Abstract

We study the focusing of a Gaussian laser beam in a microscopic planar cavity when the laser wavelength is resonant in the cavity but the beam divergence is larger than the acceptance angle of the cavity. Using the luminescence of implanted praseodymium ions as a microscopic probe for the total electric field inside the spacer of the microresonator, we investigate theoretically and experimentally how strong focusing alters the photoexcitation of luminescent species located inside such a structure.

© 1998 Optical Society of America

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References

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  1. F. DeMartini, G. Innocenti, G. R. Jacobivitz, and P. Mataloni, “Anomalous spontaneous emission time in a microscopic optical cavity,” Phys. Rev. Lett. 59, 2955–2958 (1987).
    [CrossRef]
  2. H. Yokoyama, M. Suzuki, and Y. Nambu, “Spontaneous emission and laser oscillation properties of microcavities containing a dye solution,” Appl. Phys. Lett. 58, 2598–2600 (1991).
    [CrossRef]
  3. G. Björk, S. Machida, Y. Yamamoto, and K. Igeta, “Modification of spontaneous emission rate in planar dielectric microcavity structures,” Phys. Rev. A 44, 669–681 (1991).
    [CrossRef] [PubMed]
  4. E. F. Shubert, A. M. Vredenberg, N. E. J. Hunt, Y. H. Yong, P. C. Becker, J. M. Poate, D. C. Jacobson, L. C. Feldman, and G. J. Zydzik, “Giant enhancement of luminescence intensity in Er-doped Si/SiO2 resonant cavities,” Appl. Phys. Lett. 61, 1381–1383 (1992); A. M. Vredenberg, N. E. J. Hunt, E. F. Shubert, D. C. Jacobson, J. M. Poate, and G. J. Zydzik, “Controlled atomic spontaneous emission from Er3+ in a transparent Si/SiO2 microcavity,” Phys. Rev. Lett. 71, 517–520 (1993).
    [CrossRef] [PubMed]
  5. H. Rigneault, S. Robert, C. Begon, B. Jacquier, and P. Moretti, “Radiative and guided wave emission of Er3+ atoms located in planar multidielectric structures,” Phys. Rev. A 55, 1497–1502 (1997).
    [CrossRef]
  6. H. Rigneault, F. Flory, S. Monneret, S. Robert, and L. Roux, “Fluorescence of Ta2O5 thin films doped by kilo-electron-volt Er implantation: application to microcavities,” Appl. Opt. 35, 5005–5012 (1996).
    [CrossRef] [PubMed]
  7. S. Monneret, S. Tisserand, F. Flory, and H. Rigneault, “Light-induced refractive-index modifications in dielectric thin films: experimental determination of relaxation time and amplitude,” Appl. Opt. 35, 5013–5020 (1996).
    [CrossRef] [PubMed]
  8. S. Monneret, “Coupleur à prisme à deux faisceaux pour la caractérisation d’effets non linéaires thermiques dans les couches minces,” Ph.D. dissertation (University Aix-Marseille III, Marseille, France, 1996).
  9. W. Seeber, E. A. Downing, L. Hesselink, M. M. Fejer, and D. Ehrt, “Pr3+-doped fluoride glasses,” J. Non-Cryst. Solids 189, 218–226 (1995).
    [CrossRef]
  10. F. DeMartini, G. Di Giuseppe, and M. Marrocco, “Single mode generation of quantum photon states by excited single molecules in a microcavity trap,” Phys. Rev. Lett. 76, 900–903 (1996).
    [CrossRef]
  11. P. Villeneuve, S. Fan, and J. D. Joannopoulos, “Microcavities in photonic crystals: mode symmetry, tunability, and coupling efficiency,” Phys. Rev. B 54, 7837–7842 (1996).
    [CrossRef]

1997 (1)

H. Rigneault, S. Robert, C. Begon, B. Jacquier, and P. Moretti, “Radiative and guided wave emission of Er3+ atoms located in planar multidielectric structures,” Phys. Rev. A 55, 1497–1502 (1997).
[CrossRef]

1996 (4)

F. DeMartini, G. Di Giuseppe, and M. Marrocco, “Single mode generation of quantum photon states by excited single molecules in a microcavity trap,” Phys. Rev. Lett. 76, 900–903 (1996).
[CrossRef]

P. Villeneuve, S. Fan, and J. D. Joannopoulos, “Microcavities in photonic crystals: mode symmetry, tunability, and coupling efficiency,” Phys. Rev. B 54, 7837–7842 (1996).
[CrossRef]

S. Monneret, S. Tisserand, F. Flory, and H. Rigneault, “Light-induced refractive-index modifications in dielectric thin films: experimental determination of relaxation time and amplitude,” Appl. Opt. 35, 5013–5020 (1996).
[CrossRef] [PubMed]

H. Rigneault, F. Flory, S. Monneret, S. Robert, and L. Roux, “Fluorescence of Ta2O5 thin films doped by kilo-electron-volt Er implantation: application to microcavities,” Appl. Opt. 35, 5005–5012 (1996).
[CrossRef] [PubMed]

1995 (1)

W. Seeber, E. A. Downing, L. Hesselink, M. M. Fejer, and D. Ehrt, “Pr3+-doped fluoride glasses,” J. Non-Cryst. Solids 189, 218–226 (1995).
[CrossRef]

1991 (2)

H. Yokoyama, M. Suzuki, and Y. Nambu, “Spontaneous emission and laser oscillation properties of microcavities containing a dye solution,” Appl. Phys. Lett. 58, 2598–2600 (1991).
[CrossRef]

G. Björk, S. Machida, Y. Yamamoto, and K. Igeta, “Modification of spontaneous emission rate in planar dielectric microcavity structures,” Phys. Rev. A 44, 669–681 (1991).
[CrossRef] [PubMed]

1987 (1)

F. DeMartini, G. Innocenti, G. R. Jacobivitz, and P. Mataloni, “Anomalous spontaneous emission time in a microscopic optical cavity,” Phys. Rev. Lett. 59, 2955–2958 (1987).
[CrossRef]

Begon, C.

H. Rigneault, S. Robert, C. Begon, B. Jacquier, and P. Moretti, “Radiative and guided wave emission of Er3+ atoms located in planar multidielectric structures,” Phys. Rev. A 55, 1497–1502 (1997).
[CrossRef]

Björk, G.

G. Björk, S. Machida, Y. Yamamoto, and K. Igeta, “Modification of spontaneous emission rate in planar dielectric microcavity structures,” Phys. Rev. A 44, 669–681 (1991).
[CrossRef] [PubMed]

DeMartini, F.

F. DeMartini, G. Di Giuseppe, and M. Marrocco, “Single mode generation of quantum photon states by excited single molecules in a microcavity trap,” Phys. Rev. Lett. 76, 900–903 (1996).
[CrossRef]

F. DeMartini, G. Innocenti, G. R. Jacobivitz, and P. Mataloni, “Anomalous spontaneous emission time in a microscopic optical cavity,” Phys. Rev. Lett. 59, 2955–2958 (1987).
[CrossRef]

Di Giuseppe, G.

F. DeMartini, G. Di Giuseppe, and M. Marrocco, “Single mode generation of quantum photon states by excited single molecules in a microcavity trap,” Phys. Rev. Lett. 76, 900–903 (1996).
[CrossRef]

Downing, E. A.

W. Seeber, E. A. Downing, L. Hesselink, M. M. Fejer, and D. Ehrt, “Pr3+-doped fluoride glasses,” J. Non-Cryst. Solids 189, 218–226 (1995).
[CrossRef]

Ehrt, D.

W. Seeber, E. A. Downing, L. Hesselink, M. M. Fejer, and D. Ehrt, “Pr3+-doped fluoride glasses,” J. Non-Cryst. Solids 189, 218–226 (1995).
[CrossRef]

Fan, S.

P. Villeneuve, S. Fan, and J. D. Joannopoulos, “Microcavities in photonic crystals: mode symmetry, tunability, and coupling efficiency,” Phys. Rev. B 54, 7837–7842 (1996).
[CrossRef]

Fejer, M. M.

W. Seeber, E. A. Downing, L. Hesselink, M. M. Fejer, and D. Ehrt, “Pr3+-doped fluoride glasses,” J. Non-Cryst. Solids 189, 218–226 (1995).
[CrossRef]

Flory, F.

Hesselink, L.

W. Seeber, E. A. Downing, L. Hesselink, M. M. Fejer, and D. Ehrt, “Pr3+-doped fluoride glasses,” J. Non-Cryst. Solids 189, 218–226 (1995).
[CrossRef]

Igeta, K.

G. Björk, S. Machida, Y. Yamamoto, and K. Igeta, “Modification of spontaneous emission rate in planar dielectric microcavity structures,” Phys. Rev. A 44, 669–681 (1991).
[CrossRef] [PubMed]

Innocenti, G.

F. DeMartini, G. Innocenti, G. R. Jacobivitz, and P. Mataloni, “Anomalous spontaneous emission time in a microscopic optical cavity,” Phys. Rev. Lett. 59, 2955–2958 (1987).
[CrossRef]

Jacobivitz, G. R.

F. DeMartini, G. Innocenti, G. R. Jacobivitz, and P. Mataloni, “Anomalous spontaneous emission time in a microscopic optical cavity,” Phys. Rev. Lett. 59, 2955–2958 (1987).
[CrossRef]

Jacquier, B.

H. Rigneault, S. Robert, C. Begon, B. Jacquier, and P. Moretti, “Radiative and guided wave emission of Er3+ atoms located in planar multidielectric structures,” Phys. Rev. A 55, 1497–1502 (1997).
[CrossRef]

Joannopoulos, J. D.

P. Villeneuve, S. Fan, and J. D. Joannopoulos, “Microcavities in photonic crystals: mode symmetry, tunability, and coupling efficiency,” Phys. Rev. B 54, 7837–7842 (1996).
[CrossRef]

Machida, S.

G. Björk, S. Machida, Y. Yamamoto, and K. Igeta, “Modification of spontaneous emission rate in planar dielectric microcavity structures,” Phys. Rev. A 44, 669–681 (1991).
[CrossRef] [PubMed]

Marrocco, M.

F. DeMartini, G. Di Giuseppe, and M. Marrocco, “Single mode generation of quantum photon states by excited single molecules in a microcavity trap,” Phys. Rev. Lett. 76, 900–903 (1996).
[CrossRef]

Mataloni, P.

F. DeMartini, G. Innocenti, G. R. Jacobivitz, and P. Mataloni, “Anomalous spontaneous emission time in a microscopic optical cavity,” Phys. Rev. Lett. 59, 2955–2958 (1987).
[CrossRef]

Monneret, S.

Moretti, P.

H. Rigneault, S. Robert, C. Begon, B. Jacquier, and P. Moretti, “Radiative and guided wave emission of Er3+ atoms located in planar multidielectric structures,” Phys. Rev. A 55, 1497–1502 (1997).
[CrossRef]

Nambu, Y.

H. Yokoyama, M. Suzuki, and Y. Nambu, “Spontaneous emission and laser oscillation properties of microcavities containing a dye solution,” Appl. Phys. Lett. 58, 2598–2600 (1991).
[CrossRef]

Rigneault, H.

Robert, S.

H. Rigneault, S. Robert, C. Begon, B. Jacquier, and P. Moretti, “Radiative and guided wave emission of Er3+ atoms located in planar multidielectric structures,” Phys. Rev. A 55, 1497–1502 (1997).
[CrossRef]

H. Rigneault, F. Flory, S. Monneret, S. Robert, and L. Roux, “Fluorescence of Ta2O5 thin films doped by kilo-electron-volt Er implantation: application to microcavities,” Appl. Opt. 35, 5005–5012 (1996).
[CrossRef] [PubMed]

Roux, L.

Seeber, W.

W. Seeber, E. A. Downing, L. Hesselink, M. M. Fejer, and D. Ehrt, “Pr3+-doped fluoride glasses,” J. Non-Cryst. Solids 189, 218–226 (1995).
[CrossRef]

Suzuki, M.

H. Yokoyama, M. Suzuki, and Y. Nambu, “Spontaneous emission and laser oscillation properties of microcavities containing a dye solution,” Appl. Phys. Lett. 58, 2598–2600 (1991).
[CrossRef]

Tisserand, S.

Villeneuve, P.

P. Villeneuve, S. Fan, and J. D. Joannopoulos, “Microcavities in photonic crystals: mode symmetry, tunability, and coupling efficiency,” Phys. Rev. B 54, 7837–7842 (1996).
[CrossRef]

Yamamoto, Y.

G. Björk, S. Machida, Y. Yamamoto, and K. Igeta, “Modification of spontaneous emission rate in planar dielectric microcavity structures,” Phys. Rev. A 44, 669–681 (1991).
[CrossRef] [PubMed]

Yokoyama, H.

H. Yokoyama, M. Suzuki, and Y. Nambu, “Spontaneous emission and laser oscillation properties of microcavities containing a dye solution,” Appl. Phys. Lett. 58, 2598–2600 (1991).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

H. Yokoyama, M. Suzuki, and Y. Nambu, “Spontaneous emission and laser oscillation properties of microcavities containing a dye solution,” Appl. Phys. Lett. 58, 2598–2600 (1991).
[CrossRef]

J. Non-Cryst. Solids (1)

W. Seeber, E. A. Downing, L. Hesselink, M. M. Fejer, and D. Ehrt, “Pr3+-doped fluoride glasses,” J. Non-Cryst. Solids 189, 218–226 (1995).
[CrossRef]

Phys. Rev. A (2)

G. Björk, S. Machida, Y. Yamamoto, and K. Igeta, “Modification of spontaneous emission rate in planar dielectric microcavity structures,” Phys. Rev. A 44, 669–681 (1991).
[CrossRef] [PubMed]

H. Rigneault, S. Robert, C. Begon, B. Jacquier, and P. Moretti, “Radiative and guided wave emission of Er3+ atoms located in planar multidielectric structures,” Phys. Rev. A 55, 1497–1502 (1997).
[CrossRef]

Phys. Rev. B (1)

P. Villeneuve, S. Fan, and J. D. Joannopoulos, “Microcavities in photonic crystals: mode symmetry, tunability, and coupling efficiency,” Phys. Rev. B 54, 7837–7842 (1996).
[CrossRef]

Phys. Rev. Lett. (2)

F. DeMartini, G. Innocenti, G. R. Jacobivitz, and P. Mataloni, “Anomalous spontaneous emission time in a microscopic optical cavity,” Phys. Rev. Lett. 59, 2955–2958 (1987).
[CrossRef]

F. DeMartini, G. Di Giuseppe, and M. Marrocco, “Single mode generation of quantum photon states by excited single molecules in a microcavity trap,” Phys. Rev. Lett. 76, 900–903 (1996).
[CrossRef]

Other (2)

S. Monneret, “Coupleur à prisme à deux faisceaux pour la caractérisation d’effets non linéaires thermiques dans les couches minces,” Ph.D. dissertation (University Aix-Marseille III, Marseille, France, 1996).

E. F. Shubert, A. M. Vredenberg, N. E. J. Hunt, Y. H. Yong, P. C. Becker, J. M. Poate, D. C. Jacobson, L. C. Feldman, and G. J. Zydzik, “Giant enhancement of luminescence intensity in Er-doped Si/SiO2 resonant cavities,” Appl. Phys. Lett. 61, 1381–1383 (1992); A. M. Vredenberg, N. E. J. Hunt, E. F. Shubert, D. C. Jacobson, J. M. Poate, and G. J. Zydzik, “Controlled atomic spontaneous emission from Er3+ in a transparent Si/SiO2 microcavity,” Phys. Rev. Lett. 71, 517–520 (1993).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

Left, recorded Pr luminescence intensity at λ0=490 nm in a direction normal to the microcavity versus pump angle. The theoretical curve is for plane-wave excitation. The broad wings of the experimental curve are due to the angular spread of the excitation laser. Right, microcavity design and coordinate frames.

Fig. 2
Fig. 2

Pump waist, 10 μm. (a) Incident, reflected, and transmitted PW spectrum, (b) squared modulus of the electric field in the sample (X, Z) plane (X and Z axes are graduated in micrometers). The vertical axis is normalized to the incident field.

Fig. 3
Fig. 3

Pump waist, 1 μm. (a) Incident, reflected, and transmitted PW spectrum, (b) squared modulus of the electric field in the sample (X, Z) plane (X and Z axes are graduated in micrometers). The field at Z=0 is the superposition of the incident and the reflected fields and has thus a modulus greater than 1.

Fig. 4
Fig. 4

Pr emitted power (in nanowatts) in the upper semi-infinite air space versus effective pump power Pc (in watts) seen by the atoms inside the microcavity.

Equations (6)

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Ei(x, y, z)=E0 exp-x2w2exp-y2w2,
Ei(x, y, 0)=exp-y2w2-+W(σ)exp(2iπσx)dσ,
E(X, y, Z)=exp-y2w2-+A(σ, Z)exp(2iπσX)dσ,
A(σ, Z)=1cos θm Wσ-σmcos θmE˜(σ, Z),
Pc=½nHY0|E(X, y, Zm)|2dXdy,
PL=ωΓrsS0 PcPc+S0ωΓtot/Σ,

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