Abstract

When the real parts of the permittivity and the permeability dyadics of a structurally chiral, magnetic-dielectric material are reversed in sign, the circular Bragg phenomenon displayed by the material is proved here to suffer a change which indicates that the structural handedness has been, in effect, reversed. Additionally, reflection and transmission coefficients suffer phase reversal.

© 2002 Optical Society of America

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References

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  1. N. Kato, �??The signi.cance of Ewald�??s dynamical theory of diffraction,�?? in P.P. Ewald and His Dynamical Theory of X-ray Diffraction (D. W. J. Cruickshank, H. J. Juretschke and N. Kato, eds) (Oxford University Press, Oxford, UK, 1992), pp. 3-23.
  2. H. A. Macleod, Thin-Film Optical Filters (Institute of Physics, Bristol, UK, 2001), pp. 185-208.
  3. I. J. Hodgkinson and Q. h. Wu, Birefringent Thin Films and Polarizing Elements (World Scientific, Singapore, 1997), pp. 302-322.
  4. S. D. Jacobs (ed), Selected Papers on Liquid Crystals for Optics (SPIEO ptical Engineering Press, Bellingham, WA, USA, 1992).
  5. V. C. Venugopal and A. Lakhtakia, �??Sculptured thin films: Conception, optical properties, and applications,�?? in Electromagnetic Fields in Unconventional Materials and Structures (O. N. Singh and A. Lakhtakia, eds) (Wiley, New York, NY, USA, 2000), pp. 151-216.
  6. J. Wang, A. Lakhtakia and J. B. Geddes III, �??Multiple Bragg regimes exhibited by a chiral sculptured thin film half-space on axial excitation,�?? Optik 113, 213-222 (2002).
    [CrossRef]
  7. A. Lakhtakia, �??Sculptured thin films: accomplishments and emerging uses,�?? Mater. Sci. Eng. C 19, 427-434 (2002).
    [CrossRef]
  8. J. B. Geddes III and A. Lakhtakia, �??Reflection and transmission of optical narrow-extent pulses by axially excited chiral sculptured thin films,�?? Eur. Phys. J. Appl. Phys. 13, 3-14 (2001); corrections: 16, 247 (2001).
    [CrossRef]
  9. <a href="http://www.esm.psu.edu/HTMLs/Faculty/Lakhtakia/TimeBragg/TD Bragg.html">http://www.esm.psu.edu/HTMLs/Faculty/Lakhtakia/TimeBragg/TD Bragg.html</a>
  10. H. Takezoe, K. Hashimoto, Y. Ouchi, M. Hara, A. Fukuda and E. Kuze, �??Experimental study on higher order re.ection by monodomain cholesteric liquid crystals,�?? Mol. Cryst. Liq. Cryst. 101, 329-340 (1983)
    [CrossRef]
  11. V. C. Venugopal and A. Lakhtakia, �??Electromagnetic plane-wave response characteristics of nonaxially excited slabs of dielectric thin-film helicoidal bianisotropic mediums,�?? Proc. R. Soc. Lond. A 456, 125-161 (2000).
    [CrossRef]
  12. A. Lakhtakia and W. S. Weiglhofer, �??Further results on light propagation in helicoidal bianisotropic mediums: oblique propagation,�?? Proc. R. Soc. Lond. A 453, 93-105 (1997); corrections: 454, 3275 (1998).
    [CrossRef]
  13. F. Brochard and P.G. de Gennes, �??Theory of magnetic suspensions in liquid crystals,�?? J. Phys. (Paris) 31, 691-708 (1970).
    [CrossRef]
  14. A. Lakhtakia, �??Reversal of circular Bragg phenomenon in ferrocholesteric materials with negative real permittivities and permeabilities,�?? Adv. Mater. 14, 447-449 (2002).
    [CrossRef]
  15. V. Ponsinet, P. Fabre, M. Veyssie and L. Auvray, �??A small-angle neutron-scattering study of the ferrosmectic phase,�?? J. Phys. II (Paris) 3, 1021-1039 (1993).
  16. J. Pendry, �??Electromagnetic materials enter the negative age,�?? Phys. World 14 (9), 47-51 (2001), September issue.
  17. A. Lakhtakia, M. W. McCall and W. S. Weiglhofer, �??Brief overview of recent developments on negative phase-velocity mediums (alias left-handed materials),�?? Arch. Elektr. Uber. 56, 407- 410 (2002).
  18. M. Schubert and C. M. Herzinger, �??Ellipsometry on anisotropic materials: Bragg conditions and phonons in dielectric helical thin films,�?? Phys. Stat. Sol. (a) 188, 1563-1575 (2001).
    [CrossRef]
  19. F. de Fornel, Evanescent Waves (Springer, Berlin, Germany, 2001), pp. 12-18.
  20. H. Kogelnik, �??Coupled wave theory for thick hologram gratings,�?? Bell Syst. Tech. J. 48, 2909-2947 (1969).
  21. S. F. Nagle, A. Lakhtakia and W. Thompson, Jr., �??Modal structures for axial wave propagation in a continuously twisted structurally chiral medium (CTSCM),�?? J. Acoust. Soc. Am. 97, 42-50 (1995).
    [CrossRef]
  22. P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, NY, USA, 1953), Sec. 4.3.
  23. A. Lakhtakia, �??On planewave remittances and Goos-Hanchen shifts of planar slabs with negative real permittivity and permeability,�?? Electromagnetics 23, 71-75 (2003).
    [CrossRef]

Adv. Mater. (1)

A. Lakhtakia, �??Reversal of circular Bragg phenomenon in ferrocholesteric materials with negative real permittivities and permeabilities,�?? Adv. Mater. 14, 447-449 (2002).
[CrossRef]

Arch. Elektr. Uber. (1)

A. Lakhtakia, M. W. McCall and W. S. Weiglhofer, �??Brief overview of recent developments on negative phase-velocity mediums (alias left-handed materials),�?? Arch. Elektr. Uber. 56, 407- 410 (2002).

Bell Syst. Tech. J. (1)

H. Kogelnik, �??Coupled wave theory for thick hologram gratings,�?? Bell Syst. Tech. J. 48, 2909-2947 (1969).

Electromagnetics (1)

A. Lakhtakia, �??On planewave remittances and Goos-Hanchen shifts of planar slabs with negative real permittivity and permeability,�?? Electromagnetics 23, 71-75 (2003).
[CrossRef]

Eur. Phys. J. Appl. Phys. (1)

J. B. Geddes III and A. Lakhtakia, �??Reflection and transmission of optical narrow-extent pulses by axially excited chiral sculptured thin films,�?? Eur. Phys. J. Appl. Phys. 13, 3-14 (2001); corrections: 16, 247 (2001).
[CrossRef]

J. Acoust. Soc. Am. (1)

S. F. Nagle, A. Lakhtakia and W. Thompson, Jr., �??Modal structures for axial wave propagation in a continuously twisted structurally chiral medium (CTSCM),�?? J. Acoust. Soc. Am. 97, 42-50 (1995).
[CrossRef]

J. Phys. (1)

F. Brochard and P.G. de Gennes, �??Theory of magnetic suspensions in liquid crystals,�?? J. Phys. (Paris) 31, 691-708 (1970).
[CrossRef]

J. Phys. II (1)

V. Ponsinet, P. Fabre, M. Veyssie and L. Auvray, �??A small-angle neutron-scattering study of the ferrosmectic phase,�?? J. Phys. II (Paris) 3, 1021-1039 (1993).

Mater. Sci. Eng. (1)

A. Lakhtakia, �??Sculptured thin films: accomplishments and emerging uses,�?? Mater. Sci. Eng. C 19, 427-434 (2002).
[CrossRef]

Mol. Cryst. Liq. Cryst. (1)

H. Takezoe, K. Hashimoto, Y. Ouchi, M. Hara, A. Fukuda and E. Kuze, �??Experimental study on higher order re.ection by monodomain cholesteric liquid crystals,�?? Mol. Cryst. Liq. Cryst. 101, 329-340 (1983)
[CrossRef]

Optik (1)

J. Wang, A. Lakhtakia and J. B. Geddes III, �??Multiple Bragg regimes exhibited by a chiral sculptured thin film half-space on axial excitation,�?? Optik 113, 213-222 (2002).
[CrossRef]

Phys. Stat. Sol. (1)

M. Schubert and C. M. Herzinger, �??Ellipsometry on anisotropic materials: Bragg conditions and phonons in dielectric helical thin films,�?? Phys. Stat. Sol. (a) 188, 1563-1575 (2001).
[CrossRef]

Phys. World (1)

J. Pendry, �??Electromagnetic materials enter the negative age,�?? Phys. World 14 (9), 47-51 (2001), September issue.

Proc. R. Soc. Lond. A (2)

V. C. Venugopal and A. Lakhtakia, �??Electromagnetic plane-wave response characteristics of nonaxially excited slabs of dielectric thin-film helicoidal bianisotropic mediums,�?? Proc. R. Soc. Lond. A 456, 125-161 (2000).
[CrossRef]

A. Lakhtakia and W. S. Weiglhofer, �??Further results on light propagation in helicoidal bianisotropic mediums: oblique propagation,�?? Proc. R. Soc. Lond. A 453, 93-105 (1997); corrections: 454, 3275 (1998).
[CrossRef]

Other (8)

F. de Fornel, Evanescent Waves (Springer, Berlin, Germany, 2001), pp. 12-18.

P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, NY, USA, 1953), Sec. 4.3.

<a href="http://www.esm.psu.edu/HTMLs/Faculty/Lakhtakia/TimeBragg/TD Bragg.html">http://www.esm.psu.edu/HTMLs/Faculty/Lakhtakia/TimeBragg/TD Bragg.html</a>

N. Kato, �??The signi.cance of Ewald�??s dynamical theory of diffraction,�?? in P.P. Ewald and His Dynamical Theory of X-ray Diffraction (D. W. J. Cruickshank, H. J. Juretschke and N. Kato, eds) (Oxford University Press, Oxford, UK, 1992), pp. 3-23.

H. A. Macleod, Thin-Film Optical Filters (Institute of Physics, Bristol, UK, 2001), pp. 185-208.

I. J. Hodgkinson and Q. h. Wu, Birefringent Thin Films and Polarizing Elements (World Scientific, Singapore, 1997), pp. 302-322.

S. D. Jacobs (ed), Selected Papers on Liquid Crystals for Optics (SPIEO ptical Engineering Press, Bellingham, WA, USA, 1992).

V. C. Venugopal and A. Lakhtakia, �??Sculptured thin films: Conception, optical properties, and applications,�?? in Electromagnetic Fields in Unconventional Materials and Structures (O. N. Singh and A. Lakhtakia, eds) (Wiley, New York, NY, USA, 2000), pp. 151-216.

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Figures (1)

Fig. 1.
Fig. 1.

Computed reflectances of a chiral ferrosmectic slab in free space, for Ω=140 nm, L=60Ω, and χ=30°. Case (i): h=1, ψ=35°, ∊a=2.7(1+iδ), ∊ b =3.3(1+iδ), ∊ c =3(1+iδ), µa=1.1(1+iδµ), µ b =1.4(1+iδµ), µ c =1.2(1+iδµ), δ=2δµ=2× 10-3. Case (ii): Same as (i) except h=-1 and ψ=-35°. Case (iii): Same as (i) except that ψ=215° and the real parts of ∊ a,b,c and μ a,b,c are negative.

Equations (27)

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¯ ¯ ( r ) = 0 S ¯ ¯ z S ¯ ¯ y [ a u z u z + b u x u x + c u y u y ] S ¯ ¯ y T S ¯ ¯ z T μ ¯ ¯ ( r ) = μ 0 S ¯ ¯ z S ¯ ¯ y [ μ a u z u z + μ b u x u x + μ c u y u y ] S ¯ ¯ y T S ¯ ¯ z T } , 0 z L ,
E ( r ) = E ˜ ( z ) exp [ ( x cos ψ + y sin ψ ) ] H ( r ) = H ˜ ( z ) exp [ ( x cos ψ + y sin ψ ) ] } , < z < ,
d dz [ f ¯ ( z ) ] = i [ P ¯ ¯ ( z ) ] [ f ¯ ( z ) ] , 0 < z < L .
[ P ¯ ¯ ( z ) ] = [ P ¯ ¯ 0 ( z ) ] + κ k 0 [ P ¯ ¯ 1 ( z ) ] + ( κ k 0 ) 2 [ P ¯ ¯ 2 ( z ) ] ,
[ P ¯ ¯ 0 ( z ) ] = ω { [ 0 0 0 μ 0 μ c + μ ˜ d 2 0 0 μ 0 μ c + μ ˜ d 2 0 0 0 c + ˜ d 2 0 0 0 c + ˜ d 2 0 0 0 ]
+ [ 0 0 μ 0 μ c μ ˜ d 2 sin 2 ζ μ 0 μ c μ ˜ d 2 cos 2 ζ 0 0 μ 0 μ c μ ˜ d 2 cos 2 ζ μ 0 μ c μ ˜ d 2 sin 2 ζ 0 c ˜ d 2 sin 2 ζ 0 c ˜ d 2 cos 2 ζ 0 0 0 c ˜ d 2 cos 2 ζ 0 c ˜ d 2 sin 2 ζ 0 0 ] } ,
[ P ¯ ¯ 1 ( z ) ] = ( k 0 sin χ cos χ ) ×
{ ˜ d ( a b ) a b [ cos ζ cos ψ 0 0 0 0 sin ζ sin ψ 0 0 0 0 sin ζ sin ψ 0 0 0 0 cos ζ cos ψ ]
+ μ ˜ d ( μ a μ b ) μ a μ b [ sin ζ sin ψ 0 0 0 0 cos ζ cos ψ 0 0 0 0 cos ζ cos ψ 0 0 0 0 sin ζ sin ψ ]
+ ˜ d μ ˜ d ( a μ b b μ a ) a b μ a μ b [ 0 sin ζ cos ψ 0 0 cos ζ sin ψ 0 0 0 0 0 0 sin ζ cos ψ 0 0 cos ζ sin ψ 0 ] } ,
[ P ¯ ¯ 2 ( z ) ] = ω ×
[ 0 0 μ 0 ˜ d a b cos ψ sin ψ μ 0 ˜ d a b cos 2 ψ 0 0 μ 0 ˜ d a b sin 2 ψ μ 0 ˜ d a b cos ψ sin ψ 0 μ ˜ d μ a μ b cos ψ sin ψ 0 μ ˜ d μ a μ b cos 2 ψ 0 0 0 μ ˜ d μ a μ b sin 2 ψ 0 μ ˜ d μ a μ b cos ψ sin ψ 0 0 ] .
[ f ¯ ( L ) ] = [ M ¯ ¯ ] [ f ¯ ( 0 ) ] ,
e inc ( r ) = [ ( i s p + ) 2 a L ( i s + p + ) 2 a R ] e i k 0 z cos θ , z 0 ,
e ref ( r ) = [ ( i s p ) 2 r L + ( i s + p ) 2 r R ] e i k 0 z cos θ , z 0 ,
e tr ( r ) = [ ( i s p + ) 2 t L ( i s + p + ) 2 t R ] e i k 0 ( z L ) cos θ , z L ,
[ r L r R ] = [ r LL r LR r RL r RR ] [ a L a R ] , [ t L t R ] = [ t LL t LR t RL t RR ] [ a L a R ] .
{ Re [ ¯ ¯ ( r ) ] Re [ ¯ ¯ ( r ) ] , Re [ μ ¯ ¯ ( r ) ] Re [ μ ¯ ¯ ( r ) ] , 0 z L } .
z [ 0 , L ] , [ P ¯ ¯ ( z ; ¯ ¯ ( r ) , μ ¯ ¯ ( r ) ; h , ψ ) ] = [ R ¯ ¯ ] [ P ¯ ¯ ( z ; ¯ ¯ ( r ) , μ ¯ ¯ ( r ) ; h , ψ ) ] [ R ¯ ¯ ]
= [ P ¯ ¯ ( z ; ¯ ¯ * ( r ) , μ ¯ ¯ * ( r ) ; h , π + ψ ) ] * ,
z 0 , L , [ f ¯ ( z ; ¯ ¯ ( r ) , μ ¯ ¯ ( r ) ; h , ψ ) ] = [ R ¯ ¯ ] [ f ¯ ( z ; ¯ ¯ ( r ) , μ ¯ ¯ ( r ) ; h , ψ ) ]
= [ f ¯ ( z ; ¯ ¯ * ( r ) , μ ¯ ¯ * ( r ) ; h , π + ψ ) ] * .
{ h h , ψ ψ } { a L a R , r L r R , t L t R } ;
{ Re [ a , b , c ] Re [ a , b , c ] Re [ μ a , b , c ] Re [ μ a , b , c ] ψ π + ψ } { a L a R * , a R a L * r L r R * , r R r L * t L t R * , t R t L * } .
{ h h , ψ ψ } { r LL r RR , r LR r RL t LL t RR , t LR t RL } ,
{ Re [ a , b , c ] Re [ a , b , c ] Re [ μ a , b , c ] Re [ μ a , b , c ] ψ π + ψ }
{ r LL r RR * , r RR r LL * , r LR r RL * , r RL r LR * t LL t RR * , t RR t LL * , t LR t RL * , t RL t LR * } .

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