Abstract

A theoretical study of the interaction of intense terahertz transients and broadband optical pulses in quantum wells is presented. The approach is based on a numerical solution of the anisotropic semiconductor Bloch equations and includes, self-consistently, both continuum and excitonic effects. In the optical regime we recover the dynamic Franz–Keldysh effect showing THz sidebands in the optical absorption spectrum. In the THz regime we discern a series of harmonically generated upshifted THz transients. It is demonstrated pictorially that the upshifted transients are formed by the creation of highly anisotropic interfering, relative-motion electron–hole wave packets. We also investigate the influence of ellipticity of the driving field and chirped optical pulses. The field interaction with the quantum well is shown to be highly nonperturbative for typical free-electron laser fields. A series of propagating charge-carrier wave packets are analyzed, and a connection is made to analogies in the high-field physics of atomic ensembles.

© 2000 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
  31. I. P. Christov, M. M. Murname, and H. C. Kapteyn, “High-harmonic generation of attosecond pulses in the ‘single-cycle’ regime,” Phys. Rev. Lett. 78, 1251–1254 (1997).
    [CrossRef]
  32. J. L. Krause, K. J. Schafer, M. Ben-Nun, and K. R. Wilson, “Creating and detecting shaped Rydberg wave packets,” Phys. Rev. Lett. 79, 4978–4981 (1998).
    [CrossRef]
  33. P. Moreno, L. Plaja, and L. Roso, “High-order harmonic generation in a partially ionized medium,” J. Opt. Soc. Am. B 13, 430–435 (1996).
    [CrossRef]
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    [CrossRef] [PubMed]
  36. W. Becker, A. Lohr, K. Kleber, and M. Lewenstein, “A unified theory of high-harmonic generation: application to polarization properties of the harmonics,” Phys. Rev. A 56, 645–656 (1997).
    [CrossRef]
  37. P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71, 1994–1997 (1993).
    [CrossRef] [PubMed]
  38. D. S. Citrin and S. Hughes, “Circularly polarized dynamic Franz–Keldysh effect,” submitted to Phys. Rev. B.
  39. J. Feldmann, G. von Plessen, M. Koch, E. O. Göbel, P. Thomas, G. Backer, C. Hartmann, H. Scheizer, W. Schafer, and H. Nickel, “Coherent dynamics of excitonic wave packets,” Phys. Rev. Lett. 56, 3027–3030 (1993).
    [CrossRef]
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  41. J. Feldmann, K. Leo, J. Shaw, D. A. B. Miller, J. E. Cunningham, S. Schmitt-Rink, T. Meier, G. von Plessen, A. Schultze, and P. Thomas, “Optical investigation of Bloch oscillations in a semiconductor superlattice,” Phys. Rev. B 46, 7252–7255 (1992).
    [CrossRef]

1999

S. Hughes and D. S. Citrin, “Creation of highly anisotropic wavepackets in quantum wells: dynamical Franz–Keldysh effect in the optical and terahertz regimes,” Phys. Rev. B 59, R5288–R5291 (1999).
[CrossRef]

1998

S. Hughes and D. S. Citrin, “Ultrafast heating and switching of a semiconductor optical amplifier using half-cycle terahertz pulses,” Phys. Rev. B 58, R15969–R15972 (1998).
[CrossRef]

J. L. Krause, K. J. Schafer, M. Ben-Nun, and K. R. Wilson, “Creating and detecting shaped Rydberg wave packets,” Phys. Rev. Lett. 79, 4978–4981 (1998).
[CrossRef]

1997

K. Johnsen and A. P. Jauho, “Optics of excitons in THz irradiated quantum wells,” Phys. Status Solidi A 164, 553–556 (1997).
[CrossRef]

I. P. Christov, M. M. Murname, and H. C. Kapteyn, “High-harmonic generation of attosecond pulses in the ‘single-cycle’ regime,” Phys. Rev. Lett. 78, 1251–1254 (1997).
[CrossRef]

W. Becker, A. Lohr, K. Kleber, and M. Lewenstein, “A unified theory of high-harmonic generation: application to polarization properties of the harmonics,” Phys. Rev. A 56, 645–656 (1997).
[CrossRef]

K. B. Nordstrom, K. Johnsen, S. J. Allen, A. P. Jauho, B. Birnir, J. Kono, T. Noda, H. Akiyama, and H. Sakaki, “Observation of dynamical Franz–Keldysh effect,” Phys. Status Solidi B 204, 52–54 (1997).
[CrossRef]

1996

A. P. Jauho and K. Johnsen, “Dynamical Franz–Keldysh effect,” Phys. Rev. Lett. 24, 4576–4579 (1996).
[CrossRef]

J. Zhou, J. Peatross, M. M. Murname, H. C. Kapteyn, and I. P. Christov, “Enhanced high-harmonic generation using 25 fs laser pulses,” Phys. Rev. Lett. 76, 752–755 (1996).
[CrossRef] [PubMed]

P. Moreno, L. Plaja, and L. Roso, “High-order harmonic generation in a partially ionized medium,” J. Opt. Soc. Am. B 13, 430–435 (1996).
[CrossRef]

See, for example, V. M. Axt, G. Bartels, and A. Stahl, “Intraband dynamics at the semiconductor band edge: shortcomings of the Bloch equation method,” Phys. Rev. Lett. 76, 2543–2546 (1996).
[CrossRef] [PubMed]

1994

1993

M. S. C. Luo, S. L. Chuang, P. C. M. Planken, I. Brener, and M. C. Nuss, “Coherent double-pulse control of quantum beats in a coupled quantum well,” Phys. Rev. B 48, 11043–11050 (1993).
[CrossRef]

P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71, 1994–1997 (1993).
[CrossRef] [PubMed]

J. Feldmann, G. von Plessen, M. Koch, E. O. Göbel, P. Thomas, G. Backer, C. Hartmann, H. Scheizer, W. Schafer, and H. Nickel, “Coherent dynamics of excitonic wave packets,” Phys. Rev. Lett. 56, 3027–3030 (1993).
[CrossRef]

1992

J. Feldmann, K. Leo, J. Shaw, D. A. B. Miller, J. E. Cunningham, S. Schmitt-Rink, T. Meier, G. von Plessen, A. Schultze, and P. Thomas, “Optical investigation of Bloch oscillations in a semiconductor superlattice,” Phys. Rev. B 46, 7252–7255 (1992).
[CrossRef]

D. Fröhlich, S. Spitzer, B. Uebbing, and R. Zimmermann, “Polarization dependence in the intraband optical stark effect of quantum wells,” Phys. Status Solidi B 173, 83–89 (1992).
[CrossRef]

M. Holthaus, “Collapse of minibands in far-infrared irradiated superlattices,” Phys. Rev. Lett. 69, 351–354 (1992).
[CrossRef] [PubMed]

For a review, see, for example, F. Rossi, P. Poli, and C. Jacoboni, “Weighted Monte Carlo approach to semiclassical and quantum electron transport in semiconductors,” Semicond. Sci. Technol. 7, 1017 (1992).
[CrossRef]

H. G. Roskos, M. C. Nuss, J. Shah, K. Leo, D. A. B. Miller, A. M. Fox, S. Schmitt-Rink, and K. Köhler, “Coherent submillimeter-wave emission from charge oscillations in a double-well potential,” Phys. Rev. Lett. 68, 2216–2219 (1992).
[CrossRef] [PubMed]

1988

M. Lindberg and S. W. Koch, “Effective Bloch equations for semiconductors,” Phys. Rev. B 38, 3342–3350 (1988).
[CrossRef]

1968

Y. Yacoby, “High-frequency Franz–Keldysh effect,” Phys. Rev. 169, 610–619 (1968).
[CrossRef]

1965

L. V. Keldysh, Sov. Phys. JETP 20, 1307 (1965).

1929

F. Bloch, Z. Phys. 52, 555 (1929).
[CrossRef]

Akiyama, H.

K. B. Nordstrom, K. Johnsen, S. J. Allen, A. P. Jauho, B. Birnir, J. Kono, T. Noda, H. Akiyama, and H. Sakaki, “Observation of dynamical Franz–Keldysh effect,” Phys. Status Solidi B 204, 52–54 (1997).
[CrossRef]

Allen, S. J.

K. B. Nordstrom, K. Johnsen, S. J. Allen, A. P. Jauho, B. Birnir, J. Kono, T. Noda, H. Akiyama, and H. Sakaki, “Observation of dynamical Franz–Keldysh effect,” Phys. Status Solidi B 204, 52–54 (1997).
[CrossRef]

Axt, V. M.

See, for example, V. M. Axt, G. Bartels, and A. Stahl, “Intraband dynamics at the semiconductor band edge: shortcomings of the Bloch equation method,” Phys. Rev. Lett. 76, 2543–2546 (1996).
[CrossRef] [PubMed]

Backer, G.

J. Feldmann, G. von Plessen, M. Koch, E. O. Göbel, P. Thomas, G. Backer, C. Hartmann, H. Scheizer, W. Schafer, and H. Nickel, “Coherent dynamics of excitonic wave packets,” Phys. Rev. Lett. 56, 3027–3030 (1993).
[CrossRef]

Bartels, G.

See, for example, V. M. Axt, G. Bartels, and A. Stahl, “Intraband dynamics at the semiconductor band edge: shortcomings of the Bloch equation method,” Phys. Rev. Lett. 76, 2543–2546 (1996).
[CrossRef] [PubMed]

Becker, W.

W. Becker, A. Lohr, K. Kleber, and M. Lewenstein, “A unified theory of high-harmonic generation: application to polarization properties of the harmonics,” Phys. Rev. A 56, 645–656 (1997).
[CrossRef]

Ben-Nun, M.

J. L. Krause, K. J. Schafer, M. Ben-Nun, and K. R. Wilson, “Creating and detecting shaped Rydberg wave packets,” Phys. Rev. Lett. 79, 4978–4981 (1998).
[CrossRef]

Birnir, B.

K. B. Nordstrom, K. Johnsen, S. J. Allen, A. P. Jauho, B. Birnir, J. Kono, T. Noda, H. Akiyama, and H. Sakaki, “Observation of dynamical Franz–Keldysh effect,” Phys. Status Solidi B 204, 52–54 (1997).
[CrossRef]

Bloch, F.

F. Bloch, Z. Phys. 52, 555 (1929).
[CrossRef]

Brener, I.

I. Brener, P. C. M. Planken, M. C. Nuss, M. S. C. Luo, S.-L. Chuang, L. Pfeiffer, D. E. Laird, and A. M. Weiner, “Coherent control of terahertz emission and carrier populations in semiconductor heterostructures,” J. Opt. Soc. Am. B 11, 2457–2469 (1994).
[CrossRef]

M. S. C. Luo, S. L. Chuang, P. C. M. Planken, I. Brener, and M. C. Nuss, “Coherent double-pulse control of quantum beats in a coupled quantum well,” Phys. Rev. B 48, 11043–11050 (1993).
[CrossRef]

Christov, I. P.

I. P. Christov, M. M. Murname, and H. C. Kapteyn, “High-harmonic generation of attosecond pulses in the ‘single-cycle’ regime,” Phys. Rev. Lett. 78, 1251–1254 (1997).
[CrossRef]

J. Zhou, J. Peatross, M. M. Murname, H. C. Kapteyn, and I. P. Christov, “Enhanced high-harmonic generation using 25 fs laser pulses,” Phys. Rev. Lett. 76, 752–755 (1996).
[CrossRef] [PubMed]

Chuang, S. L.

M. S. C. Luo, S. L. Chuang, P. C. M. Planken, I. Brener, and M. C. Nuss, “Coherent double-pulse control of quantum beats in a coupled quantum well,” Phys. Rev. B 48, 11043–11050 (1993).
[CrossRef]

Chuang, S.-L.

Citrin, D. S.

S. Hughes and D. S. Citrin, “Creation of highly anisotropic wavepackets in quantum wells: dynamical Franz–Keldysh effect in the optical and terahertz regimes,” Phys. Rev. B 59, R5288–R5291 (1999).
[CrossRef]

S. Hughes and D. S. Citrin, “Ultrafast heating and switching of a semiconductor optical amplifier using half-cycle terahertz pulses,” Phys. Rev. B 58, R15969–R15972 (1998).
[CrossRef]

Corkum, P. B.

P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71, 1994–1997 (1993).
[CrossRef] [PubMed]

Cunningham, J. E.

J. Feldmann, K. Leo, J. Shaw, D. A. B. Miller, J. E. Cunningham, S. Schmitt-Rink, T. Meier, G. von Plessen, A. Schultze, and P. Thomas, “Optical investigation of Bloch oscillations in a semiconductor superlattice,” Phys. Rev. B 46, 7252–7255 (1992).
[CrossRef]

Feldmann, J.

J. Feldmann, G. von Plessen, M. Koch, E. O. Göbel, P. Thomas, G. Backer, C. Hartmann, H. Scheizer, W. Schafer, and H. Nickel, “Coherent dynamics of excitonic wave packets,” Phys. Rev. Lett. 56, 3027–3030 (1993).
[CrossRef]

J. Feldmann, K. Leo, J. Shaw, D. A. B. Miller, J. E. Cunningham, S. Schmitt-Rink, T. Meier, G. von Plessen, A. Schultze, and P. Thomas, “Optical investigation of Bloch oscillations in a semiconductor superlattice,” Phys. Rev. B 46, 7252–7255 (1992).
[CrossRef]

Fox, A. M.

H. G. Roskos, M. C. Nuss, J. Shah, K. Leo, D. A. B. Miller, A. M. Fox, S. Schmitt-Rink, and K. Köhler, “Coherent submillimeter-wave emission from charge oscillations in a double-well potential,” Phys. Rev. Lett. 68, 2216–2219 (1992).
[CrossRef] [PubMed]

Fröhlich, D.

D. Fröhlich, S. Spitzer, B. Uebbing, and R. Zimmermann, “Polarization dependence in the intraband optical stark effect of quantum wells,” Phys. Status Solidi B 173, 83–89 (1992).
[CrossRef]

Göbel, E. O.

J. Feldmann, G. von Plessen, M. Koch, E. O. Göbel, P. Thomas, G. Backer, C. Hartmann, H. Scheizer, W. Schafer, and H. Nickel, “Coherent dynamics of excitonic wave packets,” Phys. Rev. Lett. 56, 3027–3030 (1993).
[CrossRef]

Hartmann, C.

J. Feldmann, G. von Plessen, M. Koch, E. O. Göbel, P. Thomas, G. Backer, C. Hartmann, H. Scheizer, W. Schafer, and H. Nickel, “Coherent dynamics of excitonic wave packets,” Phys. Rev. Lett. 56, 3027–3030 (1993).
[CrossRef]

Holthaus, M.

M. Holthaus, “Collapse of minibands in far-infrared irradiated superlattices,” Phys. Rev. Lett. 69, 351–354 (1992).
[CrossRef] [PubMed]

Hughes, S.

S. Hughes and D. S. Citrin, “Creation of highly anisotropic wavepackets in quantum wells: dynamical Franz–Keldysh effect in the optical and terahertz regimes,” Phys. Rev. B 59, R5288–R5291 (1999).
[CrossRef]

S. Hughes and D. S. Citrin, “Ultrafast heating and switching of a semiconductor optical amplifier using half-cycle terahertz pulses,” Phys. Rev. B 58, R15969–R15972 (1998).
[CrossRef]

Jacoboni, C.

For a review, see, for example, F. Rossi, P. Poli, and C. Jacoboni, “Weighted Monte Carlo approach to semiclassical and quantum electron transport in semiconductors,” Semicond. Sci. Technol. 7, 1017 (1992).
[CrossRef]

Jauho, A. P.

K. Johnsen and A. P. Jauho, “Optics of excitons in THz irradiated quantum wells,” Phys. Status Solidi A 164, 553–556 (1997).
[CrossRef]

K. B. Nordstrom, K. Johnsen, S. J. Allen, A. P. Jauho, B. Birnir, J. Kono, T. Noda, H. Akiyama, and H. Sakaki, “Observation of dynamical Franz–Keldysh effect,” Phys. Status Solidi B 204, 52–54 (1997).
[CrossRef]

A. P. Jauho and K. Johnsen, “Dynamical Franz–Keldysh effect,” Phys. Rev. Lett. 24, 4576–4579 (1996).
[CrossRef]

Johnsen, K.

K. B. Nordstrom, K. Johnsen, S. J. Allen, A. P. Jauho, B. Birnir, J. Kono, T. Noda, H. Akiyama, and H. Sakaki, “Observation of dynamical Franz–Keldysh effect,” Phys. Status Solidi B 204, 52–54 (1997).
[CrossRef]

K. Johnsen and A. P. Jauho, “Optics of excitons in THz irradiated quantum wells,” Phys. Status Solidi A 164, 553–556 (1997).
[CrossRef]

A. P. Jauho and K. Johnsen, “Dynamical Franz–Keldysh effect,” Phys. Rev. Lett. 24, 4576–4579 (1996).
[CrossRef]

Kapteyn, H. C.

I. P. Christov, M. M. Murname, and H. C. Kapteyn, “High-harmonic generation of attosecond pulses in the ‘single-cycle’ regime,” Phys. Rev. Lett. 78, 1251–1254 (1997).
[CrossRef]

J. Zhou, J. Peatross, M. M. Murname, H. C. Kapteyn, and I. P. Christov, “Enhanced high-harmonic generation using 25 fs laser pulses,” Phys. Rev. Lett. 76, 752–755 (1996).
[CrossRef] [PubMed]

Keldysh, L. V.

L. V. Keldysh, Sov. Phys. JETP 20, 1307 (1965).

Kleber, K.

W. Becker, A. Lohr, K. Kleber, and M. Lewenstein, “A unified theory of high-harmonic generation: application to polarization properties of the harmonics,” Phys. Rev. A 56, 645–656 (1997).
[CrossRef]

Koch, M.

J. Feldmann, G. von Plessen, M. Koch, E. O. Göbel, P. Thomas, G. Backer, C. Hartmann, H. Scheizer, W. Schafer, and H. Nickel, “Coherent dynamics of excitonic wave packets,” Phys. Rev. Lett. 56, 3027–3030 (1993).
[CrossRef]

Koch, S. W.

T. Meier, G. von Plessen, P. Thomas, and S. W. Koch, “Coherent electric-field effects in semiconductor,” Phys. Rev. Lett. 73, 902–905 (1994).
[CrossRef] [PubMed]

M. Lindberg and S. W. Koch, “Effective Bloch equations for semiconductors,” Phys. Rev. B 38, 3342–3350 (1988).
[CrossRef]

Köhler, K.

H. G. Roskos, M. C. Nuss, J. Shah, K. Leo, D. A. B. Miller, A. M. Fox, S. Schmitt-Rink, and K. Köhler, “Coherent submillimeter-wave emission from charge oscillations in a double-well potential,” Phys. Rev. Lett. 68, 2216–2219 (1992).
[CrossRef] [PubMed]

Kono, J.

K. B. Nordstrom, K. Johnsen, S. J. Allen, A. P. Jauho, B. Birnir, J. Kono, T. Noda, H. Akiyama, and H. Sakaki, “Observation of dynamical Franz–Keldysh effect,” Phys. Status Solidi B 204, 52–54 (1997).
[CrossRef]

Krause, J. L.

J. L. Krause, K. J. Schafer, M. Ben-Nun, and K. R. Wilson, “Creating and detecting shaped Rydberg wave packets,” Phys. Rev. Lett. 79, 4978–4981 (1998).
[CrossRef]

Laird, D. E.

Leo, K.

H. G. Roskos, M. C. Nuss, J. Shah, K. Leo, D. A. B. Miller, A. M. Fox, S. Schmitt-Rink, and K. Köhler, “Coherent submillimeter-wave emission from charge oscillations in a double-well potential,” Phys. Rev. Lett. 68, 2216–2219 (1992).
[CrossRef] [PubMed]

J. Feldmann, K. Leo, J. Shaw, D. A. B. Miller, J. E. Cunningham, S. Schmitt-Rink, T. Meier, G. von Plessen, A. Schultze, and P. Thomas, “Optical investigation of Bloch oscillations in a semiconductor superlattice,” Phys. Rev. B 46, 7252–7255 (1992).
[CrossRef]

Lewenstein, M.

W. Becker, A. Lohr, K. Kleber, and M. Lewenstein, “A unified theory of high-harmonic generation: application to polarization properties of the harmonics,” Phys. Rev. A 56, 645–656 (1997).
[CrossRef]

Lindberg, M.

M. Lindberg and S. W. Koch, “Effective Bloch equations for semiconductors,” Phys. Rev. B 38, 3342–3350 (1988).
[CrossRef]

Lohr, A.

W. Becker, A. Lohr, K. Kleber, and M. Lewenstein, “A unified theory of high-harmonic generation: application to polarization properties of the harmonics,” Phys. Rev. A 56, 645–656 (1997).
[CrossRef]

Luo, M. S. C.

I. Brener, P. C. M. Planken, M. C. Nuss, M. S. C. Luo, S.-L. Chuang, L. Pfeiffer, D. E. Laird, and A. M. Weiner, “Coherent control of terahertz emission and carrier populations in semiconductor heterostructures,” J. Opt. Soc. Am. B 11, 2457–2469 (1994).
[CrossRef]

M. S. C. Luo, S. L. Chuang, P. C. M. Planken, I. Brener, and M. C. Nuss, “Coherent double-pulse control of quantum beats in a coupled quantum well,” Phys. Rev. B 48, 11043–11050 (1993).
[CrossRef]

Meier, T.

T. Meier, G. von Plessen, P. Thomas, and S. W. Koch, “Coherent electric-field effects in semiconductor,” Phys. Rev. Lett. 73, 902–905 (1994).
[CrossRef] [PubMed]

J. Feldmann, K. Leo, J. Shaw, D. A. B. Miller, J. E. Cunningham, S. Schmitt-Rink, T. Meier, G. von Plessen, A. Schultze, and P. Thomas, “Optical investigation of Bloch oscillations in a semiconductor superlattice,” Phys. Rev. B 46, 7252–7255 (1992).
[CrossRef]

Miller, D. A. B.

J. Feldmann, K. Leo, J. Shaw, D. A. B. Miller, J. E. Cunningham, S. Schmitt-Rink, T. Meier, G. von Plessen, A. Schultze, and P. Thomas, “Optical investigation of Bloch oscillations in a semiconductor superlattice,” Phys. Rev. B 46, 7252–7255 (1992).
[CrossRef]

H. G. Roskos, M. C. Nuss, J. Shah, K. Leo, D. A. B. Miller, A. M. Fox, S. Schmitt-Rink, and K. Köhler, “Coherent submillimeter-wave emission from charge oscillations in a double-well potential,” Phys. Rev. Lett. 68, 2216–2219 (1992).
[CrossRef] [PubMed]

Moreno, P.

Murname, M. M.

I. P. Christov, M. M. Murname, and H. C. Kapteyn, “High-harmonic generation of attosecond pulses in the ‘single-cycle’ regime,” Phys. Rev. Lett. 78, 1251–1254 (1997).
[CrossRef]

J. Zhou, J. Peatross, M. M. Murname, H. C. Kapteyn, and I. P. Christov, “Enhanced high-harmonic generation using 25 fs laser pulses,” Phys. Rev. Lett. 76, 752–755 (1996).
[CrossRef] [PubMed]

Nickel, H.

J. Feldmann, G. von Plessen, M. Koch, E. O. Göbel, P. Thomas, G. Backer, C. Hartmann, H. Scheizer, W. Schafer, and H. Nickel, “Coherent dynamics of excitonic wave packets,” Phys. Rev. Lett. 56, 3027–3030 (1993).
[CrossRef]

Noda, T.

K. B. Nordstrom, K. Johnsen, S. J. Allen, A. P. Jauho, B. Birnir, J. Kono, T. Noda, H. Akiyama, and H. Sakaki, “Observation of dynamical Franz–Keldysh effect,” Phys. Status Solidi B 204, 52–54 (1997).
[CrossRef]

Nordstrom, K. B.

K. B. Nordstrom, K. Johnsen, S. J. Allen, A. P. Jauho, B. Birnir, J. Kono, T. Noda, H. Akiyama, and H. Sakaki, “Observation of dynamical Franz–Keldysh effect,” Phys. Status Solidi B 204, 52–54 (1997).
[CrossRef]

Norris, T. B.

Nuss, M. C.

I. Brener, P. C. M. Planken, M. C. Nuss, M. S. C. Luo, S.-L. Chuang, L. Pfeiffer, D. E. Laird, and A. M. Weiner, “Coherent control of terahertz emission and carrier populations in semiconductor heterostructures,” J. Opt. Soc. Am. B 11, 2457–2469 (1994).
[CrossRef]

M. S. C. Luo, S. L. Chuang, P. C. M. Planken, I. Brener, and M. C. Nuss, “Coherent double-pulse control of quantum beats in a coupled quantum well,” Phys. Rev. B 48, 11043–11050 (1993).
[CrossRef]

H. G. Roskos, M. C. Nuss, J. Shah, K. Leo, D. A. B. Miller, A. M. Fox, S. Schmitt-Rink, and K. Köhler, “Coherent submillimeter-wave emission from charge oscillations in a double-well potential,” Phys. Rev. Lett. 68, 2216–2219 (1992).
[CrossRef] [PubMed]

Peatross, J.

J. Zhou, J. Peatross, M. M. Murname, H. C. Kapteyn, and I. P. Christov, “Enhanced high-harmonic generation using 25 fs laser pulses,” Phys. Rev. Lett. 76, 752–755 (1996).
[CrossRef] [PubMed]

Peter, U.

T. Rappen, U. Peter, and W. Schäfer, “Polarization dependence of dephasing processes: a probe for many-body effects,” Phys. Rev. B 49, 10774–10777 (1994).
[CrossRef]

Pfeiffer, L.

Plaja, L.

Planken, P. C. M.

I. Brener, P. C. M. Planken, M. C. Nuss, M. S. C. Luo, S.-L. Chuang, L. Pfeiffer, D. E. Laird, and A. M. Weiner, “Coherent control of terahertz emission and carrier populations in semiconductor heterostructures,” J. Opt. Soc. Am. B 11, 2457–2469 (1994).
[CrossRef]

M. S. C. Luo, S. L. Chuang, P. C. M. Planken, I. Brener, and M. C. Nuss, “Coherent double-pulse control of quantum beats in a coupled quantum well,” Phys. Rev. B 48, 11043–11050 (1993).
[CrossRef]

Poli, P.

For a review, see, for example, F. Rossi, P. Poli, and C. Jacoboni, “Weighted Monte Carlo approach to semiclassical and quantum electron transport in semiconductors,” Semicond. Sci. Technol. 7, 1017 (1992).
[CrossRef]

Rappen, T.

T. Rappen, U. Peter, and W. Schäfer, “Polarization dependence of dephasing processes: a probe for many-body effects,” Phys. Rev. B 49, 10774–10777 (1994).
[CrossRef]

Roskos, H. G.

H. G. Roskos, M. C. Nuss, J. Shah, K. Leo, D. A. B. Miller, A. M. Fox, S. Schmitt-Rink, and K. Köhler, “Coherent submillimeter-wave emission from charge oscillations in a double-well potential,” Phys. Rev. Lett. 68, 2216–2219 (1992).
[CrossRef] [PubMed]

Roso, L.

Rossi, F.

For a review, see, for example, F. Rossi, P. Poli, and C. Jacoboni, “Weighted Monte Carlo approach to semiclassical and quantum electron transport in semiconductors,” Semicond. Sci. Technol. 7, 1017 (1992).
[CrossRef]

Sakaki, H.

K. B. Nordstrom, K. Johnsen, S. J. Allen, A. P. Jauho, B. Birnir, J. Kono, T. Noda, H. Akiyama, and H. Sakaki, “Observation of dynamical Franz–Keldysh effect,” Phys. Status Solidi B 204, 52–54 (1997).
[CrossRef]

Schafer, K. J.

J. L. Krause, K. J. Schafer, M. Ben-Nun, and K. R. Wilson, “Creating and detecting shaped Rydberg wave packets,” Phys. Rev. Lett. 79, 4978–4981 (1998).
[CrossRef]

Schafer, W.

J. Feldmann, G. von Plessen, M. Koch, E. O. Göbel, P. Thomas, G. Backer, C. Hartmann, H. Scheizer, W. Schafer, and H. Nickel, “Coherent dynamics of excitonic wave packets,” Phys. Rev. Lett. 56, 3027–3030 (1993).
[CrossRef]

Schäfer, W.

T. Rappen, U. Peter, and W. Schäfer, “Polarization dependence of dephasing processes: a probe for many-body effects,” Phys. Rev. B 49, 10774–10777 (1994).
[CrossRef]

Scheizer, H.

J. Feldmann, G. von Plessen, M. Koch, E. O. Göbel, P. Thomas, G. Backer, C. Hartmann, H. Scheizer, W. Schafer, and H. Nickel, “Coherent dynamics of excitonic wave packets,” Phys. Rev. Lett. 56, 3027–3030 (1993).
[CrossRef]

Schmitt-Rink, S.

J. Feldmann, K. Leo, J. Shaw, D. A. B. Miller, J. E. Cunningham, S. Schmitt-Rink, T. Meier, G. von Plessen, A. Schultze, and P. Thomas, “Optical investigation of Bloch oscillations in a semiconductor superlattice,” Phys. Rev. B 46, 7252–7255 (1992).
[CrossRef]

H. G. Roskos, M. C. Nuss, J. Shah, K. Leo, D. A. B. Miller, A. M. Fox, S. Schmitt-Rink, and K. Köhler, “Coherent submillimeter-wave emission from charge oscillations in a double-well potential,” Phys. Rev. Lett. 68, 2216–2219 (1992).
[CrossRef] [PubMed]

Schultze, A.

J. Feldmann, K. Leo, J. Shaw, D. A. B. Miller, J. E. Cunningham, S. Schmitt-Rink, T. Meier, G. von Plessen, A. Schultze, and P. Thomas, “Optical investigation of Bloch oscillations in a semiconductor superlattice,” Phys. Rev. B 46, 7252–7255 (1992).
[CrossRef]

Shah, J.

H. G. Roskos, M. C. Nuss, J. Shah, K. Leo, D. A. B. Miller, A. M. Fox, S. Schmitt-Rink, and K. Köhler, “Coherent submillimeter-wave emission from charge oscillations in a double-well potential,” Phys. Rev. Lett. 68, 2216–2219 (1992).
[CrossRef] [PubMed]

Shaw, J.

J. Feldmann, K. Leo, J. Shaw, D. A. B. Miller, J. E. Cunningham, S. Schmitt-Rink, T. Meier, G. von Plessen, A. Schultze, and P. Thomas, “Optical investigation of Bloch oscillations in a semiconductor superlattice,” Phys. Rev. B 46, 7252–7255 (1992).
[CrossRef]

Son, J.-H.

Spitzer, S.

D. Fröhlich, S. Spitzer, B. Uebbing, and R. Zimmermann, “Polarization dependence in the intraband optical stark effect of quantum wells,” Phys. Status Solidi B 173, 83–89 (1992).
[CrossRef]

Stahl, A.

See, for example, V. M. Axt, G. Bartels, and A. Stahl, “Intraband dynamics at the semiconductor band edge: shortcomings of the Bloch equation method,” Phys. Rev. Lett. 76, 2543–2546 (1996).
[CrossRef] [PubMed]

Thomas, P.

T. Meier, G. von Plessen, P. Thomas, and S. W. Koch, “Coherent electric-field effects in semiconductor,” Phys. Rev. Lett. 73, 902–905 (1994).
[CrossRef] [PubMed]

J. Feldmann, G. von Plessen, M. Koch, E. O. Göbel, P. Thomas, G. Backer, C. Hartmann, H. Scheizer, W. Schafer, and H. Nickel, “Coherent dynamics of excitonic wave packets,” Phys. Rev. Lett. 56, 3027–3030 (1993).
[CrossRef]

J. Feldmann, K. Leo, J. Shaw, D. A. B. Miller, J. E. Cunningham, S. Schmitt-Rink, T. Meier, G. von Plessen, A. Schultze, and P. Thomas, “Optical investigation of Bloch oscillations in a semiconductor superlattice,” Phys. Rev. B 46, 7252–7255 (1992).
[CrossRef]

Uebbing, B.

D. Fröhlich, S. Spitzer, B. Uebbing, and R. Zimmermann, “Polarization dependence in the intraband optical stark effect of quantum wells,” Phys. Status Solidi B 173, 83–89 (1992).
[CrossRef]

von Plessen, G.

T. Meier, G. von Plessen, P. Thomas, and S. W. Koch, “Coherent electric-field effects in semiconductor,” Phys. Rev. Lett. 73, 902–905 (1994).
[CrossRef] [PubMed]

J. Feldmann, G. von Plessen, M. Koch, E. O. Göbel, P. Thomas, G. Backer, C. Hartmann, H. Scheizer, W. Schafer, and H. Nickel, “Coherent dynamics of excitonic wave packets,” Phys. Rev. Lett. 56, 3027–3030 (1993).
[CrossRef]

J. Feldmann, K. Leo, J. Shaw, D. A. B. Miller, J. E. Cunningham, S. Schmitt-Rink, T. Meier, G. von Plessen, A. Schultze, and P. Thomas, “Optical investigation of Bloch oscillations in a semiconductor superlattice,” Phys. Rev. B 46, 7252–7255 (1992).
[CrossRef]

Weiner, A. M.

Whitaker, J. F.

Wilson, K. R.

J. L. Krause, K. J. Schafer, M. Ben-Nun, and K. R. Wilson, “Creating and detecting shaped Rydberg wave packets,” Phys. Rev. Lett. 79, 4978–4981 (1998).
[CrossRef]

Yacoby, Y.

Y. Yacoby, “High-frequency Franz–Keldysh effect,” Phys. Rev. 169, 610–619 (1968).
[CrossRef]

Zhou, J.

J. Zhou, J. Peatross, M. M. Murname, H. C. Kapteyn, and I. P. Christov, “Enhanced high-harmonic generation using 25 fs laser pulses,” Phys. Rev. Lett. 76, 752–755 (1996).
[CrossRef] [PubMed]

Zimmermann, R.

D. Fröhlich, S. Spitzer, B. Uebbing, and R. Zimmermann, “Polarization dependence in the intraband optical stark effect of quantum wells,” Phys. Status Solidi B 173, 83–89 (1992).
[CrossRef]

J. Opt. Soc. Am. B

Phys. Rev.

Y. Yacoby, “High-frequency Franz–Keldysh effect,” Phys. Rev. 169, 610–619 (1968).
[CrossRef]

Phys. Rev. A

W. Becker, A. Lohr, K. Kleber, and M. Lewenstein, “A unified theory of high-harmonic generation: application to polarization properties of the harmonics,” Phys. Rev. A 56, 645–656 (1997).
[CrossRef]

Phys. Rev. B

M. S. C. Luo, S. L. Chuang, P. C. M. Planken, I. Brener, and M. C. Nuss, “Coherent double-pulse control of quantum beats in a coupled quantum well,” Phys. Rev. B 48, 11043–11050 (1993).
[CrossRef]

M. Lindberg and S. W. Koch, “Effective Bloch equations for semiconductors,” Phys. Rev. B 38, 3342–3350 (1988).
[CrossRef]

T. Rappen, U. Peter, and W. Schäfer, “Polarization dependence of dephasing processes: a probe for many-body effects,” Phys. Rev. B 49, 10774–10777 (1994).
[CrossRef]

S. Hughes and D. S. Citrin, “Ultrafast heating and switching of a semiconductor optical amplifier using half-cycle terahertz pulses,” Phys. Rev. B 58, R15969–R15972 (1998).
[CrossRef]

S. Hughes and D. S. Citrin, “Creation of highly anisotropic wavepackets in quantum wells: dynamical Franz–Keldysh effect in the optical and terahertz regimes,” Phys. Rev. B 59, R5288–R5291 (1999).
[CrossRef]

J. Feldmann, K. Leo, J. Shaw, D. A. B. Miller, J. E. Cunningham, S. Schmitt-Rink, T. Meier, G. von Plessen, A. Schultze, and P. Thomas, “Optical investigation of Bloch oscillations in a semiconductor superlattice,” Phys. Rev. B 46, 7252–7255 (1992).
[CrossRef]

Phys. Rev. Lett.

A. P. Jauho and K. Johnsen, “Dynamical Franz–Keldysh effect,” Phys. Rev. Lett. 24, 4576–4579 (1996).
[CrossRef]

M. Holthaus, “Collapse of minibands in far-infrared irradiated superlattices,” Phys. Rev. Lett. 69, 351–354 (1992).
[CrossRef] [PubMed]

T. Meier, G. von Plessen, P. Thomas, and S. W. Koch, “Coherent electric-field effects in semiconductor,” Phys. Rev. Lett. 73, 902–905 (1994).
[CrossRef] [PubMed]

H. G. Roskos, M. C. Nuss, J. Shah, K. Leo, D. A. B. Miller, A. M. Fox, S. Schmitt-Rink, and K. Köhler, “Coherent submillimeter-wave emission from charge oscillations in a double-well potential,” Phys. Rev. Lett. 68, 2216–2219 (1992).
[CrossRef] [PubMed]

P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71, 1994–1997 (1993).
[CrossRef] [PubMed]

J. Feldmann, G. von Plessen, M. Koch, E. O. Göbel, P. Thomas, G. Backer, C. Hartmann, H. Scheizer, W. Schafer, and H. Nickel, “Coherent dynamics of excitonic wave packets,” Phys. Rev. Lett. 56, 3027–3030 (1993).
[CrossRef]

See, for example, V. M. Axt, G. Bartels, and A. Stahl, “Intraband dynamics at the semiconductor band edge: shortcomings of the Bloch equation method,” Phys. Rev. Lett. 76, 2543–2546 (1996).
[CrossRef] [PubMed]

J. Zhou, J. Peatross, M. M. Murname, H. C. Kapteyn, and I. P. Christov, “Enhanced high-harmonic generation using 25 fs laser pulses,” Phys. Rev. Lett. 76, 752–755 (1996).
[CrossRef] [PubMed]

I. P. Christov, M. M. Murname, and H. C. Kapteyn, “High-harmonic generation of attosecond pulses in the ‘single-cycle’ regime,” Phys. Rev. Lett. 78, 1251–1254 (1997).
[CrossRef]

J. L. Krause, K. J. Schafer, M. Ben-Nun, and K. R. Wilson, “Creating and detecting shaped Rydberg wave packets,” Phys. Rev. Lett. 79, 4978–4981 (1998).
[CrossRef]

Phys. Status Solidi A

K. Johnsen and A. P. Jauho, “Optics of excitons in THz irradiated quantum wells,” Phys. Status Solidi A 164, 553–556 (1997).
[CrossRef]

Phys. Status Solidi B

D. Fröhlich, S. Spitzer, B. Uebbing, and R. Zimmermann, “Polarization dependence in the intraband optical stark effect of quantum wells,” Phys. Status Solidi B 173, 83–89 (1992).
[CrossRef]

K. B. Nordstrom, K. Johnsen, S. J. Allen, A. P. Jauho, B. Birnir, J. Kono, T. Noda, H. Akiyama, and H. Sakaki, “Observation of dynamical Franz–Keldysh effect,” Phys. Status Solidi B 204, 52–54 (1997).
[CrossRef]

Semicond. Sci. Technol.

For a review, see, for example, F. Rossi, P. Poli, and C. Jacoboni, “Weighted Monte Carlo approach to semiclassical and quantum electron transport in semiconductors,” Semicond. Sci. Technol. 7, 1017 (1992).
[CrossRef]

Sov. Phys. JETP

L. V. Keldysh, Sov. Phys. JETP 20, 1307 (1965).

Z. Phys.

F. Bloch, Z. Phys. 52, 555 (1929).
[CrossRef]

Other

S. L. Chuang, S. Schmitt-Rink, B. I. Greene, P. N. Saeta, and A. F. J. Levi, “Optical rectification at semiconductor surfaces,” Phys. Rev. Lett. 68, 102–105 (1992); P. C. M. Planken, M. C. Nuss, I. Brener, K. W. Goossen, M. S. C. Luo, S. L. Chuang, and L. Pfeiffer, “Terahertz emission in single quantum wells after coherent optical excitation of light hole and heavy hole excitons,” Phys. Rev. Lett. 69, 3800–3803 (1992).
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A. W. Ghosh, A. V. Kuznetsov, and J. W. Wilkins, “Reflection of THz radiation by a superlattice,” Phys. Rev. Lett. 79, 3494–3497 (1997); J. Kono, M. Y. Su, T. Inoshita, T. Noda, M. S. Sherwin, S. J. Allen, Jr., and H. Sakaki, “Resonant terahertz optical sideband generation from confined magnetoexcitons,” Phys. Rev. Lett. 79, 1758–1761 (1997).
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N. G. Asmar, A. G. Markelz, E. G. Gwinn, J. Cerne, M. S. Sherwin, K. L. Campman, P. F. Hopkins, and A. C. Gossard, “Resonant-energy relaxation of terahertz-driven two-dimensional electron gases,” Phys. Rev. B 51, 18041–18044 (1995); X. L. Lei, B. Dong, and Y. Q. Chen, “Nonlinear transport in quasi-two-dimensional systems driven by intense terahertz fields,” Phys. Rev. B 56, 12120–12123 (1997).
[CrossRef]

W. Franz, Z. Naturforsch. Teil A 13, 484 (1958); L. V. Keldysh, Sov. Phys. JETP 34, 788 (1958).

For a textbook discussion, see J. Shah, Ultrafast Spectroscopy of Semiconductors and Semiconductor Nanostructures (Springer-Verlag, Berlin, 1996) and references therein.

D. S. Citrin, “Quasi-half-cycle terahertz pulse generation via optical rectification in quantum wells using shaped optical pulses,” Optics Express 4, 376–384 (1997); A. M. Weiner, “Enhancement of coherent charge oscillations in coupled quantum wells by femtosecond pulse shaping,” J. Opt. Soc. Am. B 11, 2480–2491 (1994).
[CrossRef]

For a textbook discussion, see H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors, 3rd ed. (World Scientific, Singapore, 1994) and references therein.

D. H. Dunlop and V. M. Kenkre, “Dynamic localization of a charged particle moving under the influence of an electric field,” Phys. Rev. B 34, 3625–3633 (1986); T. Meier, G. von Plessen, P. Thomas, and S. W. Koch, “Coherent effects induced by static and time-dependent electric fields in semiconductors,” Phys. Rev. B 51, 14490–14497 (1995).
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J. A. Fleck, Jr., “Ultrashort-pulse generation by Q-switched lasers,” Phys. Rev. B 1, 84–100 (1970); J. C. Eilbeck and R. K. Bullough, J. Phys. A 5, 820 (1972).
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R. Zimmermann, in Nonlinear Optics of Semiconductor Nanostructures, F. Henneberger, S. Schmitt-Rink, and E. O. Göbel, eds. (Akademie-Verlag, Berlin, 1993), pp. 51–74; R. Zimmermann, Spectroscopy and Dynamics of Collective Excitations in Solids, Di Bartoli, ed. (Plenum, New York, 1997).

M. Protopapus, D. G. Lappas, and P. L. Knight, “Strong field ionization in arbitrary laser polarizations,” Phys. Rev. Lett. 79, 4550–4553 (1997); G. G. Paulus, H. Walther, A. Lohr, W. Becker, and M. Kleber, “Above-threshold ionization by an elliptically polarized field: quantum tunneling interferences and classical dodging,” Phys. Rev. Lett. 80, 484–487 (1998).
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K. S. Budil, P. Salières, A. L’Huillier, T. Ditmire, and M. D. Perry, “Influence of ellipticity on harmonic generation,” Phys. Rev. A 48, R3437–R3400 (1993); G. G. Paulus, F. Zacher, H. Walther, A. Lohr, W. Becker, and M. Kleber, “Above-threshold ionization by an elliptically polarized field: quantum tunneling interferences and classical dodging,” Phys. Rev. Lett. 80, 484–487 (1997).
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[CrossRef]

D. S. Citrin and S. Hughes, “Circularly polarized dynamic Franz–Keldysh effect,” submitted to Phys. Rev. B.

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Figures (13)

Fig. 1
Fig. 1

Schematic of the modeled experiment.

Fig. 2
Fig. 2

(a) Optical polarization versus time corresponding to the following: solid curve, no applied THz field; dashed curve, with THz field and ξ(t)=2πνTHzt; dotted curve, with a THz field and ξ(t)=2πνTHzt+π/2. The frequency and amplitude of the THz field is 1 THz and 3 kV/cm. (b) Corresponding optical absorption spectrum of (a).

Fig. 3
Fig. 3

(a) As in Fig. 2(a) but with a 2-THz field of amplitude 6 kV/cm. (b) Corresponding optical absorption spectrum of (a).

Fig. 4
Fig. 4

(a) Solid curve, temporal behavior of the emitted THz field with ξ(t)=2πνTHzt; dashed curve, 2πνTHzt+π/2. The frequency and amplitude of the THz field is 1 THz and 3 kV/cm. (b) Solid curve, magnitude of the emitted THz spectra with ξ(t)=2πνTHzt; dashed curve, ξ(t)=2πνTHzt+π/2. Note that an energy of 40 MeV corresponds to a frequency of ∼10 THz.

Fig. 5
Fig. 5

(a) As in Fig. 4(a) but with a 2-THz field of amplitude 6 kV/cm. (b) Solid curve, magnitude of the emitted THz spectra with ξ(t)=2πνTHzt; dashed curve, ξ(t)=2πνTHzt+π/2.

Fig. 6
Fig. 6

Magnitude of the emitted THz spectra with ξ(t)=2πνTHzt+π/2 for various dephasing times. The driving field has a magnitude and frequency of 3 kV/cm and 1 THz, respectively.

Fig. 7
Fig. 7

(a) Emitted THz field both circularly polarized and linearly polarized driving fields. Heavy and thin solid curves, THz emission for linearly polarized driving fields with ϕ=0, π/2, respectively; heavy and thin dashed curves, THz emission from circularly polarized driving field from the respective x and y components. (b) As in (a) but with a 6-kV/cm field.

Fig. 8
Fig. 8

(a) Spectrum of the chirped optical pulses. (b) Emitted THz field both a negatively chirped and a positively chirped pulse.

Fig. 9
Fig. 9

Wave packet at several times [(a) t=100 fs, (b) t=250 fs, (c) t=400 fs, and (d) t=640 fs] for the polarization density with ξ(t)=2πνTHzt. The frequency and amplitude of the THz field is 1 THz and 3 kV/cm. The wave packets have been multiplied by a factor of 103 for clarity. A displacement of the WP from (x, y)=(0, 0) means it is polarized; a circular shape means that the electron and hole distributions are circular (but may be displaced).

Fig. 10
Fig. 10

As in Fig. 9 but with ξ(t)=2πνTHzt+π/2.

Fig. 11
Fig. 11

As in Fig. 9 but with a 2-THz field of amplitude 6 kV/cm. The phase ξ(t)=2πνTHzt.

Fig. 12
Fig. 12

As in Fig. 9 but with ξ(t)=2πνTHzt+π/2.

Fig. 13
Fig. 13

Wave packet at several times for the polarization density with a circularly polarized input field of magnitude 3 kV/cm and frequency 1 THz.

Equations (13)

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FTHz(t, r)=nˆxF0 cos ξ(t)+nˆyF0 sin ξ(t),
t+eFTHz(t, r)·kPk=iΔkPk+iΩk+Pktc.c.,
P˜k¯t˜=Pkttt˜+kPk kt˜,
=t+FTHz(t, r)·kPk.
P˜k˜t=iΔk(t)P˜k˜+iΩk(t)-γ0pP˜k˜,
[withFTHz(t, r)=nˆxF0 cos(ωTHzt)]
Pk(t)=Pk+Λ(t)(t0),
Δk12µ[k˜-Λ(t)]2,
qVk-qPqq˜Vk˜-q˜Pq˜.
P=2A-1kdcvPk=2/(2π)2dk˜x dk˜y dcvP˜k˜x,k˜y.
α(ω)=-4πkz ImP(ω)FOpt(ω).
PTHz(t)=ed2rP*(r, t)rP(r, t)=-4ek˜P˜k˜ikP˜k˜,
FOpt(t)=FOpt(t)exp[-iωc(t)t]+c.c.,

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