007).
[Crossref]

Conrad, G.

R. L. Jungerman, C. Johnsen, D. J. McQuate, K. Salomaa, M. P. Zurakowski, R. C. Bray, G. Conrad, D. Cropper, and P. Hernday, “High-speed optical modulator for application in instrumentation,” IEEE J. Lightwave Technol. 8(9), 1363–1370 (1990).
[Crossref]

Cropper, D.

R. L. Jungerman, C. Johnsen, D. J. McQuate, K. Salomaa, M. P. Zurakowski, R. C. Bray, G. Conrad, D. Cropper, and P. Hernday, “High-speed optical modulator for application in instrumentation,” IEEE J. Lightwave Technol. 8(9), 1363–1370 (1990).
[Crossref]

Cyr, N.

C. Gamache, M. Têtu, C. Latrasse, N. Cyr, M. A. Duguay, and B. Villeneuve, “An optical frequency scale in exact multiples of 100 GHz for standardization of multifrequency communications,” IEEE Photonics Technol. Lett. 8(2), 290–292 (1996).
[Crossref]

Delfyett, P. J.

D. Mandridis, I. Ozdur, M. Bagnell, and P. J. Delfyett, “Free spectral range measurement of a fiberized Fabry-Perot etalon with sub-Hz accuracy,” Opt. Express 18(11), 11264–11269 (2010).
[Crossref] [PubMed]

I. Ozdur, S. Ozharar, F. Quinlan, S. Gee, and P. J. Delfyett, “Modified Pound-Drever-Hall scheme for high-precision free spectral range measurement of Fabry-Perot etalon,” Electron. Lett. 44(15), 927–928 (2008).
[Crossref]

S. Gee, S. Ozharar, F. Quinlan, and P. J. Delfyett, “High-precision measurement of free spectral range of etalon,” Electron. Lett. 42(12), 715–716 (2006).
[Crossref]

Drever, R. W. P.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31(2), 97–105 (1983).
[Crossref]

Duguay, M. A.

C. Gamache, M. Têtu, C. Latrasse, N. Cyr, M. A. Duguay, and B. Villeneuve, “An optical frequency scale in exact multiples of 100 GHz for standardization of multifrequency communications,” IEEE Photonics Technol. Lett. 8(2), 290–292 (1996).
[Crossref]

Dunlop, A. E.

Edwards, G. J.

G. J. Edwards and M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16(4), 373–375 (1984).
[Crossref]

Elliott, S. S.

T. S. Tan, R. L. Jungerman, and S. S. Elliott, “Optical receiver and modulator frequency response measurement with a Nd:YAG ring laser heterodyne technique,” IEEE Trans. Microw. Theory Techn. 37(8), 1217–1222 (1989).
[Crossref]

Fabre, C.

R. Medeiros de Araújo, J. Roslund, Y. Cai, G. Ferrini, C. Fabre, and N. Treps, “Full characterization of a highly multimode entangled state embedded in an optical frequency comb using pulse shaping,” Phys. Rev. A 89, 053828 (2014).
[Crossref]

Fairburn, M.

A. K. M. Lam, M. Fairburn, and N. A. F. Jaeger, “Wide-band electrooptic intensity modulator frequency response measurement using an optical heterodyne down-conversion technique,” IEEE Trans. Microw. Theory Technnol. 54(1), 240–246 (2006).
[Crossref]

Ferrini, G.

R. Medeiros de Araújo, J. Roslund, Y. Cai, G. Ferrini, C. Fabre, and N. Treps, “Full characterization of a highly multimode entangled state embedded in an optical frequency comb using pulse shaping,” Phys. Rev. A 89, 053828 (2014).
[Crossref]

Ford, G. M.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31(2), 97–105 (1983).
[Crossref]

Fritz, D. J.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron.,  6(1), 69–82 (2000).
[Crossref]

Gamache, C.

C. Gamache, M. Têtu, C. Latrasse, N. Cyr, M. A. Duguay, and B. Villeneuve, “An optical frequency scale in exact multiples of 100 GHz for standardization of multifrequency communications,” IEEE Photonics Technol. Lett. 8(2), 290–292 (1996).
[Crossref]

Gee, S.

I. Ozdur, S. Ozharar, F. Quinlan, S. Gee, and P. J. Delfyett, “Modified Pound-Drever-Hall scheme for high-precision free spectral range measurement of Fabry-Perot etalon,” Electron. Lett. 44(15), 927–928 (2008).
[Crossref]

S. Gee, S. Ozharar, F. Quinlan, and P. J. Delfyett, “High-precision measurement of free spectral range of etalon,” Electron. Lett. 42(12), 715–716 (2006).
[Crossref]

Gerry, M. C. L.

A. G. Adam, A. J. Merer, D. M. Steunenberg, M. C. L. Gerry, and I. Ozier, “A precise calibration system for high-resolution visible-laser spectroscopy,” Rev. Sci. Instrum. 60(6), 1003–1007 (1989).
[Crossref]

Gnauck, A. H.

S. K. Korotky, A. H. Gnauck, B. L. Kasper, J. C. Campbell, J. J. Veselka, J. R. Talman, and A. R. McCormick, “8-Gbit/s transmission experiment over 68 km of optical fiber using a Ti: LiNbO3 external modulator,” IEEE J. Lightwave Technol. LT-5(10), 1505–1509 (1987).
[Crossref]

Goll, J. H.

R. T. Hawkins, M. D. Jones, S. H. Pepper, and J. H. Goll, “Comparison of fast photodetector response measurement by optical heterodyne and pulse response techniques,” IEEE J. Lightwave Technol. 9(10), 1289–1294 (1991).
[Crossref]

Haitjema, H.

H. Haitjema, P. H. J. Schellekens, and S. F. C. L. Wetzels, “Calibration of displacement sensors up to 300 μm with nanometre accuracy and direct traceability to a primary standard of length,” Metrologia 37(1), 25–33 (2000).
[Crossref]

Hall, J. L.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31(2), 97–105 (1983).
[Crossref]

Hallemeier, P. F.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron.,  6(1), 69–82 (2000).
[Crossref]

Harb, C. C.

Hawkins, R. T.

R. T. Hawkins, M. D. Jones, S. H. Pepper, and J. H. Goll, “Comparison of fast photodetector response measurement by optical heterodyne and pulse response techniques,” IEEE J. Lightwave Technol. 9(10), 1289–1294 (1991).
[Crossref]

Hernday, P.

R. L. Jungerman, C. Johnsen, D. J. McQuate, K. Salomaa, M. P. Zurakowski, R. C. Bray, G. Conrad, D. Cropper, and P. Hernday, “High-speed optical modulator for application in instrumentation,” IEEE J. Lightwave Technol. 8(9), 1363–1370 (1990).
[Crossref]

Hirata, K.

M. Aketagawa, S. Kimura, T. Yashiki, H. Iwata, T. Q. Banh, and K. Hirata, “Measurement of a free spectral range of a Fabry-Perot cavity using frequency modulation and null method under off-resonance conditions,” Meas. Sci. Technol. 22, 025302 (2011).
[Crossref]

Hiser, S. C.

P. Skeath, C. H. Bulmer, S. C. Hiser, and W. K. Burns, “Novel electrostatic mechanism in the thermal instability of z-cut LiNbO3 interferometers,” Appl. Phys. Lett. 49(19), 1221–1223 (1986).
[Crossref]

Hough, J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31(2), 97–105 (1983).
[Crossref]

Huntington, E. H.

Ito, T.

T. Ito, S. Machida, T. Izawa, T. Miyashita, and A. Kawana, “Optical-transmission experiment at 400 Mb/s using a single-mode fibre,” Trans. IECE Jpn. E59(1), 19–20 (1976).

Ivanov, E. N.

Iwata, H.

M. Aketagawa, S. Kimura, T. Yashiki, H. Iwata, T. Q. Banh, and K. Hirata, “Measurement of a free spectral range of a Fabry-Perot cavity using frequency modulation and null method under off-resonance conditions,” Meas. Sci. Technol. 22, 025302 (2011).
[Crossref]

Izawa, T.

T. Ito, S. Machida, T. Izawa, T. Miyashita, and A. Kawana, “Optical-transmission experiment at 400 Mb/s using a single-mode fibre,” Trans. IECE Jpn. E59(1), 19–20 (1976).

Jaeger, N. A. F.

A. A. Chtcherbakov, R. J. Kisch, J. D. Bull, and N. A. F. Jaeger, “Optical heterodyne method for amplitude and phase response mmeasurement for ultrawideband electrooptic modulators,” IEEE Photonics Technol. Lett. 19(1), 18–20 (2007).
[Crossref]

A. K. M. Lam, M. Fairburn, and N. A. F. Jaeger, “Wide-band electrooptic intensity modulator frequency response measurement using an optical heterodyne down-conversion technique,” IEEE Trans. Microw. Theory Technnol. 54(1), 240–246 (2006).
[Crossref]

Janousek, J.

Johnsen, C.

R. L. Jungerman, C. Johnsen, D. J. McQuate, K. Salomaa, M. P. Zurakowski, R. C. Bray, G. Conrad, D. Cropper, and P. Hernday, “High-speed optical modulator for application in instrumentation,” IEEE J. Lightwave Technol. 8(9), 1363–1370 (1990).
[Crossref]

Jones, M. D.

R. T. Hawkins, M. D. Jones, S. H. Pepper, and J. H. Goll, “Comparison of fast photodetector response measurement by optical heterodyne and pulse response techniques,” IEEE J. Lightwave Technol. 9(10), 1289–1294 (1991).
[Crossref]

Jungerman, R. L.

R. L. Jungerman, C. Johnsen, D. J. McQuate, K. Salomaa, M. P. Zurakowski, R. C. Bray, G. Conrad, D. Cropper, and P. Hernday, “High-speed optical modulator for application in instrumentation,” IEEE J. Lightwave Technol. 8(9), 1363–1370 (1990).
[Crossref]

T. S. Tan, R. L. Jungerman, and S. S. Elliott, “Optical receiver and modulator frequency response measurement with a Nd:YAG ring laser heterodyne technique,” IEEE Trans. Microw. Theory Techn. 37(8), 1217–1222 (1989).
[Crossref]

Kasper, B. L.

S. K. Korotky, A. H. Gnauck, B. L. Kasper, J. C. Campbell, J. J. Veselka, J. R. Talman, and A. R. McCormick, “8-Gbit/s transmission experiment over 68 km of optical fiber using a Ti: LiNbO3 external modulator,” IEEE J. Lightwave Technol. LT-5(10), 1505–1509 (1987).
[Crossref]

Kawana, A.

T. Ito, S. Machida, T. Izawa, T. Miyashita, and A. Kawana, “Optical-transmission experiment at 400 Mb/s using a single-mode fibre,” Trans. IECE Jpn. E59(1), 19–20 (1976).

Kimura, S.

M. Aketagawa, S. Kimura, T. Yashiki, H. Iwata, T. Q. Banh, and K. Hirata, “Measurement of a free spectral range of a Fabry-Perot cavity using frequency modulation and null method under off-resonance conditions,” Meas. Sci. Technol. 22, 025302 (2011).
[Crossref]

Kisch, R. J.

A. A. Chtcherbakov, R. J. Kisch, J. D. Bull, and N. A. F. Jaeger, “Optical heterodyne method for amplitude and phase response mmeasurement for ultrawideband electrooptic modulators,” IEEE Photonics Technol. Lett. 19(1), 18–20 (2007).
[Crossref]

Kissa, K. M.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron.,  6(1), 69–82 (2000).
[Crossref]

Kobayashi, I.

I. Kobayashi and M. Koyama, “Measurement of optical fiber transfer functions based upon the swept-frequency technique for baseband signals,” Trans. IECE Jpn. E59(4), 11–12 (1976).

Korotky, S. K.

S. K. Korotky, A. H. Gnauck, B. L. Kasper, J. C. Campbell, J. J. Veselka, J. R. Talman, and A. R. McCormick, “8-Gbit/s transmission experiment over 68 km of optical fiber using a Ti: LiNbO3 external modulator,” IEEE J. Lightwave Technol. LT-5(10), 1505–1509 (1987).
[Crossref]

Kowalski, F. V.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31(2), 97–105 (1983).
[Crossref]

Koyama, M.

I. Kobayashi and M. Koyama, “Measurement of optical fiber transfer functions based upon the swept-frequency technique for baseband signals,” Trans. IECE Jpn. E59(4), 11–12 (1976).

Lafaw, D. A.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron.,  6(1), 69–82 (2000).
[Crossref]

Lam, A. K. M.

A. K. M. Lam, M. Fairburn, and N. A. F. Jaeger, “Wide-band electrooptic intensity modulator frequency response measurement using an optical heterodyne down-conversion technique,” IEEE Trans. Microw. Theory Technnol. 54(1), 240–246 (2006).
[Crossref]

Latrasse, C.

C. Gamache, M. Têtu, C. Latrasse, N. Cyr, M. A. Duguay, and B. Villeneuve, “An optical frequency scale in exact multiples of 100 GHz for standardization of multifrequency communications,” IEEE Photonics Technol. Lett. 8(2), 290–292 (1996).
[Crossref]

Lawall, J. R.

Lawrence, M.

G. J. Edwards and M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16(4), 373–375 (1984).
[Crossref]

Locke, C. R.

Luiten, A. N.

Luther, G. G.

Z. Bay and G. G. Luther, “Locking a laser frequency to the time standard,” Appl. Phys. Lett. 13(9), 303–304 (1968).
[Crossref]

Maack, D.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron.,  6(1), 69–82 (2000).
[Crossref]

Machida, S.

T. Ito, S. Machida, T. Izawa, T. Miyashita, and A. Kawana, “Optical-transmission experiment at 400 Mb/s using a single-mode fibre,” Trans. IECE Jpn. E59(1), 19–20 (1976).

Mandridis, D.

Manson, P. J.

P. J. Manson, “High precision free spectral range measurement using a phase modulated laser beam,” Rev. Sci. Instrum. 70(10), 3834–3839 (1999).
[Crossref]

McBrien, G. J.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron.,  6(1), 69–82 (2000).
[Crossref]

McCormick, A. R.

S. K. Korotky, A. H. Gnauck, B. L. Kasper, J. C. Campbell, J. J. Veselka, J. R. Talman, and A. R. McCormick, “8-Gbit/s transmission experiment over 68 km of optical fiber using a Ti: LiNbO3 external modulator,” IEEE J. Lightwave Technol. LT-5(10), 1505–1509 (1987).
[Crossref]

McQuate, D. J.

R. L. Jungerman, C. Johnsen, D. J. McQuate, K. Salomaa, M. P. Zurakowski, R. C. Bray, G. Conrad, D. Cropper, and P. Hernday, “High-speed optical modulator for application in instrumentation,” IEEE J. Lightwave Technol. 8(9), 1363–1370 (1990).
[Crossref]

Medeiros de Araújo, R.

R. Medeiros de Araújo, J. Roslund, Y. Cai, G. Ferrini, C. Fabre, and N. Treps, “Full characterization of a highly multimode entangled state embedded in an optical frequency comb using pulse shaping,” Phys. Rev. A 89, 053828 (2014).
[Crossref]

Menicucci, N. C.

M. Chen, N. C. Menicucci, and O. Pfister, “Experimental realization of multipartite entanglement of 60 modes of a quantum optical frequency comb,” Phys. Rev. Lett. 112, 120505 (2014).
[Crossref] [PubMed]

Merer, A. J.

A. G. Adam, A. J. Merer, D. M. Steunenberg, M. C. L. Gerry, and I. Ozier, “A precise calibration system for high-resolution visible-laser spectroscopy,” Rev. Sci. Instrum. 60(6), 1003–1007 (1989).
[Crossref]

Milford, G. N.

Miwa, Y.

M. Pysher, Y. Miwa, R. Shahrokhshahi, R. Bloomer, and O. Pfister, “Parallel generation of quadripartite cluster entanglement in the optical frequency comb,” Phys. Rev. Lett. 107, 030505 (2011).
[Crossref] [PubMed]

Miyashita, T.

T. Ito, S. Machida, T. Izawa, T. Miyashita, and A. Kawana, “Optical-transmission experiment at 400 Mb/s using a single-mode fibre,” Trans. IECE Jpn. E59(1), 19–20 (1976).

Munley, A. J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31(2), 97–105 (1983).
[Crossref]

Murphy, E. J.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron.,  6(1), 69–82 (2000).
[Crossref]

Nishimoto, H.

T. Okiyama, H. Nishimoto, I. Yokota, and T. Touge, “Evaluation of 4-Gbit/s optical fiber transmission distance with direct and external modulation,” IEEE J. Lightwave Technol. 6(11), 1686–1692 (1988).
[Crossref]

Okiyama, T.

T. Okiyama, H. Nishimoto, I. Yokota, and T. Touge, “Evaluation of 4-Gbit/s optical fiber transmission distance with direct and external modulation,” IEEE J. Lightwave Technol. 6(11), 1686–1692 (1988).
[Crossref]

Ozdur, I.

D. Mandridis, I. Ozdur, M. Bagnell, and P. J. Delfyett, “Free spectral range measurement of a fiberized Fabry-Perot etalon with sub-Hz accuracy,” Opt. Express 18(11), 11264–11269 (2010).
[Crossref] [PubMed]

I. Ozdur, S. Ozharar, F. Quinlan, S. Gee, and P. J. Delfyett, “Modified Pound-Drever-Hall scheme for high-precision free spectral range measurement of Fabry-Perot etalon,” Electron. Lett. 44(15), 927–928 (2008).
[Crossref]

Ozharar, S.

I. Ozdur, S. Ozharar, F. Quinlan, S. Gee, and P. J. Delfyett, “Modified Pound-Drever-Hall scheme for high-precision free spectral range measurement of Fabry-Perot etalon,” Electron. Lett. 44(15), 927–928 (2008).
[Crossref]

S. Gee, S. Ozharar, F. Quinlan, and P. J. Delfyett, “High-precision measurement of free spectral range of etalon,” Electron. Lett. 42(12), 715–716 (2006).
[Crossref]

Ozier, I.

A. G. Adam, A. J. Merer, D. M. Steunenberg, M. C. L. Gerry, and I. Ozier, “A precise calibration system for high-resolution visible-laser spectroscopy,” Rev. Sci. Instrum. 60(6), 1003–1007 (1989).
[Crossref]

Pepper, S. H.

R. T. Hawkins, M. D. Jones, S. H. Pepper, and J. H. Goll, “Comparison of fast photodetector response measurement by optical heterodyne and pulse response techniques,” IEEE J. Lightwave Technol. 9(10), 1289–1294 (1991).
[Crossref]

Pfister, O.

M. Chen, N. C. Menicucci, and O. Pfister, “Experimental realization of multipartite entanglement of 60 modes of a quantum optical frequency comb,” Phys. Rev. Lett. 112, 120505 (2014).
[Crossref] [PubMed]

M. Pysher, Y. Miwa, R. Shahrokhshahi, R. Bloomer, and O. Pfister, “Parallel generation of quadripartite cluster entanglement in the optical frequency comb,” Phys. Rev. Lett. 107, 030505 (2011).
[Crossref] [PubMed]

Pysher, M.

M. Pysher, Y. Miwa, R. Shahrokhshahi, R. Bloomer, and O. Pfister, “Parallel generation of quadripartite cluster entanglement in the optical frequency comb,” Phys. Rev. Lett. 107, 030505 (2011).
[Crossref] [PubMed]

Quinlan, F.

I. Ozdur, S. Ozharar, F. Quinlan, S. Gee, and P. J. Delfyett, “Modified Pound-Drever-Hall scheme for high-precision free spectral range measurement of Fabry-Perot etalon,” Electron. Lett. 44(15), 927–928 (2008).
[Crossref]

S. Gee, S. Ozharar, F. Quinlan, and P. J. Delfyett, “High-precision measurement of free spectral range of etalon,” Electron. Lett. 42(12), 715–716 (2006).
[Crossref]

Ralph, T. C.

Roslund, J.

R. Medeiros de Araújo, J. Roslund, Y. Cai, G. Ferrini, C. Fabre, and N. Treps, “Full characterization of a highly multimode entangled state embedded in an optical frequency comb using pulse shaping,” Phys. Rev. A 89, 053828 (2014).
[Crossref]

Saleh, B. E. A.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 2007).

Salomaa, K.

R. L. Jungerman, C. Johnsen, D. J. McQuate, K. Salomaa, M. P. Zurakowski, R. C. Bray, G. Conrad, D. Cropper, and P. Hernday, “High-speed optical modulator for application in instrumentation,” IEEE J. Lightwave Technol. 8(9), 1363–1370 (1990).
[Crossref]

Schellekens, P. H. J.

H. Haitjema, P. H. J. Schellekens, and S. F. C. L. Wetzels, “Calibration of displacement sensors up to 300 μm with nanometre accuracy and direct traceability to a primary standard of length,” Metrologia 37(1), 25–33 (2000).
[Crossref]

Senior, R. J.

Shahrokhshahi, R.

M. Pysher, Y. Miwa, R. Shahrokhshahi, R. Bloomer, and O. Pfister, “Parallel generation of quadripartite cluster entanglement in the optical frequency comb,” Phys. Rev. Lett. 107, 030505 (2011).
[Crossref] [PubMed]

Skeath, P.

P. Skeath, C. H. Bulmer, S. C. Hiser, and W. K. Burns, “Novel electrostatic mechanism in the thermal instability of z-cut LiNbO3 interferometers,” Appl. Phys. Lett. 49(19), 1221–1223 (1986).
[Crossref]

Steunenberg, D. M.

A. G. Adam, A. J. Merer, D. M. Steunenberg, M. C. L. Gerry, and I. Ozier, “A precise calibration system for high-resolution visible-laser spectroscopy,” Rev. Sci. Instrum. 60(6), 1003–1007 (1989).
[Crossref]

Stuart, D.

Talman, J. R.

S. K. Korotky, A. H. Gnauck, B. L. Kasper, J. C. Campbell, J. J. Veselka, J. R. Talman, and A. R. McCormick, “8-Gbit/s transmission experiment over 68 km of optical fiber using a Ti: LiNbO3 external modulator,” IEEE J. Lightwave Technol. LT-5(10), 1505–1509 (1987).
[Crossref]

Tan, T. S.

T. S. Tan, R. L. Jungerman, and S. S. Elliott, “Optical receiver and modulator frequency response measurement with a Nd:YAG ring laser heterodyne technique,” IEEE Trans. Microw. Theory Techn. 37(8), 1217–1222 (1989).
[Crossref]

Teich, M. C.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 2007).

Terpstra, C.

R. Williamson and C. Terpstra, “Precise free spectral range measurement of telecom etalons,” Proc. SPIE 5180, 274–282 (2004).
[Crossref]

Têtu, M.

C. Gamache, M. Têtu, C. Latrasse, N. Cyr, M. A. Duguay, and B. Villeneuve, “An optical frequency scale in exact multiples of 100 GHz for standardization of multifrequency communications,” IEEE Photonics Technol. Lett. 8(2), 290–292 (1996).
[Crossref]

Touge, T.

T. Okiyama, H. Nishimoto, I. Yokota, and T. Touge, “Evaluation of 4-Gbit/s optical fiber transmission distance with direct and external modulation,” IEEE J. Lightwave Technol. 6(11), 1686–1692 (1988).
[Crossref]

Treps, N.

R. Medeiros de Araújo, J. Roslund, Y. Cai, G. Ferrini, C. Fabre, and N. Treps, “Full characterization of a highly multimode entangled state embedded in an optical frequency comb using pulse shaping,” Phys. Rev. A 89, 053828 (2014).
[Crossref]

Ueda, K.

N. Uehara and K. Ueda, “Accurate measurement of ultralow loss in a high-finesse Fabry-Perot interferometer using the frequency response functions,” Appl. Phys. B 61(1), 9–15 (1995).
[Crossref]

Uehara, N.

N. Uehara and K. Ueda, “Accurate measurement of ultralow loss in a high-finesse Fabry-Perot interferometer using the frequency response functions,” Appl. Phys. B 61(1), 9–15 (1995).
[Crossref]

Uehara, S.

Veselka, J. J.

S. K. Korotky, A. H. Gnauck, B. L. Kasper, J. C. Campbell, J. J. Veselka, J. R. Talman, and A. R. McCormick, “8-Gbit/s transmission experiment over 68 km of optical fiber using a Ti: LiNbO3 external modulator,” IEEE J. Lightwave Technol. LT-5(10), 1505–1509 (1987).
[Crossref]

Villeneuve, B.

C. Gamache, M. Têtu, C. Latrasse, N. Cyr, M. A. Duguay, and B. Villeneuve, “An optical frequency scale in exact multiples of 100 GHz for standardization of multifrequency communications,” IEEE Photonics Technol. Lett. 8(2), 290–292 (1996).
[Crossref]

Wagner, K.

Ward, H.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31(2), 97–105 (1983).
[Crossref]

Wetzels, S. F. C. L.

H. Haitjema, P. H. J. Schellekens, and S. F. C. L. Wetzels, “Calibration of displacement sensors up to 300 μm with nanometre accuracy and direct traceability to a primary standard of length,” Metrologia 37(1), 25–33 (2000).
[Crossref]

Williamson, R.

R. Williamson and C. Terpstra, “Precise free spectral range measurement of telecom etalons,” Proc. SPIE 5180, 274–282 (2004).
[Crossref]

Wooten, E. L.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron.,  6(1), 69–82 (2000).
[Crossref]

Yashiki, T.

M. Aketagawa, S. Kimura, T. Yashiki, H. Iwata, T. Q. Banh, and K. Hirata, “Measurement of a free spectral range of a Fabry-Perot cavity using frequency modulation and null method under off-resonance conditions,” Meas. Sci. Technol. 22, 025302 (2011).
[Crossref]

Yi-Yan, A.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron.,  6(1), 69–82 (2000).
[Crossref]

Yokota, I.

T. Okiyama, H. Nishimoto, I. Yokota, and T. Touge, “Evaluation of 4-Gbit/s optical fiber transmission distance with direct and external modulation,” IEEE J. Lightwave Technol. 6(11), 1686–1692 (1988).
[Crossref]

Zurakowski, M. P.

R. L. Jungerman, C. Johnsen, D. J. McQuate, K. Salomaa, M. P. Zurakowski, R. C. Bray, G. Conrad, D. Cropper, and P. Hernday, “High-speed optical modulator for application in instrumentation,” IEEE J. Lightwave Technol. 8(9), 1363–1370 (1990).
[Crossref]

Appl. Opt. (1)

Appl. Phys. B (2)

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Figures (7)

Fig. 1
Fig. 1 Schematic representing the model of our proposed method to measure the frequency response of an optical system consisting of an optical cavity and an amplitude modulator. First a laser with electric field amplitude Ein is sent to the modulator. The amplitude modulated light (Em) is then injected into the optical element under investigation, whose transmission/reflection coefficient is given as K(ω). The light from the optical element (Eout) is detected with a low-frequency (DC) photo-detector. The detector output is described by IDC in Eq. (6). A small pick-off of the modulator’s output is also monitored with a DC photo-detector, whose output is described by IDC,Mod in Eq. (13). The modulator is driven with a sine wave signal at ωAM, and biased with a DC voltage supply at VDC.

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Fig. 2
Fig. 2 Theoretical calculations for the cavity reflection (A) and transmission (B) measurements. The overall downward (upward) trend of the off-resonance data in the reflected (transmitted) response, located inbetween the resonances, is due to the increasing optical power at the carrier frequency as a function of the modulator’s frequency response. We used parameters similar to the characteristics of our optical cavity. We modelled the frequency-dependent modulation depth of the amplitude modulator as β = 1.5e−f/8.69 GHz (−20dB at 20GHz), normalized the incident intensity as I0 = 1, and set the DC offset of the modulator to θDC = π/2.

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Fig. 3
Fig. 3 Diagram of our experiment used to measure the frequency response of our optical system consisting of an amplitude modulator and optical cavity with a non-linear crystal (periodically poled lithium niobate, PPLN). Phase modulation (PM) at ωPM is used to lock the cavity to the laser carrier frequency, while amplitude modulation (AM) at ωAM is used to probe the cavity’s response. A DC bias voltage, VDC, is applied to control the energy ratio between the AM sidebands and the carrier. Low-frequency (DC) photo-detectors (PD) are used to monitor the transmitted and reflected power as a function of ωAM. PBS: polarization beam splitter. HWP: half-wave plate.

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Fig. 4
Fig. 4 Frequency response of our cavity spanning 15.5 GHz, showing 28 consecutive cavity resonances. A) Measured reflection output for horizontally-polarized light. B) Measured transmission output for horizontally-polarized light. The cavity was locked to the carrier frequency while the amplitude modulation frequency was swept, and the reflected/transmitted light from the cavity was captured with DC photo-detectors. The dotted lines are added to highlight the normalized on-resonance detector response, corresponding to ℐ DC on in Eq. (16).

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Fig. 5
Fig. 5 Frequency-dependent modulation depth of our modulation system estimated from the cavity’s transmission response. The grey dots are experimental data, while the solid blue line is the interpolation.

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Fig. 6
Fig. 6 Linewidths (FWHM) of the first 26 consecutive cavity resonances, corresponding to the resonances shown in Fig. 4. A Lorentzian function was fitted to the reflected on-resonance cavity data to more precisely determine the linewidth of each resonance. Black: fitting using a single Lorentzian function (first term in Eq. (21)). Red: fitting using Eq. (21), which models both the first and second-order sidebands.

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Fig. 7
Fig. 7 Frequency response of our cavity to horizontally (red dots) and vertically (black crosses) polarized light around the first resonance. The data sets were taken separately with the input beam to the cavity set to either completely horizontal or vertical polarization. The cavity was locked to the carrier frequency while the amplitude modulation frequency was swept, and the reflected light from the cavity was captured by a DC photo-detector. The data points represent measured data (normalized average of five data sets), whereas the solid lines are the Lorentzian fits (Eq. (21)). The insert illustrates how the polarization modes are distinguishable and non-degenerate.

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Equations (24)

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E m ( t ) = 1 2 E in e i ω 0 t ( 1 + e i [ θ DC + θ AC ( t ) ] ) ,
E m ( t ) = 1 2 E in e i ω 0 t ( 1 + e i θ DC e i β sin ( ω AM t ) ) = 1 2 E in e i ω 0 t ( 1 + e i θ DC ∑ n = − ∞ + ∞ J n ( β ) e in ω AM t ) ,
E m ( ω ) = 1 2 E in ( 2 π δ ( ω − ω 0 ) + e i θ DC ∑ n = − ∞ + ∞ J n ( β ) 2 π δ ( ω − ω 0 − n ω AM ) ) .
E out ( ω ) = E m ( ω ) K ( ω ) , = 1 2 E in ( 2 π δ ( ω − ω 0 ) K ( ω ) + e i θ DC ∑ n = − ∞ + ∞ J n ( β ) 2 π δ ( ω − ω 0 − n ω AM ) K ( ω ) ) .
E out ( t ) = 1 2 E in e i ω 0 t ( K ( ω 0 ) + e i θ DC ∑ n = − ∞ + ∞ J n ( β ) K ( ω 0 + n ω AM ) e in ω AM t ) .
I DC = G det | E out ( t ) E out * ( t ) | 2 , ≃ I 0 2 ( | K ( 0 ) | 2 ( 1 + | J 0 ( β ) | 2 + 2 J 0 ( β ) cos θ DC ) + ∑ n ≠ 0 | J n ( β ) | 2 | K ( n ω ) | 2 ) ,
K T ( ω ) = e i ϕ / 2 ( 1 − L ′ ) ( 1 − R in ) ( 1 − R out ) 1 − e i ϕ ( 1 − L ) R in R out ,
K R ( ω ) = − R in + e i ϕ ( 1 − L ) R out 1 − e i ϕ ( 1 − L ) R in R out ,
| K T ( ω ) | 2 ≃ γ 2 ( ω − n ω FSR ) 2 + γ 2 × | K T ( n ω FSR ) | 2 ,
| K R ( ω ) | 2 ≃ 1 − γ 2 ( ω − n ω FSR ) 2 + γ 2 × ( 1 − | K R ( n ω FSR ) | 2 ) ,
γ = π f FWHM = 1 − R in R out 1 − L [ R in R out ( 1 − L ) ] 1 / 4 f FSR ,
f FSR = c l ,
I DC , Mod = I 0 ′ ( 1 + J 0 ( β ) cos θ DC ) ,
ℐ DC = 𝒦 2 1 1 + J 0 ( β ) cos θ DC × ( | K ( 0 ) | 2 ( 1 + | J 0 ( β ) | 2 + 2 J 0 ( β ) cos θ DC ) + ∑ n ≠ 0 | J n ( β ) | 2 | K ( n ω ) | 2 ) .
ℐ DC ′ = 𝒦 ′ ∑ n = − ∞ + ∞ | J n ( β ) | 2 | K ( n ω ) | 2 + 𝒞 ,
ℐ DC on = 𝒦 2 1 1 + J 0 ( β ) cos θ DC × ( | K ( 0 ) | 2 ( 1 + | J 0 ( β ) | 2 + 2 J 0 ( β ) cos θ DC ) + ∑ n ≠ 0 | J n ( β ) | 2 | K ( 0 ) | 2 ) , = 𝒦 | K ( 0 ) | 2 .
ℐ DC off , T = 𝒦 | K ( 0 ) | 2 ( 1 + | J 0 ( β ) | 2 − 1 2 ( 1 + J 0 ( β ) cos θ DC ) ) .
ℐ DC off , T ℐ DC on − 1 = | J 0 ( β ) | 2 − 1 2 ( 1 + J 0 ( β ) cos θ DC ) .
ℐ DC , Mod = I DC , Mod I DC , Mod | ω = 0 = 1 + J 0 ( β ) cos θ DC .
| J 0 ( β ) | 2 = 2 ℐ DC , Mod ( ℐ DC off , T ℐ DC on − 1 ) + 1 .
𝒮 = J 0 ( β ) 2 + 2 J 1 ( β ) 2 γ 2 ( ω AM − n ω FSR ) 2 + γ 2 + 2 J 2 ( β ) 2 γ 2 4 ( ω AM − n ω FSR ) 2 + γ 2 .
n o 2 = 4.9017 + 0.112280 λ 2 − 0.049656 − 0.039636 λ 2 ,
n e 2 = 4.5583 + 0.091806 λ 2 − 0.048086 − 0.032068 λ 2 ,
f FSR = c n 1 l 1 + n 2 l 2 ,

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