Laboratoire d'Optique des Surfaces et des Couches Minces, Unité Propre de la Recherche et de l'Enseignement Supérieur Associée au Centre National de la Recherche Scientifique 6080, Ecole Nationale Supérieure de Physique de Marseille, Domaine Universitaire de St Jérôme, Avenue Escadrille Normandie-Niemen, 13397 Marseille Cedex 20, France
Claude Amra and Sophie Maure, "Electromagnetic power provided by sources within multilayer optics: free-space and modal patterns," J. Opt. Soc. Am. A 14, 3102-3113 (1997)
An electromagnetic theory is presented that makes possible the development
of a complete energy balance within an arbitrary multilayer microcavity that
supports different kinds of classical optical sources. The theory is based
on a single Fourier spectrum of waves and is valid for transparent or dissipative
stacks, with no use of modal methods. We show how the power provided by the
cavity is converted into Poynting flux and absorption. Free-space and guided-mode
patterns are calculated for single layers, mirrors, and narrow-band filters.
The modal pattern is shown to be strongly dependent on the cavity poles. Discretization
of the high-frequency energy into a set of guided modes is introduced as an
asymptotic limit of the problem when absorption vanishes to zero. The applications
concern defect-induced absorption in optical multilayers or guided-mode coupling
through microirregularities in a stack, as well as spontaneous emission in
classical microcavities.
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Ratios of Embedded to Radiative Power, Calculated for Different Absorption Values ( and 1) and Two Polarizations ( and ), Where the Cavity is the Low-Index Layer
of Fig. 5(a)
Polarization
Polarization
0
0
0
1
34.51
Table 2
Ratios of Modal Power Carried by Each Guided Mode, Normalized to
Radiative Power, Where the Calculation Is Performed for
(TE-Mode) and (TM-Mode) Polarizations and the Cavity
Is the High-Index Layer of Fig. 7(a)
is the maxima of normalized spectral densities at modal frequencies in the
case of slight absorption
Σ is the sum of all
ratios and gives the contribution of total embedded power.
Table 3
Ratios of Modal Power Carried by Each Guided Mode, Normalized to
Radiative Power, Where the Calculation Is Performed for
(TE-Mode) and (TM-Mode) Polarizations and the Cavity
Is That of Fig. 9(a)
is the maxima of spectral densities at modal frequencies in the case of slight
absorption
Σ is the sum of all
ratios and gives the contribution of total embedded power.
Table 4
Same as Table 3, but the Cavity Is That of Fig. 10(a)
Mode
Mode
TE0
8
TM0
2131
TE1
45
TM1
8549
TE2
1897
TM2
12,461
Table 5
Same as Table
3, but the Cavity Is That of Fig. 11(a)
Mode
Mode
TE0
0.25
1586
TM0
47
TE1
0.94
6128
TM1
185
TE2
1.94
13,752
TM2
370
TE3
3.02
26,867
TM3
508
TE4
3.76
35,974
Table 6
Same as Table
3, but the Cavity Is the Fabry–Perot Cavity of Fig. 12(a), Whose Design is
Mode
Mode
TE0
115
TM0
84
TE1
158
TM1
149
TE2
366
TM2
55
TE3
368
Table 7
Same as Table
3, but with a Fabry–Perot Cavity of Design
Mode
Mode
TE0
218
TM0
0.4
2182
TE1
268
TM1
38
TE2
68
TM2
328
TE3
0.1
1053
TM3
321
TE4
358
Tables (7)
Table 1
Ratios of Embedded to Radiative Power, Calculated for Different Absorption Values ( and 1) and Two Polarizations ( and ), Where the Cavity is the Low-Index Layer
of Fig. 5(a)
Polarization
Polarization
0
0
0
1
34.51
Table 2
Ratios of Modal Power Carried by Each Guided Mode, Normalized to
Radiative Power, Where the Calculation Is Performed for
(TE-Mode) and (TM-Mode) Polarizations and the Cavity
Is the High-Index Layer of Fig. 7(a)
is the maxima of normalized spectral densities at modal frequencies in the
case of slight absorption
Σ is the sum of all
ratios and gives the contribution of total embedded power.
Table 3
Ratios of Modal Power Carried by Each Guided Mode, Normalized to
Radiative Power, Where the Calculation Is Performed for
(TE-Mode) and (TM-Mode) Polarizations and the Cavity
Is That of Fig. 9(a)
is the maxima of spectral densities at modal frequencies in the case of slight
absorption
Σ is the sum of all
ratios and gives the contribution of total embedded power.
Table 4
Same as Table 3, but the Cavity Is That of Fig. 10(a)
Mode
Mode
TE0
8
TM0
2131
TE1
45
TM1
8549
TE2
1897
TM2
12,461
Table 5
Same as Table
3, but the Cavity Is That of Fig. 11(a)
Mode
Mode
TE0
0.25
1586
TM0
47
TE1
0.94
6128
TM1
185
TE2
1.94
13,752
TM2
370
TE3
3.02
26,867
TM3
508
TE4
3.76
35,974
Table 6
Same as Table
3, but the Cavity Is the Fabry–Perot Cavity of Fig. 12(a), Whose Design is
Mode
Mode
TE0
115
TM0
84
TE1
158
TM1
149
TE2
366
TM2
55
TE3
368
Table 7
Same as Table
3, but with a Fabry–Perot Cavity of Design
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