Abstract

We present and theoretically study a superluminal fiber laser based super-sensor employing Brillouin gain. The white light cavity condition is attained by introducing a phase shift component comprising an additional ring or Fabry-Perot cavity into the main cavity. By adjusting the parameters of the laser cavity and those of the phase component it is possible to attain sensitivity enhancement of many orders of magnitude compared to that of conventional laser sensors. The tradeoffs between the attainable sensitivity enhancement, the cavity dimensions and the impact of the cavity roundtrip loss are studied in details, providing a set of design rules for the optimization of the super-sensor.

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  4. G. Heinzel, K. A. Strain, J. Mizuno, K. D. Skeldon, B. Willke, W. Winkler, R. Schilling, A. Rudiger, and K. Danzmann, “Experimental demonstration of a suspended dual recycling interferometer for gravitational wave detection,” Phys. Rev. Lett.81(25), 5493–5496 (1998).
    [CrossRef]
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  7. P. Lambeck, “Integrated optical sensors for the chemical domain,” Meas. Sci. Technol.17(8), R93–R116 (2006).
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  21. J. D. Cresser, W. H. Louisell, P. Meystre, W. Schleich, and M. O. Scully, “Quantum noise in ring laser gyros. I. Theoretical formulation of the problem,” Phys. Rev. A25(4), 2214–2225 (1982).
    [CrossRef]
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  23. S. Huang, L. Thevenaz, K. Toyama, B. Y. Kim, and H. J. Shaw, “Optical Kerr-effect in fiber-optic Brillouin ring laser gyroscopes,” IEEE Photon. Technol. Lett.5(3), 365–367 (1993).
    [CrossRef]

2011

J. Schaar, H. Yum, and M. S. Shahriar, “Theoretical Description and Design of a Fast-Light Enhanced Helium-Neon Ring-Laser Gyroscope,” Proc. SPIE 7949, Advances in Slow and Fast LightIV, 794914 (2011).

2010

2007

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Demonstration of a tunable-bandwidth white-light interferometer using anomalous dispersion in atomic vapor,” Phys. Rev. Lett.99(13), 133601 (2007).
[CrossRef] [PubMed]

M. S. Shahriar, G. S. Pati, R. Tripathi, V. Gopal, M. Messall, and K. Salit, “Ultrahigh enhancement in absolute and relative rotation sensing using fast and slow light,” Phys. Rev. A75(5), 053807 (2007).
[CrossRef]

A. Leung, P. M. Shankar, and R. Mutharasan, “A review of fiber-optic biosensors,” Sens. Actuators B Chem.125(2), 688–703 (2007).
[CrossRef]

2006

P. Lambeck, “Integrated optical sensors for the chemical domain,” Meas. Sci. Technol.17(8), R93–R116 (2006).
[CrossRef]

2005

G. Gauglitz, “Direct optical sensors: principles and selected applications,” Anal. Bioanal. Chem.381(1), 141–155 (2005).
[CrossRef] [PubMed]

S. Wise, V. Quetschke, A. J. Deshpande, G. Mueller, D. H. Reitze, D. B. Tanner, B. F. Whiting, Y. Chen, A. Tünnermann, E. Kley, and T. Clausnitzer, “Phase effects in the diffraction of light: beyond the grating equation,” Phys. Rev. Lett.95(1), 013901 (2005).
[CrossRef] [PubMed]

2004

S. Wise, G. Mueller, D. Reitze, D. B. Tanner, and B. F. Whiting, “Linewidth-broadened Fabry-Perot cavities within future gravitational wave detectors,” Class. Quantum Gravity21(5), S1031–S1036 (2004).
[CrossRef]

2000

1998

G. Heinzel, K. A. Strain, J. Mizuno, K. D. Skeldon, B. Willke, W. Winkler, R. Schilling, A. Rudiger, and K. Danzmann, “Experimental demonstration of a suspended dual recycling interferometer for gravitational wave detection,” Phys. Rev. Lett.81(25), 5493–5496 (1998).
[CrossRef]

M. B. Gray, A. J. Stevenson, H.-A. Bachor, and D. E. McClelland, “Broadband and tuned signal recycling with a simple Michelson interferometer,” Appl. Opt.37(25), 5886–5893 (1998).
[CrossRef] [PubMed]

1997

A. Lenef, T. D. Hammond, E. T. Smith, M. S. Chapman, R. A. Rubenstein, and D. E. Pritchard, “Rotation sensing with an atom interferometer,” Phys. Rev. Lett.78(5), 760–763 (1997).
[CrossRef]

1993

S. Huang, L. Thevenaz, K. Toyama, B. Y. Kim, and H. J. Shaw, “Optical Kerr-effect in fiber-optic Brillouin ring laser gyroscopes,” IEEE Photon. Technol. Lett.5(3), 365–367 (1993).
[CrossRef]

1989

B. J. Meers, “The frequency response of interferometric gravitational wave detectors,” Phys. Lett. A142(8-9), 465–470 (1989).
[CrossRef]

1988

B. J. Meers, “Recycling in laser-interferometric gravitational-wave detectors,” Phys. Rev. D Part. Fields38(8), 2317–2326 (1988).
[CrossRef] [PubMed]

1983

1982

J. D. Cresser, W. H. Louisell, P. Meystre, W. Schleich, and M. O. Scully, “Quantum noise in ring laser gyros. I. Theoretical formulation of the problem,” Phys. Rev. A25(4), 2214–2225 (1982).
[CrossRef]

1980

R. Ulrich, “Fiber-optic rotation sensing with low drift,” Opt. Lett.5(5), 173–175 (1980).
[CrossRef] [PubMed]

T. A. Dorschner, H. A. Haus, M. Holz, I. W. Smith, and H. Statz, “Laser gyro at quantum limit,” IEEE J. Quantum Electron.16(12), 1376–1379 (1980).
[CrossRef]

Bachor, H.-A.

Chapman, M. S.

A. Lenef, T. D. Hammond, E. T. Smith, M. S. Chapman, R. A. Rubenstein, and D. E. Pritchard, “Rotation sensing with an atom interferometer,” Phys. Rev. Lett.78(5), 760–763 (1997).
[CrossRef]

Chen, Y.

S. Wise, V. Quetschke, A. J. Deshpande, G. Mueller, D. H. Reitze, D. B. Tanner, B. F. Whiting, Y. Chen, A. Tünnermann, E. Kley, and T. Clausnitzer, “Phase effects in the diffraction of light: beyond the grating equation,” Phys. Rev. Lett.95(1), 013901 (2005).
[CrossRef] [PubMed]

Chowdhury, D.

Clausnitzer, T.

S. Wise, V. Quetschke, A. J. Deshpande, G. Mueller, D. H. Reitze, D. B. Tanner, B. F. Whiting, Y. Chen, A. Tünnermann, E. Kley, and T. Clausnitzer, “Phase effects in the diffraction of light: beyond the grating equation,” Phys. Rev. Lett.95(1), 013901 (2005).
[CrossRef] [PubMed]

Cresser, J. D.

J. D. Cresser, W. H. Louisell, P. Meystre, W. Schleich, and M. O. Scully, “Quantum noise in ring laser gyros. I. Theoretical formulation of the problem,” Phys. Rev. A25(4), 2214–2225 (1982).
[CrossRef]

Danzmann, K.

G. Heinzel, K. A. Strain, J. Mizuno, K. D. Skeldon, B. Willke, W. Winkler, R. Schilling, A. Rudiger, and K. Danzmann, “Experimental demonstration of a suspended dual recycling interferometer for gravitational wave detection,” Phys. Rev. Lett.81(25), 5493–5496 (1998).
[CrossRef]

Deshpande, A. J.

S. Wise, V. Quetschke, A. J. Deshpande, G. Mueller, D. H. Reitze, D. B. Tanner, B. F. Whiting, Y. Chen, A. Tünnermann, E. Kley, and T. Clausnitzer, “Phase effects in the diffraction of light: beyond the grating equation,” Phys. Rev. Lett.95(1), 013901 (2005).
[CrossRef] [PubMed]

Dorschner, T. A.

T. A. Dorschner, H. A. Haus, M. Holz, I. W. Smith, and H. Statz, “Laser gyro at quantum limit,” IEEE J. Quantum Electron.16(12), 1376–1379 (1980).
[CrossRef]

Ezekiel, S.

Gauglitz, G.

G. Gauglitz, “Direct optical sensors: principles and selected applications,” Anal. Bioanal. Chem.381(1), 141–155 (2005).
[CrossRef] [PubMed]

Gopal, V.

M. S. Shahriar, G. S. Pati, R. Tripathi, V. Gopal, M. Messall, and K. Salit, “Ultrahigh enhancement in absolute and relative rotation sensing using fast and slow light,” Phys. Rev. A75(5), 053807 (2007).
[CrossRef]

Gray, M. B.

Hammond, T. D.

A. Lenef, T. D. Hammond, E. T. Smith, M. S. Chapman, R. A. Rubenstein, and D. E. Pritchard, “Rotation sensing with an atom interferometer,” Phys. Rev. Lett.78(5), 760–763 (1997).
[CrossRef]

Haus, H. A.

T. A. Dorschner, H. A. Haus, M. Holz, I. W. Smith, and H. Statz, “Laser gyro at quantum limit,” IEEE J. Quantum Electron.16(12), 1376–1379 (1980).
[CrossRef]

Heinzel, G.

G. Heinzel, K. A. Strain, J. Mizuno, K. D. Skeldon, B. Willke, W. Winkler, R. Schilling, A. Rudiger, and K. Danzmann, “Experimental demonstration of a suspended dual recycling interferometer for gravitational wave detection,” Phys. Rev. Lett.81(25), 5493–5496 (1998).
[CrossRef]

Holz, M.

T. A. Dorschner, H. A. Haus, M. Holz, I. W. Smith, and H. Statz, “Laser gyro at quantum limit,” IEEE J. Quantum Electron.16(12), 1376–1379 (1980).
[CrossRef]

Huang, S.

S. Huang, L. Thevenaz, K. Toyama, B. Y. Kim, and H. J. Shaw, “Optical Kerr-effect in fiber-optic Brillouin ring laser gyroscopes,” IEEE Photon. Technol. Lett.5(3), 365–367 (1993).
[CrossRef]

Kim, B. Y.

S. Huang, L. Thevenaz, K. Toyama, B. Y. Kim, and H. J. Shaw, “Optical Kerr-effect in fiber-optic Brillouin ring laser gyroscopes,” IEEE Photon. Technol. Lett.5(3), 365–367 (1993).
[CrossRef]

King, B. T.

Kley, E.

S. Wise, V. Quetschke, A. J. Deshpande, G. Mueller, D. H. Reitze, D. B. Tanner, B. F. Whiting, Y. Chen, A. Tünnermann, E. Kley, and T. Clausnitzer, “Phase effects in the diffraction of light: beyond the grating equation,” Phys. Rev. Lett.95(1), 013901 (2005).
[CrossRef] [PubMed]

Kobyakov, A.

Lambeck, P.

P. Lambeck, “Integrated optical sensors for the chemical domain,” Meas. Sci. Technol.17(8), R93–R116 (2006).
[CrossRef]

Lenef, A.

A. Lenef, T. D. Hammond, E. T. Smith, M. S. Chapman, R. A. Rubenstein, and D. E. Pritchard, “Rotation sensing with an atom interferometer,” Phys. Rev. Lett.78(5), 760–763 (1997).
[CrossRef]

Leung, A.

A. Leung, P. M. Shankar, and R. Mutharasan, “A review of fiber-optic biosensors,” Sens. Actuators B Chem.125(2), 688–703 (2007).
[CrossRef]

Louisell, W. H.

J. D. Cresser, W. H. Louisell, P. Meystre, W. Schleich, and M. O. Scully, “Quantum noise in ring laser gyros. I. Theoretical formulation of the problem,” Phys. Rev. A25(4), 2214–2225 (1982).
[CrossRef]

McClelland, D. E.

Meers, B. J.

B. J. Meers, “The frequency response of interferometric gravitational wave detectors,” Phys. Lett. A142(8-9), 465–470 (1989).
[CrossRef]

B. J. Meers, “Recycling in laser-interferometric gravitational-wave detectors,” Phys. Rev. D Part. Fields38(8), 2317–2326 (1988).
[CrossRef] [PubMed]

Messall, M.

M. S. Shahriar, G. S. Pati, R. Tripathi, V. Gopal, M. Messall, and K. Salit, “Ultrahigh enhancement in absolute and relative rotation sensing using fast and slow light,” Phys. Rev. A75(5), 053807 (2007).
[CrossRef]

Meyer, R. E.

Meystre, P.

J. D. Cresser, W. H. Louisell, P. Meystre, W. Schleich, and M. O. Scully, “Quantum noise in ring laser gyros. I. Theoretical formulation of the problem,” Phys. Rev. A25(4), 2214–2225 (1982).
[CrossRef]

Mizuno, J.

G. Heinzel, K. A. Strain, J. Mizuno, K. D. Skeldon, B. Willke, W. Winkler, R. Schilling, A. Rudiger, and K. Danzmann, “Experimental demonstration of a suspended dual recycling interferometer for gravitational wave detection,” Phys. Rev. Lett.81(25), 5493–5496 (1998).
[CrossRef]

Mueller, G.

S. Wise, V. Quetschke, A. J. Deshpande, G. Mueller, D. H. Reitze, D. B. Tanner, B. F. Whiting, Y. Chen, A. Tünnermann, E. Kley, and T. Clausnitzer, “Phase effects in the diffraction of light: beyond the grating equation,” Phys. Rev. Lett.95(1), 013901 (2005).
[CrossRef] [PubMed]

S. Wise, G. Mueller, D. Reitze, D. B. Tanner, and B. F. Whiting, “Linewidth-broadened Fabry-Perot cavities within future gravitational wave detectors,” Class. Quantum Gravity21(5), S1031–S1036 (2004).
[CrossRef]

Mutharasan, R.

A. Leung, P. M. Shankar, and R. Mutharasan, “A review of fiber-optic biosensors,” Sens. Actuators B Chem.125(2), 688–703 (2007).
[CrossRef]

Pati, G. S.

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Demonstration of a tunable-bandwidth white-light interferometer using anomalous dispersion in atomic vapor,” Phys. Rev. Lett.99(13), 133601 (2007).
[CrossRef] [PubMed]

M. S. Shahriar, G. S. Pati, R. Tripathi, V. Gopal, M. Messall, and K. Salit, “Ultrahigh enhancement in absolute and relative rotation sensing using fast and slow light,” Phys. Rev. A75(5), 053807 (2007).
[CrossRef]

Pritchard, D. E.

A. Lenef, T. D. Hammond, E. T. Smith, M. S. Chapman, R. A. Rubenstein, and D. E. Pritchard, “Rotation sensing with an atom interferometer,” Phys. Rev. Lett.78(5), 760–763 (1997).
[CrossRef]

Quetschke, V.

S. Wise, V. Quetschke, A. J. Deshpande, G. Mueller, D. H. Reitze, D. B. Tanner, B. F. Whiting, Y. Chen, A. Tünnermann, E. Kley, and T. Clausnitzer, “Phase effects in the diffraction of light: beyond the grating equation,” Phys. Rev. Lett.95(1), 013901 (2005).
[CrossRef] [PubMed]

Reitze, D.

S. Wise, G. Mueller, D. Reitze, D. B. Tanner, and B. F. Whiting, “Linewidth-broadened Fabry-Perot cavities within future gravitational wave detectors,” Class. Quantum Gravity21(5), S1031–S1036 (2004).
[CrossRef]

Reitze, D. H.

S. Wise, V. Quetschke, A. J. Deshpande, G. Mueller, D. H. Reitze, D. B. Tanner, B. F. Whiting, Y. Chen, A. Tünnermann, E. Kley, and T. Clausnitzer, “Phase effects in the diffraction of light: beyond the grating equation,” Phys. Rev. Lett.95(1), 013901 (2005).
[CrossRef] [PubMed]

Rubenstein, R. A.

A. Lenef, T. D. Hammond, E. T. Smith, M. S. Chapman, R. A. Rubenstein, and D. E. Pritchard, “Rotation sensing with an atom interferometer,” Phys. Rev. Lett.78(5), 760–763 (1997).
[CrossRef]

Rudiger, A.

G. Heinzel, K. A. Strain, J. Mizuno, K. D. Skeldon, B. Willke, W. Winkler, R. Schilling, A. Rudiger, and K. Danzmann, “Experimental demonstration of a suspended dual recycling interferometer for gravitational wave detection,” Phys. Rev. Lett.81(25), 5493–5496 (1998).
[CrossRef]

Salit, K.

H. N. Yum, M. Salit, J. Yablon, K. Salit, Y. Wang, and M. S. Shahriar, “Superluminal ring laser for hypersensitive sensing,” Opt. Express18(17), 17658–17665 (2010).
[CrossRef] [PubMed]

M. S. Shahriar, G. S. Pati, R. Tripathi, V. Gopal, M. Messall, and K. Salit, “Ultrahigh enhancement in absolute and relative rotation sensing using fast and slow light,” Phys. Rev. A75(5), 053807 (2007).
[CrossRef]

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Demonstration of a tunable-bandwidth white-light interferometer using anomalous dispersion in atomic vapor,” Phys. Rev. Lett.99(13), 133601 (2007).
[CrossRef] [PubMed]

Salit, M.

H. N. Yum, M. Salit, J. Yablon, K. Salit, Y. Wang, and M. S. Shahriar, “Superluminal ring laser for hypersensitive sensing,” Opt. Express18(17), 17658–17665 (2010).
[CrossRef] [PubMed]

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Demonstration of a tunable-bandwidth white-light interferometer using anomalous dispersion in atomic vapor,” Phys. Rev. Lett.99(13), 133601 (2007).
[CrossRef] [PubMed]

Sauer, M.

Schaar, J.

J. Schaar, H. Yum, and M. S. Shahriar, “Theoretical Description and Design of a Fast-Light Enhanced Helium-Neon Ring-Laser Gyroscope,” Proc. SPIE 7949, Advances in Slow and Fast LightIV, 794914 (2011).

Schilling, R.

G. Heinzel, K. A. Strain, J. Mizuno, K. D. Skeldon, B. Willke, W. Winkler, R. Schilling, A. Rudiger, and K. Danzmann, “Experimental demonstration of a suspended dual recycling interferometer for gravitational wave detection,” Phys. Rev. Lett.81(25), 5493–5496 (1998).
[CrossRef]

Schleich, W.

J. D. Cresser, W. H. Louisell, P. Meystre, W. Schleich, and M. O. Scully, “Quantum noise in ring laser gyros. I. Theoretical formulation of the problem,” Phys. Rev. A25(4), 2214–2225 (1982).
[CrossRef]

Scully, M. O.

J. D. Cresser, W. H. Louisell, P. Meystre, W. Schleich, and M. O. Scully, “Quantum noise in ring laser gyros. I. Theoretical formulation of the problem,” Phys. Rev. A25(4), 2214–2225 (1982).
[CrossRef]

Shahriar, M. S.

J. Schaar, H. Yum, and M. S. Shahriar, “Theoretical Description and Design of a Fast-Light Enhanced Helium-Neon Ring-Laser Gyroscope,” Proc. SPIE 7949, Advances in Slow and Fast LightIV, 794914 (2011).

H. N. Yum, M. Salit, J. Yablon, K. Salit, Y. Wang, and M. S. Shahriar, “Superluminal ring laser for hypersensitive sensing,” Opt. Express18(17), 17658–17665 (2010).
[CrossRef] [PubMed]

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Demonstration of a tunable-bandwidth white-light interferometer using anomalous dispersion in atomic vapor,” Phys. Rev. Lett.99(13), 133601 (2007).
[CrossRef] [PubMed]

M. S. Shahriar, G. S. Pati, R. Tripathi, V. Gopal, M. Messall, and K. Salit, “Ultrahigh enhancement in absolute and relative rotation sensing using fast and slow light,” Phys. Rev. A75(5), 053807 (2007).
[CrossRef]

Shankar, P. M.

A. Leung, P. M. Shankar, and R. Mutharasan, “A review of fiber-optic biosensors,” Sens. Actuators B Chem.125(2), 688–703 (2007).
[CrossRef]

Shaw, H. J.

S. Huang, L. Thevenaz, K. Toyama, B. Y. Kim, and H. J. Shaw, “Optical Kerr-effect in fiber-optic Brillouin ring laser gyroscopes,” IEEE Photon. Technol. Lett.5(3), 365–367 (1993).
[CrossRef]

Skeldon, K. D.

G. Heinzel, K. A. Strain, J. Mizuno, K. D. Skeldon, B. Willke, W. Winkler, R. Schilling, A. Rudiger, and K. Danzmann, “Experimental demonstration of a suspended dual recycling interferometer for gravitational wave detection,” Phys. Rev. Lett.81(25), 5493–5496 (1998).
[CrossRef]

Smith, E. T.

A. Lenef, T. D. Hammond, E. T. Smith, M. S. Chapman, R. A. Rubenstein, and D. E. Pritchard, “Rotation sensing with an atom interferometer,” Phys. Rev. Lett.78(5), 760–763 (1997).
[CrossRef]

Smith, I. W.

T. A. Dorschner, H. A. Haus, M. Holz, I. W. Smith, and H. Statz, “Laser gyro at quantum limit,” IEEE J. Quantum Electron.16(12), 1376–1379 (1980).
[CrossRef]

Statz, H.

T. A. Dorschner, H. A. Haus, M. Holz, I. W. Smith, and H. Statz, “Laser gyro at quantum limit,” IEEE J. Quantum Electron.16(12), 1376–1379 (1980).
[CrossRef]

Stevenson, A. J.

Stowe, D. W.

Strain, K. A.

G. Heinzel, K. A. Strain, J. Mizuno, K. D. Skeldon, B. Willke, W. Winkler, R. Schilling, A. Rudiger, and K. Danzmann, “Experimental demonstration of a suspended dual recycling interferometer for gravitational wave detection,” Phys. Rev. Lett.81(25), 5493–5496 (1998).
[CrossRef]

Tanner, D. B.

S. Wise, V. Quetschke, A. J. Deshpande, G. Mueller, D. H. Reitze, D. B. Tanner, B. F. Whiting, Y. Chen, A. Tünnermann, E. Kley, and T. Clausnitzer, “Phase effects in the diffraction of light: beyond the grating equation,” Phys. Rev. Lett.95(1), 013901 (2005).
[CrossRef] [PubMed]

S. Wise, G. Mueller, D. Reitze, D. B. Tanner, and B. F. Whiting, “Linewidth-broadened Fabry-Perot cavities within future gravitational wave detectors,” Class. Quantum Gravity21(5), S1031–S1036 (2004).
[CrossRef]

Tekippe, V. J.

Thevenaz, L.

S. Huang, L. Thevenaz, K. Toyama, B. Y. Kim, and H. J. Shaw, “Optical Kerr-effect in fiber-optic Brillouin ring laser gyroscopes,” IEEE Photon. Technol. Lett.5(3), 365–367 (1993).
[CrossRef]

Toyama, K.

S. Huang, L. Thevenaz, K. Toyama, B. Y. Kim, and H. J. Shaw, “Optical Kerr-effect in fiber-optic Brillouin ring laser gyroscopes,” IEEE Photon. Technol. Lett.5(3), 365–367 (1993).
[CrossRef]

Tripathi, R.

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Figures (12)

Fig. 1
Fig. 1

Interferometric (a) and resonator-based (b) optical measurement schemes.

Fig. 2
Fig. 2

An optical cavity incorporating a negative dispersion section.

Fig. 3
Fig. 3

(a) Ring resonator and (b) Fabry-Perot interferometer based negative dispersion components.

Fig. 4
Fig. 4

Schematic of a SBS based superluminal fiber laser; Inset: effective gain and phase profiles.

Fig. 5
Fig. 5

Relationship between the coupling coefficients for maximal sensitivity enhancement.

Fig. 6
Fig. 6

Enhancement (solid) and roundtrip transmission (dashed) of superluminal lasers with optimal κ1 and κ2 relations for maximal enhancement.

Fig. 7
Fig. 7

Enhancement-roundtrip loss tradeoffs for superluminal laser with various cavity length ratios.

Fig. 8
Fig. 8

Dependence of the sensitivity enhancement on δL.

Fig. 9
Fig. 9

Dependence of the sensitivity enhancement on the cavity length of the phase component. Inset: zoom in on smaller δL levels.

Fig. 10
Fig. 10

Dependence of the excess roundtrip loss on the cavity length of the phase component.

Fig. 11
Fig. 11

Dependence of the sensitivity enhancement on the coupling coefficients. Inset: corresponding excess roundtrip losses.

Fig. 12
Fig. 12

Dependence of the δLmin on the coupling coefficient κ1

Equations (23)

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Δφ( ω 0 )= ω 0 c 0 [ (Ll)+ n l ( ω 0 )l ]
Δφ( ω res +Δω)= ( ω res +Δω) c 0 [ (Ll)+ n l ( ω res +Δω)l ]=2πm
n l ( ω res )+ ω res d n l dω | ω res = n g ( ω res )=1L/l
Δφ( ω res +Δω)= ( ω res +Δω) c 0 n p ( ω res +Δω) L +θ( ω res +Δω)=2πm
dθ dω | ω res = L c 0 [ n p ( ω res )+ ω res d n p / dω ]= L c 0 n pg =2π/Δ ω FSR
S= δω δL = n p ( ω res ) ω res L n pg ( ω res )
S= δω δL = n p ( ω res ) ω res L n pg ( ω res )+ c 0 dθ / dω | ω res
tan(θ)= κ 1 1 κ 2 sin(ϕ) 1 κ 1 (2 κ 2 ) 1 κ 2 (2 κ 1 )cos(ϕ) = r 2 ( 1 r 1 2 )sinϕ r 1 ( 1+ r 2 2 ) r 2 ( 1+ r 1 2 )cosϕ
L'= κ 1 1 κ 2 L r ( 1 κ 1 1 κ 2 )( 1 1 κ 1 1 κ 2 ) = 2 r 2 ( 1 r 1 2 ) L fp r 1 ( 1+ r 2 2 ) r 2 ( 1+ r 1 2 )
β= 1 2α [ 1+ α 2 1 α 2 M (1+ α 2 [1 α 2 ] /M ) 2 4 α 2 ]
ω res c 0 n p ( ω res ) L +θ( ω res )=2πm
( ω res +Δ ω s ) c 0 n p ( ω res +Δ ω s )( L +δL)+θ( ω res +Δ ω s )+Δ θ Br ( ω res +Δ ω s )=2πm
χ =2 χ (ω ω 0 ) / Δ ω Br
χ = ln(T) / k 0 n L l χ =2 ln(T) k 0 n L l ω ω 0 Δ ω Br
Δβ= k 0 n χ =2 ln(T) L l ω ω 0 Δ ω Br
Δ θ Br =2ln(T) ω ω 0 Δ ω Br
T( ω res )=1 κ 1 2 κ 2 2 (1αβ) 2
( ω res +δω) c 0 ( L +δL) n p +θ( ω res +δω)=2πm whereθ( ω res +δω)Aδω+Bδ ω 3 ,A= n p L r c 0 R 2 (1 R 1 ) ( R 1 R 2 )(1 R 1 R 2 ) and B= ( n p L r ) 3 c 0 3 ( R 1 R 2 ) [ 1 6 R 2 (1 R 1 ) (1 R 1 R 2 ) + 1 2 R 2 (1 R 1 2 ) ( R 1 R 2 ) (1 R 1 R 2 ) 2 + 1 3 R 2 3 2 (1 R 1 ) 3 ( R 1 R 2 ) 2 (1 R 1 R 2 ) 3 ]= ( n p L r ) 3 c 0 3 B ¯
δω= ( n p ω res δL c 0 B ) 1/3
ξ=M ( λ 2 / n p 2 4 π 2 B ¯ δ L 2 ) 1/3
Δ ω rms = 1 Q ( ω 3 PT ) 1/2
Q=ωτ= L ω / cΛ
δ L min = Δ ω rms ξS = 1 ξS 1 Q ( ω 3 PT ) 1/2

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