Thermal emission of a doped silicon grating has been studied in the plane perpendicular to the grooves. We show how the excitation of surface plasmons produce a resonant emission weakly depending on the polarization and azimuthal angle. We analyze in detail the polarization and angular dependence of the emission out of the plane perpendicular to the grooves. Two kinds of thermal sources, directional and quasi-isotropic, are studied. They have been designed in a previous paper. We also compute the total hemispherical emissivity of these gratings. In addition we show that in applications such as radiative cooling, these sources are less efficient than other structures.

1.
Wood
,
R. W.
, 1902, “
On a Remarkable Case of Uneven Distribution of Light in a Diffraction Grating Spectrum
,”
Philos. Mag.
0031-8086,
4
, pp.
396
402
.
2.
Maystre
,
D.
, and
Hutley
,
M. C.
, 1976, “
The Total Absorption of Light by a Diffraction Grating
,”
Opt. Commun.
0030-4018,
19
, pp.
431
436
.
3.
Petit
,
R.
, 1980,
Electromagnetic theory of gratings
,
Springer Verlag
,
Berlin
.
4.
Greffet
,
J. J.
,
Carminati
,
R.
,
Joulain
,
K.
,
Mulet
,
J. P.
,
Mainguy
,
S.
, and
Chen
,
Y.
, 2002, “
Coherent Thermal Emission of Light by Thermal Sources
,”
Nature (London)
0028-0836,
416
, pp.
61
64
.
5.
Marquier
,
F.
,
Joulain
,
K.
,
Mulet
,
J. P.
,
Carminati
,
R.
,
Greffet
,
J. J.
, and
Chen
,
Y.
, 2004,
Phys. Rev. B
0163-1829
69
, p.
155412
.
6.
Marquier
,
F.
,
Joulain
,
K.
,
Mulet
,
J. P.
,
Carminati
,
R.
, and
Greffet
,
J. J.
, 2004, “
Engineering Infrared Emission Properties of Silicon in the Near Field and the Far Field
,”
Opt. Commun.
0030-4018,
237
, pp.
379
388
.
7.
Kreiter
,
M.
,
Oster
,
J.
,
Sambles
,
R.
,
Herminghaus
,
S.
,
Mittler-Neher
,
S.
, and
Knoll
,
W.
, 1999, “
Thermally Induced Emission of Light From a Metallic Diffraction Grating, Mediated by Surface Plasmons
,”
Opt. Commun.
0030-4018,
200
, pp.
1
4
.
8.
Laroche
,
M.
,
Arnold
,
C.
,
Marquier
,
F.
,
Carminati
,
R.
,
Greffet
,
J. J.
,
Collin
,
S.
,
Bardou
,
N.
, and
Pelouard
,
J. L.
, 2005, “
Highly Directional Radiation Generated by Tungsten Thermal Source
,”
Opt. Lett.
0146-9592,
30
, pp.
2623
2625
.
9.
Hesketh
,
P. J.
,
Zemel
,
J. N.
, and
Gebhart
,
B.
, 1986, “
Organ Pipe Radiant Modes of Periodic Micromachined Silicon Surfaces
,”
Nature (London)
0028-0836,
324
, pp.
549
551
.
10.
Hesketh
,
P. J.
,
Zemel
,
J. N.
, and
Gebhart
,
B.
, 1988, “
Polarized Spectral Emittance From Periodic Micromachined Surfaces. I. Doped Silicon: The Normal Direction
,”
Phys. Rev. B
0163-1829,
37
, pp.
10795
10802
.
11.
Hesketh
,
P. J.
,
Zemel
,
J. N.
, and
Gebhart
,
B.
, 1988, “
Polarized Spectral Emittance From Periodic Micromachined Surfaces. II. Doped Silicon: Angular Variation
,”
Phys. Rev. B
0163-1829,
37
, pp.
10803
10813
.
12.
Hava
,
S.
,
Auslender
,
M.
,
Lacquet
,
B. M.
,
Coetzer
,
P. J.
, and
Swart
,
P. L.
, 1995, “
IR Transmission and Reflection Study of Lamellar Silicon Grating-Wafer Structures
,”
Infrared Phys. Technol.
1350-4495,
36
, pp.
639
647
.
13.
Auslender
,
M.
, and
Hava
,
S.
, 1995, “
Zero Infrared Reflectance Anomaly in Doped Silicon Lamellar Gratings. I. From Antireflection to Total Absorption
,”
Infrared Phys. Technol.
1350-4495,
36
, pp.
1077
1088
.
14.
Chateau
,
N.
, and
Hugonin
,
J. P.
, 1994, “
Algorithm for the Rigorous Coupled-Wave Analysis of Grating Diffraction
,”
J. Opt. Soc. Am. A
0740-3232,
11
, pp.
1321
1331
.
15.
Laroche
,
M.
,
Marquier
,
F.
,
Carminati
,
R.
, and
Greffet
,
J. J.
, 2005, “
Tailoring Silicon Radiative Properties
,”
Opt. Commun.
0030-4018,
250
, pp.
316
320
.
16.
Sai
,
H.
,
Yugami
,
H.
,
Akiyama
,
Y.
,
Kanamori
,
Y.
, and
Hane
,
K.
, 2001, “
Spectral Control of Thermal Emission by Periodic Microstructured Surfaces in the Near-Infrared Region
,”
J. Opt. Soc. Am. A
0740-3232,
18
, pp.
1471
1476
.
17.
Maruyama
,
S.
,
Kashiwa
,
T.
,
Yugami
,
H.
, and
Esachi
,
M.
, 2001, “
Thermal Radiation From Two-Dimensionally Confined Modes in Microcavities
,”
Appl. Phys. Lett.
0003-6951,
79
, pp.
1393
1395
.
18.
Pralle
,
M. U.
,
Moelders
,
N.
,
McNeal
,
M. P.
,
Puscasu
,
I.
,
Greenwald
,
A. C.
,
Daly
,
J. T.
,
Johnson
,
E. A.
,
George
,
T.
,
Choi
,
D. S.
,
El-Kady
,
I.
, and
Biswas
,
R.
, 2002, “
Photonic Crystal Enhanced Narrow-Band Infrared Emitters
,”
Appl. Phys. Lett.
0003-6951,
81
, pp.
4685
4687
.
19.
Kusunoki
,
F.
,
Kohama
,
T.
,
Hiroshima
,
T.
,
Fukumoto
,
S.
,
Takahara
,
J.
, and
Kobayashi
,
T.
, 2004, “
Narrow-Band Thermal Radiation With Low Directivity by Resonant Modes Inside Tungsten Microcavities
,”
Jpn. J. Appl. Phys., Part 1
0021-4922,
43
, pp.
5253
5258
.
20.
Enoch
,
S.
,
Simon
,
J. J.
,
Ascoubas
,
L.
,
Elamy
,
Z.
,
Lemarquis
,
F.
,
Torchio
,
P.
, and
Albrand
,
G.
, 2005, “
Simple Layer-By-Layer Photonic Crystal for the Control of Thermal Emission
,”
Appl. Phys. Lett.
0003-6951,
86
, p.
261101
.
21.
Laroche
,
M.
,
Carminati
,
R.
, and
Greffet
,
J. J.
, 2006, “
Coherent Thermal Antenna Using a Photonic Crystal Slab
,”
Phys. Rev. Lett.
0031-9007,
96
, p.
123903
.
22.
Hu
,
L.
,
Schmidt
,
A.
,
Narayanaswamy
,
A.
, and
Chen
,
G.
, 2004, “
Effects of Periodic Structures on the Coherence Properties of Blackbody Radiation
,”
ASME J. Heat Transfer
0022-1481,
126
, pp.
786
792
.
23.
Celanovic
,
I.
,
Perreault
,
D.
, and
Kassakian
,
J.
, 2005, “
Resonant-Cavity Enhanced Thermal Emission
,”
Phys. Rev. B
0163-1829,
72
, p.
075127
.
24.
Lee
,
B. J.
,
Fu
,
C. J.
, and
Zhang
,
Z. M.
, 2005, “
Coherent Thermal Emission From One-Dimensional Photonic Crystals
,”
Appl. Phys. Lett.
0003-6951,
87
, p.
071904
.
25.
Lee
,
B. J.
, and
Zhang
,
Z. M.
, 2006, “
Coherent Thermal Emission From Modified Periodic Multilayer Structures
,”
ASME J. Heat Transfer
0022-1481 (to be published).
26.
Kretschmann
,
M.
,
Leskova
,
T. A.
, and
Maradudin
,
A. A.
, 2003, “
Conical Propagation of a Surface Polariton Across a Grating
,”
Opt. Commun.
0030-4018,
215
, pp.
205
223
.
27.
Elston
,
S. J.
,
Bryan-Brown
,
G. P.
, and
Sambles
,
J. R.
, 1991, “
Polarization Conversion From Diffraction Gratings
,”
Phys. Rev. B
0163-1829,
44
, pp.
6393
6400
.
28.
Moharam
,
M. G.
,
Grann
,
E. B.
,
Pommet
,
D. P.
, and
Gaylord
,
T. K.
, 1995, “
Formulation for Stable and Efficient Implementation of the Rigorous Coupled-Wave Analysis of Binary Gratings
,”
J. Opt. Soc. Am. A
0740-3232,
12
, pp.
1068
1076
.
29.
Li
,
L.
, 1997, “
New Formulation of the Fourier Modal Method for Crossed Surface-Relief Gratings
,”
J. Opt. Soc. Am. A
0740-3232,
14
, pp.
2758
2767
.
30.
Joulain
,
K.
,
Mulet
,
J. P.
,
Marquier
,
F.
,
Carminati
,
R.
, and
Greffet
,
J. J.
, 2005, “
Surface Electromagnetic Waves Thermally Excited: Radiative Heat Transfer, Coherence Properties and Casimir Forces Revisited in the Near-Field
,”
Surf. Sci. Rep.
0167-5729,
57
, pp.
59
112
.
31.
Raether
,
H.
, 1988,
Surface Plasmons on smooth and rough surfaces and on gratings
,
Springer Verlag
,
Berlin
.
32.
Simon
,
J. M.
, and
Gonzãlez Pagliere
,
J. M.
, 1986, “
Diffuse Light in Diffraction Gratings and Surface Plasma Oscillations
,”
Opt. Acta
0030-3909,
33
, pp.
1035
1049
.
33.
Simon
,
J. M.
, and
Gonzãlez Pagliere
,
J. M.
, 1988, “
Diffuse Light Bands From Diffraction Gratings: Polarization Dependence and Phase Behaviour
,”
J. Mod. Opt.
0950-0340,
35
, pp.
1549
1555
.
34.
Depine
,
R. A.
, and
Brudny
,
V. L.
, 1991, “
Speckle Patterns Generated by Rough Surfaces With a Periodic Component
,”
J. Mod. Opt.
0950-0340,
38
, pp.
2281
2293
.
35.
Brudny
,
V. L.
,
Iemmi
,
C. C.
, and
Ledesma
,
S. A.
, 1994, “
Diffuse Light Bands for p and s Polarization in Microrough Diffraction Gratings
,”
Optik (Jena)
0030-4026,
97
, pp.
23
30
.
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