Abstract

We study tight focus coherent anti-Stokes Raman scattering (CARS) emission in a microcavity where the active medium is squeezed between two independent planar mirrors. We show strong modifications in the CARS forward and backward far-field radiation patterns. For low-order cavities, we demonstrate that most of the emitted power can be concentrated into a direction perpendicular to the mirrors.

© 2009 Optical Society of America

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  1. E. Purcell, Phys. Rev. 69, 681 (1946).
    [CrossRef]
  2. P. Goy, J. M. Raimond, M. Gross, and S. Haroche, Phys. Rev. Lett. 50, 1903 (1983).
    [CrossRef]
  3. F. De Martini, G. Innocenti, G. R. Jacobovitz, and P. Mataloni, Phys. Rev. Lett. 59, 2955 (1987).
    [CrossRef] [PubMed]
  4. G. Björk, S. Machida, Y. Yamamoto, and K. Igeta, Phys. Rev. A 44, 669 (1991).
    [CrossRef] [PubMed]
  5. A. M. Vredenberg, N. E. J. Hunt, E. F. Schubert, D. C. Jacobson, J. M. Poate, and G. J. Zydzik, Phys. Rev. Lett. 71, 517 (1993).
    [CrossRef] [PubMed]
  6. H. Rigneault, S. Robert, C. Begon, B. Jacquier, and P. Moretti, Phys. Rev. A 55, 1497 (1997).
    [CrossRef]
  7. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, 1984).
  8. A. Zumbusch, G. R. Holtom, and X. S. Xie, Phys. Rev. Lett. 82, 4014 (1999).
    [CrossRef]
  9. J.-X. Cheng, Appl. Spectrosc. 61, 197 (2007).
    [CrossRef] [PubMed]
  10. J.-X. Cheng, A. Volkmer, and X. S. Xie, J. Opt. Soc. Am. B 19, 1363 (2002).
    [CrossRef]
  11. D. Gachet, N. Sandeau, and H. Rigneault, Proc. SPIE 6093, 62 (2005).
  12. H. Kim, D. K. Taggart, C. Xiang, R. M. Penner, and E. O. Potma, Nano Lett. 8, 2373 (2008).
    [CrossRef] [PubMed]
  13. F. Billard, D. Gachet, and H. Rigneault, , “Coherent anti-Stokes Raman scattering (CARS) in a Fabry-Perot cavity: a theoretical study,” J. Opt. Soc. Am. B (to be published).
  14. The mirrors considered here are made of a succession of high (H) and low (L) refractive index hafnium oxide HfO2(n=2.207) and silica SiO2(n=1.456) layers deposed on a silica substrate. The widths (in nanometers) of the different layers are given by (H) 107, (L) 272, (H) 88, (L) 109, (H) 206, (L) 119, (H) 64, (L) 298, (H) 314, (L) 36, (H) 374, (L) 201, (H) 127, (L) 212, (H) 111, (L) 209, (H) 128, (L) 95.
  15. Note that the asymmetric shape of the oscillatory curves in Fig. (Fwd and Epi-CARS) are related to the abrupt appearance of a ring at the k-space center (kx=ky=0) and its progression toward larger k values when increasing Lopt before its final disappearance when kx,ky>2π/λas×NAcollection.

2008 (1)

H. Kim, D. K. Taggart, C. Xiang, R. M. Penner, and E. O. Potma, Nano Lett. 8, 2373 (2008).
[CrossRef] [PubMed]

2007 (1)

J.-X. Cheng, Appl. Spectrosc. 61, 197 (2007).
[CrossRef] [PubMed]

2005 (1)

D. Gachet, N. Sandeau, and H. Rigneault, Proc. SPIE 6093, 62 (2005).

2002 (1)

1999 (1)

A. Zumbusch, G. R. Holtom, and X. S. Xie, Phys. Rev. Lett. 82, 4014 (1999).
[CrossRef]

1997 (1)

H. Rigneault, S. Robert, C. Begon, B. Jacquier, and P. Moretti, Phys. Rev. A 55, 1497 (1997).
[CrossRef]

1993 (1)

A. M. Vredenberg, N. E. J. Hunt, E. F. Schubert, D. C. Jacobson, J. M. Poate, and G. J. Zydzik, Phys. Rev. Lett. 71, 517 (1993).
[CrossRef] [PubMed]

1991 (1)

G. Björk, S. Machida, Y. Yamamoto, and K. Igeta, Phys. Rev. A 44, 669 (1991).
[CrossRef] [PubMed]

1987 (1)

F. De Martini, G. Innocenti, G. R. Jacobovitz, and P. Mataloni, Phys. Rev. Lett. 59, 2955 (1987).
[CrossRef] [PubMed]

1984 (1)

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, 1984).

1983 (1)

P. Goy, J. M. Raimond, M. Gross, and S. Haroche, Phys. Rev. Lett. 50, 1903 (1983).
[CrossRef]

1946 (1)

E. Purcell, Phys. Rev. 69, 681 (1946).
[CrossRef]

Begon, C.

H. Rigneault, S. Robert, C. Begon, B. Jacquier, and P. Moretti, Phys. Rev. A 55, 1497 (1997).
[CrossRef]

Billard, F.

F. Billard, D. Gachet, and H. Rigneault, , “Coherent anti-Stokes Raman scattering (CARS) in a Fabry-Perot cavity: a theoretical study,” J. Opt. Soc. Am. B (to be published).

Björk, G.

G. Björk, S. Machida, Y. Yamamoto, and K. Igeta, Phys. Rev. A 44, 669 (1991).
[CrossRef] [PubMed]

Cheng, J.-X.

De Martini, F.

F. De Martini, G. Innocenti, G. R. Jacobovitz, and P. Mataloni, Phys. Rev. Lett. 59, 2955 (1987).
[CrossRef] [PubMed]

Gachet, D.

D. Gachet, N. Sandeau, and H. Rigneault, Proc. SPIE 6093, 62 (2005).

F. Billard, D. Gachet, and H. Rigneault, , “Coherent anti-Stokes Raman scattering (CARS) in a Fabry-Perot cavity: a theoretical study,” J. Opt. Soc. Am. B (to be published).

Goy, P.

P. Goy, J. M. Raimond, M. Gross, and S. Haroche, Phys. Rev. Lett. 50, 1903 (1983).
[CrossRef]

Gross, M.

P. Goy, J. M. Raimond, M. Gross, and S. Haroche, Phys. Rev. Lett. 50, 1903 (1983).
[CrossRef]

Haroche, S.

P. Goy, J. M. Raimond, M. Gross, and S. Haroche, Phys. Rev. Lett. 50, 1903 (1983).
[CrossRef]

Holtom, G. R.

A. Zumbusch, G. R. Holtom, and X. S. Xie, Phys. Rev. Lett. 82, 4014 (1999).
[CrossRef]

Hunt, N. E. J.

A. M. Vredenberg, N. E. J. Hunt, E. F. Schubert, D. C. Jacobson, J. M. Poate, and G. J. Zydzik, Phys. Rev. Lett. 71, 517 (1993).
[CrossRef] [PubMed]

Igeta, K.

G. Björk, S. Machida, Y. Yamamoto, and K. Igeta, Phys. Rev. A 44, 669 (1991).
[CrossRef] [PubMed]

Innocenti, G.

F. De Martini, G. Innocenti, G. R. Jacobovitz, and P. Mataloni, Phys. Rev. Lett. 59, 2955 (1987).
[CrossRef] [PubMed]

Jacobovitz, G. R.

F. De Martini, G. Innocenti, G. R. Jacobovitz, and P. Mataloni, Phys. Rev. Lett. 59, 2955 (1987).
[CrossRef] [PubMed]

Jacobson, D. C.

A. M. Vredenberg, N. E. J. Hunt, E. F. Schubert, D. C. Jacobson, J. M. Poate, and G. J. Zydzik, Phys. Rev. Lett. 71, 517 (1993).
[CrossRef] [PubMed]

Jacquier, B.

H. Rigneault, S. Robert, C. Begon, B. Jacquier, and P. Moretti, Phys. Rev. A 55, 1497 (1997).
[CrossRef]

Kim, H.

H. Kim, D. K. Taggart, C. Xiang, R. M. Penner, and E. O. Potma, Nano Lett. 8, 2373 (2008).
[CrossRef] [PubMed]

Machida, S.

G. Björk, S. Machida, Y. Yamamoto, and K. Igeta, Phys. Rev. A 44, 669 (1991).
[CrossRef] [PubMed]

Mataloni, P.

F. De Martini, G. Innocenti, G. R. Jacobovitz, and P. Mataloni, Phys. Rev. Lett. 59, 2955 (1987).
[CrossRef] [PubMed]

Moretti, P.

H. Rigneault, S. Robert, C. Begon, B. Jacquier, and P. Moretti, Phys. Rev. A 55, 1497 (1997).
[CrossRef]

Penner, R. M.

H. Kim, D. K. Taggart, C. Xiang, R. M. Penner, and E. O. Potma, Nano Lett. 8, 2373 (2008).
[CrossRef] [PubMed]

Poate, J. M.

A. M. Vredenberg, N. E. J. Hunt, E. F. Schubert, D. C. Jacobson, J. M. Poate, and G. J. Zydzik, Phys. Rev. Lett. 71, 517 (1993).
[CrossRef] [PubMed]

Potma, E. O.

H. Kim, D. K. Taggart, C. Xiang, R. M. Penner, and E. O. Potma, Nano Lett. 8, 2373 (2008).
[CrossRef] [PubMed]

Purcell, E.

E. Purcell, Phys. Rev. 69, 681 (1946).
[CrossRef]

Raimond, J. M.

P. Goy, J. M. Raimond, M. Gross, and S. Haroche, Phys. Rev. Lett. 50, 1903 (1983).
[CrossRef]

Rigneault, H.

D. Gachet, N. Sandeau, and H. Rigneault, Proc. SPIE 6093, 62 (2005).

H. Rigneault, S. Robert, C. Begon, B. Jacquier, and P. Moretti, Phys. Rev. A 55, 1497 (1997).
[CrossRef]

F. Billard, D. Gachet, and H. Rigneault, , “Coherent anti-Stokes Raman scattering (CARS) in a Fabry-Perot cavity: a theoretical study,” J. Opt. Soc. Am. B (to be published).

Robert, S.

H. Rigneault, S. Robert, C. Begon, B. Jacquier, and P. Moretti, Phys. Rev. A 55, 1497 (1997).
[CrossRef]

Sandeau, N.

D. Gachet, N. Sandeau, and H. Rigneault, Proc. SPIE 6093, 62 (2005).

Schubert, E. F.

A. M. Vredenberg, N. E. J. Hunt, E. F. Schubert, D. C. Jacobson, J. M. Poate, and G. J. Zydzik, Phys. Rev. Lett. 71, 517 (1993).
[CrossRef] [PubMed]

Shen, Y. R.

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, 1984).

Taggart, D. K.

H. Kim, D. K. Taggart, C. Xiang, R. M. Penner, and E. O. Potma, Nano Lett. 8, 2373 (2008).
[CrossRef] [PubMed]

Volkmer, A.

Vredenberg, A. M.

A. M. Vredenberg, N. E. J. Hunt, E. F. Schubert, D. C. Jacobson, J. M. Poate, and G. J. Zydzik, Phys. Rev. Lett. 71, 517 (1993).
[CrossRef] [PubMed]

Xiang, C.

H. Kim, D. K. Taggart, C. Xiang, R. M. Penner, and E. O. Potma, Nano Lett. 8, 2373 (2008).
[CrossRef] [PubMed]

Xie, X. S.

J.-X. Cheng, A. Volkmer, and X. S. Xie, J. Opt. Soc. Am. B 19, 1363 (2002).
[CrossRef]

A. Zumbusch, G. R. Holtom, and X. S. Xie, Phys. Rev. Lett. 82, 4014 (1999).
[CrossRef]

Yamamoto, Y.

G. Björk, S. Machida, Y. Yamamoto, and K. Igeta, Phys. Rev. A 44, 669 (1991).
[CrossRef] [PubMed]

Zumbusch, A.

A. Zumbusch, G. R. Holtom, and X. S. Xie, Phys. Rev. Lett. 82, 4014 (1999).
[CrossRef]

Zydzik, G. J.

A. M. Vredenberg, N. E. J. Hunt, E. F. Schubert, D. C. Jacobson, J. M. Poate, and G. J. Zydzik, Phys. Rev. Lett. 71, 517 (1993).
[CrossRef] [PubMed]

Appl. Spectrosc. (1)

J.-X. Cheng, Appl. Spectrosc. 61, 197 (2007).
[CrossRef] [PubMed]

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

Nano Lett. (1)

H. Kim, D. K. Taggart, C. Xiang, R. M. Penner, and E. O. Potma, Nano Lett. 8, 2373 (2008).
[CrossRef] [PubMed]

Phys. Rev. (1)

E. Purcell, Phys. Rev. 69, 681 (1946).
[CrossRef]

Phys. Rev. A (2)

G. Björk, S. Machida, Y. Yamamoto, and K. Igeta, Phys. Rev. A 44, 669 (1991).
[CrossRef] [PubMed]

H. Rigneault, S. Robert, C. Begon, B. Jacquier, and P. Moretti, Phys. Rev. A 55, 1497 (1997).
[CrossRef]

Phys. Rev. Lett. (4)

A. M. Vredenberg, N. E. J. Hunt, E. F. Schubert, D. C. Jacobson, J. M. Poate, and G. J. Zydzik, Phys. Rev. Lett. 71, 517 (1993).
[CrossRef] [PubMed]

P. Goy, J. M. Raimond, M. Gross, and S. Haroche, Phys. Rev. Lett. 50, 1903 (1983).
[CrossRef]

F. De Martini, G. Innocenti, G. R. Jacobovitz, and P. Mataloni, Phys. Rev. Lett. 59, 2955 (1987).
[CrossRef] [PubMed]

A. Zumbusch, G. R. Holtom, and X. S. Xie, Phys. Rev. Lett. 82, 4014 (1999).
[CrossRef]

Proc. SPIE (1)

D. Gachet, N. Sandeau, and H. Rigneault, Proc. SPIE 6093, 62 (2005).

Other (4)

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, 1984).

F. Billard, D. Gachet, and H. Rigneault, , “Coherent anti-Stokes Raman scattering (CARS) in a Fabry-Perot cavity: a theoretical study,” J. Opt. Soc. Am. B (to be published).

The mirrors considered here are made of a succession of high (H) and low (L) refractive index hafnium oxide HfO2(n=2.207) and silica SiO2(n=1.456) layers deposed on a silica substrate. The widths (in nanometers) of the different layers are given by (H) 107, (L) 272, (H) 88, (L) 109, (H) 206, (L) 119, (H) 64, (L) 298, (H) 314, (L) 36, (H) 374, (L) 201, (H) 127, (L) 212, (H) 111, (L) 209, (H) 128, (L) 95.

Note that the asymmetric shape of the oscillatory curves in Fig. (Fwd and Epi-CARS) are related to the abrupt appearance of a ring at the k-space center (kx=ky=0) and its progression toward larger k values when increasing Lopt before its final disappearance when kx,ky>2π/λas×NAcollection.

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Figures (3)

Fig. 1
Fig. 1

(a) Point source and (b) extended coherent volume emission in a microcavity.

Fig. 2
Fig. 2

(a) Scheme of the experiment, (b) mirror design and CARS wavelengths, (c) Fwd- and Epi-CARS signal dependence with cavity optical width L opt ; all the maxima are separated by Δ L opt = λ as 2 .

Fig. 3
Fig. 3

Far-field Fwd-CARS into the k space for (a) a L opt = 20 μ m DMF layer squeezed between two silica substrates and (c) a L opt = 21.8 μ m DMF layer squeezed between two dielectric mirrors; (b) and (c) are cuts along the x and y axes together with the expected computation relative to respectively (a) and (c). (d) Theoretical and experimental integrated Fwd-CARS enhancement for maximum and minimum emission [points M and N in Fig. 2c] when varying the cavity optical width L opt .

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