Abstract

We have demonstrated experimentally a Diode-Pumped Alkali Laser (DPAL) with a Raman resonance induced dip in the center of the gain profile, in order to produce an anomalous dispersion, necessary for making the laser superluminal. Numerical calculations match closely with experimental results, and indicate that the laser is operating superluminally, with the group index far below unity (~0.00526) at the center of the dip. The estimated factor of enhancement in the sensitivity to cavity length perturbation is ~190, approximately equaling the inverse of the group index. This enhancement factor can be made much higher via optimal tuning of parameters. Such a laser has the potential to advance significantly the field of high-precision metrology, with applications such as vibrometry, accelerometry, and rotation sensing.

© 2016 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
  4. D. D. Smith, K. Myneni, J. A. Odutola, and J. C. Diels, “Enhanced sensitivity of a passive optical cavity by an intracavity dispersive medium,” Phys. Rev. A 80(1), 011809 (2009).
    [Crossref]
  5. D. D. Smith, H. Chang, K. Myneni, and A. T. Rosenberger, “Fast-light enhancement of an optical cavity by polarization mode coupling,” Phys. Rev. A 89(5), 053804 (2014).
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]

2016 (1)

Z. Zhou, J. Yablon, M. Zhou, Y. Wang, A. Heifetz, and M. S. Shahriar, “Modeling and analysis of an ultra-stable subluminal laser,” Opt. Commun. 358, 6–19 (2016).
[Crossref]

2015 (3)

J. Scheuer and S. M. Shahriar, “Lasing dynamics of super and sub luminal lasers,” Opt. Express 23(25), 32350–32366 (2015).
[Crossref] [PubMed]

K. Myneni, D. D. Smith, H. Chang, and H. A. Luckay, “Temperature sensitivity of the cavity scale factor enhancement for a Gaussian absorption resonance,” Phys. Rev. A 92(5), 053845 (2015).
[Crossref]

Y. Wang, Z. Zhou, J. Yablon, and M. S. Shahriar, “Effect of multi-order harmonics in a double-Raman pumped gain medium for a superluminal laser,” Opt. Eng. 54(5), 057106 (2015).
[Crossref]

2014 (2)

D. D. Smith, H. Chang, K. Myneni, and A. T. Rosenberger, “Fast-light enhancement of an optical cavity by polarization mode coupling,” Phys. Rev. A 89(5), 053804 (2014).
[Crossref]

M. S. Shahriar, Y. Wang, S. Krishnamurthy, Y. Tu, G. S. Pati, and S. Tseng, “Evolution of an N-level system via automated vectorization of the Liouville equations and application to optically controlled polarization rotation,” J. Mod. Opt. 61(4), 351–367 (2014).
[Crossref]

2012 (1)

2010 (2)

2009 (2)

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Simultaneous slow and fast light effects using probe gain and pump depletion via Raman gain in atomic vapor,” Opt. Express 17(11), 8775–8780 (2009).
[Crossref] [PubMed]

D. D. Smith, K. Myneni, J. A. Odutola, and J. C. Diels, “Enhanced sensitivity of a passive optical cavity by an intracavity dispersive medium,” Phys. Rev. A 80(1), 011809 (2009).
[Crossref]

2008 (2)

D. D. Smith, H. Chang, L. Arissian, and J. C. Diels, “Dispersion-enhanced laser gyroscope,” Phys. Rev. A 78(5), 053824 (2008).
[Crossref]

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Demonstration of displacement-measurement-sensitivity proportional to inverse group index of intra-cavity medium in a ring resonator,” Opt. Commun. 281(19), 4931–4935 (2008).
[Crossref]

2007 (2)

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. A 75(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]

2003 (1)

2000 (1)

1973 (1)

G. J. Troup and A. Bambini, “The use of the modified Kramers-Kronig relation in the rate equation approach of laser theory,” Phys. Lett. 45(5), 393–394 (1973).
[Crossref]

1969 (1)

H. C. Bolton and G. J. Troup, “The modification of the Kronig-Kramers relations under saturation conditions,” Philos. Mag. 19(159), 477–485 (1969).
[Crossref]

Arissian, L.

D. D. Smith, H. Chang, L. Arissian, and J. C. Diels, “Dispersion-enhanced laser gyroscope,” Phys. Rev. A 78(5), 053824 (2008).
[Crossref]

Bambini, A.

G. J. Troup and A. Bambini, “The use of the modified Kramers-Kronig relation in the rate equation approach of laser theory,” Phys. Lett. 45(5), 393–394 (1973).
[Crossref]

Beach, R. J.

Bolton, H. C.

H. C. Bolton and G. J. Troup, “The modification of the Kronig-Kramers relations under saturation conditions,” Philos. Mag. 19(159), 477–485 (1969).
[Crossref]

Chang, H.

K. Myneni, D. D. Smith, H. Chang, and H. A. Luckay, “Temperature sensitivity of the cavity scale factor enhancement for a Gaussian absorption resonance,” Phys. Rev. A 92(5), 053845 (2015).
[Crossref]

D. D. Smith, H. Chang, K. Myneni, and A. T. Rosenberger, “Fast-light enhancement of an optical cavity by polarization mode coupling,” Phys. Rev. A 89(5), 053804 (2014).
[Crossref]

D. D. Smith, H. Chang, L. Arissian, and J. C. Diels, “Dispersion-enhanced laser gyroscope,” Phys. Rev. A 78(5), 053824 (2008).
[Crossref]

Diels, J. C.

D. D. Smith, K. Myneni, J. A. Odutola, and J. C. Diels, “Enhanced sensitivity of a passive optical cavity by an intracavity dispersive medium,” Phys. Rev. A 80(1), 011809 (2009).
[Crossref]

D. D. Smith, H. Chang, L. Arissian, and J. C. Diels, “Dispersion-enhanced laser gyroscope,” Phys. Rev. A 78(5), 053824 (2008).
[Crossref]

Faerch, K.

Frederiksen, S. L.

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. A 75(5), 053807 (2007).
[Crossref]

Heifetz, A.

Z. Zhou, J. Yablon, M. Zhou, Y. Wang, A. Heifetz, and M. S. Shahriar, “Modeling and analysis of an ultra-stable subluminal laser,” Opt. Commun. 358, 6–19 (2016).
[Crossref]

Kanz, V. K.

Kotlicki, O.

Krishnamurthy, S.

M. S. Shahriar, Y. Wang, S. Krishnamurthy, Y. Tu, G. S. Pati, and S. Tseng, “Evolution of an N-level system via automated vectorization of the Liouville equations and application to optically controlled polarization rotation,” J. Mod. Opt. 61(4), 351–367 (2014).
[Crossref]

Krupke, W. F.

Luckay, H. A.

K. Myneni, D. D. Smith, H. Chang, and H. A. Luckay, “Temperature sensitivity of the cavity scale factor enhancement for a Gaussian absorption resonance,” Phys. Rev. A 92(5), 053845 (2015).
[Crossref]

Meelby, T.

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. A 75(5), 053807 (2007).
[Crossref]

Myneni, K.

K. Myneni, D. D. Smith, H. Chang, and H. A. Luckay, “Temperature sensitivity of the cavity scale factor enhancement for a Gaussian absorption resonance,” Phys. Rev. A 92(5), 053845 (2015).
[Crossref]

D. D. Smith, H. Chang, K. Myneni, and A. T. Rosenberger, “Fast-light enhancement of an optical cavity by polarization mode coupling,” Phys. Rev. A 89(5), 053804 (2014).
[Crossref]

D. D. Smith, K. Myneni, J. A. Odutola, and J. C. Diels, “Enhanced sensitivity of a passive optical cavity by an intracavity dispersive medium,” Phys. Rev. A 80(1), 011809 (2009).
[Crossref]

Odutola, J. A.

D. D. Smith, K. Myneni, J. A. Odutola, and J. C. Diels, “Enhanced sensitivity of a passive optical cavity by an intracavity dispersive medium,” Phys. Rev. A 80(1), 011809 (2009).
[Crossref]

Pati, G. S.

M. S. Shahriar, Y. Wang, S. Krishnamurthy, Y. Tu, G. S. Pati, and S. Tseng, “Evolution of an N-level system via automated vectorization of the Liouville equations and application to optically controlled polarization rotation,” J. Mod. Opt. 61(4), 351–367 (2014).
[Crossref]

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Simultaneous slow and fast light effects using probe gain and pump depletion via Raman gain in atomic vapor,” Opt. Express 17(11), 8775–8780 (2009).
[Crossref] [PubMed]

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Demonstration of displacement-measurement-sensitivity proportional to inverse group index of intra-cavity medium in a ring resonator,” Opt. Commun. 281(19), 4931–4935 (2008).
[Crossref]

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. A 75(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]

Payne, S. A.

Pedersen, C.

Rosenberger, A. T.

D. D. Smith, H. Chang, K. Myneni, and A. T. Rosenberger, “Fast-light enhancement of an optical cavity by polarization mode coupling,” Phys. Rev. A 89(5), 053804 (2014).
[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. Express 18(17), 17658–17665 (2010).
[Crossref] [PubMed]

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Simultaneous slow and fast light effects using probe gain and pump depletion via Raman gain in atomic vapor,” Opt. Express 17(11), 8775–8780 (2009).
[Crossref] [PubMed]

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Demonstration of displacement-measurement-sensitivity proportional to inverse group index of intra-cavity medium in a ring resonator,” Opt. Commun. 281(19), 4931–4935 (2008).
[Crossref]

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. A 75(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. Express 18(17), 17658–17665 (2010).
[Crossref] [PubMed]

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Simultaneous slow and fast light effects using probe gain and pump depletion via Raman gain in atomic vapor,” Opt. Express 17(11), 8775–8780 (2009).
[Crossref] [PubMed]

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Demonstration of displacement-measurement-sensitivity proportional to inverse group index of intra-cavity medium in a ring resonator,” Opt. Commun. 281(19), 4931–4935 (2008).
[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]

Scheuer, J.

Shahriar, M. S.

Z. Zhou, J. Yablon, M. Zhou, Y. Wang, A. Heifetz, and M. S. Shahriar, “Modeling and analysis of an ultra-stable subluminal laser,” Opt. Commun. 358, 6–19 (2016).
[Crossref]

Y. Wang, Z. Zhou, J. Yablon, and M. S. Shahriar, “Effect of multi-order harmonics in a double-Raman pumped gain medium for a superluminal laser,” Opt. Eng. 54(5), 057106 (2015).
[Crossref]

M. S. Shahriar, Y. Wang, S. Krishnamurthy, Y. Tu, G. S. Pati, and S. Tseng, “Evolution of an N-level system via automated vectorization of the Liouville equations and application to optically controlled polarization rotation,” J. Mod. Opt. 61(4), 351–367 (2014).
[Crossref]

O. Kotlicki, J. Scheuer, and M. S. Shahriar, “Theoretical study on Brillouin fiber laser sensor based on white light cavity,” Opt. Express 20(27), 28234–28248 (2012).
[Crossref] [PubMed]

H. N. Yum, M. Salit, J. Yablon, K. Salit, Y. Wang, and M. S. Shahriar, “Superluminal ring laser for hypersensitive sensing,” Opt. Express 18(17), 17658–17665 (2010).
[Crossref] [PubMed]

H. N. Yum and M. S. Shahriar, “Pump-probe model for the Kramers-Kronig relations in a laser,” J. Opt. 12(10), 104018 (2010).
[Crossref]

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Simultaneous slow and fast light effects using probe gain and pump depletion via Raman gain in atomic vapor,” Opt. Express 17(11), 8775–8780 (2009).
[Crossref] [PubMed]

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Demonstration of displacement-measurement-sensitivity proportional to inverse group index of intra-cavity medium in a ring resonator,” Opt. Commun. 281(19), 4931–4935 (2008).
[Crossref]

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. A 75(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]

Shahriar, S. M.

Skettrup, T.

Smith, D. D.

K. Myneni, D. D. Smith, H. Chang, and H. A. Luckay, “Temperature sensitivity of the cavity scale factor enhancement for a Gaussian absorption resonance,” Phys. Rev. A 92(5), 053845 (2015).
[Crossref]

D. D. Smith, H. Chang, K. Myneni, and A. T. Rosenberger, “Fast-light enhancement of an optical cavity by polarization mode coupling,” Phys. Rev. A 89(5), 053804 (2014).
[Crossref]

D. D. Smith, K. Myneni, J. A. Odutola, and J. C. Diels, “Enhanced sensitivity of a passive optical cavity by an intracavity dispersive medium,” Phys. Rev. A 80(1), 011809 (2009).
[Crossref]

D. D. Smith, H. Chang, L. Arissian, and J. C. Diels, “Dispersion-enhanced laser gyroscope,” Phys. Rev. A 78(5), 053824 (2008).
[Crossref]

Tripathi, R.

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. A 75(5), 053807 (2007).
[Crossref]

Troup, G. J.

G. J. Troup and A. Bambini, “The use of the modified Kramers-Kronig relation in the rate equation approach of laser theory,” Phys. Lett. 45(5), 393–394 (1973).
[Crossref]

H. C. Bolton and G. J. Troup, “The modification of the Kronig-Kramers relations under saturation conditions,” Philos. Mag. 19(159), 477–485 (1969).
[Crossref]

Tseng, S.

M. S. Shahriar, Y. Wang, S. Krishnamurthy, Y. Tu, G. S. Pati, and S. Tseng, “Evolution of an N-level system via automated vectorization of the Liouville equations and application to optically controlled polarization rotation,” J. Mod. Opt. 61(4), 351–367 (2014).
[Crossref]

Tu, Y.

M. S. Shahriar, Y. Wang, S. Krishnamurthy, Y. Tu, G. S. Pati, and S. Tseng, “Evolution of an N-level system via automated vectorization of the Liouville equations and application to optically controlled polarization rotation,” J. Mod. Opt. 61(4), 351–367 (2014).
[Crossref]

Wang, Y.

Z. Zhou, J. Yablon, M. Zhou, Y. Wang, A. Heifetz, and M. S. Shahriar, “Modeling and analysis of an ultra-stable subluminal laser,” Opt. Commun. 358, 6–19 (2016).
[Crossref]

Y. Wang, Z. Zhou, J. Yablon, and M. S. Shahriar, “Effect of multi-order harmonics in a double-Raman pumped gain medium for a superluminal laser,” Opt. Eng. 54(5), 057106 (2015).
[Crossref]

M. S. Shahriar, Y. Wang, S. Krishnamurthy, Y. Tu, G. S. Pati, and S. Tseng, “Evolution of an N-level system via automated vectorization of the Liouville equations and application to optically controlled polarization rotation,” J. Mod. Opt. 61(4), 351–367 (2014).
[Crossref]

H. N. Yum, M. Salit, J. Yablon, K. Salit, Y. Wang, and M. S. Shahriar, “Superluminal ring laser for hypersensitive sensing,” Opt. Express 18(17), 17658–17665 (2010).
[Crossref] [PubMed]

Yablon, J.

Z. Zhou, J. Yablon, M. Zhou, Y. Wang, A. Heifetz, and M. S. Shahriar, “Modeling and analysis of an ultra-stable subluminal laser,” Opt. Commun. 358, 6–19 (2016).
[Crossref]

Y. Wang, Z. Zhou, J. Yablon, and M. S. Shahriar, “Effect of multi-order harmonics in a double-Raman pumped gain medium for a superluminal laser,” Opt. Eng. 54(5), 057106 (2015).
[Crossref]

H. N. Yum, M. Salit, J. Yablon, K. Salit, Y. Wang, and M. S. Shahriar, “Superluminal ring laser for hypersensitive sensing,” Opt. Express 18(17), 17658–17665 (2010).
[Crossref] [PubMed]

Yum, H. N.

Zhou, M.

Z. Zhou, J. Yablon, M. Zhou, Y. Wang, A. Heifetz, and M. S. Shahriar, “Modeling and analysis of an ultra-stable subluminal laser,” Opt. Commun. 358, 6–19 (2016).
[Crossref]

Zhou, Z.

Z. Zhou, J. Yablon, M. Zhou, Y. Wang, A. Heifetz, and M. S. Shahriar, “Modeling and analysis of an ultra-stable subluminal laser,” Opt. Commun. 358, 6–19 (2016).
[Crossref]

Y. Wang, Z. Zhou, J. Yablon, and M. S. Shahriar, “Effect of multi-order harmonics in a double-Raman pumped gain medium for a superluminal laser,” Opt. Eng. 54(5), 057106 (2015).
[Crossref]

Appl. Opt. (1)

J. Mod. Opt. (1)

M. S. Shahriar, Y. Wang, S. Krishnamurthy, Y. Tu, G. S. Pati, and S. Tseng, “Evolution of an N-level system via automated vectorization of the Liouville equations and application to optically controlled polarization rotation,” J. Mod. Opt. 61(4), 351–367 (2014).
[Crossref]

J. Opt. (1)

H. N. Yum and M. S. Shahriar, “Pump-probe model for the Kramers-Kronig relations in a laser,” J. Opt. 12(10), 104018 (2010).
[Crossref]

Opt. Commun. (2)

Z. Zhou, J. Yablon, M. Zhou, Y. Wang, A. Heifetz, and M. S. Shahriar, “Modeling and analysis of an ultra-stable subluminal laser,” Opt. Commun. 358, 6–19 (2016).
[Crossref]

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Demonstration of displacement-measurement-sensitivity proportional to inverse group index of intra-cavity medium in a ring resonator,” Opt. Commun. 281(19), 4931–4935 (2008).
[Crossref]

Opt. Eng. (1)

Y. Wang, Z. Zhou, J. Yablon, and M. S. Shahriar, “Effect of multi-order harmonics in a double-Raman pumped gain medium for a superluminal laser,” Opt. Eng. 54(5), 057106 (2015).
[Crossref]

Opt. Express (4)

Opt. Lett. (1)

Philos. Mag. (1)

H. C. Bolton and G. J. Troup, “The modification of the Kronig-Kramers relations under saturation conditions,” Philos. Mag. 19(159), 477–485 (1969).
[Crossref]

Phys. Lett. (1)

G. J. Troup and A. Bambini, “The use of the modified Kramers-Kronig relation in the rate equation approach of laser theory,” Phys. Lett. 45(5), 393–394 (1973).
[Crossref]

Phys. Rev. A (5)

D. D. Smith, K. Myneni, J. A. Odutola, and J. C. Diels, “Enhanced sensitivity of a passive optical cavity by an intracavity dispersive medium,” Phys. Rev. A 80(1), 011809 (2009).
[Crossref]

D. D. Smith, H. Chang, K. Myneni, and A. T. Rosenberger, “Fast-light enhancement of an optical cavity by polarization mode coupling,” Phys. Rev. A 89(5), 053804 (2014).
[Crossref]

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. A 75(5), 053807 (2007).
[Crossref]

D. D. Smith, H. Chang, L. Arissian, and J. C. Diels, “Dispersion-enhanced laser gyroscope,” Phys. Rev. A 78(5), 053824 (2008).
[Crossref]

K. Myneni, D. D. Smith, H. Chang, and H. A. Luckay, “Temperature sensitivity of the cavity scale factor enhancement for a Gaussian absorption resonance,” Phys. Rev. A 92(5), 053845 (2015).
[Crossref]

Phys. Rev. Lett. (1)

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]

Other (3)

M. O. Scully, and W. E. Lamb, Laser Physics (Westview, 1974).

A. Daniel, Steck, “Rubidium 85 D Line Data,” available online at http://steck.us/alkalidata (revision 2.1.6, 20 September 2013).

A. Daniel, Steck, “Rubidium 87 D Line Data,” available online at http://steck.us/alkalidata (revision 2.0.1, 2 May 2008).

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Figures (8)

Fig. 1
Fig. 1 (a) Spectral profile of the gain (-χ”) vs. probe frequency in the vicinity of the dip; (b) Index (χ’) in the vicinity of the dip.
Fig. 2
Fig. 2 (a) Schematic of superluminal laser; (b) Energy levels and optical fields in the gain cell; c) Energy levels and optical fields in the dip cell.
Fig. 3
Fig. 3 Flow chart illustrating the iterative algorithm used to calculate laser output frequency and amplitude.
Fig. 4
Fig. 4 Illustration of the energy levels, optical fields and decay rates for the gain cell. The Liouville equation [18,19] is the density matrix equation of evolution:
Fig. 5
Fig. 5 (a) Illustration of the energy levels, optical fields and decay rates for the dip cell; (b) Effective 3-level system in which the optical pump is equivalently modeled as a decay rate.
Fig. 6
Fig. 6 Schematic of the experimental setup for realizing a superluminal laser. See text for details.
Fig. 7
Fig. 7 (a) Experimentally observed Raman depletion; (b) numerically-calculated Raman depletion vs. δAOM.
Fig. 8
Fig. 8 (a) Frequency shift versus cavity length change for various values of Raman probe power. The dotted line represents change in DPAL output frequency vs. cavity length change for a conventional laser without Raman depletion; (b): Sensitivity enhancement factors (log scale), calculated as the ratio of the slope of Δf/ΔL with Raman depletion to the slope of Δf/ΔL without Raman depletion (dotted line in Fig. 8(a)).

Equations (18)

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ν+ φ ˙ = Ω C χ R 2 ν
E ˙ = νE 2Q χ I E 2 ν
R=1/ ( 1+ χ R 2 + ν 2 d χ R dν )
n= ( 1+ χ R ) 1 2 =1+ χ R 2 χ R 2 4 + 3 χ R 3 8 ...
n g c v g = c ω / k = (nν) ν = ν [ ν( 1+ χ R 2 ) ]=1+ χ R 2 + ν 2 d χ R dν
χ I (ν)= G g Γ g 2 2 Ω g 2 + Γ g 2 +4 ( ν ν o ) 2 + G d Γ d 2 2 Ω d 2 + Γ d 2 +4 ( ν ν o ) 2
χ R (ν)= 2 G g ( ν ν o ) Γ g 2 Ω g 2 + Γ g 2 +4 ( ν ν o ) 2 2 G d ( ν ν o ) Γ d 2 Ω d 2 + Γ d 2 +4 ( ν ν o ) 2
t ρ ˜ G = i ħ [ H ˜ ˜ G , ρ ˜ G ]+ ρ ˜ G t SOURCE + ρ ˜ G t DEPHASING
H ˜ ˜ G = ħ 2 [(i Γ 12 )|11|+(2 ω 21 i Γ 21 )|22|+[2 δ L i( Γ 31 + Γ 32 + Γ 34 )]|33| +[2 δ OP i( Γ 41 + Γ 42 + Γ 43 )]|44|+{[ Ω L |13|+ Ω OP |14| + Ω L |23|+ Ω OP |24|]+h.c.}]
ρ ˜ G t SOURCE =( Γ 21 ρ ˜ 22 + Γ 3R ρ ˜ 33 /2 + Γ 4R ρ ˜ 44 /2 )|11| +( Γ 12 ρ ˜ 11 + Γ 3R ρ ˜ 33 /2 + Γ 4R ρ ˜ 44 /2 )|22|+ Γ 43 ρ ˜ 44 |33|+ Γ 34 ρ ˜ 33 |44|
ρ ˜ G t DEPHASING =[ Γ d ρ ˜ 12 |12|+ Γ d ρ ˜ 13 |13| + Γ d ρ ˜ 14 |14|+ Γ d ρ ˜ 23 |23|+ Γ d ρ ˜ 24 |24|+ Γ d ρ ˜ 34 |34|+h.c.]
t ρ ˜ D = i ħ [ H ˜ ˜ D , ρ ˜ D ]+ ρ ˜ D t SOURCE
H ˜ ˜ D = ħ 2 {(i Γ 12 ')|11|+(2 δ RP +2 δ L i Γ 21 )|22| +(2 δ RP i Γ 3R )|33|+[ Ω L |13|+ Ω RP |23|+h.c.]}
ρ ˜ D t SOURCE =( Γ 21 ρ ˜ 22 + Γ 3R ρ ˜ 33 /2 )|11|+( Γ 12 ' ρ ˜ 11 + Γ 3R ρ ˜ 33 /2 )|22|
χ G85 = [ ( ρ ˜ 31 ) ħc n G I SAT(13) Ω L ( Γ 31 2 ) 2 ] 85 + [ ( ρ ˜ 32 ) ħc n G I SAT(23) Ω L ( Γ 32 2 ) 2 ] 85
χ G =0.72 χ G85 +0.28 χ G87
χ D = [ ħc n D I SAT(13) Ω L ( Γ 3R 2 ) 2 ρ ˜ 31 ] 85
χ EFF = L G L χ G + L D L χ D

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