Abstract

We report on bidirectional frequency conversion between the microwave and optical domains using electro-optics. Advances in communications, time keeping, and quantum sensing have all come to depend upon the coherent interoperation of light wave and microwave signals. To connect these domains, which are separated by a factor of 10,000 in frequency, requires specialized technology that has until now only been achieved by ultrafast mode-locked lasers. In contrast, electro-optic modulation (EOM) combs arise deterministically by imposing microwave-rate oscillations on a continuous-wave laser. Here we demonstrate electro-optic generation of a 160 THz bandwidth supercontinuum and realize f-2f self-referencing. Coherence of the supercontinuum is achieved through optical filtering of electronic noise on the seed EOM comb. The mode frequencies of the supercontinuum are derived from the electronic oscillator and they achieve <5×1014 fractional accuracy and stability, which opens a novel regime for tunable combs with wide mode spacing apart from the requirements of mode locking.

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2016 (3)

P. Del’Haye, A. Coillet, T. Fortier, K. Beha, D. C. Cole, K. Y. Yang, H. Lee, K. J. Vahala, S. B. Papp, and S. A. Diddams, “Phase-coherent microwave-to-optical link with a self-referenced microcomb,” Nat. Photonics 10, 516–520 (2016).
[Crossref]

X. Yi, K. Vahala, J. Li, S. Diddams, G. Ycas, P. Plavchan, S. Leifer, J. Sandhu, G. Vasisht, P. Chen, P. Gao, J. Gagne, E. Furlan, M. Bottom, E. C. Martin, M. P. Fitzgerald, G. Doppmann, and C. Beichman, “Demonstration of a near-IR line-referenced electro-optical laser frequency comb for precision radial velocity measurements in astronomy,” Nat. Commun. 7, 10436 (2016).
[Crossref]

D. C. Cole, K. M. Beha, S. A. Diddams, and S. B. Papp, “Octave-spanning supercontinuum generation via microwave frequency multiplication,” J. Phys. 723, 012035 (2016).
[Crossref]

2015 (1)

A. D. Ludlow, M. M. Boyd, J. Ye, E. Peik, and P. O. Schmidt, “Optical atomic clocks,” Rev. Mod. Phys. 87, 637–701 (2015).
[Crossref]

2014 (2)

2013 (3)

A. Ishizawa, T. Nishikawa, A. Mizutori, H. Takara, A. Takada, T. Sogawa, and M. Koga, “Phase-noise characteristics of a 25-GHz-spaced optical frequency comb based on a phase- and intensity-modulated laser,” Opt. Express 21, 29186–29194 (2013).
[Crossref]

T. Ideguchi, S. Holzner, B. Bernhardt, G. Guelachvili, N. Picqué, and T. W. Hänsch, “Coherent Raman spectro-imaging with laser frequency combs,” Nature 502, 355–358 (2013).
[Crossref]

M. Reagor, H. Paik, G. Catelani, L. Sun, C. Axline, E. Holland, I. M. Pop, N. A. Masluk, T. Brecht, L. Frunzio, M. H. Devoret, L. Glazman, and R. J. Schoelkopf, “Reaching 10  ms single photon lifetimes for superconducting aluminum cavities,” Appl. Phys. Lett. 102, 192604 (2013).
[Crossref]

2012 (3)

2011 (1)

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics 5, 425–429 (2011).
[Crossref]

2010 (4)

S. T. Cundiff and A. M. Weiner, “Optical arbitrary waveform generation,” Nat. Photonics 4, 760–766 (2010).
[Crossref]

A. Ishizawa, T. Nishikawa, A. Mizutori, H. Takara, S. Aozasa, A. Mori, H. Nakano, A. Takada, and M. Koga, “Octave-spanning frequency comb generated by 250  fs pulse train emitted from 25  GHz externally phase-modulated laser diode for carrier-envelope-offset-locking,” Electron. Lett. 46, 1343–1344 (2010).
[Crossref]

G. Di Domenico, S. Schilt, and P. Thomann, “Simple approach to the relation between laser frequency noise and laser line shape,” Appl. Opt. 49, 4801–4807 (2010).
[Crossref]

R. Wu, V. R. Supradeepa, C. M. Long, D. E. Leaird, and A. M. Weiner, “Generation of very flat optical frequency combs from continuous-wave lasers using cascaded intensity and phase modulators driven by tailored radio frequency waveforms,” Opt. Lett. 35, 3234–3236 (2010).
[Crossref]

2009 (2)

A. Bartels, D. Heinecke, and S. A. Diddams, “10  GHz self-referenced optical frequency comb,” Science 326, 681 (2009).
[Crossref]

B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R. Holzwarth, G. Guelachvili, T. W. Hänsch, and N. Picqué, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4, 55–57 (2009).
[Crossref]

2008 (2)

2007 (2)

S. A. Diddams, L. Hollberg, and V. Mbele, “Molecular fingerprinting with the resolved modes of a femtosecond laser frequency comb,” Nature 445, 627–630 (2007).
[Crossref]

T. Sakamoto, T. Kawanishi, and M. Izutsu, “Asymptotic formalism for ultraflat optical frequency comb generation using a Mach–Zehnder modulator,” Opt. Lett. 32, 1515–1517 (2007).
[Crossref]

2006 (1)

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).
[Crossref]

2005 (1)

2004 (1)

A. Marian, M. C. Stowe, J. R. Lawall, D. Felinto, and J. Ye, “United time-frequency spectroscopy for dynamics and global structure,” Science 306, 2063–2068 (2004).
[Crossref]

2003 (4)

S. T. Cundiff and J. Ye, “Colloquium: femtosecond optical frequency combs,” Rev. Mod. Phys. 75, 325–342 (2003).
[Crossref]

A. Baltuska, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hansch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421, 611–615 (2003).
[Crossref]

M. Fujiwara, M. Teshima, J. Kani, H. Suzuki, N. Takachio, and K. Iwatsuki, “Optical carrier supply module using flattened optical multicarrier generation based on sinusoidal amplitude and phase hybrid modulation,” J. Lightwave Technol. 21, 2705–2714 (2003).
[Crossref]

K. L. Corwin, N. R. Newbury, J. M. Dudley, S. Coen, S. A. Diddams, K. Weber, and R. S. Windeler, “Fundamental noise limitations to supercontinuum generation in microstructure fiber,” Phys. Rev. Lett. 90, 113904 (2003).
[Crossref]

2000 (2)

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Haensch, “Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
[Crossref]

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
[Crossref]

1994 (1)

1993 (1)

M. Kourogi, K. Nakagawa, and M. Ohtsu, “Wide-span optical frequency comb generator for accurate optical frequency difference measurement,” IEEE J. Quantum Electron. 29, 2693–2701 (1993).
[Crossref]

1991 (1)

D. R. Hjelme, A. R. Mickelson, and R. G. Beausoleil, “Semiconductor laser stabilization by external optical feedback,” IEEE J. Quantum Electron. 27, 352–372 (1991).
[Crossref]

1988 (1)

T. Kobayashi, H. Yao, K. Amano, Y. Fukushima, A. Morimoto, and T. Sueta, “Optical pulse compression using high-frequency electrooptic phase modulation,” IEEE J. Quantum Electron. 24, 382–387 (1988).
[Crossref]

1982 (1)

D. S. Elliott, R. Roy, and S. J. Smith, “Extracavity laser band-shape and bandwidth modification,” Phys. Rev. A 26, 12–18 (1982).
[Crossref]

1975 (1)

F. L. Walls and A. Demarchi, “RF spectrum of a signal after frequency multiplication; measurement and comparison with a simple calculation,” IEEE Trans. Instrum. Meas. 24, 210–217 (1975).
[Crossref]

1972 (1)

T. Kobayashi, “High-repetition-rate optical pulse generator using a Fabry–Perot electro-optic modulator,” Appl. Phys. Lett. 21, 341–343 (1972).
[Crossref]

Alic, N.

Amano, K.

T. Kobayashi, H. Yao, K. Amano, Y. Fukushima, A. Morimoto, and T. Sueta, “Optical pulse compression using high-frequency electrooptic phase modulation,” IEEE J. Quantum Electron. 24, 382–387 (1988).
[Crossref]

Aozasa, S.

A. Ishizawa, T. Nishikawa, A. Mizutori, H. Takara, S. Aozasa, A. Mori, H. Nakano, A. Takada, and M. Koga, “Octave-spanning frequency comb generated by 250  fs pulse train emitted from 25  GHz externally phase-modulated laser diode for carrier-envelope-offset-locking,” Electron. Lett. 46, 1343–1344 (2010).
[Crossref]

Apolonski, A.

Axline, C.

M. Reagor, H. Paik, G. Catelani, L. Sun, C. Axline, E. Holland, I. M. Pop, N. A. Masluk, T. Brecht, L. Frunzio, M. H. Devoret, L. Glazman, and R. J. Schoelkopf, “Reaching 10  ms single photon lifetimes for superconducting aluminum cavities,” Appl. Phys. Lett. 102, 192604 (2013).
[Crossref]

Baltuska, A.

A. Baltuska, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hansch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421, 611–615 (2003).
[Crossref]

Bartels, A.

A. Bartels, D. Heinecke, and S. A. Diddams, “10  GHz self-referenced optical frequency comb,” Science 326, 681 (2009).
[Crossref]

Beausoleil, R. G.

D. R. Hjelme, A. R. Mickelson, and R. G. Beausoleil, “Semiconductor laser stabilization by external optical feedback,” IEEE J. Quantum Electron. 27, 352–372 (1991).
[Crossref]

Beha, K.

P. Del’Haye, A. Coillet, T. Fortier, K. Beha, D. C. Cole, K. Y. Yang, H. Lee, K. J. Vahala, S. B. Papp, and S. A. Diddams, “Phase-coherent microwave-to-optical link with a self-referenced microcomb,” Nat. Photonics 10, 516–520 (2016).
[Crossref]

Beha, K. M.

D. C. Cole, K. M. Beha, S. A. Diddams, and S. B. Papp, “Octave-spanning supercontinuum generation via microwave frequency multiplication,” J. Phys. 723, 012035 (2016).
[Crossref]

Beichman, C.

X. Yi, K. Vahala, J. Li, S. Diddams, G. Ycas, P. Plavchan, S. Leifer, J. Sandhu, G. Vasisht, P. Chen, P. Gao, J. Gagne, E. Furlan, M. Bottom, E. C. Martin, M. P. Fitzgerald, G. Doppmann, and C. Beichman, “Demonstration of a near-IR line-referenced electro-optical laser frequency comb for precision radial velocity measurements in astronomy,” Nat. Commun. 7, 10436 (2016).
[Crossref]

Bergquist, J. C.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics 5, 425–429 (2011).
[Crossref]

Bernhardt, B.

T. Ideguchi, S. Holzner, B. Bernhardt, G. Guelachvili, N. Picqué, and T. W. Hänsch, “Coherent Raman spectro-imaging with laser frequency combs,” Nature 502, 355–358 (2013).
[Crossref]

B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R. Holzwarth, G. Guelachvili, T. W. Hänsch, and N. Picqué, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4, 55–57 (2009).
[Crossref]

Bielska, K.

Bottom, M.

X. Yi, K. Vahala, J. Li, S. Diddams, G. Ycas, P. Plavchan, S. Leifer, J. Sandhu, G. Vasisht, P. Chen, P. Gao, J. Gagne, E. Furlan, M. Bottom, E. C. Martin, M. P. Fitzgerald, G. Doppmann, and C. Beichman, “Demonstration of a near-IR line-referenced electro-optical laser frequency comb for precision radial velocity measurements in astronomy,” Nat. Commun. 7, 10436 (2016).
[Crossref]

Boyd, M. M.

A. D. Ludlow, M. M. Boyd, J. Ye, E. Peik, and P. O. Schmidt, “Optical atomic clocks,” Rev. Mod. Phys. 87, 637–701 (2015).
[Crossref]

Brasch, V.

V. Brasch, E. Lucas, J. D. Jost, M. Geiselmann, and T. J. Kippenberg, “Self-referencing of an on-chip soliton Kerr frequency comb without external broadening,” arXiv:1605.02801 (2016).

Brecht, T.

M. Reagor, H. Paik, G. Catelani, L. Sun, C. Axline, E. Holland, I. M. Pop, N. A. Masluk, T. Brecht, L. Frunzio, M. H. Devoret, L. Glazman, and R. J. Schoelkopf, “Reaching 10  ms single photon lifetimes for superconducting aluminum cavities,” Appl. Phys. Lett. 102, 192604 (2013).
[Crossref]

Bucalovic, N.

Catelani, G.

M. Reagor, H. Paik, G. Catelani, L. Sun, C. Axline, E. Holland, I. M. Pop, N. A. Masluk, T. Brecht, L. Frunzio, M. H. Devoret, L. Glazman, and R. J. Schoelkopf, “Reaching 10  ms single photon lifetimes for superconducting aluminum cavities,” Appl. Phys. Lett. 102, 192604 (2013).
[Crossref]

Chen, P.

X. Yi, K. Vahala, J. Li, S. Diddams, G. Ycas, P. Plavchan, S. Leifer, J. Sandhu, G. Vasisht, P. Chen, P. Gao, J. Gagne, E. Furlan, M. Bottom, E. C. Martin, M. P. Fitzgerald, G. Doppmann, and C. Beichman, “Demonstration of a near-IR line-referenced electro-optical laser frequency comb for precision radial velocity measurements in astronomy,” Nat. Commun. 7, 10436 (2016).
[Crossref]

Coddington, I.

L. C. Sinclair, I. Coddington, W. C. Swann, G. B. Rieker, A. Hati, K. Iwakuni, and N. R. Newbury, “Operation of an optically coherent frequency comb outside the metrology lab,” Opt. Express 22, 6996–7006 (2014).
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Supplementary Material (1)

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Figures (4)

Fig. 1.
Fig. 1.

Apparatus for self-referencing a CW laser. The system is comprised of electro-optic phase and intensity modulators, two stages of nonlinear-fiber (HNLF-1 and -2) spectral broadening, a Fabry–Perot optical cavity filter, and f 2 f detection. (a) EOM comb with 10 GHz spacing. (b) Idem after HNLF-1. (c) EOM comb with 33 GHz spacing. (d) Idem after HNLF-1 and line-by-line intensity control.

Fig. 2.
Fig. 2.

Supercontinuum generated using our second broadening stage with HNLF-2. (a) EOM-comb spacing is 33 GHz. (b) Idem but for 10 GHz spacing. (c) Pulse picking prior to HNLF-2 reduces the initial spacing to 2.5 GHz.

Fig. 3.
Fig. 3.

EOM-comb offset-frequency detection. (a) Spectra of fundamental and second-harmonic supercontinuum light at 1070 nm. (b) i, Carrier-offset heterodyne beat ( f 0 ) in black; ii, intensity noise in red; iii, detector noise in gray. (c)–(e) Spectrum of f 0 with different f e o sources, including a synthesizer, dielectric-resonator oscillator, and sapphire-cavity oscillator. The 2.5 GHz cases utilize pulse picking. All the photocurrent spectra are acquired with 100 kHz bandwidth, and frequency axes are offset 706.6, 1793, 491, and 726 MHz, respectively, in (b)–(d).

Fig. 4.
Fig. 4.

Demonstration of optical frequency measurements and synthesis. (a) System components and connections. Both the EOM comb and an auxiliary fiber comb are referenced to a hydrogen maser. (b) Frequency counting record over 4000 s of the pump laser ν p with the EOM (black points) and fiber (green circles) combs. (c) Allan deviation of the frequency count record from (b) for EOM comb (black points) and fiber comb (green circles) and the synthesis data (green points) in (d). The solid line indicates the Allan deviation of a 193 THz laser drifting at 65 mHz/s. (d) Phase-lock synthesis of ν p with respect to the maser-referenced f eo ; ν set = 193 397    334 972    kHz . Green points are measurements of locked ν p with the fiber comb, and blue points are the in-loop noise.

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