Abstract

The scattering by slightly inhomogeneous objects has been studied by a first-order method and reciprocity theorem. The scattering calculation reported in this manuscript is based on a simple computation of the field in a defectless structure at different incidence angles. The numerical results have been compared to those given by an exact calculation. It is shown that the method enables to handle complex structures with an affordable computational burden. A major advantage of the method is its ability to treat different defects without recomputing the field, i.e, the main part of the computation time. In addition, for defects in periodic structures, the field computation can be limited to a single period thus leading to an important decrease of the computational time and required memory. This method is believed to provide significant advantages for the engineering of optical devices.

© 2014 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  25. B. Polat, “On Poynting’s theorem and reciprocity relations for discontinuous fields,” IEEE Antennas and propagation magazine49, 74–83 (2007).
    [CrossRef]
  26. K. Yegin, “Application of electromagnetic reciprocity principle to the computation of signal coupling to missile-like structures,” Progress in electromagnetics research M23, 79–91 (2012).
    [CrossRef]
  27. http://www.comsol.com/ .
  28. C. C. Fisenmaier, Y. Huo, and P. B. Catrysse, “Optical confinement methods for continued scaling of CMOS image sensor pixels,” Opt. Exp.16, 20457–20470 (2008).
    [CrossRef]

2013

J. Polanco, R. M. Fitzgerald, and A. A. Maradudin, “Scattering of surface plasmon polaritons by one-dimensional surface defects,” Phys. Rev. B87, 155417 (2013).
[CrossRef]

É. Dieudonné, N. Malléjac, C. Amra, and S. Enoch, “Surface and bulk scattering by magnetic and dielectric inhomogeneities: a first-order method,” J. Opt. Soc. Am. A30, 1772–1779 (2013).
[CrossRef]

2012

K. Yegin, “Application of electromagnetic reciprocity principle to the computation of signal coupling to missile-like structures,” Progress in electromagnetics research M23, 79–91 (2012).
[CrossRef]

2008

C. C. Fisenmaier, Y. Huo, and P. B. Catrysse, “Optical confinement methods for continued scaling of CMOS image sensor pixels,” Opt. Exp.16, 20457–20470 (2008).
[CrossRef]

2007

B. Polat, “On Poynting’s theorem and reciprocity relations for discontinuous fields,” IEEE Antennas and propagation magazine49, 74–83 (2007).
[CrossRef]

2006

2005

J.-M. L. Bernard, D. Bouche, I. Andronov, and F. Guyon, “Expression du champ diffracté par une inclusion,” Ann. Télécommun.60, 630–648, (2005).

2004

T. M. Elfouhaily and C.-A. Guérin, “A critical survey of approximate scattering wave theories from random rough surfaces,” Waves Random Media14, R1–R40 (2004).
[CrossRef]

2002

G. Soriano, C. A. Guerin, and M. Saillard, “Scattering by two-dimensional rough surfaces: comparison between the method of moments, Kirchhoff and small-slope approximations,” Waves Random Media12, 63–83 (2002).
[CrossRef]

2001

M. Saillard and A. Sentenac, “Rigorous solutions for electromagnetic scattering from rough surfaces,” Waves Random Media11, R103–R137 (2001).
[CrossRef]

K. F. Warnick and W. C. Chew, “Numerical simulation methods for rough surface scattering,” Waves Random Media11, R1–R30 (2001).
[CrossRef]

1998

1997

1993

1992

C.-T. Tai, “Complementary reciprocity theorems in electromagnetic theory,” IEEE Transactions on antennas and propagation40, 675–681 (1992).
[CrossRef]

1989

1988

M. Nieto-Vesperinas, “Reciprocity of the impultse response for scattering from inhomogeneous media and arbitrary dielectric bodies,” J. Opt. Soc. Am. A.5, 360–365 (1988).
[CrossRef]

1986

M. Nieto-Vesperinas and E. Wolf, “Generalized Stokes reciprocity relations for scattering from dielectric objects of arbitrary shape,” J. Opt. Soc. Am. A.3, 2038–2046 (1986).
[CrossRef]

1984

J. M. Elson, “Theory of light scattering from a rough surface with an inhomogeneous dielectric permittivity,” Phys. Rev. B.30, 5460–5480 (1984).
[CrossRef]

1981

1955

D. S. Saxon, “Tensor scattering matrix for the electromagnetic field,” Phys. Rev.100, 1771–1775 (1955).
[CrossRef]

1954

T. H. Crowley, “On reciprocity theorems in electromagnetic theory,” J. Appl. Phys.25, 119–120 (1954).
[CrossRef]

V. H. Rumsey, “Reaction concept in electromagnetic theory,” Phys. Rev.94, 1483–1491 (1954).
[CrossRef]

1896

H. A. Lorentz, “The theorem of Poynting concerning the energy in the electromagnetic field and two general propositions concerning the propagation of light,” Amsterdammer Akademie der Wetenschappen4, 176 (1896).

Amra, C.

Andronov, I.

J.-M. L. Bernard, D. Bouche, I. Andronov, and F. Guyon, “Expression du champ diffracté par une inclusion,” Ann. Télécommun.60, 630–648, (2005).

Bernard, J.-M. L.

J.-M. L. Bernard, D. Bouche, I. Andronov, and F. Guyon, “Expression du champ diffracté par une inclusion,” Ann. Télécommun.60, 630–648, (2005).

Bouche, D.

J.-M. L. Bernard, D. Bouche, I. Andronov, and F. Guyon, “Expression du champ diffracté par une inclusion,” Ann. Télécommun.60, 630–648, (2005).

Bousquet, P.

Carminati, R.

Catrysse, P. B.

C. C. Fisenmaier, Y. Huo, and P. B. Catrysse, “Optical confinement methods for continued scaling of CMOS image sensor pixels,” Opt. Exp.16, 20457–20470 (2008).
[CrossRef]

Chew, W. C.

K. F. Warnick and W. C. Chew, “Numerical simulation methods for rough surface scattering,” Waves Random Media11, R1–R30 (2001).
[CrossRef]

Crowley, T. H.

T. H. Crowley, “On reciprocity theorems in electromagnetic theory,” J. Appl. Phys.25, 119–120 (1954).
[CrossRef]

Dieudonné, É.

Elfouhaily, T. M.

T. M. Elfouhaily and C.-A. Guérin, “A critical survey of approximate scattering wave theories from random rough surfaces,” Waves Random Media14, R1–R40 (2004).
[CrossRef]

Elson, J. M.

J. M. Elson, “Theory of light scattering from a rough surface with an inhomogeneous dielectric permittivity,” Phys. Rev. B.30, 5460–5480 (1984).
[CrossRef]

Enoch, S.

Fisenmaier, C. C.

C. C. Fisenmaier, Y. Huo, and P. B. Catrysse, “Optical confinement methods for continued scaling of CMOS image sensor pixels,” Opt. Exp.16, 20457–20470 (2008).
[CrossRef]

Fitzgerald, R. M.

J. Polanco, R. M. Fitzgerald, and A. A. Maradudin, “Scattering of surface plasmon polaritons by one-dimensional surface defects,” Phys. Rev. B87, 155417 (2013).
[CrossRef]

Flory, F.

Greffet, J.-J.

Guerin, C. A.

G. Soriano, C. A. Guerin, and M. Saillard, “Scattering by two-dimensional rough surfaces: comparison between the method of moments, Kirchhoff and small-slope approximations,” Waves Random Media12, 63–83 (2002).
[CrossRef]

Guérin, C.-A.

T. M. Elfouhaily and C.-A. Guérin, “A critical survey of approximate scattering wave theories from random rough surfaces,” Waves Random Media14, R1–R40 (2004).
[CrossRef]

Guyon, F.

J.-M. L. Bernard, D. Bouche, I. Andronov, and F. Guyon, “Expression du champ diffracté par une inclusion,” Ann. Télécommun.60, 630–648, (2005).

Harrington, R. F.

R. F. Harrington, Time-harmonic Electromagnetic Fields (McGraw-Hill, 1961), pp. 116–123

He, S.

Hill, S. C.

Huo, Y.

C. C. Fisenmaier, Y. Huo, and P. B. Catrysse, “Optical confinement methods for continued scaling of CMOS image sensor pixels,” Opt. Exp.16, 20457–20470 (2008).
[CrossRef]

Ladouceur, F.

F. Ladouceur, “Roughness, Inhomogeneity, and Integrated Optics,” Journal of lightwave technology15, 1020–1025 (1997).
[CrossRef]

L. Poladian, F. Ladouceur, and P. D. Miller, “Effects of surface roughness on gratings,” J. Opt. Soc. Am. B14, 1339–1344 (1997).
[CrossRef]

Lorentz, H. A.

H. A. Lorentz, “The theorem of Poynting concerning the energy in the electromagnetic field and two general propositions concerning the propagation of light,” Amsterdammer Akademie der Wetenschappen4, 176 (1896).

Malléjac, N.

Maradudin, A. A.

J. Polanco, R. M. Fitzgerald, and A. A. Maradudin, “Scattering of surface plasmon polaritons by one-dimensional surface defects,” Phys. Rev. B87, 155417 (2013).
[CrossRef]

Miller, P. D.

Nieto-Vesperinas, M.

R. Carminati, M. Nieto-Vesperinas, and J.-J. Greffet, “Reciprocity of evanescent electromagnetic waves,” J. Opt. Soc. Am. A15, 706–712,, (1998).
[CrossRef]

J. M. Soto-Crespo and M. Nieto-Vesperinas, “Electromagnetic scattering from very rough random surfaces and deep reflection gratings,” J. Opt. Soc. Am. A6, 367–384 (1989).
[CrossRef]

M. Nieto-Vesperinas, “Reciprocity of the impultse response for scattering from inhomogeneous media and arbitrary dielectric bodies,” J. Opt. Soc. Am. A.5, 360–365 (1988).
[CrossRef]

M. Nieto-Vesperinas and E. Wolf, “Generalized Stokes reciprocity relations for scattering from dielectric objects of arbitrary shape,” J. Opt. Soc. Am. A.3, 2038–2046 (1986).
[CrossRef]

Pendleton, J. D.

Poladian, L.

Polanco, J.

J. Polanco, R. M. Fitzgerald, and A. A. Maradudin, “Scattering of surface plasmon polaritons by one-dimensional surface defects,” Phys. Rev. B87, 155417 (2013).
[CrossRef]

Polat, B.

B. Polat, “On Poynting’s theorem and reciprocity relations for discontinuous fields,” IEEE Antennas and propagation magazine49, 74–83 (2007).
[CrossRef]

Roche, P.

Rumsey, V. H.

V. H. Rumsey, “Reaction concept in electromagnetic theory,” Phys. Rev.94, 1483–1491 (1954).
[CrossRef]

Saillard, M.

G. Soriano, C. A. Guerin, and M. Saillard, “Scattering by two-dimensional rough surfaces: comparison between the method of moments, Kirchhoff and small-slope approximations,” Waves Random Media12, 63–83 (2002).
[CrossRef]

M. Saillard and A. Sentenac, “Rigorous solutions for electromagnetic scattering from rough surfaces,” Waves Random Media11, R103–R137 (2001).
[CrossRef]

Saxon, D. S.

D. S. Saxon, “Tensor scattering matrix for the electromagnetic field,” Phys. Rev.100, 1771–1775 (1955).
[CrossRef]

Sentenac, A.

M. Saillard and A. Sentenac, “Rigorous solutions for electromagnetic scattering from rough surfaces,” Waves Random Media11, R103–R137 (2001).
[CrossRef]

Song, J.

Soriano, G.

G. Soriano, C. A. Guerin, and M. Saillard, “Scattering by two-dimensional rough surfaces: comparison between the method of moments, Kirchhoff and small-slope approximations,” Waves Random Media12, 63–83 (2002).
[CrossRef]

Soto-Crespo, J. M.

Tai, C.-T.

C.-T. Tai, “Complementary reciprocity theorems in electromagnetic theory,” IEEE Transactions on antennas and propagation40, 675–681 (1992).
[CrossRef]

Videen, G.

Warnick, K. F.

K. F. Warnick and W. C. Chew, “Numerical simulation methods for rough surface scattering,” Waves Random Media11, R1–R30 (2001).
[CrossRef]

Wolf, E.

M. Nieto-Vesperinas and E. Wolf, “Generalized Stokes reciprocity relations for scattering from dielectric objects of arbitrary shape,” J. Opt. Soc. Am. A.3, 2038–2046 (1986).
[CrossRef]

Yegin, K.

K. Yegin, “Application of electromagnetic reciprocity principle to the computation of signal coupling to missile-like structures,” Progress in electromagnetics research M23, 79–91 (2012).
[CrossRef]

Zhu, N.

Amsterdammer Akademie der Wetenschappen

H. A. Lorentz, “The theorem of Poynting concerning the energy in the electromagnetic field and two general propositions concerning the propagation of light,” Amsterdammer Akademie der Wetenschappen4, 176 (1896).

Ann. Télécommun.

J.-M. L. Bernard, D. Bouche, I. Andronov, and F. Guyon, “Expression du champ diffracté par une inclusion,” Ann. Télécommun.60, 630–648, (2005).

IEEE Antennas and propagation magazine

B. Polat, “On Poynting’s theorem and reciprocity relations for discontinuous fields,” IEEE Antennas and propagation magazine49, 74–83 (2007).
[CrossRef]

IEEE Transactions on antennas and propagation

C.-T. Tai, “Complementary reciprocity theorems in electromagnetic theory,” IEEE Transactions on antennas and propagation40, 675–681 (1992).
[CrossRef]

J. Appl. Phys.

T. H. Crowley, “On reciprocity theorems in electromagnetic theory,” J. Appl. Phys.25, 119–120 (1954).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Opt. Soc. Am. A.

M. Nieto-Vesperinas and E. Wolf, “Generalized Stokes reciprocity relations for scattering from dielectric objects of arbitrary shape,” J. Opt. Soc. Am. A.3, 2038–2046 (1986).
[CrossRef]

M. Nieto-Vesperinas, “Reciprocity of the impultse response for scattering from inhomogeneous media and arbitrary dielectric bodies,” J. Opt. Soc. Am. A.5, 360–365 (1988).
[CrossRef]

J. Opt. Soc. Am. B

Journal of lightwave technology

F. Ladouceur, “Roughness, Inhomogeneity, and Integrated Optics,” Journal of lightwave technology15, 1020–1025 (1997).
[CrossRef]

Opt. Exp.

C. C. Fisenmaier, Y. Huo, and P. B. Catrysse, “Optical confinement methods for continued scaling of CMOS image sensor pixels,” Opt. Exp.16, 20457–20470 (2008).
[CrossRef]

Phys. Rev.

V. H. Rumsey, “Reaction concept in electromagnetic theory,” Phys. Rev.94, 1483–1491 (1954).
[CrossRef]

D. S. Saxon, “Tensor scattering matrix for the electromagnetic field,” Phys. Rev.100, 1771–1775 (1955).
[CrossRef]

Phys. Rev. B

J. Polanco, R. M. Fitzgerald, and A. A. Maradudin, “Scattering of surface plasmon polaritons by one-dimensional surface defects,” Phys. Rev. B87, 155417 (2013).
[CrossRef]

Phys. Rev. B.

J. M. Elson, “Theory of light scattering from a rough surface with an inhomogeneous dielectric permittivity,” Phys. Rev. B.30, 5460–5480 (1984).
[CrossRef]

Progress in electromagnetics research M

K. Yegin, “Application of electromagnetic reciprocity principle to the computation of signal coupling to missile-like structures,” Progress in electromagnetics research M23, 79–91 (2012).
[CrossRef]

Waves Random Media

G. Soriano, C. A. Guerin, and M. Saillard, “Scattering by two-dimensional rough surfaces: comparison between the method of moments, Kirchhoff and small-slope approximations,” Waves Random Media12, 63–83 (2002).
[CrossRef]

M. Saillard and A. Sentenac, “Rigorous solutions for electromagnetic scattering from rough surfaces,” Waves Random Media11, R103–R137 (2001).
[CrossRef]

K. F. Warnick and W. C. Chew, “Numerical simulation methods for rough surface scattering,” Waves Random Media11, R1–R30 (2001).
[CrossRef]

T. M. Elfouhaily and C.-A. Guérin, “A critical survey of approximate scattering wave theories from random rough surfaces,” Waves Random Media14, R1–R40 (2004).
[CrossRef]

Other

R. F. Harrington, Time-harmonic Electromagnetic Fields (McGraw-Hill, 1961), pp. 116–123

http://www.comsol.com/ .

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Figures (9)

Fig. 1
Fig. 1

Schematic representation of an arbitrary object. The permittivity and permeability are given by Eqs. 2a and 2b, respectively.

Fig. 2
Fig. 2

Illustration of the reciprocity principle for the electric sources only.

Fig. 3
Fig. 3

Schematic representation of the studied media. k is the wavevector and it is defined by the two angles θ (normal angle) and ϕ (polar angle) as well as its norm k. Layers 1 and 3 are infinite medium air (εr = 1, μr = 1). Layer 2 of slightly fluctuating permittivity and permeability (ε̃, μ̃) has a thickness e.

Fig. 4
Fig. 4

Schematic representation of the considered medium in S polarization. Here, e is the thickness, λ is the wavelength, L is the length of the layer and θ is the observation angle between 0 and 90.

Fig. 5
Fig. 5

Comparison between the first-order method and the exact calculation.

Fig. 6
Fig. 6

Representation of the function p(x) in [−0.375, 0.375], p(x) = 0 if x ∉ [−0.375, 0.375].

Fig. 7
Fig. 7

Configuration for the application example: a 35-square cylinder, width e = 0.03 m, period pr = 0.09 m, permittivity εc = 15, permeability μc = 1, S polarization, normal incidence i0 = 0, wavelength λ = 1 m.

Fig. 8
Fig. 8

Comparison between reciprocity and exact calculation - Localized property defect with a 10% higher permittivity on one cylinder.

Fig. 9
Fig. 9

Two-dimentional CMOS pixel model with layer materials.

Tables (3)

Tables Icon

Table 1 The average difference between RECY and exact calculation for differents permittivities εc and differents perecentage of defect.

Tables Icon

Table 2 Height and permittivity of the components of the CMOS structure.

Tables Icon

Table 3 Scattered transmission of the defective CMOS structure.

Equations (33)

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

× E i ( x , y , z ) = ι ω μ ˜ i H i ( x , y , z ) ,
× H i ( x , y , z ) = ι ω ε ˜ i E i ( x , y , z ) .
ε ˜ i = ε i [ 1 + p i ( ρ ) ] ,
μ ˜ i = μ i [ 1 + q i ( ρ ) ] ,
( E , H ) = ( E 0 , H 0 ) + ( E d , H d ) .
× E i d = ι ω μ i H i d + M i ,
× H i d = ι ω ε i E i d + J i ,
M i = ι ω μ i q i H i 0 ,
J i = ι ω ε i p i E i 0 .
V ( E b J a H b M a ) d ρ = V ( E a J b H a M b ) d ρ .
J a = Il d δ ( ρ ρ d ) ,
M a = Il d δ ( ρ ρ d ) ,
J b = ι ω ε i p i ( ρ ) E i 0 ( ρ V i )
M b = ι ω μ i q i ( ρ ) H i 0 ( ρ V i )
E d ( ρ d ) d = ι ω ε i V i p i ( ρ ) E i dip ( ρ ) E i 0 ( ρ ) d ρ
H d ( ρ d ) d = ι ω μ i V i q i ( ρ ) H i dip ( ρ ) H i 0 ( ρ ) d ρ
X ( r , z ) = σ X ^ ( σ , z ) exp ( ι σ r ) d σ ,
X ^ ( σ , z ) = 1 4 π 2 r X ( r , z ) exp ( ι σ r ) d r .
k × E ^ a = M ^ a + ι ω μ H ^ a ,
k × H ^ a = J ^ a ι ω ε E ^ a ,
k × E ^ b = M ^ b + ι ω μ H ^ b ,
k × H ^ b = J ^ b ι ω ε E ^ b ,
H ^ b ( 13 a ) + H ^ a ( 14 a ) + E ^ b ( 13 b ) + E ^ a ( 14 b ) ,
( C × A ) B + ( C × B ) A = 0 ,
E ^ b J ^ a + H ^ b M ^ a = E ^ a J ^ b + H ^ a M ^ b ,
z ( E ^ b J ^ a + H ^ b M ^ a ) d z = z ( E ^ a J ^ b + H ^ a M ^ b ) d z .
E ^ 0 a ( σ , z ) = 1 4 π 2 Il e ι σ r ω μ 0 2 α 1 e ι α 1 z Γ ¯ d e ι α 1 z
Γ ¯ = ( 1 σ x 2 k 1 2 σ x σ y k 1 2 σ x α 1 k 1 2 σ y σ x k 1 2 1 σ y 2 k 1 2 σ y α 1 k 1 2 α 1 σ x k 1 2 α 1 σ y k 1 2 1 α 1 2 k 1 2 ) .
A ^ 1 b ( σ ) d = ι ω ε ω μ 0 2 α 1 p ^ ( σ σ 0 ) z = 0 e E ^ 2 a ( σ , z ) E ^ 2 0 ( σ 0 , z ) d z
E y d ( i 0 , θ ) = ι ω ε c E dip 2 D p ˜ x c x c + e z c z c + e E c y a ( x , z , θ ) E c y 0 ( x , z , i 0 ) d x d z
ε r filter = 2.25 10 ι | λ f λ λ |
ε r deflens = ε r lens ( 1 + p ( x ) ) ,
E d ( ρ s ) d = ι ω ε r lens p ( ρ ) E dip ( ρ ) E 0 ( ρ ) d ρ

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