Abstract

We present a detailed electromagnetic analysis for the radiation of an electric source located inside grating structures. Our analysis is based on the differential method and uses the scattering-matrix algorithm. We show that gratings that exhibit periodic modulations along two spatial directions (crossed gratings) enable one to couple out the totality of the light emitted by the source into the guided modes of the structure. This property is investigated through the computation of the far-field radiation patterns for crossed gratings with various etching depths. One key result is the possibility to confine the emitted light in a direction about the sample normal, a property that is of interest in the context of spontaneous emission control by microcavity structures.

© 2000 Optical Society of America

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1999 (1)

1998 (3)

F. Lemarchand, A. Sentenac, H. Giovannini, “Increasing the angular tolerance of resonant grating filters with doubly periodic structure,” Opt. Lett. 23, 1149–1151 (1998).
[CrossRef]

H. Benisty, H. De Neve, C. Weisbuch, “Impact of planar microcavity effects on light extraction. Part 1. Basic concepts and analytical trends,” IEEE J. Quantum Electron. 34, 1612–1631 (1998);H. Benisty, H. De Neve, C. Weisbuch, “Impact of planar microcavity effects on light extraction. Part II. Selected exact simulations and role of photon recycling,” IEEE J. Quantum Electron. 34, 1632–1643 (1998).
[CrossRef]

J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, V. Thierry-Mieg, “Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity,” Phys. Rev. Lett. 81, 1110–1113 (1998).
[CrossRef]

1997 (6)

1996 (8)

J. B. Harris, T. W. Preist, J. R. Sambles, R. N. Thorpe, R. A. Watts, “Optical response of bigratings,” J. Opt. Soc. Am. A 13, 2041–2049 (1996).
[CrossRef]

L. Li, “Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings,” J. Opt. Soc. Am. A 13, 1024–1035 (1996).
[CrossRef]

F. De Martini, G. Di Giuseppe, M. Marrocco, “Single-mode generation of quantum photon states by excited single molecules in a microcavity trap,” Phys. Rev. Lett. 76, 900–903 (1996);S. C. Kitson, P. Jonsson, J. G. Rarity, P. R. Tapster, “Intensity fluctuation spectroscopy of small numbers of dye molecules in a microcavity,” Phys. Rev. A 58, 620–627 (1998).
[CrossRef] [PubMed]

H. Rigneault, S. Monneret, “Modal analysis of spontaneous emission in a planar microcavity,” Phys. Rev. A 54, 2356–2368 (1996).
[CrossRef] [PubMed]

J. M. Gérard, D. Barrier, J. Y. Marzin, R. Kuszelewicz, L. Manin, E. Costard, V. Thierry-Mieg, T. Rivera, “Quantum boxes as active probes for photonic microstructures: the pillar microcavity case,” Phys. Rev. Lett. 69, 449–451 (1996).

S. C. Kitson, W. L. Barnes, J. R. Sambles, “Photoluminescence from dye molecules on silver gratings,” Opt. Commun. 122, 147–154 (1996).
[CrossRef]

S. C. Kitson, W. L. Barnes, J. R. Sambles, “Full photonic band gap for surface modes in the visible,” Phys. Rev. Lett. 77, 2670–2673 (1996).
[CrossRef] [PubMed]

W. L. Barnes, T. W. Preist, S. C. Kitson, J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B 54, 6227–6244 (1996).
[CrossRef]

1995 (2)

S. C. Kitson, W. L. Barnes, J. R. Sambles, “Surface-plasmon energy gaps and photoluminescence,” Phys. Rev. B 52, 11441–11445 (1995).
[CrossRef]

J. P. Zhang, D. Y. Chu, S. L. Wu, S. T. Ho, W. G. Bi, C. W. Tu, R. C. Tiberio, “Photonic-wire laser,” Phys. Rev. Lett. 75, 2678–2681 (1995).
[CrossRef] [PubMed]

1994 (1)

F. Montiel, M. Nevière, “Differential theory of gratings: extension to deep gratings of arbitrary profile and permittivity through the R-matrix propagation algorithm,” J. Opt. Soc. Am. A 12, 3241–3250 (1994).
[CrossRef]

1991 (2)

W. Lukosz, D. Clerc, Ph. M. Nellen, Ch. Stamm, P. Weiss, “Output grating couplers on planar optical waveguides as direct immunosensors,” Biosens. Bioelectron. 6, 227–232 (1991);K. G. Sullivan, O. King, C. Sigg, D. G. Hall, “Directional, enhanced fluorescence from molecules near a periodic surface,” Appl. Opt. 33, 2447–2454 (1994).
[CrossRef] [PubMed]

G. Björk, S. Machida, Y. Yamamoto, K. Igeta, “Modification of spontaneous emission rate in planar dielectric microcavity structures,” Phys. Rev. A 44, 669–681 (1991);D. G. Deppe, C. Lei, C. C. Lin, D. L. Huffaker, “Spontaneous emission from planar microstructures,” J. Mod. Opt. 41, 325–344 (1994).
[CrossRef]

1987 (3)

F. DeMartini, G. Innocenti, G. R. Jacobivitz, P. Mataloni, “Anomalous spontaneous emission time in a microscopic optical cavity,” Phys. Rev. Lett. 59, 1995–2957 (1987); H. Yokoyama, M. Suzuki, Y. Nambu, “Spontaneous emission and laser oscillation properties of microcavities containing dye solution,” Appl. Phys. Lett. 58, 2598–2600 (1991).
[CrossRef]

R. Zengerle, “Light propagation in singly and doubly periodic planar waveguides,” J. Mod. Opt. 34, 1589–1617 (1987).
[CrossRef]

J. E. Sipe, “New Green-function formalism for surface optics,” J. Opt. Soc. Am. A 4, 481–489 (1987).
[CrossRef]

1983 (1)

P. Goy, J. M. Raimond, M. Gross, S. Haroche, “Observation of cavity-enhanced single atom spontaneous emission,” Phys. Rev. Lett. 50, 1903–1906 (1983).
[CrossRef]

1978 (1)

P. Vincent, “A finite-difference method for dielectric and conducting cross-grating,” Opt. Commun. 26, 293–296 (1978).
[CrossRef]

1973 (1)

M. Nevière, R. Petit, M. Cadilhac, “About the theory of optical grating coupler-waveguide systems,” Opt. Commun. 8, 113–117 (1973).
[CrossRef]

1946 (1)

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).

Amra, C.

Barnes, W. L.

S. C. Kitson, W. L. Barnes, J. R. Sambles, “Photoluminescence from dye molecules on silver gratings,” Opt. Commun. 122, 147–154 (1996).
[CrossRef]

S. C. Kitson, W. L. Barnes, J. R. Sambles, “Full photonic band gap for surface modes in the visible,” Phys. Rev. Lett. 77, 2670–2673 (1996).
[CrossRef] [PubMed]

W. L. Barnes, T. W. Preist, S. C. Kitson, J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B 54, 6227–6244 (1996).
[CrossRef]

S. C. Kitson, W. L. Barnes, J. R. Sambles, “Surface-plasmon energy gaps and photoluminescence,” Phys. Rev. B 52, 11441–11445 (1995).
[CrossRef]

Barrier, D.

J. M. Gérard, D. Barrier, J. Y. Marzin, R. Kuszelewicz, L. Manin, E. Costard, V. Thierry-Mieg, T. Rivera, “Quantum boxes as active probes for photonic microstructures: the pillar microcavity case,” Phys. Rev. Lett. 69, 449–451 (1996).

Begon, C.

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

Benisty, H.

H. Benisty, H. De Neve, C. Weisbuch, “Impact of planar microcavity effects on light extraction. Part 1. Basic concepts and analytical trends,” IEEE J. Quantum Electron. 34, 1612–1631 (1998);H. Benisty, H. De Neve, C. Weisbuch, “Impact of planar microcavity effects on light extraction. Part II. Selected exact simulations and role of photon recycling,” IEEE J. Quantum Electron. 34, 1632–1643 (1998).
[CrossRef]

Bi, W. G.

J. P. Zhang, D. Y. Chu, S. L. Wu, S. T. Ho, W. G. Bi, C. W. Tu, R. C. Tiberio, “Photonic-wire laser,” Phys. Rev. Lett. 75, 2678–2681 (1995).
[CrossRef] [PubMed]

Björk, G.

G. Björk, S. Machida, Y. Yamamoto, K. Igeta, “Modification of spontaneous emission rate in planar dielectric microcavity structures,” Phys. Rev. A 44, 669–681 (1991);D. G. Deppe, C. Lei, C. C. Lin, D. L. Huffaker, “Spontaneous emission from planar microstructures,” J. Mod. Opt. 41, 325–344 (1994).
[CrossRef]

Cadilhac, M.

M. Nevière, R. Petit, M. Cadilhac, “About the theory of optical grating coupler-waveguide systems,” Opt. Commun. 8, 113–117 (1973).
[CrossRef]

Carminati, R.

J.-J. Greffet, R. Carminati, “Image formation in near-field optics,” Prog. Surf. Sci. 56, 133–237 (1997).
[CrossRef]

Chu, D. Y.

J. P. Zhang, D. Y. Chu, S. L. Wu, S. T. Ho, W. G. Bi, C. W. Tu, R. C. Tiberio, “Photonic-wire laser,” Phys. Rev. Lett. 75, 2678–2681 (1995).
[CrossRef] [PubMed]

Clerc, D.

W. Lukosz, D. Clerc, Ph. M. Nellen, Ch. Stamm, P. Weiss, “Output grating couplers on planar optical waveguides as direct immunosensors,” Biosens. Bioelectron. 6, 227–232 (1991);K. G. Sullivan, O. King, C. Sigg, D. G. Hall, “Directional, enhanced fluorescence from molecules near a periodic surface,” Appl. Opt. 33, 2447–2454 (1994).
[CrossRef] [PubMed]

Costard, E.

J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, V. Thierry-Mieg, “Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity,” Phys. Rev. Lett. 81, 1110–1113 (1998).
[CrossRef]

J. M. Gérard, D. Barrier, J. Y. Marzin, R. Kuszelewicz, L. Manin, E. Costard, V. Thierry-Mieg, T. Rivera, “Quantum boxes as active probes for photonic microstructures: the pillar microcavity case,” Phys. Rev. Lett. 69, 449–451 (1996).

De Martini, F.

F. De Martini, G. Di Giuseppe, M. Marrocco, “Single-mode generation of quantum photon states by excited single molecules in a microcavity trap,” Phys. Rev. Lett. 76, 900–903 (1996);S. C. Kitson, P. Jonsson, J. G. Rarity, P. R. Tapster, “Intensity fluctuation spectroscopy of small numbers of dye molecules in a microcavity,” Phys. Rev. A 58, 620–627 (1998).
[CrossRef] [PubMed]

De Neve, H.

H. Benisty, H. De Neve, C. Weisbuch, “Impact of planar microcavity effects on light extraction. Part 1. Basic concepts and analytical trends,” IEEE J. Quantum Electron. 34, 1612–1631 (1998);H. Benisty, H. De Neve, C. Weisbuch, “Impact of planar microcavity effects on light extraction. Part II. Selected exact simulations and role of photon recycling,” IEEE J. Quantum Electron. 34, 1632–1643 (1998).
[CrossRef]

DeMartini, F.

F. DeMartini, G. Innocenti, G. R. Jacobivitz, P. Mataloni, “Anomalous spontaneous emission time in a microscopic optical cavity,” Phys. Rev. Lett. 59, 1995–2957 (1987); H. Yokoyama, M. Suzuki, Y. Nambu, “Spontaneous emission and laser oscillation properties of microcavities containing dye solution,” Appl. Phys. Lett. 58, 2598–2600 (1991).
[CrossRef]

Di Giuseppe, G.

F. De Martini, G. Di Giuseppe, M. Marrocco, “Single-mode generation of quantum photon states by excited single molecules in a microcavity trap,” Phys. Rev. Lett. 76, 900–903 (1996);S. C. Kitson, P. Jonsson, J. G. Rarity, P. R. Tapster, “Intensity fluctuation spectroscopy of small numbers of dye molecules in a microcavity,” Phys. Rev. A 58, 620–627 (1998).
[CrossRef] [PubMed]

Friesem, A. A.

Gayral, B.

J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, V. Thierry-Mieg, “Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity,” Phys. Rev. Lett. 81, 1110–1113 (1998).
[CrossRef]

Gérard, J. M.

J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, V. Thierry-Mieg, “Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity,” Phys. Rev. Lett. 81, 1110–1113 (1998).
[CrossRef]

J. M. Gérard, D. Barrier, J. Y. Marzin, R. Kuszelewicz, L. Manin, E. Costard, V. Thierry-Mieg, T. Rivera, “Quantum boxes as active probes for photonic microstructures: the pillar microcavity case,” Phys. Rev. Lett. 69, 449–451 (1996).

Giovannini, H.

Gourley, P. L.

P. L. Gourley, “Microlaser-optical-mechanical systems for biomedicine,” Opt. Photon. News 8(4), 31–36 (1997).
[CrossRef]

Goy, P.

P. Goy, J. M. Raimond, M. Gross, S. Haroche, “Observation of cavity-enhanced single atom spontaneous emission,” Phys. Rev. Lett. 50, 1903–1906 (1983).
[CrossRef]

Greffet, J.-J.

J.-J. Greffet, R. Carminati, “Image formation in near-field optics,” Prog. Surf. Sci. 56, 133–237 (1997).
[CrossRef]

Gross, M.

P. Goy, J. M. Raimond, M. Gross, S. Haroche, “Observation of cavity-enhanced single atom spontaneous emission,” Phys. Rev. Lett. 50, 1903–1906 (1983).
[CrossRef]

Hare, J.

V. Lefèvre-Seguin, J. C. Knight, V. Sandoghdar, D. S. Weiss, J. Hare, J. M. Raymond, S. Haroche, “Very high Q whispering-gallery modes in silica microsheres for cavity QED experiments,” in Optical Processes in Microcavities, R. K. Chang, A. J. Campillo, eds. (World Scientific, Singapore, 1996), pp. 101–133.

Haroche, S.

P. Goy, J. M. Raimond, M. Gross, S. Haroche, “Observation of cavity-enhanced single atom spontaneous emission,” Phys. Rev. Lett. 50, 1903–1906 (1983).
[CrossRef]

V. Lefèvre-Seguin, J. C. Knight, V. Sandoghdar, D. S. Weiss, J. Hare, J. M. Raymond, S. Haroche, “Very high Q whispering-gallery modes in silica microsheres for cavity QED experiments,” in Optical Processes in Microcavities, R. K. Chang, A. J. Campillo, eds. (World Scientific, Singapore, 1996), pp. 101–133.

Harris, J. B.

Henricini, P.

P. Henricini, Discrete Variable Methods in Ordinary Differential Equations (Wiley, New York, 1963).

Ho, S. T.

J. P. Zhang, D. Y. Chu, S. L. Wu, S. T. Ho, W. G. Bi, C. W. Tu, R. C. Tiberio, “Photonic-wire laser,” Phys. Rev. Lett. 75, 2678–2681 (1995).
[CrossRef] [PubMed]

Igeta, K.

G. Björk, S. Machida, Y. Yamamoto, K. Igeta, “Modification of spontaneous emission rate in planar dielectric microcavity structures,” Phys. Rev. A 44, 669–681 (1991);D. G. Deppe, C. Lei, C. C. Lin, D. L. Huffaker, “Spontaneous emission from planar microstructures,” J. Mod. Opt. 41, 325–344 (1994).
[CrossRef]

Innocenti, G.

F. DeMartini, G. Innocenti, G. R. Jacobivitz, P. Mataloni, “Anomalous spontaneous emission time in a microscopic optical cavity,” Phys. Rev. Lett. 59, 1995–2957 (1987); H. Yokoyama, M. Suzuki, Y. Nambu, “Spontaneous emission and laser oscillation properties of microcavities containing dye solution,” Appl. Phys. Lett. 58, 2598–2600 (1991).
[CrossRef]

Jacobivitz, G. R.

F. DeMartini, G. Innocenti, G. R. Jacobivitz, P. Mataloni, “Anomalous spontaneous emission time in a microscopic optical cavity,” Phys. Rev. Lett. 59, 1995–2957 (1987); H. Yokoyama, M. Suzuki, Y. Nambu, “Spontaneous emission and laser oscillation properties of microcavities containing dye solution,” Appl. Phys. Lett. 58, 2598–2600 (1991).
[CrossRef]

Jacquier, B.

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

Kitson, S. C.

S. C. Kitson, W. L. Barnes, J. R. Sambles, “Photoluminescence from dye molecules on silver gratings,” Opt. Commun. 122, 147–154 (1996).
[CrossRef]

W. L. Barnes, T. W. Preist, S. C. Kitson, J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B 54, 6227–6244 (1996).
[CrossRef]

S. C. Kitson, W. L. Barnes, J. R. Sambles, “Full photonic band gap for surface modes in the visible,” Phys. Rev. Lett. 77, 2670–2673 (1996).
[CrossRef] [PubMed]

S. C. Kitson, W. L. Barnes, J. R. Sambles, “Surface-plasmon energy gaps and photoluminescence,” Phys. Rev. B 52, 11441–11445 (1995).
[CrossRef]

Knight, J. C.

V. Lefèvre-Seguin, J. C. Knight, V. Sandoghdar, D. S. Weiss, J. Hare, J. M. Raymond, S. Haroche, “Very high Q whispering-gallery modes in silica microsheres for cavity QED experiments,” in Optical Processes in Microcavities, R. K. Chang, A. J. Campillo, eds. (World Scientific, Singapore, 1996), pp. 101–133.

Kuszelewicz, R.

J. M. Gérard, D. Barrier, J. Y. Marzin, R. Kuszelewicz, L. Manin, E. Costard, V. Thierry-Mieg, T. Rivera, “Quantum boxes as active probes for photonic microstructures: the pillar microcavity case,” Phys. Rev. Lett. 69, 449–451 (1996).

Lefèvre-Seguin, V.

V. Lefèvre-Seguin, J. C. Knight, V. Sandoghdar, D. S. Weiss, J. Hare, J. M. Raymond, S. Haroche, “Very high Q whispering-gallery modes in silica microsheres for cavity QED experiments,” in Optical Processes in Microcavities, R. K. Chang, A. J. Campillo, eds. (World Scientific, Singapore, 1996), pp. 101–133.

Legrand, B.

J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, V. Thierry-Mieg, “Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity,” Phys. Rev. Lett. 81, 1110–1113 (1998).
[CrossRef]

Lemarchand, F.

Li, L.

Lukosz, W.

W. Lukosz, D. Clerc, Ph. M. Nellen, Ch. Stamm, P. Weiss, “Output grating couplers on planar optical waveguides as direct immunosensors,” Biosens. Bioelectron. 6, 227–232 (1991);K. G. Sullivan, O. King, C. Sigg, D. G. Hall, “Directional, enhanced fluorescence from molecules near a periodic surface,” Appl. Opt. 33, 2447–2454 (1994).
[CrossRef] [PubMed]

Machida, S.

G. Björk, S. Machida, Y. Yamamoto, K. Igeta, “Modification of spontaneous emission rate in planar dielectric microcavity structures,” Phys. Rev. A 44, 669–681 (1991);D. G. Deppe, C. Lei, C. C. Lin, D. L. Huffaker, “Spontaneous emission from planar microstructures,” J. Mod. Opt. 41, 325–344 (1994).
[CrossRef]

Manin, L.

J. M. Gérard, D. Barrier, J. Y. Marzin, R. Kuszelewicz, L. Manin, E. Costard, V. Thierry-Mieg, T. Rivera, “Quantum boxes as active probes for photonic microstructures: the pillar microcavity case,” Phys. Rev. Lett. 69, 449–451 (1996).

Marrocco, M.

F. De Martini, G. Di Giuseppe, M. Marrocco, “Single-mode generation of quantum photon states by excited single molecules in a microcavity trap,” Phys. Rev. Lett. 76, 900–903 (1996);S. C. Kitson, P. Jonsson, J. G. Rarity, P. R. Tapster, “Intensity fluctuation spectroscopy of small numbers of dye molecules in a microcavity,” Phys. Rev. A 58, 620–627 (1998).
[CrossRef] [PubMed]

Marzin, J. Y.

J. M. Gérard, D. Barrier, J. Y. Marzin, R. Kuszelewicz, L. Manin, E. Costard, V. Thierry-Mieg, T. Rivera, “Quantum boxes as active probes for photonic microstructures: the pillar microcavity case,” Phys. Rev. Lett. 69, 449–451 (1996).

Mataloni, P.

F. DeMartini, G. Innocenti, G. R. Jacobivitz, P. Mataloni, “Anomalous spontaneous emission time in a microscopic optical cavity,” Phys. Rev. Lett. 59, 1995–2957 (1987); H. Yokoyama, M. Suzuki, Y. Nambu, “Spontaneous emission and laser oscillation properties of microcavities containing dye solution,” Appl. Phys. Lett. 58, 2598–2600 (1991).
[CrossRef]

Maure, S.

Monneret, S.

H. Rigneault, S. Monneret, “Modal analysis of spontaneous emission in a planar microcavity,” Phys. Rev. A 54, 2356–2368 (1996).
[CrossRef] [PubMed]

Montiel, F.

F. Montiel, M. Nevière, “Differential theory of gratings: extension to deep gratings of arbitrary profile and permittivity through the R-matrix propagation algorithm,” J. Opt. Soc. Am. A 12, 3241–3250 (1994).
[CrossRef]

Moretti, P.

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

Nellen, Ph. M.

W. Lukosz, D. Clerc, Ph. M. Nellen, Ch. Stamm, P. Weiss, “Output grating couplers on planar optical waveguides as direct immunosensors,” Biosens. Bioelectron. 6, 227–232 (1991);K. G. Sullivan, O. King, C. Sigg, D. G. Hall, “Directional, enhanced fluorescence from molecules near a periodic surface,” Appl. Opt. 33, 2447–2454 (1994).
[CrossRef] [PubMed]

Nevière, M.

F. Montiel, M. Nevière, “Differential theory of gratings: extension to deep gratings of arbitrary profile and permittivity through the R-matrix propagation algorithm,” J. Opt. Soc. Am. A 12, 3241–3250 (1994).
[CrossRef]

M. Nevière, R. Petit, M. Cadilhac, “About the theory of optical grating coupler-waveguide systems,” Opt. Commun. 8, 113–117 (1973).
[CrossRef]

Nieto-Vesperinas, M.

M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics, Wiley Series in Pure and Applied Optics (Wiley, New York, 1991).

Petit, R.

M. Nevière, R. Petit, M. Cadilhac, “About the theory of optical grating coupler-waveguide systems,” Opt. Commun. 8, 113–117 (1973).
[CrossRef]

Preist, T. W.

J. B. Harris, T. W. Preist, J. R. Sambles, R. N. Thorpe, R. A. Watts, “Optical response of bigratings,” J. Opt. Soc. Am. A 13, 2041–2049 (1996).
[CrossRef]

W. L. Barnes, T. W. Preist, S. C. Kitson, J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B 54, 6227–6244 (1996).
[CrossRef]

Purcell, E. M.

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).

Raimond, J. M.

P. Goy, J. M. Raimond, M. Gross, S. Haroche, “Observation of cavity-enhanced single atom spontaneous emission,” Phys. Rev. Lett. 50, 1903–1906 (1983).
[CrossRef]

Raymond, J. M.

V. Lefèvre-Seguin, J. C. Knight, V. Sandoghdar, D. S. Weiss, J. Hare, J. M. Raymond, S. Haroche, “Very high Q whispering-gallery modes in silica microsheres for cavity QED experiments,” in Optical Processes in Microcavities, R. K. Chang, A. J. Campillo, eds. (World Scientific, Singapore, 1996), pp. 101–133.

Rigneault, H.

H. Rigneault, F. Lemarchand, A. Sentenac, H. Giovannini, “Extraction of light from sources located inside waveguide grating structures,” Opt. Lett. 24, 148–150 (1999).
[CrossRef]

H. Rigneault, S. Robert, C. Begon, B. Jacquier, 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, S. Monneret, “Modal analysis of spontaneous emission in a planar microcavity,” Phys. Rev. A 54, 2356–2368 (1996).
[CrossRef] [PubMed]

Rivera, T.

J. M. Gérard, D. Barrier, J. Y. Marzin, R. Kuszelewicz, L. Manin, E. Costard, V. Thierry-Mieg, T. Rivera, “Quantum boxes as active probes for photonic microstructures: the pillar microcavity case,” Phys. Rev. Lett. 69, 449–451 (1996).

Robert, S.

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

Rosenblatt, D.

Sambles, J. R.

J. B. Harris, T. W. Preist, J. R. Sambles, R. N. Thorpe, R. A. Watts, “Optical response of bigratings,” J. Opt. Soc. Am. A 13, 2041–2049 (1996).
[CrossRef]

W. L. Barnes, T. W. Preist, S. C. Kitson, J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B 54, 6227–6244 (1996).
[CrossRef]

S. C. Kitson, W. L. Barnes, J. R. Sambles, “Full photonic band gap for surface modes in the visible,” Phys. Rev. Lett. 77, 2670–2673 (1996).
[CrossRef] [PubMed]

S. C. Kitson, W. L. Barnes, J. R. Sambles, “Photoluminescence from dye molecules on silver gratings,” Opt. Commun. 122, 147–154 (1996).
[CrossRef]

S. C. Kitson, W. L. Barnes, J. R. Sambles, “Surface-plasmon energy gaps and photoluminescence,” Phys. Rev. B 52, 11441–11445 (1995).
[CrossRef]

Sandoghdar, V.

V. Lefèvre-Seguin, J. C. Knight, V. Sandoghdar, D. S. Weiss, J. Hare, J. M. Raymond, S. Haroche, “Very high Q whispering-gallery modes in silica microsheres for cavity QED experiments,” in Optical Processes in Microcavities, R. K. Chang, A. J. Campillo, eds. (World Scientific, Singapore, 1996), pp. 101–133.

Sentenac, A.

Sermage, B.

J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, V. Thierry-Mieg, “Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity,” Phys. Rev. Lett. 81, 1110–1113 (1998).
[CrossRef]

Sharon,

Sipe, J. E.

Stamm, Ch.

W. Lukosz, D. Clerc, Ph. M. Nellen, Ch. Stamm, P. Weiss, “Output grating couplers on planar optical waveguides as direct immunosensors,” Biosens. Bioelectron. 6, 227–232 (1991);K. G. Sullivan, O. King, C. Sigg, D. G. Hall, “Directional, enhanced fluorescence from molecules near a periodic surface,” Appl. Opt. 33, 2447–2454 (1994).
[CrossRef] [PubMed]

Tamir, T.

T. Tamir in Integrated Optics, T. Tamir, ed. (Springer, New York, 1975), p. 83.

Thierry-Mieg, V.

J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, V. Thierry-Mieg, “Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity,” Phys. Rev. Lett. 81, 1110–1113 (1998).
[CrossRef]

J. M. Gérard, D. Barrier, J. Y. Marzin, R. Kuszelewicz, L. Manin, E. Costard, V. Thierry-Mieg, T. Rivera, “Quantum boxes as active probes for photonic microstructures: the pillar microcavity case,” Phys. Rev. Lett. 69, 449–451 (1996).

Thorpe, R. N.

Tiberio, R. C.

J. P. Zhang, D. Y. Chu, S. L. Wu, S. T. Ho, W. G. Bi, C. W. Tu, R. C. Tiberio, “Photonic-wire laser,” Phys. Rev. Lett. 75, 2678–2681 (1995).
[CrossRef] [PubMed]

Tu, C. W.

J. P. Zhang, D. Y. Chu, S. L. Wu, S. T. Ho, W. G. Bi, C. W. Tu, R. C. Tiberio, “Photonic-wire laser,” Phys. Rev. Lett. 75, 2678–2681 (1995).
[CrossRef] [PubMed]

Vincent, P.

P. Vincent, “A finite-difference method for dielectric and conducting cross-grating,” Opt. Commun. 26, 293–296 (1978).
[CrossRef]

Watts, R. A.

Weisbuch, C.

H. Benisty, H. De Neve, C. Weisbuch, “Impact of planar microcavity effects on light extraction. Part 1. Basic concepts and analytical trends,” IEEE J. Quantum Electron. 34, 1612–1631 (1998);H. Benisty, H. De Neve, C. Weisbuch, “Impact of planar microcavity effects on light extraction. Part II. Selected exact simulations and role of photon recycling,” IEEE J. Quantum Electron. 34, 1632–1643 (1998).
[CrossRef]

Weiss, D. S.

V. Lefèvre-Seguin, J. C. Knight, V. Sandoghdar, D. S. Weiss, J. Hare, J. M. Raymond, S. Haroche, “Very high Q whispering-gallery modes in silica microsheres for cavity QED experiments,” in Optical Processes in Microcavities, R. K. Chang, A. J. Campillo, eds. (World Scientific, Singapore, 1996), pp. 101–133.

Weiss, P.

W. Lukosz, D. Clerc, Ph. M. Nellen, Ch. Stamm, P. Weiss, “Output grating couplers on planar optical waveguides as direct immunosensors,” Biosens. Bioelectron. 6, 227–232 (1991);K. G. Sullivan, O. King, C. Sigg, D. G. Hall, “Directional, enhanced fluorescence from molecules near a periodic surface,” Appl. Opt. 33, 2447–2454 (1994).
[CrossRef] [PubMed]

Wu, S. L.

J. P. Zhang, D. Y. Chu, S. L. Wu, S. T. Ho, W. G. Bi, C. W. Tu, R. C. Tiberio, “Photonic-wire laser,” Phys. Rev. Lett. 75, 2678–2681 (1995).
[CrossRef] [PubMed]

Yamamoto, Y.

G. Björk, S. Machida, Y. Yamamoto, K. Igeta, “Modification of spontaneous emission rate in planar dielectric microcavity structures,” Phys. Rev. A 44, 669–681 (1991);D. G. Deppe, C. Lei, C. C. Lin, D. L. Huffaker, “Spontaneous emission from planar microstructures,” J. Mod. Opt. 41, 325–344 (1994).
[CrossRef]

Zengerle, R.

R. Zengerle, “Light propagation in singly and doubly periodic planar waveguides,” J. Mod. Opt. 34, 1589–1617 (1987).
[CrossRef]

Zhang, J. P.

J. P. Zhang, D. Y. Chu, S. L. Wu, S. T. Ho, W. G. Bi, C. W. Tu, R. C. Tiberio, “Photonic-wire laser,” Phys. Rev. Lett. 75, 2678–2681 (1995).
[CrossRef] [PubMed]

Biosens. Bioelectron. (1)

W. Lukosz, D. Clerc, Ph. M. Nellen, Ch. Stamm, P. Weiss, “Output grating couplers on planar optical waveguides as direct immunosensors,” Biosens. Bioelectron. 6, 227–232 (1991);K. G. Sullivan, O. King, C. Sigg, D. G. Hall, “Directional, enhanced fluorescence from molecules near a periodic surface,” Appl. Opt. 33, 2447–2454 (1994).
[CrossRef] [PubMed]

IEEE J. Quantum Electron. (1)

H. Benisty, H. De Neve, C. Weisbuch, “Impact of planar microcavity effects on light extraction. Part 1. Basic concepts and analytical trends,” IEEE J. Quantum Electron. 34, 1612–1631 (1998);H. Benisty, H. De Neve, C. Weisbuch, “Impact of planar microcavity effects on light extraction. Part II. Selected exact simulations and role of photon recycling,” IEEE J. Quantum Electron. 34, 1632–1643 (1998).
[CrossRef]

J. Mod. Opt. (1)

R. Zengerle, “Light propagation in singly and doubly periodic planar waveguides,” J. Mod. Opt. 34, 1589–1617 (1987).
[CrossRef]

J. Opt. Soc. Am. A (7)

Opt. Commun. (3)

P. Vincent, “A finite-difference method for dielectric and conducting cross-grating,” Opt. Commun. 26, 293–296 (1978).
[CrossRef]

S. C. Kitson, W. L. Barnes, J. R. Sambles, “Photoluminescence from dye molecules on silver gratings,” Opt. Commun. 122, 147–154 (1996).
[CrossRef]

M. Nevière, R. Petit, M. Cadilhac, “About the theory of optical grating coupler-waveguide systems,” Opt. Commun. 8, 113–117 (1973).
[CrossRef]

Opt. Lett. (2)

Opt. Photon. News (1)

P. L. Gourley, “Microlaser-optical-mechanical systems for biomedicine,” Opt. Photon. News 8(4), 31–36 (1997).
[CrossRef]

Phys. Rev. (1)

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).

Phys. Rev. A (3)

H. Rigneault, S. Monneret, “Modal analysis of spontaneous emission in a planar microcavity,” Phys. Rev. A 54, 2356–2368 (1996).
[CrossRef] [PubMed]

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

G. Björk, S. Machida, Y. Yamamoto, K. Igeta, “Modification of spontaneous emission rate in planar dielectric microcavity structures,” Phys. Rev. A 44, 669–681 (1991);D. G. Deppe, C. Lei, C. C. Lin, D. L. Huffaker, “Spontaneous emission from planar microstructures,” J. Mod. Opt. 41, 325–344 (1994).
[CrossRef]

Phys. Rev. B (2)

S. C. Kitson, W. L. Barnes, J. R. Sambles, “Surface-plasmon energy gaps and photoluminescence,” Phys. Rev. B 52, 11441–11445 (1995).
[CrossRef]

W. L. Barnes, T. W. Preist, S. C. Kitson, J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B 54, 6227–6244 (1996).
[CrossRef]

Phys. Rev. Lett. (7)

S. C. Kitson, W. L. Barnes, J. R. Sambles, “Full photonic band gap for surface modes in the visible,” Phys. Rev. Lett. 77, 2670–2673 (1996).
[CrossRef] [PubMed]

J. P. Zhang, D. Y. Chu, S. L. Wu, S. T. Ho, W. G. Bi, C. W. Tu, R. C. Tiberio, “Photonic-wire laser,” Phys. Rev. Lett. 75, 2678–2681 (1995).
[CrossRef] [PubMed]

J. M. Gérard, D. Barrier, J. Y. Marzin, R. Kuszelewicz, L. Manin, E. Costard, V. Thierry-Mieg, T. Rivera, “Quantum boxes as active probes for photonic microstructures: the pillar microcavity case,” Phys. Rev. Lett. 69, 449–451 (1996).

J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, V. Thierry-Mieg, “Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity,” Phys. Rev. Lett. 81, 1110–1113 (1998).
[CrossRef]

P. Goy, J. M. Raimond, M. Gross, S. Haroche, “Observation of cavity-enhanced single atom spontaneous emission,” Phys. Rev. Lett. 50, 1903–1906 (1983).
[CrossRef]

F. DeMartini, G. Innocenti, G. R. Jacobivitz, P. Mataloni, “Anomalous spontaneous emission time in a microscopic optical cavity,” Phys. Rev. Lett. 59, 1995–2957 (1987); H. Yokoyama, M. Suzuki, Y. Nambu, “Spontaneous emission and laser oscillation properties of microcavities containing dye solution,” Appl. Phys. Lett. 58, 2598–2600 (1991).
[CrossRef]

F. De Martini, G. Di Giuseppe, M. Marrocco, “Single-mode generation of quantum photon states by excited single molecules in a microcavity trap,” Phys. Rev. Lett. 76, 900–903 (1996);S. C. Kitson, P. Jonsson, J. G. Rarity, P. R. Tapster, “Intensity fluctuation spectroscopy of small numbers of dye molecules in a microcavity,” Phys. Rev. A 58, 620–627 (1998).
[CrossRef] [PubMed]

Prog. Surf. Sci. (1)

J.-J. Greffet, R. Carminati, “Image formation in near-field optics,” Prog. Surf. Sci. 56, 133–237 (1997).
[CrossRef]

Other (5)

R. Petit, ed., Electromagnetic Theory of Grating (Springer-Verlag, Berlin, 1980).

M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics, Wiley Series in Pure and Applied Optics (Wiley, New York, 1991).

P. Henricini, Discrete Variable Methods in Ordinary Differential Equations (Wiley, New York, 1963).

V. Lefèvre-Seguin, J. C. Knight, V. Sandoghdar, D. S. Weiss, J. Hare, J. M. Raymond, S. Haroche, “Very high Q whispering-gallery modes in silica microsheres for cavity QED experiments,” in Optical Processes in Microcavities, R. K. Chang, A. J. Campillo, eds. (World Scientific, Singapore, 1996), pp. 101–133.

T. Tamir in Integrated Optics, T. Tamir, ed. (Springer, New York, 1975), p. 83.

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Figures (5)

Fig. 1
Fig. 1

(a) Monomode slab waveguide, (b) associated WVD.

Fig. 2
Fig. 2

(a) Doubly periodic grating and associated optogeometric parameters, (b) WVD.

Fig. 3
Fig. 3

Radiation pattern in the WVD of a localized source located within doubly periodic grating. We assume dominant emission in the guided mode. (m, n) are the multiplicities associated with each arc [see Fig. 2(b)].

Fig. 4
Fig. 4

Source radiation in an inhomogeneous structure. The source is assumed to be located in a thin homogeneous material slab (ha<z<hb) surrounded by inhomogeneous scatterers.

Fig. 5
Fig. 5

Results of the computation for the Poynting flux power density per unit solid angle dσ/dΩ in the kp/k0 plane for three different values of the perturbation parameter ξ=0.2 (A) and (B), ξ=0.5 (C) and (D), and ξ=1 (E) and (F). (A), (C), and (E) are power density emitted in the air; (B), (D), and (F) are power density emitted in the substrate.

Equations (70)

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

×E(r)-iωμ0H(r)=0,
×H(r)+iω0(r)E(r)=-iωPδ(r-z0z),
Ehom(rp, z)=U(kp)exp(ikprp+iγ2z)+D(kp)×exp(ikprp-iγ2z)dkp,
Epar(rp, z)
=[Us(kp)exp[ikprp+iγ2(z-z0)]Θ(z-z0)+Ds(kp)exp[ikprp-iγ2(z-z0)]Θ(z0-z)]dkp,
Us(kp)=ω2μ0 i8π2γ2 [P-(Pk^+)k^+],
Ds(kp)=ω2μ0 i8π2γ2 [P-(Pk^-)k^-],
k^+=1(2k0)1/2 (kp+γ2z),k^-=1(2k0)1/2 (kp-γ2z)
E(rp, z)=R(kp)exp(ikprp+iγ1z)dkp
forz>hmax,
E(rp, z)=T(kp)exp(ikprp-iγ3z)dkp
forz<hmin,
RD=Shb,hmaxUs+U0,UT=Shmin,ha0D+Ds,
E(r)=-2πiγ1R(kp) exp(ik1r)rforz>hmax,
E(r)=-2πiγ3T(kp) exp(ik3r)rforz<hmin,
dσdΩ=4π22η1 |γ1R(kp)|2
dσdΩ=4π22η3 |γ3T(kp)|2
Ψtot=Ψtotup+Ψtotdown=4πsr dσdΩ dΩ=|kp|<k1 4π22η1 |γ1R(kp)|2 dkpγ1k1+|kp|<k3 4π22η3 |γ3T(kp)|2 dkpγ3k3.
E(x, y, z)=-+dα-+dβE˜(α, β, z)(iαx+iβy),
(m, n)Z2,P(x, y, z)=Pδ(r-z0z)=δ(z-z0)-+dα-+dβP˜(α, β)×exp(iαx+iβy).
P(x, y, z)
=δ(z-z0)02π/dxdα02π/dydβm=-+n=-+Pα,βm,n
×exp(iαmx+iβny),
Pα,β(x, y, z)=δ(z-z0)m=-+n=-+Pα,βm,n×exp(iαmx+iβny),
Eα,β(x, y, z)=n=-+m=-+Eα,βm,n(z)exp(iαmx+iβny).
Eα,β(x, y, z)=n=-+m=-+Rα,βm,n exp(iαmx+iβny+iγ1m,nz),
[Eα,β(x, y, z)=n=-+m=-+Tα,βm,n exp(iαmx+iβny-iγ3m,nz)],
E(x, y, z)=02π/dxdα02π/dydβEα,β(x, y, z).
Epar(x, y, z)=n=-+m=-+Eparm,n(z)exp(iαmx+iβny)
Eparm,n(z)=Usm,n exp(iγ2m,nz)Θ(z-z0)+Dsm,n exp(-iγ2m,nz)Θ(z0-z)+em,nδ(z-z0),
em,n=-(zP˜m,n)z 120,
Dsm,n=Ds(kpm,n),Usm,n=Us(kpm,n),
Usxm,nUsym,nDsxm,nDsym,n=1202 Y2m,n-C2m,n-iαm-C2m,nX2m,n-iβnY2m,n-C2m,niαm-C2m,nX2m,niβn Pxm,nPym,nPzm,n,
Cjm,n=iαmβn/γjm,n,
Xjm,n=i[αm2+(γjm,n)2]/γjm,n,
Yjm,n=i[βn2+(γjm,n)2]/γjm,n,
Ehom(x, y, z)=n=-+m=-+Um,n exp(iαmx+iβny+iγ2m,nz)+Dm,n exp(iαmx+iβny-iγ2m,nz).
UT=S0,z0-uuS0,z0-udS0,z0-duS0,z0-dd 0D+Ds,
RD=Sz0+,huuSz0+,hudSz0+,hduSz0+,hdd U+Us0,
RT=Sz0,huu(I+S0, z0udM)Sz0,huuS0,z0ud(I+MS0,z0ud)S0,z0ddMS0,z0dd(I+MS0,z0ud)×Us-Ds,
M=(I-Sz0,hduS0,z0ud)-1Sz0,hdu.
dσdΩ=2π2η1 [X1m,n|Rxm,n|2+Y1m,n|Rym,n|2+2 Re(C1m,nR¯xm,nRym,n)],
dσdΩ=2π2η3 [X3m,n|Txm,n|2+Y3m,n|Tym,n|2+2 Re(C3m,nT¯xm,nTym,n)].
E(x, y, z)=n=-+m=-+Em,n(z)exp(iαmx+iβny),
H(x, y, z)=1iωμ0 n=-+m=-+Hm,n(z)×exp i(αmx+βny).
dExm,ndz=Hym,n-αmp,q1k2m-p,n-q(αpHyp,q-βqHxp,q),
dEym,ndz=-Hym,n-βnp,q1k2m-p,n-q×(αpHyp,q-βqHxp,q),
dHxm,ndz=p,q[k2]m-p,n-qEyp,q-αm(αmEym,n-βnExm,n),
dHym,ndz=-p,q[k2]m-p,n-qExp,q-βn×(αmEym,n-βnExm,n),
ε(x, y, z)k02and1/[k02ε(x, y, z)],
ε(x, y, z)k02=n=-+m=-+[k2]m,n exp(imKxx+inKyy),
EpHp(zq)=[M]EpHp(zp).
Em,n(zp)=upm,n exp[iγjm,n(z-zp)]+dpm,n×exp[-iγjm,n(z-zp)],
Hm,n(zp)=uhpm,n exp[iγjm,n(z-zp)]+dhpm,n exp[-iγjm,n(z-zp)]
uhpxm,n=-Cjm,nupxm,n-Yjm,nupym,n,
uhpym,n=Xjm,nupxm,n+Cjm,nupym,n,
dhpxm,n=Cjm,ndpxm,n+Yjm,ndpym,n,
dhpym,n=-Xjm,ndpxm,n-Cjm,ndpym,n,
UqDq=[Tp,q]UpDp
[Tp,q]=Tp,quuTp,qudTp,qduTp,qdd,
UqDp=[Sp,q]UpDq=Sp,quuSp,qudSp,qduSp,qdd UpDq.
Uv+1Dv+1=[Tv]UvDv,
Sp,pdd=1,Sp,qdd=Sp,q-1ddMq,
Sp,pud=0,Sp,qud=(TquuSp,q-1ud+Tqud)Mq,
Sp,pdu=0,Sp,qdu=-Sp,q-1ddMq[TqduHq-1-TqddGq-1],
Sp,puu=1,Sp,quu=TquuHq-1-TqudGq-1
-Sp,qud[TqduHq-1-TqddGq-1],
Mq=(TqduSp,q-1ud+Tqdd)-1,
Gq-1=(Sp,q-1dd)-1Sp,q-1du,
Hq-1=Sp,q-1uu-Sp,q-1ud(Sp,q-1dd)-1Sp,q-1du.

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