Abstract

Amplitude modulation of laser light is required for resonant sideband extraction employed in gravitational-wave detectors. Amplitude modulation with electro-optic phase modulators is realized by interferometric phase-to- amplitude conversion. Although two outputs modulated at opposite phases to each other are obtained, usually only one of them is utilized and the other is abandoned. The reuse of this abandoned light improves the power efficiency of the modulation. This can be realized by inverting the modulation phase of one output with a delay line and adding it to the other coherently. Moreover, this system selects a high-efficiency operating point and modulates the light in a linear range. We demonstrate that the modulation system can be operated with a power loss that is due only to the losses of the optical components.

© 2011 Optical Society of America

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  1. R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  5. G. M. Harry and LIGO Scientific Collaboration, Class. Quantum Grav. 27, 084006 (2010).
    [CrossRef]
  6. T. Accadis, B. L. Swinkels, and VIRGO Collaboration, Class. Quantum Grav. 27, 084002 (2010).
    [CrossRef]
  7. K. Kuroda, N. Kanda, M. Ohashi, Y. Saito, R. Takahashi, M. Ando, N. Mio, S. Telada, S. Moriwaki, T. Uchiyama, T. Tomaru, T. Suzuki, S. Miyoki, A. Takamori, D. Tatsumi, and LCGT Collaboration, Prog. Theor. Phys. Suppl. 163, 54 (2006).
    [CrossRef]
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2010 (2)

G. M. Harry and LIGO Scientific Collaboration, Class. Quantum Grav. 27, 084006 (2010).
[CrossRef]

T. Accadis, B. L. Swinkels, and VIRGO Collaboration, Class. Quantum Grav. 27, 084002 (2010).
[CrossRef]

2008 (1)

F. Kawazoe, A. Sugamoto, V. Leonhardt, S. Sato, T. Yamazaki, M. Fukushima, S. Kawamura, O. Miyakawa, K. Somiya, T. Morioka, and A. Nishizawa, Class. Quantum Grav. 25, 195008 (2008).
[CrossRef]

2006 (1)

K. Kuroda, N. Kanda, M. Ohashi, Y. Saito, R. Takahashi, M. Ando, N. Mio, S. Telada, S. Moriwaki, T. Uchiyama, T. Tomaru, T. Suzuki, S. Miyoki, A. Takamori, D. Tatsumi, and LCGT Collaboration, Prog. Theor. Phys. Suppl. 163, 54 (2006).
[CrossRef]

2003 (1)

1993 (1)

J. Mizuno, K. A. Strain, P. G. Nelson, J. M. Chen, R. Schilling, A. Rüdiger, W. Winkler, and K. Danzmann, Phys. Lett. A 175, 273 (1993).
[CrossRef]

1983 (1)

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Accadis, T.

T. Accadis, B. L. Swinkels, and VIRGO Collaboration, Class. Quantum Grav. 27, 084002 (2010).
[CrossRef]

Ando, M.

K. Kuroda, N. Kanda, M. Ohashi, Y. Saito, R. Takahashi, M. Ando, N. Mio, S. Telada, S. Moriwaki, T. Uchiyama, T. Tomaru, T. Suzuki, S. Miyoki, A. Takamori, D. Tatsumi, and LCGT Collaboration, Prog. Theor. Phys. Suppl. 163, 54 (2006).
[CrossRef]

Chen, J. M.

J. Mizuno, K. A. Strain, P. G. Nelson, J. M. Chen, R. Schilling, A. Rüdiger, W. Winkler, and K. Danzmann, Phys. Lett. A 175, 273 (1993).
[CrossRef]

Danzmann, K.

J. Mizuno, K. A. Strain, P. G. Nelson, J. M. Chen, R. Schilling, A. Rüdiger, W. Winkler, and K. Danzmann, Phys. Lett. A 175, 273 (1993).
[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, Appl. Phys. B 31, 97 (1983).
[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, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Fukushima, M.

F. Kawazoe, A. Sugamoto, V. Leonhardt, S. Sato, T. Yamazaki, M. Fukushima, S. Kawamura, O. Miyakawa, K. Somiya, T. Morioka, and A. Nishizawa, Class. Quantum Grav. 25, 195008 (2008).
[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, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Harry, G. M.

G. M. Harry and LIGO Scientific Collaboration, Class. Quantum Grav. 27, 084006 (2010).
[CrossRef]

Hough, J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Kanda, N.

K. Kuroda, N. Kanda, M. Ohashi, Y. Saito, R. Takahashi, M. Ando, N. Mio, S. Telada, S. Moriwaki, T. Uchiyama, T. Tomaru, T. Suzuki, S. Miyoki, A. Takamori, D. Tatsumi, and LCGT Collaboration, Prog. Theor. Phys. Suppl. 163, 54 (2006).
[CrossRef]

Kawamura, S.

F. Kawazoe, A. Sugamoto, V. Leonhardt, S. Sato, T. Yamazaki, M. Fukushima, S. Kawamura, O. Miyakawa, K. Somiya, T. Morioka, and A. Nishizawa, Class. Quantum Grav. 25, 195008 (2008).
[CrossRef]

Kawazoe, F.

F. Kawazoe, A. Sugamoto, V. Leonhardt, S. Sato, T. Yamazaki, M. Fukushima, S. Kawamura, O. Miyakawa, K. Somiya, T. Morioka, and A. Nishizawa, Class. Quantum Grav. 25, 195008 (2008).
[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, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Kuroda, K.

K. Kuroda, N. Kanda, M. Ohashi, Y. Saito, R. Takahashi, M. Ando, N. Mio, S. Telada, S. Moriwaki, T. Uchiyama, T. Tomaru, T. Suzuki, S. Miyoki, A. Takamori, D. Tatsumi, and LCGT Collaboration, Prog. Theor. Phys. Suppl. 163, 54 (2006).
[CrossRef]

Leonhardt, V.

F. Kawazoe, A. Sugamoto, V. Leonhardt, S. Sato, T. Yamazaki, M. Fukushima, S. Kawamura, O. Miyakawa, K. Somiya, T. Morioka, and A. Nishizawa, Class. Quantum Grav. 25, 195008 (2008).
[CrossRef]

Mason, J. E.

Mio, N.

K. Kuroda, N. Kanda, M. Ohashi, Y. Saito, R. Takahashi, M. Ando, N. Mio, S. Telada, S. Moriwaki, T. Uchiyama, T. Tomaru, T. Suzuki, S. Miyoki, A. Takamori, D. Tatsumi, and LCGT Collaboration, Prog. Theor. Phys. Suppl. 163, 54 (2006).
[CrossRef]

Miyakawa, O.

F. Kawazoe, A. Sugamoto, V. Leonhardt, S. Sato, T. Yamazaki, M. Fukushima, S. Kawamura, O. Miyakawa, K. Somiya, T. Morioka, and A. Nishizawa, Class. Quantum Grav. 25, 195008 (2008).
[CrossRef]

Miyoki, S.

K. Kuroda, N. Kanda, M. Ohashi, Y. Saito, R. Takahashi, M. Ando, N. Mio, S. Telada, S. Moriwaki, T. Uchiyama, T. Tomaru, T. Suzuki, S. Miyoki, A. Takamori, D. Tatsumi, and LCGT Collaboration, Prog. Theor. Phys. Suppl. 163, 54 (2006).
[CrossRef]

Mizuno, J.

J. Mizuno, K. A. Strain, P. G. Nelson, J. M. Chen, R. Schilling, A. Rüdiger, W. Winkler, and K. Danzmann, Phys. Lett. A 175, 273 (1993).
[CrossRef]

Morioka, T.

F. Kawazoe, A. Sugamoto, V. Leonhardt, S. Sato, T. Yamazaki, M. Fukushima, S. Kawamura, O. Miyakawa, K. Somiya, T. Morioka, and A. Nishizawa, Class. Quantum Grav. 25, 195008 (2008).
[CrossRef]

Moriwaki, S.

K. Kuroda, N. Kanda, M. Ohashi, Y. Saito, R. Takahashi, M. Ando, N. Mio, S. Telada, S. Moriwaki, T. Uchiyama, T. Tomaru, T. Suzuki, S. Miyoki, A. Takamori, D. Tatsumi, and LCGT Collaboration, Prog. Theor. Phys. Suppl. 163, 54 (2006).
[CrossRef]

Munley, A. J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Nelson, P. G.

J. Mizuno, K. A. Strain, P. G. Nelson, J. M. Chen, R. Schilling, A. Rüdiger, W. Winkler, and K. Danzmann, Phys. Lett. A 175, 273 (1993).
[CrossRef]

Nishizawa, A.

F. Kawazoe, A. Sugamoto, V. Leonhardt, S. Sato, T. Yamazaki, M. Fukushima, S. Kawamura, O. Miyakawa, K. Somiya, T. Morioka, and A. Nishizawa, Class. Quantum Grav. 25, 195008 (2008).
[CrossRef]

Ohashi, M.

K. Kuroda, N. Kanda, M. Ohashi, Y. Saito, R. Takahashi, M. Ando, N. Mio, S. Telada, S. Moriwaki, T. Uchiyama, T. Tomaru, T. Suzuki, S. Miyoki, A. Takamori, D. Tatsumi, and LCGT Collaboration, Prog. Theor. Phys. Suppl. 163, 54 (2006).
[CrossRef]

Rüdiger, A.

J. Mizuno, K. A. Strain, P. G. Nelson, J. M. Chen, R. Schilling, A. Rüdiger, W. Winkler, and K. Danzmann, Phys. Lett. A 175, 273 (1993).
[CrossRef]

Saito, Y.

K. Kuroda, N. Kanda, M. Ohashi, Y. Saito, R. Takahashi, M. Ando, N. Mio, S. Telada, S. Moriwaki, T. Uchiyama, T. Tomaru, T. Suzuki, S. Miyoki, A. Takamori, D. Tatsumi, and LCGT Collaboration, Prog. Theor. Phys. Suppl. 163, 54 (2006).
[CrossRef]

Saleh, B. E. A.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd ed. (Wiley-Interscience, 2007).

Sato, S.

F. Kawazoe, A. Sugamoto, V. Leonhardt, S. Sato, T. Yamazaki, M. Fukushima, S. Kawamura, O. Miyakawa, K. Somiya, T. Morioka, and A. Nishizawa, Class. Quantum Grav. 25, 195008 (2008).
[CrossRef]

Schilling, R.

J. Mizuno, K. A. Strain, P. G. Nelson, J. M. Chen, R. Schilling, A. Rüdiger, W. Winkler, and K. Danzmann, Phys. Lett. A 175, 273 (1993).
[CrossRef]

Somiya, K.

F. Kawazoe, A. Sugamoto, V. Leonhardt, S. Sato, T. Yamazaki, M. Fukushima, S. Kawamura, O. Miyakawa, K. Somiya, T. Morioka, and A. Nishizawa, Class. Quantum Grav. 25, 195008 (2008).
[CrossRef]

Strain, K. A.

J. Mizuno, K. A. Strain, P. G. Nelson, J. M. Chen, R. Schilling, A. Rüdiger, W. Winkler, and K. Danzmann, Phys. Lett. A 175, 273 (1993).
[CrossRef]

Sugamoto, A.

F. Kawazoe, A. Sugamoto, V. Leonhardt, S. Sato, T. Yamazaki, M. Fukushima, S. Kawamura, O. Miyakawa, K. Somiya, T. Morioka, and A. Nishizawa, Class. Quantum Grav. 25, 195008 (2008).
[CrossRef]

Suzuki, T.

K. Kuroda, N. Kanda, M. Ohashi, Y. Saito, R. Takahashi, M. Ando, N. Mio, S. Telada, S. Moriwaki, T. Uchiyama, T. Tomaru, T. Suzuki, S. Miyoki, A. Takamori, D. Tatsumi, and LCGT Collaboration, Prog. Theor. Phys. Suppl. 163, 54 (2006).
[CrossRef]

Swinkels, B. L.

T. Accadis, B. L. Swinkels, and VIRGO Collaboration, Class. Quantum Grav. 27, 084002 (2010).
[CrossRef]

Takahashi, R.

K. Kuroda, N. Kanda, M. Ohashi, Y. Saito, R. Takahashi, M. Ando, N. Mio, S. Telada, S. Moriwaki, T. Uchiyama, T. Tomaru, T. Suzuki, S. Miyoki, A. Takamori, D. Tatsumi, and LCGT Collaboration, Prog. Theor. Phys. Suppl. 163, 54 (2006).
[CrossRef]

Takamori, A.

K. Kuroda, N. Kanda, M. Ohashi, Y. Saito, R. Takahashi, M. Ando, N. Mio, S. Telada, S. Moriwaki, T. Uchiyama, T. Tomaru, T. Suzuki, S. Miyoki, A. Takamori, D. Tatsumi, and LCGT Collaboration, Prog. Theor. Phys. Suppl. 163, 54 (2006).
[CrossRef]

Tatsumi, D.

K. Kuroda, N. Kanda, M. Ohashi, Y. Saito, R. Takahashi, M. Ando, N. Mio, S. Telada, S. Moriwaki, T. Uchiyama, T. Tomaru, T. Suzuki, S. Miyoki, A. Takamori, D. Tatsumi, and LCGT Collaboration, Prog. Theor. Phys. Suppl. 163, 54 (2006).
[CrossRef]

Teich, M. C.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd ed. (Wiley-Interscience, 2007).

Telada, S.

K. Kuroda, N. Kanda, M. Ohashi, Y. Saito, R. Takahashi, M. Ando, N. Mio, S. Telada, S. Moriwaki, T. Uchiyama, T. Tomaru, T. Suzuki, S. Miyoki, A. Takamori, D. Tatsumi, and LCGT Collaboration, Prog. Theor. Phys. Suppl. 163, 54 (2006).
[CrossRef]

Tomaru, T.

K. Kuroda, N. Kanda, M. Ohashi, Y. Saito, R. Takahashi, M. Ando, N. Mio, S. Telada, S. Moriwaki, T. Uchiyama, T. Tomaru, T. Suzuki, S. Miyoki, A. Takamori, D. Tatsumi, and LCGT Collaboration, Prog. Theor. Phys. Suppl. 163, 54 (2006).
[CrossRef]

Uchiyama, T.

K. Kuroda, N. Kanda, M. Ohashi, Y. Saito, R. Takahashi, M. Ando, N. Mio, S. Telada, S. Moriwaki, T. Uchiyama, T. Tomaru, T. Suzuki, S. Miyoki, A. Takamori, D. Tatsumi, and LCGT Collaboration, Prog. Theor. Phys. Suppl. 163, 54 (2006).
[CrossRef]

Ward, H.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Willems, P. A.

Winkler, W.

J. Mizuno, K. A. Strain, P. G. Nelson, J. M. Chen, R. Schilling, A. Rüdiger, W. Winkler, and K. Danzmann, Phys. Lett. A 175, 273 (1993).
[CrossRef]

Yamazaki, T.

F. Kawazoe, A. Sugamoto, V. Leonhardt, S. Sato, T. Yamazaki, M. Fukushima, S. Kawamura, O. Miyakawa, K. Somiya, T. Morioka, and A. Nishizawa, Class. Quantum Grav. 25, 195008 (2008).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (1)

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Class. Quantum Grav. (3)

F. Kawazoe, A. Sugamoto, V. Leonhardt, S. Sato, T. Yamazaki, M. Fukushima, S. Kawamura, O. Miyakawa, K. Somiya, T. Morioka, and A. Nishizawa, Class. Quantum Grav. 25, 195008 (2008).
[CrossRef]

G. M. Harry and LIGO Scientific Collaboration, Class. Quantum Grav. 27, 084006 (2010).
[CrossRef]

T. Accadis, B. L. Swinkels, and VIRGO Collaboration, Class. Quantum Grav. 27, 084002 (2010).
[CrossRef]

Phys. Lett. A (1)

J. Mizuno, K. A. Strain, P. G. Nelson, J. M. Chen, R. Schilling, A. Rüdiger, W. Winkler, and K. Danzmann, Phys. Lett. A 175, 273 (1993).
[CrossRef]

Prog. Theor. Phys. Suppl. (1)

K. Kuroda, N. Kanda, M. Ohashi, Y. Saito, R. Takahashi, M. Ando, N. Mio, S. Telada, S. Moriwaki, T. Uchiyama, T. Tomaru, T. Suzuki, S. Miyoki, A. Takamori, D. Tatsumi, and LCGT Collaboration, Prog. Theor. Phys. Suppl. 163, 54 (2006).
[CrossRef]

Other (1)

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd ed. (Wiley-Interscience, 2007).

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Figures (3)

Fig. 1
Fig. 1

Experimental setup. NPRO, nonplanar ring oscillator; QWP, quarter-wave plate; HWP, half-wave plate; FI, Faraday isolator; EOAM (EOPM), electro-optic amplitude (phase) modulator; PBS, polarizing beam splitter; PZT, piezoelectric transducer; PD, photodetector; HM, half-mirror. The polarization states and the time variations of laser power at several points are described.

Fig. 2
Fig. 2

Time variation of intensity of modulated light: (a) output recombined using interference; (b), (c), and (d) output of conventional amplitude modulation scheme with operating points at transmittances of 50%, 90%, and 100%, respectively. The solid line shows the laser power after the FI, the dashed line shows the laser power before the PBS, and the dotted line shows the output power after recombination without modulation signal.

Fig. 3
Fig. 3

Frequency analysis measured with the optical cavity, the length of which was being scanned. (a)–(d) Same situations as in Fig. 2. The dashed curve shows the signal of the solid curve magnified 15 times.

Equations (7)

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I ( t ) = I 0 cos 2 [ π 2 V π V ( t ) + ϕ 0 ] ,
E 1 ( t ) = E 0 e i Ω t cos ( m sin ω t + ϕ 0 ) ,
E 2 ( t ) = E 0 e i Ω t e i ( π / 2 ) sin ( m sin ω t + ϕ 0 ) ,
E 1 ( t ) = E 0 J 0 ( m ) cos ϕ 0 e i Ω t + i E 0 J 1 ( m ) sin ϕ 0 [ e i ( Ω + ω ) t e i ( Ω ω ) t ] + .
E 1 ( t ) = E 0 e i Ω t cos ( m sin ω t + π 4 ) ,
E 2 ( t ) = E 0 e i Ω t e i ( π / 2 ) sin ( m sin ω t + π 4 ) .
E 2 ( t ) E 0 e i Ω t e i ( π / 2 ) sin [ m sin ω ( t π ω ) + π 4 ] = E 0 e i Ω t e i ( π / 2 ) cos ( m sin ω t + π 4 ) ,

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