Abstract

The emission of light by sources, e.g., by luminescent centers, located in a thin nonabsorbing dielectric layer 0 between two half-spaces 1 and 2 is investigated theoretically. It is assumed that the light is emitted in electric or magnetic dipole transitions. But the theory is given in such a form that it can easily be extended to electric and magnetic quadrupole and higher-order multipole transitions. The electromagnetic boundary-value problem is solved rigorously for sources in layers 0 of arbitrary thickness. The radiation patterns, i.e., the angular distributions of light emitted into the half-spaces 1 and 2, are calculated. The theory takes into account the following effects that strongly influence the radiation patterns: (1) the wide-angle interferences that are a consequence of the coherence of the plane waves emitted into different directions, (2) the multiple-beam interferences that result from the multiple reflections of the plane waves between the interfaces 0/1 and 0/2, and (3) that evanescent waves present in the near field of the source radiate into media 1 and/or 2 if these media are denser than layer 0. This emission process is influenced by evanescent-wave effects analogous to the wide-angle interferences and the multiple-beam interferences of the plane waves. The limiting case of extremely thin layers 0 with optical thickness much smaller than the wavelength is also treated. Explicit analytical expressions are presented for the dipole radiation patterns in this case. Furthermore, the theory is generalized for sources in plane-stratified-layer systems. The dipole radiation patterns are derived for the case in which any numbers of loss-free or absorbing, dielectric or metallic thin films are present between the loss-free layer 0 of arbitrary thickness containing the source and the half-spaces 1 and 2.

© 1981 Optical Society of America

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  1. W Lukosz and R E Kunz, "Light emission by magnetic and electric dipoles close to a plane interface I Total radiated power," J Opt Soc Am 67, 1607–1615 (1977),II Radiation patterns of perpendicular oriented dipoles J Opt Soc Am 67, 1615–1619 (1977)
  2. Reference I contains lists of references to related experimental and theoretical work
  3. W Lukosz, "Light emission by magnetic and electric dipoles close to a plane dielectric interface III Radiation patterns of dipoles with arbitrary orientation," J Opt Soc Am 69, 1495–1503 (1979)
  4. W Lukosz and R E Kunz, "Changes in fluorescence lifetimes induced by variation of the radiating molecules' optical environment," Opt Commun 31, 42–46 (1979), R E Kunz and W Lukosz, "Changes in fluorescence lifetimes induced by variable optical environments," Phys Rev B 21, 4814–4828 (1980)
  5. W Lukosz, "Theory of optical-environment-dependent spontaneous-emission rates for emitters in thin layers," Phys Rev B 22, 3030–3038 (1980)
  6. W Lukosz and R E Kunz, "New method for determining refractive index and thickness of fluorescent thin films," Opt Commun 31, 251–256 (1979)
  7. E D Palik, S W McKnight, R T Holm, W Lukosz, and R Thalmann, "Cathodo-luminescence multiple reflection effects in thin films," J Opt Soc Am 70, 1626A (1980)
  8. When comparing Section 2 B of this paper with Refs 1 and 3, pilease note that we now use the notation ø +(H E)(kx, ky,) and ø∞− (H E)(kx, ky,) to distinguish more clearly between the amplitudes of the waves in the half-spaces zz0 and z < z0, respectively
  9. The notation L∞ (n0) is meant to indicate that the source is located in an infinite medium 0, Eqs (3 7) and (3 8) show that L∞,(n0) depends not only on n0 but also on µ0
  10. The total power L (z0) is a function of the position z0 of the source in layer 0 and depends on the optical properties of the media 1 and 2′ (cf Ref 5) In the case in which the layer 0 is a dielectric waveguide, i e, if n0 > n1, n2 and if the thickness d0 of the layer exceeds the cutoff thickness, the source not only radiates into media 1 and 2 but also excites guided modes of the waveguide Then the power carried away by these modes is not included in L(z0) given by Eq (3 2) The total dipole power radiated by the dipole into media 1 and 2 and into the guided modes is given by the expressions for L (z0) derived in Section IV of Ref 6
  11. We use the subscripts 1, 0, 2 only in Section 5 of this paper to designate the radiation patterns of dipoles located in extremely thin layers 0 between the half-spaces 1 and 2 In Eqs (5 2) and (5 4) the subscript ‖ denotes a single dipole whose dipole moment is parallel to the layer and not (as in Section 4 D) an ensemble of parallel dipoles with random orientations in the xy plane
  12. W Lukosz and M Meier, "Lifetimes and radiation patterns of luminescent centers close to a thin metal film," Opt Lett 6, 251–253 (1981)

1981

W Lukosz and M Meier, "Lifetimes and radiation patterns of luminescent centers close to a thin metal film," Opt Lett 6, 251–253 (1981)

1980

E D Palik, S W McKnight, R T Holm, W Lukosz, and R Thalmann, "Cathodo-luminescence multiple reflection effects in thin films," J Opt Soc Am 70, 1626A (1980)

W Lukosz, "Theory of optical-environment-dependent spontaneous-emission rates for emitters in thin layers," Phys Rev B 22, 3030–3038 (1980)

1979

W Lukosz and R E Kunz, "New method for determining refractive index and thickness of fluorescent thin films," Opt Commun 31, 251–256 (1979)

W Lukosz, "Light emission by magnetic and electric dipoles close to a plane dielectric interface III Radiation patterns of dipoles with arbitrary orientation," J Opt Soc Am 69, 1495–1503 (1979)

W Lukosz and R E Kunz, "Changes in fluorescence lifetimes induced by variation of the radiating molecules' optical environment," Opt Commun 31, 42–46 (1979), R E Kunz and W Lukosz, "Changes in fluorescence lifetimes induced by variable optical environments," Phys Rev B 21, 4814–4828 (1980)

1977

W Lukosz and R E Kunz, "Light emission by magnetic and electric dipoles close to a plane interface I Total radiated power," J Opt Soc Am 67, 1607–1615 (1977),II Radiation patterns of perpendicular oriented dipoles J Opt Soc Am 67, 1615–1619 (1977)

Kunz, R E

W Lukosz and R E Kunz, "Changes in fluorescence lifetimes induced by variation of the radiating molecules' optical environment," Opt Commun 31, 42–46 (1979), R E Kunz and W Lukosz, "Changes in fluorescence lifetimes induced by variable optical environments," Phys Rev B 21, 4814–4828 (1980)

W Lukosz and R E Kunz, "New method for determining refractive index and thickness of fluorescent thin films," Opt Commun 31, 251–256 (1979)

W Lukosz and R E Kunz, "Light emission by magnetic and electric dipoles close to a plane interface I Total radiated power," J Opt Soc Am 67, 1607–1615 (1977),II Radiation patterns of perpendicular oriented dipoles J Opt Soc Am 67, 1615–1619 (1977)

Lukosz, W

W Lukosz and M Meier, "Lifetimes and radiation patterns of luminescent centers close to a thin metal film," Opt Lett 6, 251–253 (1981)

W Lukosz, "Theory of optical-environment-dependent spontaneous-emission rates for emitters in thin layers," Phys Rev B 22, 3030–3038 (1980)

W Lukosz and R E Kunz, "New method for determining refractive index and thickness of fluorescent thin films," Opt Commun 31, 251–256 (1979)

W Lukosz, "Light emission by magnetic and electric dipoles close to a plane dielectric interface III Radiation patterns of dipoles with arbitrary orientation," J Opt Soc Am 69, 1495–1503 (1979)

W Lukosz and R E Kunz, "Changes in fluorescence lifetimes induced by variation of the radiating molecules' optical environment," Opt Commun 31, 42–46 (1979), R E Kunz and W Lukosz, "Changes in fluorescence lifetimes induced by variable optical environments," Phys Rev B 21, 4814–4828 (1980)

W Lukosz and R E Kunz, "Light emission by magnetic and electric dipoles close to a plane interface I Total radiated power," J Opt Soc Am 67, 1607–1615 (1977),II Radiation patterns of perpendicular oriented dipoles J Opt Soc Am 67, 1615–1619 (1977)

McKnight, S W

E D Palik, S W McKnight, R T Holm, W Lukosz, and R Thalmann, "Cathodo-luminescence multiple reflection effects in thin films," J Opt Soc Am 70, 1626A (1980)

Meier, M

W Lukosz and M Meier, "Lifetimes and radiation patterns of luminescent centers close to a thin metal film," Opt Lett 6, 251–253 (1981)

Palik, E D

E D Palik, S W McKnight, R T Holm, W Lukosz, and R Thalmann, "Cathodo-luminescence multiple reflection effects in thin films," J Opt Soc Am 70, 1626A (1980)

J Opt Soc Am

W Lukosz and R E Kunz, "Light emission by magnetic and electric dipoles close to a plane interface I Total radiated power," J Opt Soc Am 67, 1607–1615 (1977),II Radiation patterns of perpendicular oriented dipoles J Opt Soc Am 67, 1615–1619 (1977)

W Lukosz, "Light emission by magnetic and electric dipoles close to a plane dielectric interface III Radiation patterns of dipoles with arbitrary orientation," J Opt Soc Am 69, 1495–1503 (1979)

E D Palik, S W McKnight, R T Holm, W Lukosz, and R Thalmann, "Cathodo-luminescence multiple reflection effects in thin films," J Opt Soc Am 70, 1626A (1980)

Opt Commun

W Lukosz and R E Kunz, "Changes in fluorescence lifetimes induced by variation of the radiating molecules' optical environment," Opt Commun 31, 42–46 (1979), R E Kunz and W Lukosz, "Changes in fluorescence lifetimes induced by variable optical environments," Phys Rev B 21, 4814–4828 (1980)

W Lukosz and R E Kunz, "New method for determining refractive index and thickness of fluorescent thin films," Opt Commun 31, 251–256 (1979)

Opt Lett

W Lukosz and M Meier, "Lifetimes and radiation patterns of luminescent centers close to a thin metal film," Opt Lett 6, 251–253 (1981)

Phys Rev B

W Lukosz, "Theory of optical-environment-dependent spontaneous-emission rates for emitters in thin layers," Phys Rev B 22, 3030–3038 (1980)

Other

Reference I contains lists of references to related experimental and theoretical work

When comparing Section 2 B of this paper with Refs 1 and 3, pilease note that we now use the notation ø +(H E)(kx, ky,) and ø∞− (H E)(kx, ky,) to distinguish more clearly between the amplitudes of the waves in the half-spaces zz0 and z < z0, respectively

The notation L∞ (n0) is meant to indicate that the source is located in an infinite medium 0, Eqs (3 7) and (3 8) show that L∞,(n0) depends not only on n0 but also on µ0

The total power L (z0) is a function of the position z0 of the source in layer 0 and depends on the optical properties of the media 1 and 2′ (cf Ref 5) In the case in which the layer 0 is a dielectric waveguide, i e, if n0 > n1, n2 and if the thickness d0 of the layer exceeds the cutoff thickness, the source not only radiates into media 1 and 2 but also excites guided modes of the waveguide Then the power carried away by these modes is not included in L(z0) given by Eq (3 2) The total dipole power radiated by the dipole into media 1 and 2 and into the guided modes is given by the expressions for L (z0) derived in Section IV of Ref 6

We use the subscripts 1, 0, 2 only in Section 5 of this paper to designate the radiation patterns of dipoles located in extremely thin layers 0 between the half-spaces 1 and 2 In Eqs (5 2) and (5 4) the subscript ‖ denotes a single dipole whose dipole moment is parallel to the layer and not (as in Section 4 D) an ensemble of parallel dipoles with random orientations in the xy plane

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