Abstract

Theoretical analysis of electromagnetic wave propagation in planar waveguides filled with uniaxial chiral anisotropic media is presented. The guide parallel plates are assumed to be perfect electric conductors. The material filling the waveguide is a generalized medium that incorporates chiral and metamaterials. The behavior of the field intensities, the dispersion curves, and the energy flux for three varieties of uniaxial chiral media are examined numerically. The results demonstrate the phenomena of backward waves in uniaxial anisotropic chiral media. The comparisons of the computed results of the presented general formulations with published results for some material cases confirm the accuracy of the presented analysis.

© 2014 Optical Society of America

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  1. P. Pelet and N. Engheta, “The theory of chirowaveguides,” IEEE Trans. Antenn. Propag.38(1), 90–98 (1990).
    [CrossRef]
  2. I. V. Lindell, A. H. Sihvola, S. A. Tretyakov, and A. J. Viitanen, Electromagnetic Waves in Chiral and Bi-Isotropic Media (Artech House, Incorporated, 1994).
  3. R. Oussaid and B. Haraoubia, “Behavior of chiral material in terms of a guided wave propagation,” I. J.of Appl. Electromagnetics and Mechanics19(1–4), 631–635 (2004).
  4. R. Oussaid and B. Haraoubia, “Longitudinal and transverse operators formalism for chiral media: Application to guided structures filled with chiral material,” Can. J. Phys.82(5), 367–378 (2004).
    [CrossRef]
  5. S. Gulistan, A. A. Syed, and Q. A. Naqvi, “Fields in fractional dual DB waveguides containing chiral nihility metamaterials,” J. Electromagn. Waves Appl.26(16), 2130–2141 (2012).
    [CrossRef]
  6. M. M. Ali, M. J. Mughal, A. A. Rahim, and Q. A. Naqvi, “The Guided waves in planar waveguide partially filled with strong chiral material,” I. J.of Appl. Electromagnetics and Mechanics38(2–3), 139–149 (2012).
  7. A. Viitanen and I. V. Lindell, “Plane wave propagation in uniaxial bianisotropic medium with an application to a polarization transformer,” Int. J. Infrared Millim. Waves14(10), 1993–20010 (1993).
    [CrossRef]
  8. Q. Cheng and T. J. Cui, “Negative refractions in uniaxially anisotropic chiral media,” Phys. Rev. B73(11), 113(2006).
    [CrossRef]
  9. S. F. Mahmoud and A. J. Viittanen, “Modes in a hard surface waveguide with uniaxially anisotropic chiral material filling,” Prog. in Electromag. Res.39, 265–279 (2003).
  10. J. F. Dong and J. Li, “Characteristics of guided modes in uniaxial chiral circular waveguide,” Prog. in Electromag. Res.124, 331–345 (2012).
  11. J. F. Dong and J. Li, “Guided modes in circular waveguide filled uniaxial chiral medium,” I. J. of Applied Electromagnetics and Mech.40(4), 283–292 (2012).
  12. M. A. Baqir and P. K. Choudhury, “On energy Flux through a uniaxial chiral metamaterials made circular waveguide under PMC boundary,” J. Electromagn. Waves Appl.26(16), 2165–2175 (2012).
    [CrossRef]
  13. M. A. Baqir and P. K. Choudhury, “Propagation through uniaxial anisotropic chiral circular waveguide under DB boundary,” J. Electromagn. Waves Appl.27(6), 783–793 (2013).
    [CrossRef]
  14. M. A. Baqir and P. K. Choudhury, “Flux through guides with microstructured twisted clad DB medium,” J. Nanomater.2014, 1–6 (2014).
    [CrossRef]
  15. M. A. Baqir and P. K. Choudhury, “Propagation through uniaxial anisotropic chiral circular waveguide under DB boundary,” J. Electromagn. Waves Appl.27(6), 783–793 (2013).
    [CrossRef]

2014

M. A. Baqir and P. K. Choudhury, “Flux through guides with microstructured twisted clad DB medium,” J. Nanomater.2014, 1–6 (2014).
[CrossRef]

2013

M. A. Baqir and P. K. Choudhury, “Propagation through uniaxial anisotropic chiral circular waveguide under DB boundary,” J. Electromagn. Waves Appl.27(6), 783–793 (2013).
[CrossRef]

M. A. Baqir and P. K. Choudhury, “Propagation through uniaxial anisotropic chiral circular waveguide under DB boundary,” J. Electromagn. Waves Appl.27(6), 783–793 (2013).
[CrossRef]

2012

S. Gulistan, A. A. Syed, and Q. A. Naqvi, “Fields in fractional dual DB waveguides containing chiral nihility metamaterials,” J. Electromagn. Waves Appl.26(16), 2130–2141 (2012).
[CrossRef]

M. M. Ali, M. J. Mughal, A. A. Rahim, and Q. A. Naqvi, “The Guided waves in planar waveguide partially filled with strong chiral material,” I. J.of Appl. Electromagnetics and Mechanics38(2–3), 139–149 (2012).

J. F. Dong and J. Li, “Characteristics of guided modes in uniaxial chiral circular waveguide,” Prog. in Electromag. Res.124, 331–345 (2012).

J. F. Dong and J. Li, “Guided modes in circular waveguide filled uniaxial chiral medium,” I. J. of Applied Electromagnetics and Mech.40(4), 283–292 (2012).

M. A. Baqir and P. K. Choudhury, “On energy Flux through a uniaxial chiral metamaterials made circular waveguide under PMC boundary,” J. Electromagn. Waves Appl.26(16), 2165–2175 (2012).
[CrossRef]

2006

Q. Cheng and T. J. Cui, “Negative refractions in uniaxially anisotropic chiral media,” Phys. Rev. B73(11), 113(2006).
[CrossRef]

2004

R. Oussaid and B. Haraoubia, “Behavior of chiral material in terms of a guided wave propagation,” I. J.of Appl. Electromagnetics and Mechanics19(1–4), 631–635 (2004).

R. Oussaid and B. Haraoubia, “Longitudinal and transverse operators formalism for chiral media: Application to guided structures filled with chiral material,” Can. J. Phys.82(5), 367–378 (2004).
[CrossRef]

2003

S. F. Mahmoud and A. J. Viittanen, “Modes in a hard surface waveguide with uniaxially anisotropic chiral material filling,” Prog. in Electromag. Res.39, 265–279 (2003).

1993

A. Viitanen and I. V. Lindell, “Plane wave propagation in uniaxial bianisotropic medium with an application to a polarization transformer,” Int. J. Infrared Millim. Waves14(10), 1993–20010 (1993).
[CrossRef]

1990

P. Pelet and N. Engheta, “The theory of chirowaveguides,” IEEE Trans. Antenn. Propag.38(1), 90–98 (1990).
[CrossRef]

Ali, M. M.

M. M. Ali, M. J. Mughal, A. A. Rahim, and Q. A. Naqvi, “The Guided waves in planar waveguide partially filled with strong chiral material,” I. J.of Appl. Electromagnetics and Mechanics38(2–3), 139–149 (2012).

Baqir, M. A.

M. A. Baqir and P. K. Choudhury, “Flux through guides with microstructured twisted clad DB medium,” J. Nanomater.2014, 1–6 (2014).
[CrossRef]

M. A. Baqir and P. K. Choudhury, “Propagation through uniaxial anisotropic chiral circular waveguide under DB boundary,” J. Electromagn. Waves Appl.27(6), 783–793 (2013).
[CrossRef]

M. A. Baqir and P. K. Choudhury, “Propagation through uniaxial anisotropic chiral circular waveguide under DB boundary,” J. Electromagn. Waves Appl.27(6), 783–793 (2013).
[CrossRef]

M. A. Baqir and P. K. Choudhury, “On energy Flux through a uniaxial chiral metamaterials made circular waveguide under PMC boundary,” J. Electromagn. Waves Appl.26(16), 2165–2175 (2012).
[CrossRef]

Cheng, Q.

Q. Cheng and T. J. Cui, “Negative refractions in uniaxially anisotropic chiral media,” Phys. Rev. B73(11), 113(2006).
[CrossRef]

Choudhury, P. K.

M. A. Baqir and P. K. Choudhury, “Flux through guides with microstructured twisted clad DB medium,” J. Nanomater.2014, 1–6 (2014).
[CrossRef]

M. A. Baqir and P. K. Choudhury, “Propagation through uniaxial anisotropic chiral circular waveguide under DB boundary,” J. Electromagn. Waves Appl.27(6), 783–793 (2013).
[CrossRef]

M. A. Baqir and P. K. Choudhury, “Propagation through uniaxial anisotropic chiral circular waveguide under DB boundary,” J. Electromagn. Waves Appl.27(6), 783–793 (2013).
[CrossRef]

M. A. Baqir and P. K. Choudhury, “On energy Flux through a uniaxial chiral metamaterials made circular waveguide under PMC boundary,” J. Electromagn. Waves Appl.26(16), 2165–2175 (2012).
[CrossRef]

Cui, T. J.

Q. Cheng and T. J. Cui, “Negative refractions in uniaxially anisotropic chiral media,” Phys. Rev. B73(11), 113(2006).
[CrossRef]

Dong, J. F.

J. F. Dong and J. Li, “Guided modes in circular waveguide filled uniaxial chiral medium,” I. J. of Applied Electromagnetics and Mech.40(4), 283–292 (2012).

J. F. Dong and J. Li, “Characteristics of guided modes in uniaxial chiral circular waveguide,” Prog. in Electromag. Res.124, 331–345 (2012).

Engheta, N.

P. Pelet and N. Engheta, “The theory of chirowaveguides,” IEEE Trans. Antenn. Propag.38(1), 90–98 (1990).
[CrossRef]

Gulistan, S.

S. Gulistan, A. A. Syed, and Q. A. Naqvi, “Fields in fractional dual DB waveguides containing chiral nihility metamaterials,” J. Electromagn. Waves Appl.26(16), 2130–2141 (2012).
[CrossRef]

Haraoubia, B.

R. Oussaid and B. Haraoubia, “Longitudinal and transverse operators formalism for chiral media: Application to guided structures filled with chiral material,” Can. J. Phys.82(5), 367–378 (2004).
[CrossRef]

R. Oussaid and B. Haraoubia, “Behavior of chiral material in terms of a guided wave propagation,” I. J.of Appl. Electromagnetics and Mechanics19(1–4), 631–635 (2004).

Li, J.

J. F. Dong and J. Li, “Characteristics of guided modes in uniaxial chiral circular waveguide,” Prog. in Electromag. Res.124, 331–345 (2012).

J. F. Dong and J. Li, “Guided modes in circular waveguide filled uniaxial chiral medium,” I. J. of Applied Electromagnetics and Mech.40(4), 283–292 (2012).

Lindell, I. V.

A. Viitanen and I. V. Lindell, “Plane wave propagation in uniaxial bianisotropic medium with an application to a polarization transformer,” Int. J. Infrared Millim. Waves14(10), 1993–20010 (1993).
[CrossRef]

Mahmoud, S. F.

S. F. Mahmoud and A. J. Viittanen, “Modes in a hard surface waveguide with uniaxially anisotropic chiral material filling,” Prog. in Electromag. Res.39, 265–279 (2003).

Mughal, M. J.

M. M. Ali, M. J. Mughal, A. A. Rahim, and Q. A. Naqvi, “The Guided waves in planar waveguide partially filled with strong chiral material,” I. J.of Appl. Electromagnetics and Mechanics38(2–3), 139–149 (2012).

Naqvi, Q. A.

M. M. Ali, M. J. Mughal, A. A. Rahim, and Q. A. Naqvi, “The Guided waves in planar waveguide partially filled with strong chiral material,” I. J.of Appl. Electromagnetics and Mechanics38(2–3), 139–149 (2012).

S. Gulistan, A. A. Syed, and Q. A. Naqvi, “Fields in fractional dual DB waveguides containing chiral nihility metamaterials,” J. Electromagn. Waves Appl.26(16), 2130–2141 (2012).
[CrossRef]

Oussaid, R.

R. Oussaid and B. Haraoubia, “Longitudinal and transverse operators formalism for chiral media: Application to guided structures filled with chiral material,” Can. J. Phys.82(5), 367–378 (2004).
[CrossRef]

R. Oussaid and B. Haraoubia, “Behavior of chiral material in terms of a guided wave propagation,” I. J.of Appl. Electromagnetics and Mechanics19(1–4), 631–635 (2004).

Pelet, P.

P. Pelet and N. Engheta, “The theory of chirowaveguides,” IEEE Trans. Antenn. Propag.38(1), 90–98 (1990).
[CrossRef]

Rahim, A. A.

M. M. Ali, M. J. Mughal, A. A. Rahim, and Q. A. Naqvi, “The Guided waves in planar waveguide partially filled with strong chiral material,” I. J.of Appl. Electromagnetics and Mechanics38(2–3), 139–149 (2012).

Syed, A. A.

S. Gulistan, A. A. Syed, and Q. A. Naqvi, “Fields in fractional dual DB waveguides containing chiral nihility metamaterials,” J. Electromagn. Waves Appl.26(16), 2130–2141 (2012).
[CrossRef]

Viitanen, A.

A. Viitanen and I. V. Lindell, “Plane wave propagation in uniaxial bianisotropic medium with an application to a polarization transformer,” Int. J. Infrared Millim. Waves14(10), 1993–20010 (1993).
[CrossRef]

Viittanen, A. J.

S. F. Mahmoud and A. J. Viittanen, “Modes in a hard surface waveguide with uniaxially anisotropic chiral material filling,” Prog. in Electromag. Res.39, 265–279 (2003).

Can. J. Phys.

R. Oussaid and B. Haraoubia, “Longitudinal and transverse operators formalism for chiral media: Application to guided structures filled with chiral material,” Can. J. Phys.82(5), 367–378 (2004).
[CrossRef]

I. J. of Applied Electromagnetics and Mech.

J. F. Dong and J. Li, “Guided modes in circular waveguide filled uniaxial chiral medium,” I. J. of Applied Electromagnetics and Mech.40(4), 283–292 (2012).

I. J.of Appl. Electromagnetics and Mechanics

R. Oussaid and B. Haraoubia, “Behavior of chiral material in terms of a guided wave propagation,” I. J.of Appl. Electromagnetics and Mechanics19(1–4), 631–635 (2004).

M. M. Ali, M. J. Mughal, A. A. Rahim, and Q. A. Naqvi, “The Guided waves in planar waveguide partially filled with strong chiral material,” I. J.of Appl. Electromagnetics and Mechanics38(2–3), 139–149 (2012).

IEEE Trans. Antenn. Propag.

P. Pelet and N. Engheta, “The theory of chirowaveguides,” IEEE Trans. Antenn. Propag.38(1), 90–98 (1990).
[CrossRef]

Int. J. Infrared Millim. Waves

A. Viitanen and I. V. Lindell, “Plane wave propagation in uniaxial bianisotropic medium with an application to a polarization transformer,” Int. J. Infrared Millim. Waves14(10), 1993–20010 (1993).
[CrossRef]

J. Electromagn. Waves Appl.

S. Gulistan, A. A. Syed, and Q. A. Naqvi, “Fields in fractional dual DB waveguides containing chiral nihility metamaterials,” J. Electromagn. Waves Appl.26(16), 2130–2141 (2012).
[CrossRef]

M. A. Baqir and P. K. Choudhury, “Propagation through uniaxial anisotropic chiral circular waveguide under DB boundary,” J. Electromagn. Waves Appl.27(6), 783–793 (2013).
[CrossRef]

M. A. Baqir and P. K. Choudhury, “On energy Flux through a uniaxial chiral metamaterials made circular waveguide under PMC boundary,” J. Electromagn. Waves Appl.26(16), 2165–2175 (2012).
[CrossRef]

M. A. Baqir and P. K. Choudhury, “Propagation through uniaxial anisotropic chiral circular waveguide under DB boundary,” J. Electromagn. Waves Appl.27(6), 783–793 (2013).
[CrossRef]

J. Nanomater.

M. A. Baqir and P. K. Choudhury, “Flux through guides with microstructured twisted clad DB medium,” J. Nanomater.2014, 1–6 (2014).
[CrossRef]

Phys. Rev. B

Q. Cheng and T. J. Cui, “Negative refractions in uniaxially anisotropic chiral media,” Phys. Rev. B73(11), 113(2006).
[CrossRef]

Prog. in Electromag. Res.

S. F. Mahmoud and A. J. Viittanen, “Modes in a hard surface waveguide with uniaxially anisotropic chiral material filling,” Prog. in Electromag. Res.39, 265–279 (2003).

J. F. Dong and J. Li, “Characteristics of guided modes in uniaxial chiral circular waveguide,” Prog. in Electromag. Res.124, 331–345 (2012).

Other

I. V. Lindell, A. H. Sihvola, S. A. Tretyakov, and A. J. Viitanen, Electromagnetic Waves in Chiral and Bi-Isotropic Media (Artech House, Incorporated, 1994).

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Figures (4)

Fig. 1
Fig. 1

A parallel plate uniaxial anisotropic chirowaveguide.

Fig. 2
Fig. 2

Comparison of intensity components of our work (dotted) and results in [1](solid line).

Fig. 3
Fig. 3

Characteristics curves for mode Ω 1 (thick solid line) and mode Ω 2 (thick dotted line) in (a) type-i material, (b) type-ii material, and (c) type-iii material.

Fig. 4
Fig. 4

The energy flux density in (a) type-i and type-ii and (b) type-iii materials for different values of chirality parameter.

Equations (13)

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D = [ ε t I ¯ ¯ t + ε z e ^ z e ^ z ] . E j γ μ 0 ε 0 e ^ z e ^ z . H B = [ μ t I ¯ ¯ t + μ z e ^ z e ^ z ] . H + j γ μ 0 ε 0 e ^ z e ^ z . E
k ±c 2 = λ 2 /2[ μ z / μ t + ε z / ε t ± ( μ z / μ t ε z / ε t ) 2 +4 γ 2 μ z ε z / μ t ε t ]
δ 2 E ±z /δ x 2 + k ±c 2 E +z =0
E ±z = A ± cos( k ±c x)+ G ± sin( k ±c x)
( E ±z, H ±z )=( E ±z, j α ± / η t E ±z )
E= E + + E H=j/ η t ( H + + H )
E= E t + e ^ z E z H= H t + e ^ z H z
E t =( jβ/ k +c 2 t k t α + / k +c 2 e ^ z × t ) E +z +( jβ/ k c 2 t k t α / k c 2 e ^ z × t ) E z
( cos( k +c a/2 ) sin( k +c a/2 ) cos( k c a/2 ) sin( k c a/2 ) cos( k +c a/2 ) sin( k +c a/2 ) cos( k c a/2 ) sin( k c a/2 ) α + k +c sin( k +c a/2 ) α + k +c cos( k +c a/2 ) α k c sin( k c a/2 ) α k c cos( k c a/2 ) α + k +c sin( k +c a/2 ) α + k +c cos( k +c a/2 ) α + / k +c α k c sin( k c a/2 ) α k c cos( k c a/2 ) )( A + G + A G )=0
α sin( k ±c a/2 )cos( k ±c a/2 )/ k c + α + sin( k ±c a/2 )cos( k ±c a/2 )/ k +c =0
Ω 1,2 =( k +c + k c )sin( k +c a/2+ k c a/2 )±( k +c k c )sin( k +c a/2 k c a/2 )=0
A + Ω 2 ( β )= G + Ω 1 ( β )
S z =1/2Re( E×H ). e ^ z z =1/2Re( E x H y E y H x )

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