Abstract

Open-access optical microcavities are emerging as an original tool for light-matter studies thanks to their intrinsic tunability and the direct access to the maximum of the electric field along with their small mode volume. In this article, we present recent developments in the fabrication of such devices demonstrating topographic control of the micromirrors at the nanometer scale as well as a high degree of reproducibility. Our method takes into account the template shape as well as the effect of the dielectric mirror growth. In addition, we present the optical characterization of these microcavities with effective radii of curvature down to 4.3 µm and mode volume of 16×(λ2)3. This work opens the possibility to fully engineer the photonic potential depending on the required properties.

© 2015 Optical Society of America

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    [Crossref] [PubMed]
  2. J. Ward and O. Benson, “WGM microresonators: sensing, lasing and fundamental optics with microspheres,” Laser Photon. Rev 5(4), 553–570 (2010).
    [Crossref]
  3. D. Kleckner and D. Bouwmeester, “Sub-kelvin optical cooling of a micromechanical resonator,” Nature 444, 76 (2006).
    [Crossref]
  4. F. Vollmer and L. Yang, “Label-free detection with high-Q microcavities: a review of biosensing mechanisms for integrated devices,” Nanophotonics 1, 267–291 (2012).
    [Crossref]
  5. J.-M. Gérard, “Single Quantum Dots,” Top. Appl. Phys. 90, 269–314 (2003).
  6. T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004).
    [Crossref] [PubMed]
  7. K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Flt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007).
    [Crossref] [PubMed]
  8. Z. Di, H. V. Jones, P. R. Dolan, S. M. Fairclough, M. B. Wincott, J. Fill, G. M. Hughes, and J. M. Smith, “Controlling the emission from semiconductor quantum dots using ultra-small tunable optical microcavities,” New J. Phys. 14, 103048 (2012).
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  10. S. Stapfner, L. Ost, D. Hunger, J. Reichel, I. Favero, and E. M. Weig, “Cavity-enhanced optical detection of carbon nanotube brownian motion,” Appl. Phys. Lett. 102, 151910 (2013).
    [Crossref]
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    [Crossref]
  12. A. A. P. Trichet, J. Foster, N. E. Omori, D. James, P. R. Dolan, G. M. Hughes, C. Vallance, and J. M. Smith, “Open-access optical microcavities for lab-on-a-chip refractive index sensing,” Lab Chip 14, 4244–4249 (2014).
    [Crossref] [PubMed]
  13. D. Hunger, C. Deutsch, R. J. Barbour, R. J. Warburton, and J. Reichel, “Laser micro-fabrication of concave, low roughness features in silica,” AIP Adv. 2, 012119 (2012).
    [Crossref]
  14. D. Hunger, T. Steinmetz, Y. Colombe, C. Deutsch, T. W. Hansch, and J. Reichel, “A fiber Fabry-Perot cavity with high finesse,” New J. Phys. 12, 065038 (2010).
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    [Crossref]
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    [Crossref] [PubMed]
  19. L. Mai, F. Ding, T. Stferle, A. Knoll, B. Jan Offrein, and R. F. Mahrt, “Integrated vertical microcavity using a nano-scale deformation for strong lateral confinement,” Appl. Phys. Lett. 103, 243305 (2013).
    [Crossref]
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    [Crossref]
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    [Crossref]
  23. F. Frost, R. Fechner, B. Ziberi, J. Völlner, D. Flamm, and A. Schindler, “Large area smoothing of surfaces by ion bombardment: fundamentals and applications,” J. Phys. Condens. Matter 21, 224026 (2009).
    [Crossref] [PubMed]
  24. The software we have developed to generate the stream files is available under licence for non-commercial use upon request.
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    [Crossref]
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    [Crossref]
  28. C. J. R. Sheppard and S. Saghafi, “Beam modes beyond the paraxial approximation: a scalar treatment,” Phys. Rev. A 57, 2971 (1998).
    [Crossref]
  29. L. R. Brovelli and U. Keller, “Simple analytical expressions for the reflectivity and the penetration depth of a Bragg mirror between arbitrary media,” Opt. Commun. 116, 343–350 (1995).
    [Crossref]
  30. S. Reyntjens and R. Puers, “A review of focused ion beam applications in microsystem technology,” J. Micromech. Microeng. 11, 287–300 (2001).
    [Crossref]

2014 (4)

S. Dufferwiel, F. Fras, A. Trichet, P. M. Walker, F. Li, L. Giriunas, M. N. Makhonin, L. R. Wilson, J. M. Smith, E. Clarke, M. S. Skolnick, and D. N. Krizhanovskii, “Strong exciton-photon coupling in open semiconductor microcavities,” Appl. Phys. Lett. 104, 192107 (2014).
[Crossref]

A. A. P. Trichet, J. Foster, N. E. Omori, D. James, P. R. Dolan, G. M. Hughes, C. Vallance, and J. M. Smith, “Open-access optical microcavities for lab-on-a-chip refractive index sensing,” Lab Chip 14, 4244–4249 (2014).
[Crossref] [PubMed]

L. Greuter, S. Starosielec, D. Najer, A. Ludwig, L. Duempelmann, D. Rohner, and R. J. Warburton, “A small mode volume tunable microcavity: development and characterization,” Appl. Phys. Lett. 105, 121105 (2014).
[Crossref]

F. Ferdous, A. A. Demchenko, S. P. Vyatchanin, A. B. Matsko, and L. Maleki, “Microcavity morphology optimization,” Phys. Rev. A 90, 033826 (2014).
[Crossref]

2013 (3)

L. Mai, F. Ding, T. Stferle, A. Knoll, B. Jan Offrein, and R. F. Mahrt, “Integrated vertical microcavity using a nano-scale deformation for strong lateral confinement,” Appl. Phys. Lett. 103, 243305 (2013).
[Crossref]

H. Kaupp, C. Deutsch, H.-C. Chang, J. Reichel, T. W. Hnsch, and D. Hunger, “Scaling laws of the cavity enhancement for NV centers in diamond,” Phys. Rev. A 88, 053812 (2013).
[Crossref]

S. Stapfner, L. Ost, D. Hunger, J. Reichel, I. Favero, and E. M. Weig, “Cavity-enhanced optical detection of carbon nanotube brownian motion,” Appl. Phys. Lett. 102, 151910 (2013).
[Crossref]

2012 (3)

D. Hunger, C. Deutsch, R. J. Barbour, R. J. Warburton, and J. Reichel, “Laser micro-fabrication of concave, low roughness features in silica,” AIP Adv. 2, 012119 (2012).
[Crossref]

F. Vollmer and L. Yang, “Label-free detection with high-Q microcavities: a review of biosensing mechanisms for integrated devices,” Nanophotonics 1, 267–291 (2012).
[Crossref]

Z. Di, H. V. Jones, P. R. Dolan, S. M. Fairclough, M. B. Wincott, J. Fill, G. M. Hughes, and J. M. Smith, “Controlling the emission from semiconductor quantum dots using ultra-small tunable optical microcavities,” New J. Phys. 14, 103048 (2012).
[Crossref]

2011 (1)

R. J. Barbour, P. A. Dalgarno, A. Curran, K. M. Nowak, H. J. Baker, D. R. Hall, N. G. Stoltz, P. M. Petroff, and R. J. Warburton, “A tunable microcavity,” J. Appl. Phys. 110, 053107 (2011).
[Crossref]

2010 (4)

J. Ward and O. Benson, “WGM microresonators: sensing, lasing and fundamental optics with microspheres,” Laser Photon. Rev 5(4), 553–570 (2010).
[Crossref]

D. Hunger, T. Steinmetz, Y. Colombe, C. Deutsch, T. W. Hansch, and J. Reichel, “A fiber Fabry-Perot cavity with high finesse,” New J. Phys. 12, 065038 (2010).
[Crossref]

A. Muller, E. B. Flagg, J. R. Lawall, and G. S. Solomon, “Ultrahigh-finesse, low-mode-volume FabryPerot microcavity,” Opt. Lett. 35(13), 2293 (2010).
[Crossref] [PubMed]

P. R. Dolan, G. M. Hughes, F. Grazioso, B. R. Patton, and J. M. Smith, “Femtoliter tunable optical cavity arrays,” Opt. Lett. 3521, 3556–3558 (2010).
[Crossref] [PubMed]

2009 (1)

F. Frost, R. Fechner, B. Ziberi, J. Völlner, D. Flamm, and A. Schindler, “Large area smoothing of surfaces by ion bombardment: fundamentals and applications,” J. Phys. Condens. Matter 21, 224026 (2009).
[Crossref] [PubMed]

2007 (1)

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Flt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007).
[Crossref] [PubMed]

2006 (1)

D. Kleckner and D. Bouwmeester, “Sub-kelvin optical cooling of a micromechanical resonator,” Nature 444, 76 (2006).
[Crossref]

2004 (2)

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004).
[Crossref] [PubMed]

F. Frost, R. Fechner, D. Flamm, B. Ziberi, W. Frank, and A. Schindler, “Ion beam assisted smoothing of optical surfaces,” Appl. Phys. A Mater. Sci. Process. 78(5), 651–654 (2004).
[Crossref]

2003 (2)

K. J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003).
[Crossref] [PubMed]

J.-M. Gérard, “Single Quantum Dots,” Top. Appl. Phys. 90, 269–314 (2003).

2001 (1)

S. Reyntjens and R. Puers, “A review of focused ion beam applications in microsystem technology,” J. Micromech. Microeng. 11, 287–300 (2001).
[Crossref]

1998 (1)

C. J. R. Sheppard and S. Saghafi, “Beam modes beyond the paraxial approximation: a scalar treatment,” Phys. Rev. A 57, 2971 (1998).
[Crossref]

1995 (1)

L. R. Brovelli and U. Keller, “Simple analytical expressions for the reflectivity and the penetration depth of a Bragg mirror between arbitrary media,” Opt. Commun. 116, 343–350 (1995).
[Crossref]

1994 (1)

D. Adalsteinsson and J. A. Sethian, “A level set approach to a unified model for etching, deposition, and lithography I: algorithms and two-dimensional simulations,” J. Comput. Phys. 120(1), 128–144 (1994).
[Crossref]

1988 (1)

1971 (1)

G. A. Deschamps, “Gaussian beam as a bundle of complex rays,” Electron. Lett. 7(23), 684–685 (1971).
[Crossref]

Adalsteinsson, D.

D. Adalsteinsson and J. A. Sethian, “A level set approach to a unified model for etching, deposition, and lithography I: algorithms and two-dimensional simulations,” J. Comput. Phys. 120(1), 128–144 (1994).
[Crossref]

Atatüre, M.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Flt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007).
[Crossref] [PubMed]

Badolato, A.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Flt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007).
[Crossref] [PubMed]

Baker, H. J.

R. J. Barbour, P. A. Dalgarno, A. Curran, K. M. Nowak, H. J. Baker, D. R. Hall, N. G. Stoltz, P. M. Petroff, and R. J. Warburton, “A tunable microcavity,” J. Appl. Phys. 110, 053107 (2011).
[Crossref]

Barbour, R. J.

D. Hunger, C. Deutsch, R. J. Barbour, R. J. Warburton, and J. Reichel, “Laser micro-fabrication of concave, low roughness features in silica,” AIP Adv. 2, 012119 (2012).
[Crossref]

R. J. Barbour, P. A. Dalgarno, A. Curran, K. M. Nowak, H. J. Baker, D. R. Hall, N. G. Stoltz, P. M. Petroff, and R. J. Warburton, “A tunable microcavity,” J. Appl. Phys. 110, 053107 (2011).
[Crossref]

Barrett, H. H.

Benedikter, J.

J. Benedikter, T. Hümmer, M. Mader, B. Schlederer, J. Reichel, T. W. Hänsch, and D. Hunger, “Transverse-mode coupling and diffraction loss in tunable Fabry-Pérot microcavities,” arXiv:1502.01532 (2015).

Benson, O.

J. Ward and O. Benson, “WGM microresonators: sensing, lasing and fundamental optics with microspheres,” Laser Photon. Rev 5(4), 553–570 (2010).
[Crossref]

Bouwmeester, D.

D. Kleckner and D. Bouwmeester, “Sub-kelvin optical cooling of a micromechanical resonator,” Nature 444, 76 (2006).
[Crossref]

Brovelli, L. R.

L. R. Brovelli and U. Keller, “Simple analytical expressions for the reflectivity and the penetration depth of a Bragg mirror between arbitrary media,” Opt. Commun. 116, 343–350 (1995).
[Crossref]

Chang, H.-C.

H. Kaupp, C. Deutsch, H.-C. Chang, J. Reichel, T. W. Hnsch, and D. Hunger, “Scaling laws of the cavity enhancement for NV centers in diamond,” Phys. Rev. A 88, 053812 (2013).
[Crossref]

Clarke, E.

S. Dufferwiel, F. Fras, A. Trichet, P. M. Walker, F. Li, L. Giriunas, M. N. Makhonin, L. R. Wilson, J. M. Smith, E. Clarke, M. S. Skolnick, and D. N. Krizhanovskii, “Strong exciton-photon coupling in open semiconductor microcavities,” Appl. Phys. Lett. 104, 192107 (2014).
[Crossref]

Colombe, Y.

D. Hunger, T. Steinmetz, Y. Colombe, C. Deutsch, T. W. Hansch, and J. Reichel, “A fiber Fabry-Perot cavity with high finesse,” New J. Phys. 12, 065038 (2010).
[Crossref]

Curran, A.

R. J. Barbour, P. A. Dalgarno, A. Curran, K. M. Nowak, H. J. Baker, D. R. Hall, N. G. Stoltz, P. M. Petroff, and R. J. Warburton, “A tunable microcavity,” J. Appl. Phys. 110, 053107 (2011).
[Crossref]

Dalgarno, P. A.

R. J. Barbour, P. A. Dalgarno, A. Curran, K. M. Nowak, H. J. Baker, D. R. Hall, N. G. Stoltz, P. M. Petroff, and R. J. Warburton, “A tunable microcavity,” J. Appl. Phys. 110, 053107 (2011).
[Crossref]

Demchenko, A. A.

F. Ferdous, A. A. Demchenko, S. P. Vyatchanin, A. B. Matsko, and L. Maleki, “Microcavity morphology optimization,” Phys. Rev. A 90, 033826 (2014).
[Crossref]

Deppe, D. G.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004).
[Crossref] [PubMed]

Deschamps, G. A.

G. A. Deschamps, “Gaussian beam as a bundle of complex rays,” Electron. Lett. 7(23), 684–685 (1971).
[Crossref]

Deutsch, C.

H. Kaupp, C. Deutsch, H.-C. Chang, J. Reichel, T. W. Hnsch, and D. Hunger, “Scaling laws of the cavity enhancement for NV centers in diamond,” Phys. Rev. A 88, 053812 (2013).
[Crossref]

D. Hunger, C. Deutsch, R. J. Barbour, R. J. Warburton, and J. Reichel, “Laser micro-fabrication of concave, low roughness features in silica,” AIP Adv. 2, 012119 (2012).
[Crossref]

D. Hunger, T. Steinmetz, Y. Colombe, C. Deutsch, T. W. Hansch, and J. Reichel, “A fiber Fabry-Perot cavity with high finesse,” New J. Phys. 12, 065038 (2010).
[Crossref]

Di, Z.

Z. Di, H. V. Jones, P. R. Dolan, S. M. Fairclough, M. B. Wincott, J. Fill, G. M. Hughes, and J. M. Smith, “Controlling the emission from semiconductor quantum dots using ultra-small tunable optical microcavities,” New J. Phys. 14, 103048 (2012).
[Crossref]

Ding, F.

L. Mai, F. Ding, T. Stferle, A. Knoll, B. Jan Offrein, and R. F. Mahrt, “Integrated vertical microcavity using a nano-scale deformation for strong lateral confinement,” Appl. Phys. Lett. 103, 243305 (2013).
[Crossref]

Dolan, P. R.

A. A. P. Trichet, J. Foster, N. E. Omori, D. James, P. R. Dolan, G. M. Hughes, C. Vallance, and J. M. Smith, “Open-access optical microcavities for lab-on-a-chip refractive index sensing,” Lab Chip 14, 4244–4249 (2014).
[Crossref] [PubMed]

Z. Di, H. V. Jones, P. R. Dolan, S. M. Fairclough, M. B. Wincott, J. Fill, G. M. Hughes, and J. M. Smith, “Controlling the emission from semiconductor quantum dots using ultra-small tunable optical microcavities,” New J. Phys. 14, 103048 (2012).
[Crossref]

P. R. Dolan, G. M. Hughes, F. Grazioso, B. R. Patton, and J. M. Smith, “Femtoliter tunable optical cavity arrays,” Opt. Lett. 3521, 3556–3558 (2010).
[Crossref] [PubMed]

Duempelmann, L.

L. Greuter, S. Starosielec, D. Najer, A. Ludwig, L. Duempelmann, D. Rohner, and R. J. Warburton, “A small mode volume tunable microcavity: development and characterization,” Appl. Phys. Lett. 105, 121105 (2014).
[Crossref]

Dufferwiel, S.

S. Dufferwiel, F. Fras, A. Trichet, P. M. Walker, F. Li, L. Giriunas, M. N. Makhonin, L. R. Wilson, J. M. Smith, E. Clarke, M. S. Skolnick, and D. N. Krizhanovskii, “Strong exciton-photon coupling in open semiconductor microcavities,” Appl. Phys. Lett. 104, 192107 (2014).
[Crossref]

Ell, C.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004).
[Crossref] [PubMed]

Fairclough, S. M.

Z. Di, H. V. Jones, P. R. Dolan, S. M. Fairclough, M. B. Wincott, J. Fill, G. M. Hughes, and J. M. Smith, “Controlling the emission from semiconductor quantum dots using ultra-small tunable optical microcavities,” New J. Phys. 14, 103048 (2012).
[Crossref]

Favero, I.

S. Stapfner, L. Ost, D. Hunger, J. Reichel, I. Favero, and E. M. Weig, “Cavity-enhanced optical detection of carbon nanotube brownian motion,” Appl. Phys. Lett. 102, 151910 (2013).
[Crossref]

Fechner, R.

F. Frost, R. Fechner, B. Ziberi, J. Völlner, D. Flamm, and A. Schindler, “Large area smoothing of surfaces by ion bombardment: fundamentals and applications,” J. Phys. Condens. Matter 21, 224026 (2009).
[Crossref] [PubMed]

F. Frost, R. Fechner, D. Flamm, B. Ziberi, W. Frank, and A. Schindler, “Ion beam assisted smoothing of optical surfaces,” Appl. Phys. A Mater. Sci. Process. 78(5), 651–654 (2004).
[Crossref]

Ferdous, F.

F. Ferdous, A. A. Demchenko, S. P. Vyatchanin, A. B. Matsko, and L. Maleki, “Microcavity morphology optimization,” Phys. Rev. A 90, 033826 (2014).
[Crossref]

Fill, J.

Z. Di, H. V. Jones, P. R. Dolan, S. M. Fairclough, M. B. Wincott, J. Fill, G. M. Hughes, and J. M. Smith, “Controlling the emission from semiconductor quantum dots using ultra-small tunable optical microcavities,” New J. Phys. 14, 103048 (2012).
[Crossref]

Flagg, E. B.

Flamm, D.

F. Frost, R. Fechner, B. Ziberi, J. Völlner, D. Flamm, and A. Schindler, “Large area smoothing of surfaces by ion bombardment: fundamentals and applications,” J. Phys. Condens. Matter 21, 224026 (2009).
[Crossref] [PubMed]

F. Frost, R. Fechner, D. Flamm, B. Ziberi, W. Frank, and A. Schindler, “Ion beam assisted smoothing of optical surfaces,” Appl. Phys. A Mater. Sci. Process. 78(5), 651–654 (2004).
[Crossref]

Flt, S.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Flt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007).
[Crossref] [PubMed]

Foster, J.

A. A. P. Trichet, J. Foster, N. E. Omori, D. James, P. R. Dolan, G. M. Hughes, C. Vallance, and J. M. Smith, “Open-access optical microcavities for lab-on-a-chip refractive index sensing,” Lab Chip 14, 4244–4249 (2014).
[Crossref] [PubMed]

Frank, W.

F. Frost, R. Fechner, D. Flamm, B. Ziberi, W. Frank, and A. Schindler, “Ion beam assisted smoothing of optical surfaces,” Appl. Phys. A Mater. Sci. Process. 78(5), 651–654 (2004).
[Crossref]

Fras, F.

S. Dufferwiel, F. Fras, A. Trichet, P. M. Walker, F. Li, L. Giriunas, M. N. Makhonin, L. R. Wilson, J. M. Smith, E. Clarke, M. S. Skolnick, and D. N. Krizhanovskii, “Strong exciton-photon coupling in open semiconductor microcavities,” Appl. Phys. Lett. 104, 192107 (2014).
[Crossref]

Frost, F.

F. Frost, R. Fechner, B. Ziberi, J. Völlner, D. Flamm, and A. Schindler, “Large area smoothing of surfaces by ion bombardment: fundamentals and applications,” J. Phys. Condens. Matter 21, 224026 (2009).
[Crossref] [PubMed]

F. Frost, R. Fechner, D. Flamm, B. Ziberi, W. Frank, and A. Schindler, “Ion beam assisted smoothing of optical surfaces,” Appl. Phys. A Mater. Sci. Process. 78(5), 651–654 (2004).
[Crossref]

Gerace, D.

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Figures (6)

Fig. 1
Fig. 1

a) Process to fabricate the mirrors. Step 1: A Gallium ion beam is used to sputter the surface of a silica substrate. Step 2: DBR coating is grown on top of the template to create the concave part of the microcavity. b) RMS roughness of a feature as a function of its depth. Transparent blue area corresponds to the resolution of our AFM. Dashed line is the initial roughness of the silica substrate.

Fig. 2
Fig. 2

a) The top and middle schemes are represent the mono-directional and isotropic growth models respectively. Bottom scheme gives the definition of the position (r,z) as well as the angle θ used in equation 1. b) SEM cross-section images of hemispherical microcavities with RoCs of 5 µm (top) and 3 µm (bottom). Left graphics show the raw images with the cracks displayed with red dots. Right graphics show the sames images with the growth model in dashed lines for f=65%.

Fig. 3
Fig. 3

Left graphic: Phase map of a Gaussian cavity mode for a RoC of 4 µm and a cavity length of 327 nm. The isophase surface associated is displayed with the blue dashed line. The equivalent hemispherical surface is displayed with the black dashed line. The dash dot line gives the extension of the waist of the beam as a function of the longitudinal position in the cavity. Right graphic: Difference between the Gaussian mode isophase and the hemispherical equivalent.

Fig. 4
Fig. 4

a) AFM image of a template for a cavity of RoC of 4 µm. The initial targeted shape is given by the black line b) Residual deviation between AFM data and the targeted shape presented in a). c) Correlation function of the residual deviation between the AFM data and a smooth polynomial function. Most of the roughness correlation is below λ d) SEM cross-section of the same cavity after coating. Dashed white lines correspond to the DBR growth model. Black dashed line gives the extension of four times the waist expected for the nominal cavity parameters.

Fig. 5
Fig. 5

a) Transmission spectrum for the cavity with nominal RoC of 4 µm as a function of the optical length. The cavity modes for q=5 are indicated with black arrows up to l+m=4. b) Histogram of the spread of the optical length mode positions for 142 cavities. Red curve is a Gaussian fit giving a standard deviation of 1.1 nm.

Fig. 6
Fig. 6

a) Effective RoC as a function of the optical cavity length. Left part is measured data and right part is the nominal values for the six types of cavities presented on table 1. b) Finesse as a function of length for the same cavities. The transparent blue area corresponds to the Finesse expected from the intrinsic reflectivity of the coating.

Tables (1)

Tables Icon

Table 1 Characteristics of the six different Gaussian phase-matched cavities type fabricated using the method developed in this work.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

z = z 0 + f h + ( 1 f ) Δ h cos ( θ )
r = r 0 ( 1 f ) Δ h sin ( θ )
ϕ ( r , z ) = k ( z + r 2 2 R ( z ) ) a t a n ( z a R )
ϕ ( r , z ) = ϕ ( 0 , L ) = k L a t a n ( 1 R L 1 )
L = λ 2 [ q + 1 π ( l + m + 1 ) a c o s ( 1 L R ) ]
R = L sin 2 ( 2 π Δ t L λ )
F = Δ L δ L

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