Abstract

Rabi splitting in quantum well (QW) embedded in microcavities under strong coupling condition is modeled by a time-dependent transfer matrix model. The spectral response of QW under the influence of excitonic effects is simulated by infinite impulse digital filters. It is shown that the splitting energy obtained from the proposed model match well with that deduced from the reflection spectrum analysis. The lasing spectra observed from different transmission angles of the QW microcavity can also be calculated. Hence, it is proved that the proposed model can be used to design and analyze the lasing characteristics of QW microcavities under strong coupling condition.

© 2008 Optical Society of America

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References

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  1. A. V. Kovakin and G. Malpuech, Cavity Polaritons (Elsevier, Amsterdam, 2003).
  2. G. Khitrova, H. Gibbs, F. Jahnke, M. Kira, and S. W. Koch, “Nonlinear optics of normal-mode-coupling semiconductor microcavities,” Rev. Mod. Phys. 71, 1591–1639 (1999).
    [Crossref]
  3. S. I. Tsintzos, N. T. Pelekanos, G. Konstantinidis, Z. Hatzopoulos, and P. G. Savvidis, “A GaAs polariton light-emitting diode operating near room temperature,” Nature 453, 372–375 (2008).
    [Crossref] [PubMed]
  4. D. Bajoni, E. Semenova, A. Lemaitre, S. Bouchoule, E. Wertz, P. Senellart, and J. Bloch, “Polariton light-emitting diode in a GaAs-based microcavity,” Phys. Rev. B 77, 113303 (2008).
    [Crossref]
  5. S. Christopoulos, G. Baldassarri Höger von Högersthal, A. J. D. Grundy, P. G. Lagoudakis, A. V. Kavokin, and J. J. Baumberg, “Room-temperature polariton lasing in semiconductor microcavities,” Phys. Rev. Lett. 98, 126405 (2007).
    [Crossref] [PubMed]
  6. F. Tassone and Y. Yamamoto, “Lasing and squeezing of composite bosons in a semiconductor microcavity,” Phys. Rev. A 62, 063809 (2000).
    [Crossref]
  7. A. V. Kavokin and M. A. Kaliteevski, “Excitonic light reflection and absorption in semiconductor microvcavities at oblique incidence,” Solid State Commun. 95, 859–862 (1995).
    [Crossref]
  8. E. L. Ivchenko, M. A. Kaliteevski, A. V. Kavokin, and A. I. Nesvizhskii, “Reflection and absorption spectra from microcavities with resonant Bragg quantum wells,” J. Opt. Soc. Am. B 13, 1061–1068 (1996).
    [Crossref]
  9. E. L. Ivchenko, “Excitonic polaritons in periodic quantum well structures,” Sov. Phys. Solid State 33, 1344–1346 (1991).
  10. L. C. Andreani, F. Tassone, and F. Bassani, “Radiative lifetime of free excitons in quantum wells,” Solid State Commun. 77, 641–645 (1991).
    [Crossref]
  11. L. V. Butov, “A polariton laser,” Nature 447, 540–541 (2007).
    [Crossref] [PubMed]
  12. S. F. Yu, “Dynamic behavior of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 32, 1168–1179 (1996).
    [Crossref]
  13. C. Nyack, “Infinite impulse response filters,” http://dspcan.homestead.com/files/IIRFilt/zfiltiiri.htm.

2008 (2)

S. I. Tsintzos, N. T. Pelekanos, G. Konstantinidis, Z. Hatzopoulos, and P. G. Savvidis, “A GaAs polariton light-emitting diode operating near room temperature,” Nature 453, 372–375 (2008).
[Crossref] [PubMed]

D. Bajoni, E. Semenova, A. Lemaitre, S. Bouchoule, E. Wertz, P. Senellart, and J. Bloch, “Polariton light-emitting diode in a GaAs-based microcavity,” Phys. Rev. B 77, 113303 (2008).
[Crossref]

2007 (2)

S. Christopoulos, G. Baldassarri Höger von Högersthal, A. J. D. Grundy, P. G. Lagoudakis, A. V. Kavokin, and J. J. Baumberg, “Room-temperature polariton lasing in semiconductor microcavities,” Phys. Rev. Lett. 98, 126405 (2007).
[Crossref] [PubMed]

L. V. Butov, “A polariton laser,” Nature 447, 540–541 (2007).
[Crossref] [PubMed]

2000 (1)

F. Tassone and Y. Yamamoto, “Lasing and squeezing of composite bosons in a semiconductor microcavity,” Phys. Rev. A 62, 063809 (2000).
[Crossref]

1999 (1)

G. Khitrova, H. Gibbs, F. Jahnke, M. Kira, and S. W. Koch, “Nonlinear optics of normal-mode-coupling semiconductor microcavities,” Rev. Mod. Phys. 71, 1591–1639 (1999).
[Crossref]

1996 (2)

1995 (1)

A. V. Kavokin and M. A. Kaliteevski, “Excitonic light reflection and absorption in semiconductor microvcavities at oblique incidence,” Solid State Commun. 95, 859–862 (1995).
[Crossref]

1991 (2)

E. L. Ivchenko, “Excitonic polaritons in periodic quantum well structures,” Sov. Phys. Solid State 33, 1344–1346 (1991).

L. C. Andreani, F. Tassone, and F. Bassani, “Radiative lifetime of free excitons in quantum wells,” Solid State Commun. 77, 641–645 (1991).
[Crossref]

Andreani, L. C.

L. C. Andreani, F. Tassone, and F. Bassani, “Radiative lifetime of free excitons in quantum wells,” Solid State Commun. 77, 641–645 (1991).
[Crossref]

Bajoni, D.

D. Bajoni, E. Semenova, A. Lemaitre, S. Bouchoule, E. Wertz, P. Senellart, and J. Bloch, “Polariton light-emitting diode in a GaAs-based microcavity,” Phys. Rev. B 77, 113303 (2008).
[Crossref]

Baldassarri Höger von Högersthal, G.

S. Christopoulos, G. Baldassarri Höger von Högersthal, A. J. D. Grundy, P. G. Lagoudakis, A. V. Kavokin, and J. J. Baumberg, “Room-temperature polariton lasing in semiconductor microcavities,” Phys. Rev. Lett. 98, 126405 (2007).
[Crossref] [PubMed]

Bassani, F.

L. C. Andreani, F. Tassone, and F. Bassani, “Radiative lifetime of free excitons in quantum wells,” Solid State Commun. 77, 641–645 (1991).
[Crossref]

Baumberg, J. J.

S. Christopoulos, G. Baldassarri Höger von Högersthal, A. J. D. Grundy, P. G. Lagoudakis, A. V. Kavokin, and J. J. Baumberg, “Room-temperature polariton lasing in semiconductor microcavities,” Phys. Rev. Lett. 98, 126405 (2007).
[Crossref] [PubMed]

Bloch, J.

D. Bajoni, E. Semenova, A. Lemaitre, S. Bouchoule, E. Wertz, P. Senellart, and J. Bloch, “Polariton light-emitting diode in a GaAs-based microcavity,” Phys. Rev. B 77, 113303 (2008).
[Crossref]

Bouchoule, S.

D. Bajoni, E. Semenova, A. Lemaitre, S. Bouchoule, E. Wertz, P. Senellart, and J. Bloch, “Polariton light-emitting diode in a GaAs-based microcavity,” Phys. Rev. B 77, 113303 (2008).
[Crossref]

Butov, L. V.

L. V. Butov, “A polariton laser,” Nature 447, 540–541 (2007).
[Crossref] [PubMed]

Christopoulos, S.

S. Christopoulos, G. Baldassarri Höger von Högersthal, A. J. D. Grundy, P. G. Lagoudakis, A. V. Kavokin, and J. J. Baumberg, “Room-temperature polariton lasing in semiconductor microcavities,” Phys. Rev. Lett. 98, 126405 (2007).
[Crossref] [PubMed]

Gibbs, H.

G. Khitrova, H. Gibbs, F. Jahnke, M. Kira, and S. W. Koch, “Nonlinear optics of normal-mode-coupling semiconductor microcavities,” Rev. Mod. Phys. 71, 1591–1639 (1999).
[Crossref]

Grundy, A. J. D.

S. Christopoulos, G. Baldassarri Höger von Högersthal, A. J. D. Grundy, P. G. Lagoudakis, A. V. Kavokin, and J. J. Baumberg, “Room-temperature polariton lasing in semiconductor microcavities,” Phys. Rev. Lett. 98, 126405 (2007).
[Crossref] [PubMed]

Hatzopoulos, Z.

S. I. Tsintzos, N. T. Pelekanos, G. Konstantinidis, Z. Hatzopoulos, and P. G. Savvidis, “A GaAs polariton light-emitting diode operating near room temperature,” Nature 453, 372–375 (2008).
[Crossref] [PubMed]

Ivchenko, E. L.

Jahnke, F.

G. Khitrova, H. Gibbs, F. Jahnke, M. Kira, and S. W. Koch, “Nonlinear optics of normal-mode-coupling semiconductor microcavities,” Rev. Mod. Phys. 71, 1591–1639 (1999).
[Crossref]

Kaliteevski, M. A.

E. L. Ivchenko, M. A. Kaliteevski, A. V. Kavokin, and A. I. Nesvizhskii, “Reflection and absorption spectra from microcavities with resonant Bragg quantum wells,” J. Opt. Soc. Am. B 13, 1061–1068 (1996).
[Crossref]

A. V. Kavokin and M. A. Kaliteevski, “Excitonic light reflection and absorption in semiconductor microvcavities at oblique incidence,” Solid State Commun. 95, 859–862 (1995).
[Crossref]

Kavokin, A. V.

S. Christopoulos, G. Baldassarri Höger von Högersthal, A. J. D. Grundy, P. G. Lagoudakis, A. V. Kavokin, and J. J. Baumberg, “Room-temperature polariton lasing in semiconductor microcavities,” Phys. Rev. Lett. 98, 126405 (2007).
[Crossref] [PubMed]

E. L. Ivchenko, M. A. Kaliteevski, A. V. Kavokin, and A. I. Nesvizhskii, “Reflection and absorption spectra from microcavities with resonant Bragg quantum wells,” J. Opt. Soc. Am. B 13, 1061–1068 (1996).
[Crossref]

A. V. Kavokin and M. A. Kaliteevski, “Excitonic light reflection and absorption in semiconductor microvcavities at oblique incidence,” Solid State Commun. 95, 859–862 (1995).
[Crossref]

Khitrova, G.

G. Khitrova, H. Gibbs, F. Jahnke, M. Kira, and S. W. Koch, “Nonlinear optics of normal-mode-coupling semiconductor microcavities,” Rev. Mod. Phys. 71, 1591–1639 (1999).
[Crossref]

Kira, M.

G. Khitrova, H. Gibbs, F. Jahnke, M. Kira, and S. W. Koch, “Nonlinear optics of normal-mode-coupling semiconductor microcavities,” Rev. Mod. Phys. 71, 1591–1639 (1999).
[Crossref]

Koch, S. W.

G. Khitrova, H. Gibbs, F. Jahnke, M. Kira, and S. W. Koch, “Nonlinear optics of normal-mode-coupling semiconductor microcavities,” Rev. Mod. Phys. 71, 1591–1639 (1999).
[Crossref]

Konstantinidis, G.

S. I. Tsintzos, N. T. Pelekanos, G. Konstantinidis, Z. Hatzopoulos, and P. G. Savvidis, “A GaAs polariton light-emitting diode operating near room temperature,” Nature 453, 372–375 (2008).
[Crossref] [PubMed]

Kovakin, A. V.

A. V. Kovakin and G. Malpuech, Cavity Polaritons (Elsevier, Amsterdam, 2003).

Lagoudakis, P. G.

S. Christopoulos, G. Baldassarri Höger von Högersthal, A. J. D. Grundy, P. G. Lagoudakis, A. V. Kavokin, and J. J. Baumberg, “Room-temperature polariton lasing in semiconductor microcavities,” Phys. Rev. Lett. 98, 126405 (2007).
[Crossref] [PubMed]

Lemaitre, A.

D. Bajoni, E. Semenova, A. Lemaitre, S. Bouchoule, E. Wertz, P. Senellart, and J. Bloch, “Polariton light-emitting diode in a GaAs-based microcavity,” Phys. Rev. B 77, 113303 (2008).
[Crossref]

Malpuech, G.

A. V. Kovakin and G. Malpuech, Cavity Polaritons (Elsevier, Amsterdam, 2003).

Nesvizhskii, A. I.

Nyack, C.

C. Nyack, “Infinite impulse response filters,” http://dspcan.homestead.com/files/IIRFilt/zfiltiiri.htm.

Pelekanos, N. T.

S. I. Tsintzos, N. T. Pelekanos, G. Konstantinidis, Z. Hatzopoulos, and P. G. Savvidis, “A GaAs polariton light-emitting diode operating near room temperature,” Nature 453, 372–375 (2008).
[Crossref] [PubMed]

Savvidis, P. G.

S. I. Tsintzos, N. T. Pelekanos, G. Konstantinidis, Z. Hatzopoulos, and P. G. Savvidis, “A GaAs polariton light-emitting diode operating near room temperature,” Nature 453, 372–375 (2008).
[Crossref] [PubMed]

Semenova, E.

D. Bajoni, E. Semenova, A. Lemaitre, S. Bouchoule, E. Wertz, P. Senellart, and J. Bloch, “Polariton light-emitting diode in a GaAs-based microcavity,” Phys. Rev. B 77, 113303 (2008).
[Crossref]

Senellart, P.

D. Bajoni, E. Semenova, A. Lemaitre, S. Bouchoule, E. Wertz, P. Senellart, and J. Bloch, “Polariton light-emitting diode in a GaAs-based microcavity,” Phys. Rev. B 77, 113303 (2008).
[Crossref]

Tassone, F.

F. Tassone and Y. Yamamoto, “Lasing and squeezing of composite bosons in a semiconductor microcavity,” Phys. Rev. A 62, 063809 (2000).
[Crossref]

L. C. Andreani, F. Tassone, and F. Bassani, “Radiative lifetime of free excitons in quantum wells,” Solid State Commun. 77, 641–645 (1991).
[Crossref]

Tsintzos, S. I.

S. I. Tsintzos, N. T. Pelekanos, G. Konstantinidis, Z. Hatzopoulos, and P. G. Savvidis, “A GaAs polariton light-emitting diode operating near room temperature,” Nature 453, 372–375 (2008).
[Crossref] [PubMed]

Wertz, E.

D. Bajoni, E. Semenova, A. Lemaitre, S. Bouchoule, E. Wertz, P. Senellart, and J. Bloch, “Polariton light-emitting diode in a GaAs-based microcavity,” Phys. Rev. B 77, 113303 (2008).
[Crossref]

Yamamoto, Y.

F. Tassone and Y. Yamamoto, “Lasing and squeezing of composite bosons in a semiconductor microcavity,” Phys. Rev. A 62, 063809 (2000).
[Crossref]

Yu, S. F.

S. F. Yu, “Dynamic behavior of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 32, 1168–1179 (1996).
[Crossref]

IEEE J. Quantum Electron. (1)

S. F. Yu, “Dynamic behavior of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 32, 1168–1179 (1996).
[Crossref]

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

Nature (2)

S. I. Tsintzos, N. T. Pelekanos, G. Konstantinidis, Z. Hatzopoulos, and P. G. Savvidis, “A GaAs polariton light-emitting diode operating near room temperature,” Nature 453, 372–375 (2008).
[Crossref] [PubMed]

L. V. Butov, “A polariton laser,” Nature 447, 540–541 (2007).
[Crossref] [PubMed]

Phys. Rev. A (1)

F. Tassone and Y. Yamamoto, “Lasing and squeezing of composite bosons in a semiconductor microcavity,” Phys. Rev. A 62, 063809 (2000).
[Crossref]

Phys. Rev. B (1)

D. Bajoni, E. Semenova, A. Lemaitre, S. Bouchoule, E. Wertz, P. Senellart, and J. Bloch, “Polariton light-emitting diode in a GaAs-based microcavity,” Phys. Rev. B 77, 113303 (2008).
[Crossref]

Phys. Rev. Lett. (1)

S. Christopoulos, G. Baldassarri Höger von Högersthal, A. J. D. Grundy, P. G. Lagoudakis, A. V. Kavokin, and J. J. Baumberg, “Room-temperature polariton lasing in semiconductor microcavities,” Phys. Rev. Lett. 98, 126405 (2007).
[Crossref] [PubMed]

Rev. Mod. Phys. (1)

G. Khitrova, H. Gibbs, F. Jahnke, M. Kira, and S. W. Koch, “Nonlinear optics of normal-mode-coupling semiconductor microcavities,” Rev. Mod. Phys. 71, 1591–1639 (1999).
[Crossref]

Solid State Commun. (2)

A. V. Kavokin and M. A. Kaliteevski, “Excitonic light reflection and absorption in semiconductor microvcavities at oblique incidence,” Solid State Commun. 95, 859–862 (1995).
[Crossref]

L. C. Andreani, F. Tassone, and F. Bassani, “Radiative lifetime of free excitons in quantum wells,” Solid State Commun. 77, 641–645 (1991).
[Crossref]

Sov. Phys. Solid State (1)

E. L. Ivchenko, “Excitonic polaritons in periodic quantum well structures,” Sov. Phys. Solid State 33, 1344–1346 (1991).

Other (2)

A. V. Kovakin and G. Malpuech, Cavity Polaritons (Elsevier, Amsterdam, 2003).

C. Nyack, “Infinite impulse response filters,” http://dspcan.homestead.com/files/IIRFilt/zfiltiiri.htm.

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Figures (4)

Fig. 1.
Fig. 1.

(a) Schematic of field transmission in a microcavity, where n is the refractive index of dielectric layer and z is the interface position; (b) digital filter treatment of reflection and transmission of active region, where RDF and TDF (i.e., reflection and transmission digital filters) are reflection and transmission digital filters, respectively.

Fig. 2.
Fig. 2.

Reproductions of r QW and t QW using RDF and TDF.

Fig. 3.
Fig. 3.

Normalized lasing spectra [(a) & (c)] and reflection [(b)] of the QW-embedded microcavity. The function of splitting energy with digital filter sampling time is given in (d).

Fig. 4.
Fig. 4.

Reflection [(a)] and, lasing [(b)] spectra with different transmission angles θ. In (b), arrows indicate the positions of the suppressed LPB modes.

Equations (11)

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E j ( z , t ) = E j + ( z , t ) + E j ( z , t ) , z j 1 z z j ,
[ E j + ( z j , t ) E j ( z j 1 , t ) ] = [ exp ( i k j d j ) 0 0 exp ( i k j d j ) ] [ E j + ( z j 1 , t Δ t ) E j ( z j , t Δ t ) ] ,
[ E j + 1 + ( z j , t ) E j ( z j , t ) ] = M j [ E j + ( z j , t ) E j + 1 ( z j , t ) ] ,
M j = 1 n j cos ( θ j ) + n j + 1 cos ( θ j + 1 ) [ 2 n j cos ( θ j ) n j + 1 cos ( θ j + 1 ) n j cos ( θ j ) n j cos ( θ j ) n j + 1 cos ( θ j + 1 ) 2 n j + 1 cos ( θ j + 1 ) ] .
E 1 + ( z 0 , t ) = r 1 E 1 ( z 0 , t ) , E N + ( z N , t ) = r N E N ( z N , t ) ,
r QW = i Γ o ω o + ω i ( Γ o + γ ) , t QW = 1 + r QW ,
E s 2 + ( t , z QW 2 ) = t QW [ exp ( i k QW d QW ) E s 1 + ( t 2 Δ t , z QW 1 ) + S + ] + r QW E s 2 ( t , z QW 2 ) ,
E s 1 ( t , z QW 1 ) = t QW [ exp ( i k QW d QW ) E s 2 ( t 2 Δ t , z QW 2 ) + S ] + r QW E s 1 + ( t , z QW 1 ) ,
H r ( w ) = A 1 B exp ( j ω Δ T ) , H t ( w ) = 1 + H r ( w ) ,
y r ( t ) = A x r ( t ) + B y r ( t Δ T ) ,
y t ( t ) = ( 1 A ) x t ( t ) B x t ( t Δ T ) + B y t ( t Δ T ) ,

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