Abstract

Strong enhancement of group refractive index in a dense buffered atomic vapor is recorded using a technique of reflection from a low-finesse Fabry–Perot cavity filled with dense atomic vapor allowing the retrieval of a dispersion curve for the hyperfine structure of Rb D2 line buffered by a high-density Cs vapor. Oscillations of the recorded signal resulting from interference of beams reflected from the front and rear windows of the cell appearing with the laser frequency scanning across the resonance allow easy reconstruction of the dispersion curve. Contribution from concomitant interconnected processes, in particular, the determinative role of radiation channeling in enhancement of the resonator Q-factor, is analyzed.

© 2017 Optical Society of America

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References

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  29. S. Shmavonyan, A. Khanbekyan, A. Gogyan, M. Movsisyan, and A. Papoyan, “Selective reflection of light from Rb2 molecular vapor,” J. Mol. Spectrosc. 313, 14–18 (2015).
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    [Crossref]

2016 (2)

S. Jennewein, Y. R. P. Sortais, J. J. Greffet, and A. Browaeys, “Propagation of light through small clouds of cold interacting atoms,” Phys. Rev. A 94, 053828 (2016).

J. H. D. Munns, C. Qiu, P. M. Ledingham, I. A. Walmsley, J. Nunn, and D. J. Saunders, “In situ characterization of an optically thick atom-filled cavity,” Phys. Rev. A 93, 013858 (2016).

2015 (2)

S. Shmavonyan, A. Khanbekyan, A. Gogyan, M. Movsisyan, and A. Papoyan, “Selective reflection of light from Rb2 molecular vapor,” J. Mol. Spectrosc. 313, 14–18 (2015).
[Crossref]

A. I. Parkhomenko and A. M. Shalagin, “Transversely diode-pumped alkali metal vapour laser,” Quantum Electron. 45, 797–806 (2015).
[Crossref]

2013 (2)

S. Amaran, R. Kosloff, M. Tomza, R. Moszynski, L. Rybak, L. Levin, Z. Amitay, and C. P. Koch, “Femtosecond two-photon photoassociation of hot magnesium atoms: a quantum dynamical study using thermal random phase wavefunctions,” J. Chem. Phys. 139, 164124 (2013).

Y. A. Ilyushin, “Coherent backscattering enhancement in refracting media: diffusion approximation,” J. Opt. Soc. Am. A 30, 1305–1309 (2013).
[Crossref]

2012 (1)

J. Keaveney, I. G. Hughes, A. Sargsyan, D. Sarkisyan, and C. S. Adams, “Maximal refraction and superluminal propagation in a gaseous nanolayer,” Phys. Rev. Lett. 109, 233001 (2012).

2011 (1)

M. Movsisyan, S. Shmavonyan, and A. Papoyan, “Selective reflection studies of molecular cesium vapor,” Proc. SPIE 7998, 79980U (2011).

2010 (2)

2009 (2)

P. Siddons, N. C. Bell, Y. Cai, C. S. Adams, and I. G. Hughes, “A gigahertz-bandwidth atomic probe based on the slow-light Faraday effect,” Nat. Photonics 3, 225–229 (2009).
[Crossref]

P. Siddons, C. S. Adams, and I. G. Hughes, “Off-resonance absorption and dispersion in a Doppler-broadened medium,” J. Phys. B 42, 175004 (2009).

2007 (2)

M. A. Rosenberry, J. P. Reyes, D. Tupa, and T. J. Gay, “Radiation trapping in rubidium optical pumping at low buffer-gas pressures,” Phys. Rev. A 75, 023401 (2007).

M. Shuker, O. Firstenberg, R. Pugatch, A. Ben-Kish, A. Ron, and N. Davidson, “Angular dependence of Dicke-narrowed electromagnetically induced transparency resonances,” Phys. Rev. A 76, 023813 (2007).

2006 (1)

A. Badalyan, V. Chaltykyan, G. Grigoryan, A. Papoyan, S. Shmavonyan, and M. Movsessian, “Selective reflection by atomic vapor: experiments and self-consistent theory,” Eur. Phys. J. D 37, 157–162 (2006).
[Crossref]

2005 (1)

I. M. Savukov and M. V. Romalis, “Effects of spin-exchange collisions in a high-density alkali-metal vapor in low magnetic fields,” Phys. Rev. A 71, 023405 (2005).

2004 (1)

D. Sarkisyan, T. Varzhapetyan, A. Sarkisyan, Y. Malakyan, A. Papoyan, A. Lezama, D. Bloch, and M. Ducloy, “Spectroscopy in an extremely thin vapor cell: comparing the cell-length dependence in fluorescence and in absorption techniques,” Phys. Rev. A 69, 065802 (2004).

2003 (1)

E. E. Mikhailov, Y. V. Rostovtsev, and G. R. Welch, “Group velocity study in hot 87Rb vapour with buffer gas,” J. Mod. Opt. 50, 2645–2654 (2003).

2001 (1)

T. A. Vartanyan and A. Weis, “Origin of the “blueshift” in selective reflection spectroscopy and its partial compensation by the local-field correction,” Phys. Rev. A 63, 063813 (2001).

1999 (1)

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
[Crossref]

1998 (1)

A. V. Papoyan, G. S. Sarkisyan, and S. V. Shmavonyan, “Selective reflection of light from dense sodium vapors,” Opt. Spectrosc. 85, 649–652 (1998).

1997 (3)

H. van Kampen, A. V. Papoyan, V. A. Sautenkov, P. H. A. M. Castermans, E. R. Eliel, and J. P. Woerdman, “Observation of collisional modification of the Zeeman effect in a high-density atomic vapor,” Phys. Rev. A 56, 310–315 (1997).
[Crossref]

S. Brandt, A. Nagel, R. Wynands, and D. Meschede, “Buffer-gas-induced linewidth reduction of coherent dark resonances to below 50  Hz,” Phys. Rev. A 56, R1063–R1067 (1997).
[Crossref]

M. D. Rotondaro and G. P. Perram, “Collisional broadening and shift of rubidium D1 and D2 lines by rare gases, H2, D2, N2, CH4 and CF4,” J. Quant. Spectrosc. Radiat. Transf. 57, 497–507 (1997).
[Crossref]

1996 (2)

A. S. Zibrov, M. D. Lukin, L. Hollberg, D. E. Nikonov, M. O. Scully, H. G. Robinson, and V. L. Velichansky, “Experimental demonstration of enhanced index of refraction via quantum coherence in Rb,” Phys. Rev. Lett. 76, 3935–3938 (1996).
[Crossref]

J. Guo, J. Cooper, and A. Gallagher, “Selective reflection from a dense atomic vapor,” Phys. Rev. A 53, 1130–1138 (1996).
[Crossref]

1995 (1)

T. A. Vartanyan and D. L. Lin, “Enhanced selective reflection from a thin layer of dilute gaseous medium,” Phys. Rev. A 51, 1959–1964 (1995).
[Crossref]

1984 (1)

C. B. Alcock, V. P. Itkin, and M. K. Horrigan, “Vapor pressure of the metallic elements,” Can. Metall. Quart. 23, 309–313 (1984).
[Crossref]

1953 (1)

R. H. Dicke, “The effect of collisions upon the Doppler width of spectral lines,” Phys. Rev. 89, 472–473 (1953).
[Crossref]

1887 (1)

F. M. Raoult, “Loi générale des tensions de vapeur des dissolvants,” C. R. Acad. Sci. 104, 1430–1433 (1887).

Adams, C. S.

J. Keaveney, I. G. Hughes, A. Sargsyan, D. Sarkisyan, and C. S. Adams, “Maximal refraction and superluminal propagation in a gaseous nanolayer,” Phys. Rev. Lett. 109, 233001 (2012).

P. Siddons, N. C. Bell, Y. Cai, C. S. Adams, and I. G. Hughes, “A gigahertz-bandwidth atomic probe based on the slow-light Faraday effect,” Nat. Photonics 3, 225–229 (2009).
[Crossref]

P. Siddons, C. S. Adams, and I. G. Hughes, “Off-resonance absorption and dispersion in a Doppler-broadened medium,” J. Phys. B 42, 175004 (2009).

Alcock, C. B.

C. B. Alcock, V. P. Itkin, and M. K. Horrigan, “Vapor pressure of the metallic elements,” Can. Metall. Quart. 23, 309–313 (1984).
[Crossref]

Amaran, S.

S. Amaran, R. Kosloff, M. Tomza, R. Moszynski, L. Rybak, L. Levin, Z. Amitay, and C. P. Koch, “Femtosecond two-photon photoassociation of hot magnesium atoms: a quantum dynamical study using thermal random phase wavefunctions,” J. Chem. Phys. 139, 164124 (2013).

Amitay, Z.

S. Amaran, R. Kosloff, M. Tomza, R. Moszynski, L. Rybak, L. Levin, Z. Amitay, and C. P. Koch, “Femtosecond two-photon photoassociation of hot magnesium atoms: a quantum dynamical study using thermal random phase wavefunctions,” J. Chem. Phys. 139, 164124 (2013).

Arnold, A. S.

Badalyan, A.

A. Badalyan, V. Chaltykyan, G. Grigoryan, A. Papoyan, S. Shmavonyan, and M. Movsessian, “Selective reflection by atomic vapor: experiments and self-consistent theory,” Eur. Phys. J. D 37, 157–162 (2006).
[Crossref]

Bell, N. C.

P. Siddons, N. C. Bell, Y. Cai, C. S. Adams, and I. G. Hughes, “A gigahertz-bandwidth atomic probe based on the slow-light Faraday effect,” Nat. Photonics 3, 225–229 (2009).
[Crossref]

Ben-Kish, A.

M. Shuker, O. Firstenberg, R. Pugatch, A. Ben-Kish, A. Ron, and N. Davidson, “Angular dependence of Dicke-narrowed electromagnetically induced transparency resonances,” Phys. Rev. A 76, 023813 (2007).

Bloch, D.

D. Sarkisyan, T. Varzhapetyan, A. Sarkisyan, Y. Malakyan, A. Papoyan, A. Lezama, D. Bloch, and M. Ducloy, “Spectroscopy in an extremely thin vapor cell: comparing the cell-length dependence in fluorescence and in absorption techniques,” Phys. Rev. A 69, 065802 (2004).

Brandt, S.

S. Brandt, A. Nagel, R. Wynands, and D. Meschede, “Buffer-gas-induced linewidth reduction of coherent dark resonances to below 50  Hz,” Phys. Rev. A 56, R1063–R1067 (1997).
[Crossref]

Browaeys, A.

S. Jennewein, Y. R. P. Sortais, J. J. Greffet, and A. Browaeys, “Propagation of light through small clouds of cold interacting atoms,” Phys. Rev. A 94, 053828 (2016).

Cai, Y.

P. Siddons, N. C. Bell, Y. Cai, C. S. Adams, and I. G. Hughes, “A gigahertz-bandwidth atomic probe based on the slow-light Faraday effect,” Nat. Photonics 3, 225–229 (2009).
[Crossref]

Castermans, P. H. A. M.

H. van Kampen, A. V. Papoyan, V. A. Sautenkov, P. H. A. M. Castermans, E. R. Eliel, and J. P. Woerdman, “Observation of collisional modification of the Zeeman effect in a high-density atomic vapor,” Phys. Rev. A 56, 310–315 (1997).
[Crossref]

Chaltykyan, V.

A. Badalyan, V. Chaltykyan, G. Grigoryan, A. Papoyan, S. Shmavonyan, and M. Movsessian, “Selective reflection by atomic vapor: experiments and self-consistent theory,” Eur. Phys. J. D 37, 157–162 (2006).
[Crossref]

Cooper, J.

J. Guo, J. Cooper, and A. Gallagher, “Selective reflection from a dense atomic vapor,” Phys. Rev. A 53, 1130–1138 (1996).
[Crossref]

Davidson, N.

M. Shuker, O. Firstenberg, R. Pugatch, A. Ben-Kish, A. Ron, and N. Davidson, “Angular dependence of Dicke-narrowed electromagnetically induced transparency resonances,” Phys. Rev. A 76, 023813 (2007).

Dicke, R. H.

R. H. Dicke, “The effect of collisions upon the Doppler width of spectral lines,” Phys. Rev. 89, 472–473 (1953).
[Crossref]

Ducloy, M.

D. Sarkisyan, T. Varzhapetyan, A. Sarkisyan, Y. Malakyan, A. Papoyan, A. Lezama, D. Bloch, and M. Ducloy, “Spectroscopy in an extremely thin vapor cell: comparing the cell-length dependence in fluorescence and in absorption techniques,” Phys. Rev. A 69, 065802 (2004).

Eliel, E. R.

H. van Kampen, A. V. Papoyan, V. A. Sautenkov, P. H. A. M. Castermans, E. R. Eliel, and J. P. Woerdman, “Observation of collisional modification of the Zeeman effect in a high-density atomic vapor,” Phys. Rev. A 56, 310–315 (1997).
[Crossref]

Firstenberg, O.

M. Shuker, O. Firstenberg, R. Pugatch, A. Ben-Kish, A. Ron, and N. Davidson, “Angular dependence of Dicke-narrowed electromagnetically induced transparency resonances,” Phys. Rev. A 76, 023813 (2007).

Franke-Arnold, S.

Fry, E. S.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
[Crossref]

Gallagher, A.

J. Guo, J. Cooper, and A. Gallagher, “Selective reflection from a dense atomic vapor,” Phys. Rev. A 53, 1130–1138 (1996).
[Crossref]

Gay, T. J.

M. A. Rosenberry, J. P. Reyes, D. Tupa, and T. J. Gay, “Radiation trapping in rubidium optical pumping at low buffer-gas pressures,” Phys. Rev. A 75, 023401 (2007).

Gogyan, A.

S. Shmavonyan, A. Khanbekyan, A. Gogyan, M. Movsisyan, and A. Papoyan, “Selective reflection of light from Rb2 molecular vapor,” J. Mol. Spectrosc. 313, 14–18 (2015).
[Crossref]

Greffet, J. J.

S. Jennewein, Y. R. P. Sortais, J. J. Greffet, and A. Browaeys, “Propagation of light through small clouds of cold interacting atoms,” Phys. Rev. A 94, 053828 (2016).

Grigoryan, G.

A. Badalyan, V. Chaltykyan, G. Grigoryan, A. Papoyan, S. Shmavonyan, and M. Movsessian, “Selective reflection by atomic vapor: experiments and self-consistent theory,” Eur. Phys. J. D 37, 157–162 (2006).
[Crossref]

Guo, J.

J. Guo, J. Cooper, and A. Gallagher, “Selective reflection from a dense atomic vapor,” Phys. Rev. A 53, 1130–1138 (1996).
[Crossref]

Hollberg, L.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
[Crossref]

A. S. Zibrov, M. D. Lukin, L. Hollberg, D. E. Nikonov, M. O. Scully, H. G. Robinson, and V. L. Velichansky, “Experimental demonstration of enhanced index of refraction via quantum coherence in Rb,” Phys. Rev. Lett. 76, 3935–3938 (1996).
[Crossref]

Horrigan, M. K.

C. B. Alcock, V. P. Itkin, and M. K. Horrigan, “Vapor pressure of the metallic elements,” Can. Metall. Quart. 23, 309–313 (1984).
[Crossref]

Hughes, I. G.

J. Keaveney, I. G. Hughes, A. Sargsyan, D. Sarkisyan, and C. S. Adams, “Maximal refraction and superluminal propagation in a gaseous nanolayer,” Phys. Rev. Lett. 109, 233001 (2012).

P. Siddons, N. C. Bell, Y. Cai, C. S. Adams, and I. G. Hughes, “A gigahertz-bandwidth atomic probe based on the slow-light Faraday effect,” Nat. Photonics 3, 225–229 (2009).
[Crossref]

P. Siddons, C. S. Adams, and I. G. Hughes, “Off-resonance absorption and dispersion in a Doppler-broadened medium,” J. Phys. B 42, 175004 (2009).

Ilyushin, Y. A.

Itkin, V. P.

C. B. Alcock, V. P. Itkin, and M. K. Horrigan, “Vapor pressure of the metallic elements,” Can. Metall. Quart. 23, 309–313 (1984).
[Crossref]

Jennewein, S.

S. Jennewein, Y. R. P. Sortais, J. J. Greffet, and A. Browaeys, “Propagation of light through small clouds of cold interacting atoms,” Phys. Rev. A 94, 053828 (2016).

Kash, M. M.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
[Crossref]

Keaveney, J.

J. Keaveney, I. G. Hughes, A. Sargsyan, D. Sarkisyan, and C. S. Adams, “Maximal refraction and superluminal propagation in a gaseous nanolayer,” Phys. Rev. Lett. 109, 233001 (2012).

Khanbekyan, A.

S. Shmavonyan, A. Khanbekyan, A. Gogyan, M. Movsisyan, and A. Papoyan, “Selective reflection of light from Rb2 molecular vapor,” J. Mol. Spectrosc. 313, 14–18 (2015).
[Crossref]

Koch, C. P.

S. Amaran, R. Kosloff, M. Tomza, R. Moszynski, L. Rybak, L. Levin, Z. Amitay, and C. P. Koch, “Femtosecond two-photon photoassociation of hot magnesium atoms: a quantum dynamical study using thermal random phase wavefunctions,” J. Chem. Phys. 139, 164124 (2013).

Kosloff, R.

S. Amaran, R. Kosloff, M. Tomza, R. Moszynski, L. Rybak, L. Levin, Z. Amitay, and C. P. Koch, “Femtosecond two-photon photoassociation of hot magnesium atoms: a quantum dynamical study using thermal random phase wavefunctions,” J. Chem. Phys. 139, 164124 (2013).

Krupke, W. F.

Ledingham, P. M.

J. H. D. Munns, C. Qiu, P. M. Ledingham, I. A. Walmsley, J. Nunn, and D. J. Saunders, “In situ characterization of an optically thick atom-filled cavity,” Phys. Rev. A 93, 013858 (2016).

Levin, L.

S. Amaran, R. Kosloff, M. Tomza, R. Moszynski, L. Rybak, L. Levin, Z. Amitay, and C. P. Koch, “Femtosecond two-photon photoassociation of hot magnesium atoms: a quantum dynamical study using thermal random phase wavefunctions,” J. Chem. Phys. 139, 164124 (2013).

Lezama, A.

D. Sarkisyan, T. Varzhapetyan, A. Sarkisyan, Y. Malakyan, A. Papoyan, A. Lezama, D. Bloch, and M. Ducloy, “Spectroscopy in an extremely thin vapor cell: comparing the cell-length dependence in fluorescence and in absorption techniques,” Phys. Rev. A 69, 065802 (2004).

Lin, D. L.

T. A. Vartanyan and D. L. Lin, “Enhanced selective reflection from a thin layer of dilute gaseous medium,” Phys. Rev. A 51, 1959–1964 (1995).
[Crossref]

Lukin, M. D.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
[Crossref]

A. S. Zibrov, M. D. Lukin, L. Hollberg, D. E. Nikonov, M. O. Scully, H. G. Robinson, and V. L. Velichansky, “Experimental demonstration of enhanced index of refraction via quantum coherence in Rb,” Phys. Rev. Lett. 76, 3935–3938 (1996).
[Crossref]

Malakyan, Y.

D. Sarkisyan, T. Varzhapetyan, A. Sarkisyan, Y. Malakyan, A. Papoyan, A. Lezama, D. Bloch, and M. Ducloy, “Spectroscopy in an extremely thin vapor cell: comparing the cell-length dependence in fluorescence and in absorption techniques,” Phys. Rev. A 69, 065802 (2004).

Meschede, D.

S. Brandt, A. Nagel, R. Wynands, and D. Meschede, “Buffer-gas-induced linewidth reduction of coherent dark resonances to below 50  Hz,” Phys. Rev. A 56, R1063–R1067 (1997).
[Crossref]

Mikhailov, E. E.

E. E. Mikhailov, Y. V. Rostovtsev, and G. R. Welch, “Group velocity study in hot 87Rb vapour with buffer gas,” J. Mod. Opt. 50, 2645–2654 (2003).

Molisch, A.

A. Molisch and B. P. Oehry, Radiation Trapping in Atomic Vapours (Clarendon, 1998).

Moszynski, R.

S. Amaran, R. Kosloff, M. Tomza, R. Moszynski, L. Rybak, L. Levin, Z. Amitay, and C. P. Koch, “Femtosecond two-photon photoassociation of hot magnesium atoms: a quantum dynamical study using thermal random phase wavefunctions,” J. Chem. Phys. 139, 164124 (2013).

Movsessian, M.

A. Badalyan, V. Chaltykyan, G. Grigoryan, A. Papoyan, S. Shmavonyan, and M. Movsessian, “Selective reflection by atomic vapor: experiments and self-consistent theory,” Eur. Phys. J. D 37, 157–162 (2006).
[Crossref]

Movsisyan, M.

S. Shmavonyan, A. Khanbekyan, A. Gogyan, M. Movsisyan, and A. Papoyan, “Selective reflection of light from Rb2 molecular vapor,” J. Mol. Spectrosc. 313, 14–18 (2015).
[Crossref]

M. Movsisyan, S. Shmavonyan, and A. Papoyan, “Selective reflection studies of molecular cesium vapor,” Proc. SPIE 7998, 79980U (2011).

Munns, J. H. D.

J. H. D. Munns, C. Qiu, P. M. Ledingham, I. A. Walmsley, J. Nunn, and D. J. Saunders, “In situ characterization of an optically thick atom-filled cavity,” Phys. Rev. A 93, 013858 (2016).

Nagel, A.

S. Brandt, A. Nagel, R. Wynands, and D. Meschede, “Buffer-gas-induced linewidth reduction of coherent dark resonances to below 50  Hz,” Phys. Rev. A 56, R1063–R1067 (1997).
[Crossref]

Nikonov, D. E.

A. S. Zibrov, M. D. Lukin, L. Hollberg, D. E. Nikonov, M. O. Scully, H. G. Robinson, and V. L. Velichansky, “Experimental demonstration of enhanced index of refraction via quantum coherence in Rb,” Phys. Rev. Lett. 76, 3935–3938 (1996).
[Crossref]

Nunn, J.

J. H. D. Munns, C. Qiu, P. M. Ledingham, I. A. Walmsley, J. Nunn, and D. J. Saunders, “In situ characterization of an optically thick atom-filled cavity,” Phys. Rev. A 93, 013858 (2016).

Oehry, B. P.

A. Molisch and B. P. Oehry, Radiation Trapping in Atomic Vapours (Clarendon, 1998).

Papoyan, A.

S. Shmavonyan, A. Khanbekyan, A. Gogyan, M. Movsisyan, and A. Papoyan, “Selective reflection of light from Rb2 molecular vapor,” J. Mol. Spectrosc. 313, 14–18 (2015).
[Crossref]

M. Movsisyan, S. Shmavonyan, and A. Papoyan, “Selective reflection studies of molecular cesium vapor,” Proc. SPIE 7998, 79980U (2011).

A. Badalyan, V. Chaltykyan, G. Grigoryan, A. Papoyan, S. Shmavonyan, and M. Movsessian, “Selective reflection by atomic vapor: experiments and self-consistent theory,” Eur. Phys. J. D 37, 157–162 (2006).
[Crossref]

D. Sarkisyan, T. Varzhapetyan, A. Sarkisyan, Y. Malakyan, A. Papoyan, A. Lezama, D. Bloch, and M. Ducloy, “Spectroscopy in an extremely thin vapor cell: comparing the cell-length dependence in fluorescence and in absorption techniques,” Phys. Rev. A 69, 065802 (2004).

Papoyan, A. V.

A. V. Papoyan, G. S. Sarkisyan, and S. V. Shmavonyan, “Selective reflection of light from dense sodium vapors,” Opt. Spectrosc. 85, 649–652 (1998).

H. van Kampen, A. V. Papoyan, V. A. Sautenkov, P. H. A. M. Castermans, E. R. Eliel, and J. P. Woerdman, “Observation of collisional modification of the Zeeman effect in a high-density atomic vapor,” Phys. Rev. A 56, 310–315 (1997).
[Crossref]

Parkhomenko, A. I.

A. I. Parkhomenko and A. M. Shalagin, “Transversely diode-pumped alkali metal vapour laser,” Quantum Electron. 45, 797–806 (2015).
[Crossref]

Perram, G. P.

M. D. Rotondaro and G. P. Perram, “Collisional broadening and shift of rubidium D1 and D2 lines by rare gases, H2, D2, N2, CH4 and CF4,” J. Quant. Spectrosc. Radiat. Transf. 57, 497–507 (1997).
[Crossref]

Pugatch, R.

M. Shuker, O. Firstenberg, R. Pugatch, A. Ben-Kish, A. Ron, and N. Davidson, “Angular dependence of Dicke-narrowed electromagnetically induced transparency resonances,” Phys. Rev. A 76, 023813 (2007).

Qiu, C.

J. H. D. Munns, C. Qiu, P. M. Ledingham, I. A. Walmsley, J. Nunn, and D. J. Saunders, “In situ characterization of an optically thick atom-filled cavity,” Phys. Rev. A 93, 013858 (2016).

Raoult, F. M.

F. M. Raoult, “Loi générale des tensions de vapeur des dissolvants,” C. R. Acad. Sci. 104, 1430–1433 (1887).

Reyes, J. P.

M. A. Rosenberry, J. P. Reyes, D. Tupa, and T. J. Gay, “Radiation trapping in rubidium optical pumping at low buffer-gas pressures,” Phys. Rev. A 75, 023401 (2007).

Riis, E.

Robinson, H. G.

A. S. Zibrov, M. D. Lukin, L. Hollberg, D. E. Nikonov, M. O. Scully, H. G. Robinson, and V. L. Velichansky, “Experimental demonstration of enhanced index of refraction via quantum coherence in Rb,” Phys. Rev. Lett. 76, 3935–3938 (1996).
[Crossref]

Romalis, M. V.

I. M. Savukov and M. V. Romalis, “Effects of spin-exchange collisions in a high-density alkali-metal vapor in low magnetic fields,” Phys. Rev. A 71, 023405 (2005).

Ron, A.

M. Shuker, O. Firstenberg, R. Pugatch, A. Ben-Kish, A. Ron, and N. Davidson, “Angular dependence of Dicke-narrowed electromagnetically induced transparency resonances,” Phys. Rev. A 76, 023813 (2007).

Rosenberry, M. A.

M. A. Rosenberry, J. P. Reyes, D. Tupa, and T. J. Gay, “Radiation trapping in rubidium optical pumping at low buffer-gas pressures,” Phys. Rev. A 75, 023401 (2007).

Rostovtsev, Y.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
[Crossref]

Rostovtsev, Y. V.

E. E. Mikhailov, Y. V. Rostovtsev, and G. R. Welch, “Group velocity study in hot 87Rb vapour with buffer gas,” J. Mod. Opt. 50, 2645–2654 (2003).

Rotondaro, M. D.

M. D. Rotondaro and G. P. Perram, “Collisional broadening and shift of rubidium D1 and D2 lines by rare gases, H2, D2, N2, CH4 and CF4,” J. Quant. Spectrosc. Radiat. Transf. 57, 497–507 (1997).
[Crossref]

Rybak, L.

S. Amaran, R. Kosloff, M. Tomza, R. Moszynski, L. Rybak, L. Levin, Z. Amitay, and C. P. Koch, “Femtosecond two-photon photoassociation of hot magnesium atoms: a quantum dynamical study using thermal random phase wavefunctions,” J. Chem. Phys. 139, 164124 (2013).

Sargsyan, A.

J. Keaveney, I. G. Hughes, A. Sargsyan, D. Sarkisyan, and C. S. Adams, “Maximal refraction and superluminal propagation in a gaseous nanolayer,” Phys. Rev. Lett. 109, 233001 (2012).

Sarkisyan, A.

D. Sarkisyan, T. Varzhapetyan, A. Sarkisyan, Y. Malakyan, A. Papoyan, A. Lezama, D. Bloch, and M. Ducloy, “Spectroscopy in an extremely thin vapor cell: comparing the cell-length dependence in fluorescence and in absorption techniques,” Phys. Rev. A 69, 065802 (2004).

Sarkisyan, D.

J. Keaveney, I. G. Hughes, A. Sargsyan, D. Sarkisyan, and C. S. Adams, “Maximal refraction and superluminal propagation in a gaseous nanolayer,” Phys. Rev. Lett. 109, 233001 (2012).

D. Sarkisyan, T. Varzhapetyan, A. Sarkisyan, Y. Malakyan, A. Papoyan, A. Lezama, D. Bloch, and M. Ducloy, “Spectroscopy in an extremely thin vapor cell: comparing the cell-length dependence in fluorescence and in absorption techniques,” Phys. Rev. A 69, 065802 (2004).

Sarkisyan, G. S.

A. V. Papoyan, G. S. Sarkisyan, and S. V. Shmavonyan, “Selective reflection of light from dense sodium vapors,” Opt. Spectrosc. 85, 649–652 (1998).

Saunders, D. J.

J. H. D. Munns, C. Qiu, P. M. Ledingham, I. A. Walmsley, J. Nunn, and D. J. Saunders, “In situ characterization of an optically thick atom-filled cavity,” Phys. Rev. A 93, 013858 (2016).

Sautenkov, V. A.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
[Crossref]

H. van Kampen, A. V. Papoyan, V. A. Sautenkov, P. H. A. M. Castermans, E. R. Eliel, and J. P. Woerdman, “Observation of collisional modification of the Zeeman effect in a high-density atomic vapor,” Phys. Rev. A 56, 310–315 (1997).
[Crossref]

Savukov, I. M.

I. M. Savukov and M. V. Romalis, “Effects of spin-exchange collisions in a high-density alkali-metal vapor in low magnetic fields,” Phys. Rev. A 71, 023405 (2005).

Scully, M. O.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
[Crossref]

A. S. Zibrov, M. D. Lukin, L. Hollberg, D. E. Nikonov, M. O. Scully, H. G. Robinson, and V. L. Velichansky, “Experimental demonstration of enhanced index of refraction via quantum coherence in Rb,” Phys. Rev. Lett. 76, 3935–3938 (1996).
[Crossref]

Shalagin, A. M.

A. I. Parkhomenko and A. M. Shalagin, “Transversely diode-pumped alkali metal vapour laser,” Quantum Electron. 45, 797–806 (2015).
[Crossref]

Shmavonyan, S.

S. Shmavonyan, A. Khanbekyan, A. Gogyan, M. Movsisyan, and A. Papoyan, “Selective reflection of light from Rb2 molecular vapor,” J. Mol. Spectrosc. 313, 14–18 (2015).
[Crossref]

M. Movsisyan, S. Shmavonyan, and A. Papoyan, “Selective reflection studies of molecular cesium vapor,” Proc. SPIE 7998, 79980U (2011).

A. Badalyan, V. Chaltykyan, G. Grigoryan, A. Papoyan, S. Shmavonyan, and M. Movsessian, “Selective reflection by atomic vapor: experiments and self-consistent theory,” Eur. Phys. J. D 37, 157–162 (2006).
[Crossref]

Shmavonyan, S. V.

A. V. Papoyan, G. S. Sarkisyan, and S. V. Shmavonyan, “Selective reflection of light from dense sodium vapors,” Opt. Spectrosc. 85, 649–652 (1998).

Shuker, M.

M. Shuker, O. Firstenberg, R. Pugatch, A. Ben-Kish, A. Ron, and N. Davidson, “Angular dependence of Dicke-narrowed electromagnetically induced transparency resonances,” Phys. Rev. A 76, 023813 (2007).

Siddons, P.

P. Siddons, C. S. Adams, and I. G. Hughes, “Off-resonance absorption and dispersion in a Doppler-broadened medium,” J. Phys. B 42, 175004 (2009).

P. Siddons, N. C. Bell, Y. Cai, C. S. Adams, and I. G. Hughes, “A gigahertz-bandwidth atomic probe based on the slow-light Faraday effect,” Nat. Photonics 3, 225–229 (2009).
[Crossref]

Sortais, Y. R. P.

S. Jennewein, Y. R. P. Sortais, J. J. Greffet, and A. Browaeys, “Propagation of light through small clouds of cold interacting atoms,” Phys. Rev. A 94, 053828 (2016).

Tomza, M.

S. Amaran, R. Kosloff, M. Tomza, R. Moszynski, L. Rybak, L. Levin, Z. Amitay, and C. P. Koch, “Femtosecond two-photon photoassociation of hot magnesium atoms: a quantum dynamical study using thermal random phase wavefunctions,” J. Chem. Phys. 139, 164124 (2013).

Tupa, D.

M. A. Rosenberry, J. P. Reyes, D. Tupa, and T. J. Gay, “Radiation trapping in rubidium optical pumping at low buffer-gas pressures,” Phys. Rev. A 75, 023401 (2007).

van Kampen, H.

H. van Kampen, A. V. Papoyan, V. A. Sautenkov, P. H. A. M. Castermans, E. R. Eliel, and J. P. Woerdman, “Observation of collisional modification of the Zeeman effect in a high-density atomic vapor,” Phys. Rev. A 56, 310–315 (1997).
[Crossref]

Vartanyan, T. A.

T. A. Vartanyan and A. Weis, “Origin of the “blueshift” in selective reflection spectroscopy and its partial compensation by the local-field correction,” Phys. Rev. A 63, 063813 (2001).

T. A. Vartanyan and D. L. Lin, “Enhanced selective reflection from a thin layer of dilute gaseous medium,” Phys. Rev. A 51, 1959–1964 (1995).
[Crossref]

Varzhapetyan, T.

D. Sarkisyan, T. Varzhapetyan, A. Sarkisyan, Y. Malakyan, A. Papoyan, A. Lezama, D. Bloch, and M. Ducloy, “Spectroscopy in an extremely thin vapor cell: comparing the cell-length dependence in fluorescence and in absorption techniques,” Phys. Rev. A 69, 065802 (2004).

Velichansky, V. L.

A. S. Zibrov, M. D. Lukin, L. Hollberg, D. E. Nikonov, M. O. Scully, H. G. Robinson, and V. L. Velichansky, “Experimental demonstration of enhanced index of refraction via quantum coherence in Rb,” Phys. Rev. Lett. 76, 3935–3938 (1996).
[Crossref]

Vernier, A.

Walmsley, I. A.

J. H. D. Munns, C. Qiu, P. M. Ledingham, I. A. Walmsley, J. Nunn, and D. J. Saunders, “In situ characterization of an optically thick atom-filled cavity,” Phys. Rev. A 93, 013858 (2016).

Weis, A.

T. A. Vartanyan and A. Weis, “Origin of the “blueshift” in selective reflection spectroscopy and its partial compensation by the local-field correction,” Phys. Rev. A 63, 063813 (2001).

Welch, G. R.

E. E. Mikhailov, Y. V. Rostovtsev, and G. R. Welch, “Group velocity study in hot 87Rb vapour with buffer gas,” J. Mod. Opt. 50, 2645–2654 (2003).

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
[Crossref]

Woerdman, J. P.

H. van Kampen, A. V. Papoyan, V. A. Sautenkov, P. H. A. M. Castermans, E. R. Eliel, and J. P. Woerdman, “Observation of collisional modification of the Zeeman effect in a high-density atomic vapor,” Phys. Rev. A 56, 310–315 (1997).
[Crossref]

Wynands, R.

S. Brandt, A. Nagel, R. Wynands, and D. Meschede, “Buffer-gas-induced linewidth reduction of coherent dark resonances to below 50  Hz,” Phys. Rev. A 56, R1063–R1067 (1997).
[Crossref]

Zibrov, A. S.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
[Crossref]

A. S. Zibrov, M. D. Lukin, L. Hollberg, D. E. Nikonov, M. O. Scully, H. G. Robinson, and V. L. Velichansky, “Experimental demonstration of enhanced index of refraction via quantum coherence in Rb,” Phys. Rev. Lett. 76, 3935–3938 (1996).
[Crossref]

Zweiback, J.

C. R. Acad. Sci. (1)

F. M. Raoult, “Loi générale des tensions de vapeur des dissolvants,” C. R. Acad. Sci. 104, 1430–1433 (1887).

Can. Metall. Quart. (1)

C. B. Alcock, V. P. Itkin, and M. K. Horrigan, “Vapor pressure of the metallic elements,” Can. Metall. Quart. 23, 309–313 (1984).
[Crossref]

Eur. Phys. J. D (1)

A. Badalyan, V. Chaltykyan, G. Grigoryan, A. Papoyan, S. Shmavonyan, and M. Movsessian, “Selective reflection by atomic vapor: experiments and self-consistent theory,” Eur. Phys. J. D 37, 157–162 (2006).
[Crossref]

J. Chem. Phys. (1)

S. Amaran, R. Kosloff, M. Tomza, R. Moszynski, L. Rybak, L. Levin, Z. Amitay, and C. P. Koch, “Femtosecond two-photon photoassociation of hot magnesium atoms: a quantum dynamical study using thermal random phase wavefunctions,” J. Chem. Phys. 139, 164124 (2013).

J. Mod. Opt. (1)

E. E. Mikhailov, Y. V. Rostovtsev, and G. R. Welch, “Group velocity study in hot 87Rb vapour with buffer gas,” J. Mod. Opt. 50, 2645–2654 (2003).

J. Mol. Spectrosc. (1)

S. Shmavonyan, A. Khanbekyan, A. Gogyan, M. Movsisyan, and A. Papoyan, “Selective reflection of light from Rb2 molecular vapor,” J. Mol. Spectrosc. 313, 14–18 (2015).
[Crossref]

J. Opt. Soc. Am. A (1)

J. Phys. B (1)

P. Siddons, C. S. Adams, and I. G. Hughes, “Off-resonance absorption and dispersion in a Doppler-broadened medium,” J. Phys. B 42, 175004 (2009).

J. Quant. Spectrosc. Radiat. Transf. (1)

M. D. Rotondaro and G. P. Perram, “Collisional broadening and shift of rubidium D1 and D2 lines by rare gases, H2, D2, N2, CH4 and CF4,” J. Quant. Spectrosc. Radiat. Transf. 57, 497–507 (1997).
[Crossref]

Nat. Photonics (1)

P. Siddons, N. C. Bell, Y. Cai, C. S. Adams, and I. G. Hughes, “A gigahertz-bandwidth atomic probe based on the slow-light Faraday effect,” Nat. Photonics 3, 225–229 (2009).
[Crossref]

Opt. Express (2)

Opt. Spectrosc. (1)

A. V. Papoyan, G. S. Sarkisyan, and S. V. Shmavonyan, “Selective reflection of light from dense sodium vapors,” Opt. Spectrosc. 85, 649–652 (1998).

Phys. Rev. (1)

R. H. Dicke, “The effect of collisions upon the Doppler width of spectral lines,” Phys. Rev. 89, 472–473 (1953).
[Crossref]

Phys. Rev. A (11)

S. Brandt, A. Nagel, R. Wynands, and D. Meschede, “Buffer-gas-induced linewidth reduction of coherent dark resonances to below 50  Hz,” Phys. Rev. A 56, R1063–R1067 (1997).
[Crossref]

H. van Kampen, A. V. Papoyan, V. A. Sautenkov, P. H. A. M. Castermans, E. R. Eliel, and J. P. Woerdman, “Observation of collisional modification of the Zeeman effect in a high-density atomic vapor,” Phys. Rev. A 56, 310–315 (1997).
[Crossref]

T. A. Vartanyan and D. L. Lin, “Enhanced selective reflection from a thin layer of dilute gaseous medium,” Phys. Rev. A 51, 1959–1964 (1995).
[Crossref]

J. Guo, J. Cooper, and A. Gallagher, “Selective reflection from a dense atomic vapor,” Phys. Rev. A 53, 1130–1138 (1996).
[Crossref]

T. A. Vartanyan and A. Weis, “Origin of the “blueshift” in selective reflection spectroscopy and its partial compensation by the local-field correction,” Phys. Rev. A 63, 063813 (2001).

M. A. Rosenberry, J. P. Reyes, D. Tupa, and T. J. Gay, “Radiation trapping in rubidium optical pumping at low buffer-gas pressures,” Phys. Rev. A 75, 023401 (2007).

I. M. Savukov and M. V. Romalis, “Effects of spin-exchange collisions in a high-density alkali-metal vapor in low magnetic fields,” Phys. Rev. A 71, 023405 (2005).

M. Shuker, O. Firstenberg, R. Pugatch, A. Ben-Kish, A. Ron, and N. Davidson, “Angular dependence of Dicke-narrowed electromagnetically induced transparency resonances,” Phys. Rev. A 76, 023813 (2007).

D. Sarkisyan, T. Varzhapetyan, A. Sarkisyan, Y. Malakyan, A. Papoyan, A. Lezama, D. Bloch, and M. Ducloy, “Spectroscopy in an extremely thin vapor cell: comparing the cell-length dependence in fluorescence and in absorption techniques,” Phys. Rev. A 69, 065802 (2004).

S. Jennewein, Y. R. P. Sortais, J. J. Greffet, and A. Browaeys, “Propagation of light through small clouds of cold interacting atoms,” Phys. Rev. A 94, 053828 (2016).

J. H. D. Munns, C. Qiu, P. M. Ledingham, I. A. Walmsley, J. Nunn, and D. J. Saunders, “In situ characterization of an optically thick atom-filled cavity,” Phys. Rev. A 93, 013858 (2016).

Phys. Rev. Lett. (3)

A. S. Zibrov, M. D. Lukin, L. Hollberg, D. E. Nikonov, M. O. Scully, H. G. Robinson, and V. L. Velichansky, “Experimental demonstration of enhanced index of refraction via quantum coherence in Rb,” Phys. Rev. Lett. 76, 3935–3938 (1996).
[Crossref]

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
[Crossref]

J. Keaveney, I. G. Hughes, A. Sargsyan, D. Sarkisyan, and C. S. Adams, “Maximal refraction and superluminal propagation in a gaseous nanolayer,” Phys. Rev. Lett. 109, 233001 (2012).

Proc. SPIE (1)

M. Movsisyan, S. Shmavonyan, and A. Papoyan, “Selective reflection studies of molecular cesium vapor,” Proc. SPIE 7998, 79980U (2011).

Quantum Electron. (1)

A. I. Parkhomenko and A. M. Shalagin, “Transversely diode-pumped alkali metal vapour laser,” Quantum Electron. 45, 797–806 (2015).
[Crossref]

Other (3)

D. A. Steck, “Rubidium 85 D line data,” http://steck.us/alkalidata/rubidium85numbers.pdf .

D. A. Steck, “Rubidium 87 D line data,” http://steck.us/alkalidata/rubidium87numbers.pdf .

A. Molisch and B. P. Oehry, Radiation Trapping in Atomic Vapours (Clarendon, 1998).

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Figures (6)

Fig. 1.
Fig. 1. Schematic drawing of the experimental setup (optical part).
Fig. 2.
Fig. 2. Reflection (upper trace) and transmission (middle trace) spectra in the region of D2 line of residual Rb vapor recorded at Tsa=269°C and Tw=440°C (NRb=2.02×1013  cm3, NCs=1.30×1016  cm3, NCs2=9.24×1012  cm3), and room temperature Rb reference spectrum (lower trace). D2 line hyperfine transition groups Rb87 Fg=2Fe=1,2,3, Rb85 Fg=3Fe=2,3,4, Rb85 Fg=2Fe=1,2,3, and Rb87 Fg=1Fe=0,1,2 (left to right) are denoted by vertical lines.
Fig. 3.
Fig. 3. Dependence of group refractive index ng on frequency retrieved from experimental reflection spectra (dots) and calculated by Eqs. (4) and (11) (solid lines; see Section 3) in the region of D2 line of residual Rb vapor for four temperature regimes: (a) Tsa=220°C, Tw=350°C; (b) Tsa=260°C, Tw=370°C; (c) Tsa=300°C, Tw=400°C; (d) Tsa=350°C, Tw=410°C. The zero detuning frequency is set to the Fg=2Fe=1 hyperfine transition of Rb87.
Fig. 4.
Fig. 4. Reflection (upper graph) and transmission (lower graph) spectra in the region of D2 line of Rb atoms calculated by Eq. (12) for the conditions in Fig. 2, with a fitting parameter of Γ¯=2π×23.3  MHz146.7  MHz. The zero detuning frequency is set to the Fg=2Fe=1 hyperfine transition of Rb87D2 line.
Fig. 5.
Fig. 5. Frequency dependencies of the real (upper graph) and imaginary (middle graph) parts of refractive index calculated by Eq. (11) in the region of D2 line of Rb for the conditions in Fig. 2. The lower graph shows the corresponding group refractive index calculated by Eq. (4). The zero detuning frequency is set to the Fg=2Fe=1 transition of Rb87.
Fig. 6.
Fig. 6. Buildup of channeled backward beam under non-normal incidence ϕ0, waveguided along a high-refractive-index laser beam. I, T, and R represent incident, transmitted, and geometrically reflected beams, respectively; intense color—overlapping area of forward and backward beams.

Equations (13)

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pRb=pRb×xRb,
pRb=133.3×10(7.1934040Tsa+273).
NRb=106pRbkB(Tw+273),
ng=n+νdndν=c2LΔν,
d2E(x)dx2+k2E(x)=4πk2P(x,u)u;P(x,u)=N(u)Sp(dρ);udρdx=i[Hρ]+Λ,
P(x=0,u>0)=0;P(x=L,u<0)=0.
d2E(x)dx2+k2E(x)=4πk2iq×{0xE(y)χ(xy)u>0dy+LxE(y)χ(xy)u<0dy},
s2+k2+4πk2iqχ˜(s)=0,
χ˜(s)=k=112|dk|2|d|2αki(ωkω)+su+Γku>0,
s1(n)=ik(1+2πqχ˜(s1n1))=ikn(s1n1));s2(n)=ik(1+2πqχ˜(s2n1))=ikn(s2n1)).
n=12(n(s1)+n(s2)).
R=|r(s1)Aeϕr(s2)1Aeϕr2(s2)|2;T=|2n0(n(s1)+n(s2))(n0+n(s1))2(1Aeϕr2(s2)|2,
r(s)=n0n(s)n0+n(s),ϕ=ikL(n(s1)+n(s2)),A=(n0+n(s2))2(n0+n(s1))2,

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