Abstract

Time-harmonic and time-dependent Green’s functions are derived for a lossless, uniaxial gyroelectromagnetic medium whose permeability tensor is a scalar multiple of its permittivity tensor, and their properties are investigated. The derived Green’s functions can be used for the solution of initial and boundary value problems, as well as for obtaining the electromagnetic fields radiated by electric and magnetic sources.

© 1989 Optical Society of America

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References

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  1. E. J. Post, Formal Structure of Electromagnetics (North-Holland, Amsterdam, 1962).
  2. D. K. Cheng, J. A. Kong, “Covariant Descriptions of Bianisotropic Media,” Proc. IEEE 56, 248 (1968).
    [CrossRef]
  3. J. A. Kong, “Theorems of Bianisotropic Media,” Proc. IEEE 60, 1036 (1972).
    [CrossRef]
  4. C. M. Krowne, “Electromagnetic Theorems for Complex Anisotropic Media,” IEEE Trans. Antennas Propag. AP-32, 1224 (1984).
    [CrossRef]
  5. C. Altman, A. Schatzberg, K. Suchy, “Symmetry Transformations and Reversal of Currents and Fields in Bounded (Bi)anisotropic Media,” IEEE Trans. Antennas Propag. AP-32, 1204 (1984).
    [CrossRef]
  6. K. K. Mei, “On the Perturbational Solution to the Dyadic Green’s Function of Maxwell’s Equations in Anisotropic Media,” IEEE Trans. Antennas Propag. AP-19, 665 (1971).
    [CrossRef]
  7. S. Przezdziecki, R. A. Hurd, “A Note on Scalar Hertz Potentials for Gyrotropic Media,” Appl. Phys. 20, 313 (1979).
    [CrossRef]
  8. W. Weiglhofer, ”Scalarization of Maxwell’s Equations in General Inhomogeneous Bianisotropic Media,” Proc. Inst. Electr. Eng. Part H 134, 357 (1987).
  9. H. C. Chen, Theory of Electromagnetic Waves (McGraw-Hill, New York, 1983).
  10. H. C. Chen, “Dyadic Green’s Function and Radiation in a Uniaxially Anisotropic Medium,” Int. J. Electron. 35, 633 (1975).
    [CrossRef]
  11. A. Lakhtakia, V. K. Varadan, V. V. Varadan, “Radiation and Canonical Sources in Uniaxial Dielectric Media,” Int. J. Electron. 65, 1171 (1988).
    [CrossRef]
  12. A. Lakhtakia, V. V. Varadan, V. K. Varadan, “Time-Dependent Dyadic Green’s Functions for Uniaxial Dielectric Media,” J. Wave-Mater. Interact. 3, 1 (1988).
  13. J. F. Nye, Physical Properties of Crystals (Clarendon, Oxford, 1972), Chap. 3.
  14. Y. Chow, “A Note on Radiation in a Gyro-Electric-Magnetic Medium—An Extension of Bunkin’s Calculations,” IRE Trans. Antennas Propag. AP-10, 464 (1962).
    [CrossRef]
  15. V. H. Rumsey, “Propagation in Generalized Gyrotropic Media,” IEEE Trans. Antennas Propag. AP-12, 83 (1964).
    [CrossRef]
  16. L. B. Felsen, “Propagation and Diffraction of Transient Fields in Non-Dispersive and Dispersive Media,” in Transient Electromagnetic Fields, L. B. Felsen, Ed. (Springer-Verlag, Berlin, 1976).
    [CrossRef]
  17. D. S. Jones, Methods in Electromagnetic Wave Propagation (Clarendon, Oxford, 1979).
  18. Y. H. Ku, Transient Circuit Analysis (Van Nostrand, Princeton, NJ, 1961).

1988 (2)

A. Lakhtakia, V. K. Varadan, V. V. Varadan, “Radiation and Canonical Sources in Uniaxial Dielectric Media,” Int. J. Electron. 65, 1171 (1988).
[CrossRef]

A. Lakhtakia, V. V. Varadan, V. K. Varadan, “Time-Dependent Dyadic Green’s Functions for Uniaxial Dielectric Media,” J. Wave-Mater. Interact. 3, 1 (1988).

1987 (1)

W. Weiglhofer, ”Scalarization of Maxwell’s Equations in General Inhomogeneous Bianisotropic Media,” Proc. Inst. Electr. Eng. Part H 134, 357 (1987).

1984 (2)

C. M. Krowne, “Electromagnetic Theorems for Complex Anisotropic Media,” IEEE Trans. Antennas Propag. AP-32, 1224 (1984).
[CrossRef]

C. Altman, A. Schatzberg, K. Suchy, “Symmetry Transformations and Reversal of Currents and Fields in Bounded (Bi)anisotropic Media,” IEEE Trans. Antennas Propag. AP-32, 1204 (1984).
[CrossRef]

1979 (1)

S. Przezdziecki, R. A. Hurd, “A Note on Scalar Hertz Potentials for Gyrotropic Media,” Appl. Phys. 20, 313 (1979).
[CrossRef]

1975 (1)

H. C. Chen, “Dyadic Green’s Function and Radiation in a Uniaxially Anisotropic Medium,” Int. J. Electron. 35, 633 (1975).
[CrossRef]

1972 (1)

J. A. Kong, “Theorems of Bianisotropic Media,” Proc. IEEE 60, 1036 (1972).
[CrossRef]

1971 (1)

K. K. Mei, “On the Perturbational Solution to the Dyadic Green’s Function of Maxwell’s Equations in Anisotropic Media,” IEEE Trans. Antennas Propag. AP-19, 665 (1971).
[CrossRef]

1968 (1)

D. K. Cheng, J. A. Kong, “Covariant Descriptions of Bianisotropic Media,” Proc. IEEE 56, 248 (1968).
[CrossRef]

1964 (1)

V. H. Rumsey, “Propagation in Generalized Gyrotropic Media,” IEEE Trans. Antennas Propag. AP-12, 83 (1964).
[CrossRef]

1962 (1)

Y. Chow, “A Note on Radiation in a Gyro-Electric-Magnetic Medium—An Extension of Bunkin’s Calculations,” IRE Trans. Antennas Propag. AP-10, 464 (1962).
[CrossRef]

Altman, C.

C. Altman, A. Schatzberg, K. Suchy, “Symmetry Transformations and Reversal of Currents and Fields in Bounded (Bi)anisotropic Media,” IEEE Trans. Antennas Propag. AP-32, 1204 (1984).
[CrossRef]

Chen, H. C.

H. C. Chen, “Dyadic Green’s Function and Radiation in a Uniaxially Anisotropic Medium,” Int. J. Electron. 35, 633 (1975).
[CrossRef]

H. C. Chen, Theory of Electromagnetic Waves (McGraw-Hill, New York, 1983).

Cheng, D. K.

D. K. Cheng, J. A. Kong, “Covariant Descriptions of Bianisotropic Media,” Proc. IEEE 56, 248 (1968).
[CrossRef]

Chow, Y.

Y. Chow, “A Note on Radiation in a Gyro-Electric-Magnetic Medium—An Extension of Bunkin’s Calculations,” IRE Trans. Antennas Propag. AP-10, 464 (1962).
[CrossRef]

Felsen, L. B.

L. B. Felsen, “Propagation and Diffraction of Transient Fields in Non-Dispersive and Dispersive Media,” in Transient Electromagnetic Fields, L. B. Felsen, Ed. (Springer-Verlag, Berlin, 1976).
[CrossRef]

Hurd, R. A.

S. Przezdziecki, R. A. Hurd, “A Note on Scalar Hertz Potentials for Gyrotropic Media,” Appl. Phys. 20, 313 (1979).
[CrossRef]

Jones, D. S.

D. S. Jones, Methods in Electromagnetic Wave Propagation (Clarendon, Oxford, 1979).

Kong, J. A.

J. A. Kong, “Theorems of Bianisotropic Media,” Proc. IEEE 60, 1036 (1972).
[CrossRef]

D. K. Cheng, J. A. Kong, “Covariant Descriptions of Bianisotropic Media,” Proc. IEEE 56, 248 (1968).
[CrossRef]

Krowne, C. M.

C. M. Krowne, “Electromagnetic Theorems for Complex Anisotropic Media,” IEEE Trans. Antennas Propag. AP-32, 1224 (1984).
[CrossRef]

Ku, Y. H.

Y. H. Ku, Transient Circuit Analysis (Van Nostrand, Princeton, NJ, 1961).

Lakhtakia, A.

A. Lakhtakia, V. K. Varadan, V. V. Varadan, “Radiation and Canonical Sources in Uniaxial Dielectric Media,” Int. J. Electron. 65, 1171 (1988).
[CrossRef]

A. Lakhtakia, V. V. Varadan, V. K. Varadan, “Time-Dependent Dyadic Green’s Functions for Uniaxial Dielectric Media,” J. Wave-Mater. Interact. 3, 1 (1988).

Mei, K. K.

K. K. Mei, “On the Perturbational Solution to the Dyadic Green’s Function of Maxwell’s Equations in Anisotropic Media,” IEEE Trans. Antennas Propag. AP-19, 665 (1971).
[CrossRef]

Nye, J. F.

J. F. Nye, Physical Properties of Crystals (Clarendon, Oxford, 1972), Chap. 3.

Post, E. J.

E. J. Post, Formal Structure of Electromagnetics (North-Holland, Amsterdam, 1962).

Przezdziecki, S.

S. Przezdziecki, R. A. Hurd, “A Note on Scalar Hertz Potentials for Gyrotropic Media,” Appl. Phys. 20, 313 (1979).
[CrossRef]

Rumsey, V. H.

V. H. Rumsey, “Propagation in Generalized Gyrotropic Media,” IEEE Trans. Antennas Propag. AP-12, 83 (1964).
[CrossRef]

Schatzberg, A.

C. Altman, A. Schatzberg, K. Suchy, “Symmetry Transformations and Reversal of Currents and Fields in Bounded (Bi)anisotropic Media,” IEEE Trans. Antennas Propag. AP-32, 1204 (1984).
[CrossRef]

Suchy, K.

C. Altman, A. Schatzberg, K. Suchy, “Symmetry Transformations and Reversal of Currents and Fields in Bounded (Bi)anisotropic Media,” IEEE Trans. Antennas Propag. AP-32, 1204 (1984).
[CrossRef]

Varadan, V. K.

A. Lakhtakia, V. K. Varadan, V. V. Varadan, “Radiation and Canonical Sources in Uniaxial Dielectric Media,” Int. J. Electron. 65, 1171 (1988).
[CrossRef]

A. Lakhtakia, V. V. Varadan, V. K. Varadan, “Time-Dependent Dyadic Green’s Functions for Uniaxial Dielectric Media,” J. Wave-Mater. Interact. 3, 1 (1988).

Varadan, V. V.

A. Lakhtakia, V. V. Varadan, V. K. Varadan, “Time-Dependent Dyadic Green’s Functions for Uniaxial Dielectric Media,” J. Wave-Mater. Interact. 3, 1 (1988).

A. Lakhtakia, V. K. Varadan, V. V. Varadan, “Radiation and Canonical Sources in Uniaxial Dielectric Media,” Int. J. Electron. 65, 1171 (1988).
[CrossRef]

Weiglhofer, W.

W. Weiglhofer, ”Scalarization of Maxwell’s Equations in General Inhomogeneous Bianisotropic Media,” Proc. Inst. Electr. Eng. Part H 134, 357 (1987).

Appl. Phys. (1)

S. Przezdziecki, R. A. Hurd, “A Note on Scalar Hertz Potentials for Gyrotropic Media,” Appl. Phys. 20, 313 (1979).
[CrossRef]

IEEE Trans. Antennas Propag. (4)

V. H. Rumsey, “Propagation in Generalized Gyrotropic Media,” IEEE Trans. Antennas Propag. AP-12, 83 (1964).
[CrossRef]

C. M. Krowne, “Electromagnetic Theorems for Complex Anisotropic Media,” IEEE Trans. Antennas Propag. AP-32, 1224 (1984).
[CrossRef]

C. Altman, A. Schatzberg, K. Suchy, “Symmetry Transformations and Reversal of Currents and Fields in Bounded (Bi)anisotropic Media,” IEEE Trans. Antennas Propag. AP-32, 1204 (1984).
[CrossRef]

K. K. Mei, “On the Perturbational Solution to the Dyadic Green’s Function of Maxwell’s Equations in Anisotropic Media,” IEEE Trans. Antennas Propag. AP-19, 665 (1971).
[CrossRef]

Int. J. Electron. (2)

H. C. Chen, “Dyadic Green’s Function and Radiation in a Uniaxially Anisotropic Medium,” Int. J. Electron. 35, 633 (1975).
[CrossRef]

A. Lakhtakia, V. K. Varadan, V. V. Varadan, “Radiation and Canonical Sources in Uniaxial Dielectric Media,” Int. J. Electron. 65, 1171 (1988).
[CrossRef]

IRE Trans. Antennas Propag. (1)

Y. Chow, “A Note on Radiation in a Gyro-Electric-Magnetic Medium—An Extension of Bunkin’s Calculations,” IRE Trans. Antennas Propag. AP-10, 464 (1962).
[CrossRef]

J. Wave-Mater. Interact. (1)

A. Lakhtakia, V. V. Varadan, V. K. Varadan, “Time-Dependent Dyadic Green’s Functions for Uniaxial Dielectric Media,” J. Wave-Mater. Interact. 3, 1 (1988).

Proc. IEEE (2)

D. K. Cheng, J. A. Kong, “Covariant Descriptions of Bianisotropic Media,” Proc. IEEE 56, 248 (1968).
[CrossRef]

J. A. Kong, “Theorems of Bianisotropic Media,” Proc. IEEE 60, 1036 (1972).
[CrossRef]

Proc. Inst. Electr. Eng. Part H (1)

W. Weiglhofer, ”Scalarization of Maxwell’s Equations in General Inhomogeneous Bianisotropic Media,” Proc. Inst. Electr. Eng. Part H 134, 357 (1987).

Other (6)

H. C. Chen, Theory of Electromagnetic Waves (McGraw-Hill, New York, 1983).

E. J. Post, Formal Structure of Electromagnetics (North-Holland, Amsterdam, 1962).

L. B. Felsen, “Propagation and Diffraction of Transient Fields in Non-Dispersive and Dispersive Media,” in Transient Electromagnetic Fields, L. B. Felsen, Ed. (Springer-Verlag, Berlin, 1976).
[CrossRef]

D. S. Jones, Methods in Electromagnetic Wave Propagation (Clarendon, Oxford, 1979).

Y. H. Ku, Transient Circuit Analysis (Van Nostrand, Princeton, NJ, 1961).

J. F. Nye, Physical Properties of Crystals (Clarendon, Oxford, 1972), Chap. 3.

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Equations (43)

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D = 0 a · E ; B = μ 0 q a · H  ,
a = a A + ( a a ) e c e c ,
( × A ) a 1 ( × A ) E + 0 μ 0 q a { 2 E / t 2 } = μ 0 q { J / t } × ( a 1 K ) ,
( × A ) a 1 ( × A ) H + 0 μ 0 q a { 2 H / t 2 } = 0 { K / t } × ( a 1 J )   .
( × A ) a 1 ( × A ) E k 2 a E = i ω μ 0 q J × ( a 1 K ) ,
( × A ) a 1 ( × A ) H k 2 a H = i ω 0 q K × ( a 1 J ) ,
E ( r | ω ) = d 3 r s   [ i ω μ 0 q B e ( R | ω ) J ( r s | ω ) B m ( R | ω ) { a 1 K ( r s | ω ) } ] ,
H ( r | ω ) = d 3 r s [ i ω 0 B e ( R | ω ) K ( r s | ω ) ] + B m ( R | ω ) { a 1 J ( r s | ω ) } ]
[ ( × A ) a 1 ( × A ) k 2 a ] B e ( R | ω ) = A δ ( R ) ,
[ ( × A ) a 1 ( × A ) k 2 a ] B m ( R | ω ) = × A δ ( R ) ,
B e ( R | ω ) = ( 2 π ) 3 d 3 p exp [ i p R ] B e 1 ( p | ω ) ,
W e ( p | ω ) = ( p × A ) a 1 ( p × A ) k 2 a ,
W e 1 ( p | ω ) = [ a 2 a a 1 pp / k 2 ] / [ p a p k 2 a 2 a ]   .
B e ( R | ω ) = [ a 2 a a 1 + / k 2 ] exp [ i k R e ] / 4 π R e ,
R e = [ a 2 a  R a 1 R ] .
B m ( R | ω ) = ( 2 π ) 3 d 3 p exp [ i p R ] [ W e 1 ( p | ω ) i p × A ]   ,
B m ( R | ω ) = [ a 2 a a 1 ] × A exp [ i k R e ] / 4 π R e = a 2 a a 1 × {   exp [ i k R e ] / 4 π R e } .
B e ( R | ω ) = ( a 2 a exp [ i k R e ] / 4 π R e ) ( [ 1 ( i k R e ) 1 + ( i k R e ) 2 ] a 1 [ 1 3 ( i k R e ) 1 + 3 ( i k R e ) 2 ]   ( a 1 R )   ( a 1 R ) / [ R a 1 R ]   ) ,
B m ( R | ω ) = ( k 2 a 4 a 2 exp [ i k R e ] / 4 π R e ) ( [ ( i k R e ) 2 ( i k R e ) 1 ] a 1 × [ a 1 R ] )   .
B e ( R | ω ) = B e ( R | ω ) ; B m ( R | ω ) = B m ( R | ω ) ;
[ B e ( R | ω ) ] t r = B e ( R | ω ) ;
[ B m ( R | ω ) a 1 ] t r = B m ( R | ω ) a 1 .
B m ( R | ω ) = a 1 [ × B e ( R | ω ) ] a   ;
× B m ( R | ω ) k 2 a B e ( R | ω ) a = a δ ( R ) .
B e ( R | ω ) = ( a 2 a exp [ i k R e ] / 4 π R e ) ( i k R e ) 2 × ( a 1 3 ( a 1 R ) ( a 1 R ) / [ R a 1 R ] ) ,
B m ( R | ω ) = 0 .
B e ( R | ω ) = ( a 2 a exp [ i k R e ] / 4 π R e ) × ( a 1 ( a 1 R ) ( a 1 R ) / [ R a 1 R ] ) ,
B m ( R | ω ) = ( k 2 a 4 a 2 exp [ i k R e ] / 4 π R e ) × ( i k R e ) 1 ( a 1 × [ a 1 R ] ) .
p 2 ( e p ) = k 2 a 2 a / [ a ( e p × e c ) ( e p × e c ) + a   ( e p e c ) 2 ]   .
( i ) E 1 = e p × e c ; H 1 = [ k 2 a / ω μ 0 q p ] E 2 ;
( ii ) E 2 = e c e p ( e p e c ) ( p / k a ) 2 ; H 2 = [ ω 0 p 2 / k 2 a ] E 1 .
E ( r | t ) = d 3 r s d t s [ μ 0 q B 1 ( R | τ ) J ( r s t s ) + B 2 ( R | τ ) a 1 K ( r s t s ) ] ,
H ( r | t ) = d 3 r s d t s [ B 2 ( R | τ ) a 1 J ( r s t s ) + 0 B 2 ( R | τ ) K ( r s | t s ) ]   ,
B 1 ( R | τ ) = ( 2 π ) 1 + Δ + Δ d ω ( i ω ) exp [ i ω t ] B e ( R | ω ) ,
B 2 ( R | τ ) = ( 2 π ) 1 + Δ + Δ d ω exp [ i ω t ] B m ( R | ω ) .
u ( t ) = ( 1 2 ) + ( 1 + π ) 0 ( d ω / ω ) sin ω t , t 0 = 0 , t < 0 ,
B 1 ( R | τ ) = ( a 2 a / 4 π R e ) ( [ δ ( τ e ) + ( c e / R e ) δ ( τ e ) ( c e / R e ) 2 u ( τ e ) ] a 1 [ δ ( τ e ) + 3 ( c e / R e ) δ ( τ e ) 3 ( c e / R e ) 2 u ( τ e ) ] ( a 1 R ) ( a 1 R ) / [ R a 1 R ] ) ,
B 2 ( R | τ ) = ( a 4 a 2 / 4 π c e R e 2 ) ( [ δ ( τ e ) + ( c e / R e ) δ ( τ e ) ] a 1 × [ a 1 R ] ) ,
c e = [ μ 0 q 0 ] 1 / 2 , τ e = τ R e / c e ,
B 1 ( R | τ ) = B 1 ( R | τ ) ; B 2 ( R | τ ) = B 2 ( R | τ ) ;
[ B 1 ( R | τ ) ] t r = B 1 ( R | τ ) ; [ B 2 ( R | τ ) a 1 ] t r = B 2 ( R | τ ) a 1 .
B 1 ( R | τ ) = ( a 2 a / 4 π R e ) ( c e / R e ) 2 ( a 1 + 3 ( a 1 R ) ( a 1 R ) / [ R a 1 R ] ) ; τ e > 0 ,
B 2 ( R | τ ) = 0 ; τ e > 0 .

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