Abstract

We investigate the carrier-wave Rabi flopping effects in an asymmetric semiparabolic semiconductor quantum well (QW) with few-cycle pulse. It is found that higher spectral components of few-cycle ultrashort pulses in the semiparabolic QW depend crucially on the carrier-envelope phase (CEP) of the few-cycle ultrashort pulses: continuum and distinct peaks can be achieved by controlling the CEP. Our results demonstrate that by adjusting the CEP of few-cycle ultrashort pulses, the intersubband dynamics in the asymmetric semiparabolic QW can be controlled in an ultrashort timescale with moderate laser intensity.

© 2008 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  4. T. Tritschler, O. D. Mücke, M. Wegener, U. Morgner, and F. X. Kärtner, "Evidence for third-harmonic generation in disguise of second-harmonic generation in extreme nonlinear optics," Phys. Rev. Lett 90, 217404 (2003).
    [CrossRef] [PubMed]
  5. C. Van Vlack and S. Hughes, "Third-harmonic generation in disguise of second-harmonic generation revisited: role of thin-film thickness and carrier-envelope phase," Opt. Lett 32, 187-189 (2007).
    [CrossRef]
  6. F. Eickemeyer, M. Woerner, A. M. Weiner, T. Elsaesser, R. Hey, and K. H. Ploog, "Coherent nonlinear propagation of ultrafast electric field transients through intersubband resonances," Appl. Phys. Lett 79, 165-167 (2001).
    [CrossRef]
  7. C. W. Luo, K. Reimann, M. Woerner, T. Elsaesser, R. Hey, and K. H. Ploog, "Phase-resolved nonlinear response of a two-dimensional electron gas under femtosecond intersubband excitation," Phys. Rev. Lett 92, 047402 (2004).
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  8. G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. D. Silvestri, "Absolute-phase phenomena in photoionization with few-cycle laser pulses," Nature 414, 182-184 (2001).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  11. M. Drescher and F. Krausz, "Attosecond physics: facing the wave-particle duality," J. Phys. B: At. Mol. Opt. Phys 38, 727-740 (2005).
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  12. C. A. Haworth, L. E. Chipperfield, J. S. Robinson, P. L. Knight, J. P. Marangos, and J. W. G. Tisch, "Half-cycle cutoffs in harmonic spectra and robust carrier-envelope phase retrieval," Nature.Phys 3, 52-57 (2007).
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  18. O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, F. X. Kärtner, G. Khitrova, and H. M. Gibbs, "Carrier-wave Rabi flopping: role of the carrier-envelope phase," Opt. Lett 29, 2160-2162 (2004).
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    [CrossRef] [PubMed]
  21. R. C. Miller, A. C. Gossard, D. A. Kleinman, and O. Munteanu, "Parabolic quantum wells with the GaAs- AlxGa1−xAs system," Phys. Rev. B 29, 3740-3743 (1984).
    [CrossRef]
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  24. R. C. Miller, A. C. Gossard, and D. A. Kleinman, "Band offsets from special GaAs-AlxGa1−xAs quantum-well structures," Phys. Rev. B 32, 5443-5446 (1985).
    [CrossRef]
  25. W. W. Bewley, C. L. Felix, J. J. Plombon, M. S. Sherwin, M. Sundaram, P. F. Hopkins, and A. C. Gossard, "Far-infrared second-harmonic generation in GaAs-AlxGa1−xAs heterostructures: perturbative and nonperturbative response," Phys. Rev. B 48, 2376-2390 (1993).
    [CrossRef]
  26. M. Drobizhev, F. Meng, A. Rebane, Y. Stepanenko, E. Nickel, and C. W. Spangler, "Strong two-photon absorption in new asymmetrically substituted Porphyrins: interference between charge-transfer and intermediate-resonance pathways," J. Phys. Chem. B 110, 9802-9814 (2006).
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    [CrossRef] [PubMed]
  31. X. Song, S. Gong, S. Jin, and Z. Xu, "Formation of higher spectral components in a two-level medium driven by two-color ultrashort laser pulses," Phys. Rev. A 69, 015801 (2004).
    [CrossRef]
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    [CrossRef] [PubMed]
  33. L. W. Casperson, "Few-cycle pulses in two-level media," Phys. Rev. A 57, 609-621 (1998).
    [CrossRef]
  34. A. V. Tarasishin, S. A. Magnitskii, V. A. Shuvaev, and A. M. Zheltikov, "Evolution of ultrashort light pulses in a two-level medium visualized with the finite-difference time domain technique," Opt. Express 8, 452-457 (2001).
    [CrossRef] [PubMed]
  35. V. P. Kalosha and J. Herrmann, "Formation of optical subcycle pulses and full Maxwell-Bloch solitary waves by coherent propagation effects," Phys. Rev. Lett 83, 544-547 (1999).
    [CrossRef]
  36. X. Song, S. Gong, and Z. Xu, "Propagation of a few-cycle laser pulse in a V-type three-level system," Opt. Spectrosc 99, 517-521 (2005).
    [CrossRef]
  37. Y. Loiko and C. Serrat, "Coherent and phase-sensitive phenomena of ultrashort laser pulses propagating in three-level Λ type systems studied with the finite-difference time-domain method," Phys. Rev. A 73, 063809 (2006).
    [CrossRef]
  38. A. Taflove and M. E. Brodwin, "Numerical solution of steady-state electromagnetic scattering problems using the time-dependent Maxwell’s equations," IEEE. Trans. Microwave. Theory. Tech 23, 623-630 (1975).
    [CrossRef]
  39. K. X. Guo and S. W. Gu, "Nonlinear optical rectification in parabolic quantum wells with an applied electric field," Phys. Rev. B 47, 16322-16325 (1993).
    [CrossRef]
  40. H. J. Xie, C. Y. Chen, and B. K. Ma, "Bound polaron in a cylindrical quantum wire of a polar crystal," Phys. Rev. B 61, 4827-4834 (2000).
    [CrossRef]
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    [CrossRef]
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2007 (6)

C. Van Vlack and S. Hughes, "Third-harmonic generation in disguise of second-harmonic generation revisited: role of thin-film thickness and carrier-envelope phase," Opt. Lett 32, 187-189 (2007).
[CrossRef]

C. A. Haworth, L. E. Chipperfield, J. S. Robinson, P. L. Knight, J. P. Marangos, and J. W. G. Tisch, "Half-cycle cutoffs in harmonic spectra and robust carrier-envelope phase retrieval," Nature.Phys 3, 52-57 (2007).
[CrossRef]

S. T. Cundiff, "Attosecond Physics: better by half," Nature.Phys 3, 16-18 (2007).
[CrossRef]

X. M. Tong and C. D. Lin, "Dynamics of light-field control of molecular dissociation at the few-cycle limit," Phys. Rev. Lett 98, 123002 (2007).
[CrossRef] [PubMed]

C. Van Vlack and S. Hughes, "Carrier-envelope-offset phase control of ultrafast optical rectification in resonantly excited semiconductors," Phys. Rev. Lett 98, 167404 (2007).
[CrossRef] [PubMed]

W. Yang, X. Song, S. Gong, Y. Cheng, and Z. Xu, "Carrier-envelope phase dependence of few-cycle ultrashort laser pulse propagation in a polar molecule medium," Phys. Rev. Lett 99, 133602 (2007).
[CrossRef] [PubMed]

2006 (4)

M. Drobizhev, F. Meng, A. Rebane, Y. Stepanenko, E. Nickel, and C. W. Spangler, "Strong two-photon absorption in new asymmetrically substituted Porphyrins: interference between charge-transfer and intermediate-resonance pathways," J. Phys. Chem. B 110, 9802-9814 (2006).
[CrossRef] [PubMed]

Y. Loiko and C. Serrat, "Coherent and phase-sensitive phenomena of ultrashort laser pulses propagating in three-level Λ type systems studied with the finite-difference time-domain method," Phys. Rev. A 73, 063809 (2006).
[CrossRef]

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, "Isolated single-cycle attosecond pulses," Science 314, 443-446 (2006).
[CrossRef] [PubMed]

W. Yang, S. Gong, and Z. Xu, "Enhancement of ultrashort four-wave mixing in a polar molecule medium," Opt. Express 14, 7216-7223 (2006).
[CrossRef] [PubMed]

2005 (3)

M. Drescher and F. Krausz, "Attosecond physics: facing the wave-particle duality," J. Phys. B: At. Mol. Opt. Phys 38, 727-740 (2005).
[CrossRef]

G. L. Kamta and A. D. Bandrauk, "Phase dependence of enhanced ionization in asymmetric molecules," Phys. Rev. Lett 94, 203003 (2005).
[CrossRef] [PubMed]

X. Song, S. Gong, and Z. Xu, "Propagation of a few-cycle laser pulse in a V-type three-level system," Opt. Spectrosc 99, 517-521 (2005).
[CrossRef]

2004 (4)

O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, F. X. Kärtner, G. Khitrova, and H. M. Gibbs, "Carrier-wave Rabi flopping: role of the carrier-envelope phase," Opt. Lett 29, 2160-2162 (2004).
[CrossRef] [PubMed]

C. W. Luo, K. Reimann, M. Woerner, T. Elsaesser, R. Hey, and K. H. Ploog, "Phase-resolved nonlinear response of a two-dimensional electron gas under femtosecond intersubband excitation," Phys. Rev. Lett 92, 047402 (2004).
[CrossRef] [PubMed]

V. M. Axt and T. Kuhn, "Femtosecond spectroscopy in semiconductors: a key to coherences, correlations and quantum kinetics," Rep. Prog. Phys 67, 433-512 (2004).
[CrossRef]

X. Song, S. Gong, S. Jin, and Z. Xu, "Formation of higher spectral components in a two-level medium driven by two-color ultrashort laser pulses," Phys. Rev. A 69, 015801 (2004).
[CrossRef]

2003 (4)

T. Tritschler, O. D. Mücke, M. Wegener, U. Morgner, and F. X. Kärtner, "Evidence for third-harmonic generation in disguise of second-harmonic generation in extreme nonlinear optics," Phys. Rev. Lett 90, 217404 (2003).
[CrossRef] [PubMed]

A. Baltuška, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, "Attosecond control of electronic processes by intense light fields," Nature 421, 611-615 (2003).
[CrossRef] [PubMed]

G. G. Paulus, F. Lindner, H. Walther, A. Baltuška, E. Goulielmakis, M. Lezius, and F. Krausz, "Measurement of the phase of few-cycle laser pulses," Phys. Rev. Lett 91, 253004 (2003).
[CrossRef]

L. Zhang and H. J. Xie, "Electric field effect on the second-order nonlinear optical properties of parabolic and semiparabolic quantum wells," Phys. Rev. B 68, 235315 (2003).
[CrossRef]

2002 (2)

J. Xiao, Z. Wang, and Z. Xu, "Area evolution of a few-cycle pulse laser in a two-level-atom medium," Phys. Rev. A 65, 031402(R) (2002).
[CrossRef]

O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, "Role of the carrier-envelope offset phase of few-cycle pulses in nonperturbative resonant nonlinear optics," Phys. Rev. Lett 89, 127401 (2002).
[CrossRef] [PubMed]

2001 (4)

O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, "Signatures of carrier-wave Rabi flopping in GaAs," Phys. Rev. Lett 87, 057401 (2001).
[CrossRef] [PubMed]

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. D. Silvestri, "Absolute-phase phenomena in photoionization with few-cycle laser pulses," Nature 414, 182-184 (2001).
[CrossRef] [PubMed]

F. Eickemeyer, M. Woerner, A. M. Weiner, T. Elsaesser, R. Hey, and K. H. Ploog, "Coherent nonlinear propagation of ultrafast electric field transients through intersubband resonances," Appl. Phys. Lett 79, 165-167 (2001).
[CrossRef]

A. V. Tarasishin, S. A. Magnitskii, V. A. Shuvaev, and A. M. Zheltikov, "Evolution of ultrashort light pulses in a two-level medium visualized with the finite-difference time domain technique," Opt. Express 8, 452-457 (2001).
[CrossRef] [PubMed]

2000 (3)

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

T. Brabec and F. Krausz, "Intense few-cycle laser field: frontiers of nonlinear optics," Rev. Mod. Phys 72, 545-591 (2000).
[CrossRef]

H. J. Xie, C. Y. Chen, and B. K. Ma, "Bound polaron in a cylindrical quantum wire of a polar crystal," Phys. Rev. B 61, 4827-4834 (2000).
[CrossRef]

1999 (1)

V. P. Kalosha and J. Herrmann, "Formation of optical subcycle pulses and full Maxwell-Bloch solitary waves by coherent propagation effects," Phys. Rev. Lett 83, 544-547 (1999).
[CrossRef]

1998 (2)

S. Hughes, "Breakdown of the area theorem: carrier-wave Rabi flopping of femtosecond optical pulses," Phys. Rev. Lett 81, 3363-3366 (1998).
[CrossRef]

L. W. Casperson, "Few-cycle pulses in two-level media," Phys. Rev. A 57, 609-621 (1998).
[CrossRef]

1995 (1)

R. W. Ziolkowski, J. M. Arnold, and D. M. Gogny, "Ultrafast pulse interactions with two-level atoms," Phys. Rev. A 52, 3082-3094 (1995).
[CrossRef] [PubMed]

1993 (2)

K. X. Guo and S. W. Gu, "Nonlinear optical rectification in parabolic quantum wells with an applied electric field," Phys. Rev. B 47, 16322-16325 (1993).
[CrossRef]

W. W. Bewley, C. L. Felix, J. J. Plombon, M. S. Sherwin, M. Sundaram, P. F. Hopkins, and A. C. Gossard, "Far-infrared second-harmonic generation in GaAs-AlxGa1−xAs heterostructures: perturbative and nonperturbative response," Phys. Rev. B 48, 2376-2390 (1993).
[CrossRef]

1991 (1)

M. Sundaram, S. A. Chalmers, P. F. Hopkins, and A. C. Gossard, "New quantum structures," Science 254, 1326-1335 (1991).
[CrossRef] [PubMed]

1986 (1)

A. C. Gossard, "Growth of microstructures by molecular beam epitaxy," IEEE J. Quantum Electron 22, 1649-1655 (1986).
[CrossRef]

1985 (2)

R. C. Miller, A. C. Gossard, and D. A. Kleinman, "Band offsets from special GaAs-AlxGa1−xAs quantum-well structures," Phys. Rev. B 32, 5443-5446 (1985).
[CrossRef]

S. Adachi, "GaAs, AlAs, and AlxGa1−xAs material parameters for use in research and device applications," J. Appl. Phys 58, 1-29 (1985).
[CrossRef]

1984 (1)

R. C. Miller, A. C. Gossard, D. A. Kleinman, and O. Munteanu, "Parabolic quantum wells with the GaAs- AlxGa1−xAs system," Phys. Rev. B 29, 3740-3743 (1984).
[CrossRef]

1975 (1)

A. Taflove and M. E. Brodwin, "Numerical solution of steady-state electromagnetic scattering problems using the time-dependent Maxwell’s equations," IEEE. Trans. Microwave. Theory. Tech 23, 623-630 (1975).
[CrossRef]

Appl. Phys. Lett (1)

F. Eickemeyer, M. Woerner, A. M. Weiner, T. Elsaesser, R. Hey, and K. H. Ploog, "Coherent nonlinear propagation of ultrafast electric field transients through intersubband resonances," Appl. Phys. Lett 79, 165-167 (2001).
[CrossRef]

IEEE J. Quantum Electron (1)

A. C. Gossard, "Growth of microstructures by molecular beam epitaxy," IEEE J. Quantum Electron 22, 1649-1655 (1986).
[CrossRef]

IEEE. Trans. Microwave. Theory. Tech (1)

A. Taflove and M. E. Brodwin, "Numerical solution of steady-state electromagnetic scattering problems using the time-dependent Maxwell’s equations," IEEE. Trans. Microwave. Theory. Tech 23, 623-630 (1975).
[CrossRef]

J. Appl. Phys (1)

S. Adachi, "GaAs, AlAs, and AlxGa1−xAs material parameters for use in research and device applications," J. Appl. Phys 58, 1-29 (1985).
[CrossRef]

J. Phys. B: At. Mol. Opt. Phys (1)

M. Drescher and F. Krausz, "Attosecond physics: facing the wave-particle duality," J. Phys. B: At. Mol. Opt. Phys 38, 727-740 (2005).
[CrossRef]

J. Phys. Chem. B (1)

M. Drobizhev, F. Meng, A. Rebane, Y. Stepanenko, E. Nickel, and C. W. Spangler, "Strong two-photon absorption in new asymmetrically substituted Porphyrins: interference between charge-transfer and intermediate-resonance pathways," J. Phys. Chem. B 110, 9802-9814 (2006).
[CrossRef] [PubMed]

Nature (2)

A. Baltuška, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, "Attosecond control of electronic processes by intense light fields," Nature 421, 611-615 (2003).
[CrossRef] [PubMed]

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. D. Silvestri, "Absolute-phase phenomena in photoionization with few-cycle laser pulses," Nature 414, 182-184 (2001).
[CrossRef] [PubMed]

Opt. Express (2)

Opt. Lett (2)

C. Van Vlack and S. Hughes, "Third-harmonic generation in disguise of second-harmonic generation revisited: role of thin-film thickness and carrier-envelope phase," Opt. Lett 32, 187-189 (2007).
[CrossRef]

O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, F. X. Kärtner, G. Khitrova, and H. M. Gibbs, "Carrier-wave Rabi flopping: role of the carrier-envelope phase," Opt. Lett 29, 2160-2162 (2004).
[CrossRef] [PubMed]

Opt. Spectrosc (1)

X. Song, S. Gong, and Z. Xu, "Propagation of a few-cycle laser pulse in a V-type three-level system," Opt. Spectrosc 99, 517-521 (2005).
[CrossRef]

Phys (2)

C. A. Haworth, L. E. Chipperfield, J. S. Robinson, P. L. Knight, J. P. Marangos, and J. W. G. Tisch, "Half-cycle cutoffs in harmonic spectra and robust carrier-envelope phase retrieval," Nature.Phys 3, 52-57 (2007).
[CrossRef]

S. T. Cundiff, "Attosecond Physics: better by half," Nature.Phys 3, 16-18 (2007).
[CrossRef]

Phys. Rev. A (5)

Y. Loiko and C. Serrat, "Coherent and phase-sensitive phenomena of ultrashort laser pulses propagating in three-level Λ type systems studied with the finite-difference time-domain method," Phys. Rev. A 73, 063809 (2006).
[CrossRef]

X. Song, S. Gong, S. Jin, and Z. Xu, "Formation of higher spectral components in a two-level medium driven by two-color ultrashort laser pulses," Phys. Rev. A 69, 015801 (2004).
[CrossRef]

R. W. Ziolkowski, J. M. Arnold, and D. M. Gogny, "Ultrafast pulse interactions with two-level atoms," Phys. Rev. A 52, 3082-3094 (1995).
[CrossRef] [PubMed]

L. W. Casperson, "Few-cycle pulses in two-level media," Phys. Rev. A 57, 609-621 (1998).
[CrossRef]

J. Xiao, Z. Wang, and Z. Xu, "Area evolution of a few-cycle pulse laser in a two-level-atom medium," Phys. Rev. A 65, 031402(R) (2002).
[CrossRef]

Phys. Rev. B (6)

L. Zhang and H. J. Xie, "Electric field effect on the second-order nonlinear optical properties of parabolic and semiparabolic quantum wells," Phys. Rev. B 68, 235315 (2003).
[CrossRef]

R. C. Miller, A. C. Gossard, and D. A. Kleinman, "Band offsets from special GaAs-AlxGa1−xAs quantum-well structures," Phys. Rev. B 32, 5443-5446 (1985).
[CrossRef]

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Figures (6)

Fig. 1.
Fig. 1.

Conduction-band profile of GaAs-AlGaAs symmetric QW (a) and asymmetric QW (b).

Fig. 2.
Fig. 2.

(Color online) The spectra of few-cycle ultrashort pulses in symmetric QW with ω 0=0.4 fs-1 at z=120 µm.

Fig. 3(a).
Fig. 3(a).

The spectra of few-cycle ultrashort pulses in asymmetric QW with ω0 =0.4 fs-1 at z=120 µm.

Fig. 3(b).
Fig. 3(b).

The carrier of few-cycle ultrashort pulses Ω(fs-1) (solid line) and the population difference w (dotted line) at z=0 µm.

Fig. 4(a).
Fig. 4(a).

As in Fig. 3(a) but for ω0 =0.5 fs-1.

Fig. 4(b).
Fig. 4(b).

As in Fig. 3(b) but for ω0 =0.5 fs-1.

Equations (11)

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H = H 0 + H 1 ,
H 1 = e r E ( r , t ) ,
H 0 = P 2 2 m * + p x 2 2 m * + V ( x ) ,
V ( x ) = 1 2 m * ω 0 2 x 2 ,   < x < ,
V ( x ) = { 1 2 m * ω 0 2 x 2 , x 0 , , x < 0 ,
E s = ( n 1 + 1 2 ) ω 0 + 2 2 m * k 2 , n 1 = 0 , 1 , 2 , ...
φ s = N s exp ( 1 2 β 2 x 2 ) H n 1 ( β x ) U c ( r ) exp ( i k r ) ,
β = m * ω 0 ,
E a = ( 2 n 2 + 3 2 ) ω 0 + 2 2 m * k 2 , n 2 = 0 , 1 , 2 , ...
φ a = N a exp ( 1 2 β 2 x 2 ) H 2 n 2 + 1 ( β x ) U c ( r ) exp ( i k r ) ,
Ω ( t = 0 , z ) = Ω m sec h [ 1.76 ( z c z 0 c ) τ p ] cos [ ω p ( z z 0 ) c + ϕ ] ,

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