Abstract

Localized to the planar interface of two identical dielectric biaxial crystals with optic ray axes parallel to the interface but with a relative twist about an axis perpendicular to the interface, electromagnetic wave propagation along the bisectrix of the two crystallographic orientations is possible with either real-valued or complex-valued transverse decay constants as the twist angle varies from 0° to an upper limit (90°) that is dependent on the angle between the two optic ray axes.

© 2007 Optical Society of America

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References

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  1. M. I. D'yakonov, "New type of electromagnetic wave propogating at an interface," Sov. Phys. JETP 67, 714-716 (1988).
  2. N. S. Averkiev and M. I. Dyakonov, "Electromagnetic waves localized at the interface of transparent anisotropic media," Opt. Spectrosc. 68, 653-655 (1990).
  3. D. B. Walker, E. N. Glytsis, and T. K. Gaylord, "Surface mode at isotropic-uniaxial and isotropic-biaxial interfaces," J. Opt. Soc. Am. A 15, 248-260 (1998).
    [CrossRef]
  4. A. N. Darinskiĭ, "Dispersionless polaritons on a twist boundary in optically uniaxial crystals," Crystallogr. Rep. 46, 842-844 (2001).
    [CrossRef]
  5. J. A. Polo, Jr., S. Nelatury, and A. Lakhtakia, "Surface electromagnetic wave at a tilted uniaxial bicrystalline interface," Electromagnetics 26, 629-642 (2006).
    [CrossRef]
  6. S. R. Nelatury, J. A. Polo, Jr., and A. Lakhtakia, "Surface waves with simple exponential transverse decay at a biaxial bicrystalline interface," J. Opt. Soc. Am. A 24, 856-865 (2007).
    [CrossRef]
  7. S. R. Nelatury, J. A. Polo, Jr., and A. Lakhtakia, "Surface waves with simple exponential transverse decay at a biaxial bicrystalline interface: errata," J. Opt. Soc. Am. A 24, 2012 (2007).
  8. Mineralogy Database, http://www.webmineral.com/ (20 April 2006).
  9. W. S. Weiglhofer and A. Lakhtakia, "On electromagnetic waves in biaxial bianisotropic media," Electromagnetics 19, 351-362 (1999).
    [CrossRef]
  10. The right sides of Eqs. of have typographical errors. The correct versions are Eqs. of this paper.
  11. J. Homola, S. Yee, and G. Gauglitz, "Surface plasmon resonance sensors: review," Sens. Actuators B 54, 3-15 (1999).
    [CrossRef]
  12. E. Matveeva, Z. Gryczynski, J. Malicka, J. Lukomska, S. Makowiec, K. Berndt, J. Lakowicz, and I. Gryczynski, "Directional surface plasmon-coupled emission: Application for an immunoassay in whole blood," Anal. Biochem. 344, 161-167 (2005).
    [CrossRef] [PubMed]

2007 (2)

S. R. Nelatury, J. A. Polo, Jr., and A. Lakhtakia, "Surface waves with simple exponential transverse decay at a biaxial bicrystalline interface," J. Opt. Soc. Am. A 24, 856-865 (2007).
[CrossRef]

S. R. Nelatury, J. A. Polo, Jr., and A. Lakhtakia, "Surface waves with simple exponential transverse decay at a biaxial bicrystalline interface: errata," J. Opt. Soc. Am. A 24, 2012 (2007).

2006 (1)

J. A. Polo, Jr., S. Nelatury, and A. Lakhtakia, "Surface electromagnetic wave at a tilted uniaxial bicrystalline interface," Electromagnetics 26, 629-642 (2006).
[CrossRef]

2005 (1)

E. Matveeva, Z. Gryczynski, J. Malicka, J. Lukomska, S. Makowiec, K. Berndt, J. Lakowicz, and I. Gryczynski, "Directional surface plasmon-coupled emission: Application for an immunoassay in whole blood," Anal. Biochem. 344, 161-167 (2005).
[CrossRef] [PubMed]

2001 (1)

A. N. Darinskiĭ, "Dispersionless polaritons on a twist boundary in optically uniaxial crystals," Crystallogr. Rep. 46, 842-844 (2001).
[CrossRef]

1999 (2)

W. S. Weiglhofer and A. Lakhtakia, "On electromagnetic waves in biaxial bianisotropic media," Electromagnetics 19, 351-362 (1999).
[CrossRef]

J. Homola, S. Yee, and G. Gauglitz, "Surface plasmon resonance sensors: review," Sens. Actuators B 54, 3-15 (1999).
[CrossRef]

1998 (1)

1990 (1)

N. S. Averkiev and M. I. Dyakonov, "Electromagnetic waves localized at the interface of transparent anisotropic media," Opt. Spectrosc. 68, 653-655 (1990).

1988 (1)

M. I. D'yakonov, "New type of electromagnetic wave propogating at an interface," Sov. Phys. JETP 67, 714-716 (1988).

Averkiev, N. S.

N. S. Averkiev and M. I. Dyakonov, "Electromagnetic waves localized at the interface of transparent anisotropic media," Opt. Spectrosc. 68, 653-655 (1990).

Berndt, K.

E. Matveeva, Z. Gryczynski, J. Malicka, J. Lukomska, S. Makowiec, K. Berndt, J. Lakowicz, and I. Gryczynski, "Directional surface plasmon-coupled emission: Application for an immunoassay in whole blood," Anal. Biochem. 344, 161-167 (2005).
[CrossRef] [PubMed]

Darinskii, A. N.

A. N. Darinskiĭ, "Dispersionless polaritons on a twist boundary in optically uniaxial crystals," Crystallogr. Rep. 46, 842-844 (2001).
[CrossRef]

Dyakonov, M. I.

N. S. Averkiev and M. I. Dyakonov, "Electromagnetic waves localized at the interface of transparent anisotropic media," Opt. Spectrosc. 68, 653-655 (1990).

D'yakonov, M. I.

M. I. D'yakonov, "New type of electromagnetic wave propogating at an interface," Sov. Phys. JETP 67, 714-716 (1988).

Gauglitz, G.

J. Homola, S. Yee, and G. Gauglitz, "Surface plasmon resonance sensors: review," Sens. Actuators B 54, 3-15 (1999).
[CrossRef]

Gaylord, T. K.

Glytsis, E. N.

Gryczynski, I.

E. Matveeva, Z. Gryczynski, J. Malicka, J. Lukomska, S. Makowiec, K. Berndt, J. Lakowicz, and I. Gryczynski, "Directional surface plasmon-coupled emission: Application for an immunoassay in whole blood," Anal. Biochem. 344, 161-167 (2005).
[CrossRef] [PubMed]

Gryczynski, Z.

E. Matveeva, Z. Gryczynski, J. Malicka, J. Lukomska, S. Makowiec, K. Berndt, J. Lakowicz, and I. Gryczynski, "Directional surface plasmon-coupled emission: Application for an immunoassay in whole blood," Anal. Biochem. 344, 161-167 (2005).
[CrossRef] [PubMed]

Homola, J.

J. Homola, S. Yee, and G. Gauglitz, "Surface plasmon resonance sensors: review," Sens. Actuators B 54, 3-15 (1999).
[CrossRef]

Lakhtakia, A.

S. R. Nelatury, J. A. Polo, Jr., and A. Lakhtakia, "Surface waves with simple exponential transverse decay at a biaxial bicrystalline interface: errata," J. Opt. Soc. Am. A 24, 2012 (2007).

S. R. Nelatury, J. A. Polo, Jr., and A. Lakhtakia, "Surface waves with simple exponential transverse decay at a biaxial bicrystalline interface," J. Opt. Soc. Am. A 24, 856-865 (2007).
[CrossRef]

J. A. Polo, Jr., S. Nelatury, and A. Lakhtakia, "Surface electromagnetic wave at a tilted uniaxial bicrystalline interface," Electromagnetics 26, 629-642 (2006).
[CrossRef]

W. S. Weiglhofer and A. Lakhtakia, "On electromagnetic waves in biaxial bianisotropic media," Electromagnetics 19, 351-362 (1999).
[CrossRef]

Lakowicz, J.

E. Matveeva, Z. Gryczynski, J. Malicka, J. Lukomska, S. Makowiec, K. Berndt, J. Lakowicz, and I. Gryczynski, "Directional surface plasmon-coupled emission: Application for an immunoassay in whole blood," Anal. Biochem. 344, 161-167 (2005).
[CrossRef] [PubMed]

Lukomska, J.

E. Matveeva, Z. Gryczynski, J. Malicka, J. Lukomska, S. Makowiec, K. Berndt, J. Lakowicz, and I. Gryczynski, "Directional surface plasmon-coupled emission: Application for an immunoassay in whole blood," Anal. Biochem. 344, 161-167 (2005).
[CrossRef] [PubMed]

Makowiec, S.

E. Matveeva, Z. Gryczynski, J. Malicka, J. Lukomska, S. Makowiec, K. Berndt, J. Lakowicz, and I. Gryczynski, "Directional surface plasmon-coupled emission: Application for an immunoassay in whole blood," Anal. Biochem. 344, 161-167 (2005).
[CrossRef] [PubMed]

Malicka, J.

E. Matveeva, Z. Gryczynski, J. Malicka, J. Lukomska, S. Makowiec, K. Berndt, J. Lakowicz, and I. Gryczynski, "Directional surface plasmon-coupled emission: Application for an immunoassay in whole blood," Anal. Biochem. 344, 161-167 (2005).
[CrossRef] [PubMed]

Matveeva, E.

E. Matveeva, Z. Gryczynski, J. Malicka, J. Lukomska, S. Makowiec, K. Berndt, J. Lakowicz, and I. Gryczynski, "Directional surface plasmon-coupled emission: Application for an immunoassay in whole blood," Anal. Biochem. 344, 161-167 (2005).
[CrossRef] [PubMed]

Nelatury, S.

J. A. Polo, Jr., S. Nelatury, and A. Lakhtakia, "Surface electromagnetic wave at a tilted uniaxial bicrystalline interface," Electromagnetics 26, 629-642 (2006).
[CrossRef]

Nelatury, S. R.

S. R. Nelatury, J. A. Polo, Jr., and A. Lakhtakia, "Surface waves with simple exponential transverse decay at a biaxial bicrystalline interface," J. Opt. Soc. Am. A 24, 856-865 (2007).
[CrossRef]

S. R. Nelatury, J. A. Polo, Jr., and A. Lakhtakia, "Surface waves with simple exponential transverse decay at a biaxial bicrystalline interface: errata," J. Opt. Soc. Am. A 24, 2012 (2007).

Polo, J. A.

S. R. Nelatury, J. A. Polo, Jr., and A. Lakhtakia, "Surface waves with simple exponential transverse decay at a biaxial bicrystalline interface: errata," J. Opt. Soc. Am. A 24, 2012 (2007).

S. R. Nelatury, J. A. Polo, Jr., and A. Lakhtakia, "Surface waves with simple exponential transverse decay at a biaxial bicrystalline interface," J. Opt. Soc. Am. A 24, 856-865 (2007).
[CrossRef]

J. A. Polo, Jr., S. Nelatury, and A. Lakhtakia, "Surface electromagnetic wave at a tilted uniaxial bicrystalline interface," Electromagnetics 26, 629-642 (2006).
[CrossRef]

Walker, D. B.

Weiglhofer, W. S.

W. S. Weiglhofer and A. Lakhtakia, "On electromagnetic waves in biaxial bianisotropic media," Electromagnetics 19, 351-362 (1999).
[CrossRef]

Yee, S.

J. Homola, S. Yee, and G. Gauglitz, "Surface plasmon resonance sensors: review," Sens. Actuators B 54, 3-15 (1999).
[CrossRef]

Anal. Biochem. (1)

E. Matveeva, Z. Gryczynski, J. Malicka, J. Lukomska, S. Makowiec, K. Berndt, J. Lakowicz, and I. Gryczynski, "Directional surface plasmon-coupled emission: Application for an immunoassay in whole blood," Anal. Biochem. 344, 161-167 (2005).
[CrossRef] [PubMed]

Crystallogr. Rep. (1)

A. N. Darinskiĭ, "Dispersionless polaritons on a twist boundary in optically uniaxial crystals," Crystallogr. Rep. 46, 842-844 (2001).
[CrossRef]

Electromagnetics (2)

J. A. Polo, Jr., S. Nelatury, and A. Lakhtakia, "Surface electromagnetic wave at a tilted uniaxial bicrystalline interface," Electromagnetics 26, 629-642 (2006).
[CrossRef]

W. S. Weiglhofer and A. Lakhtakia, "On electromagnetic waves in biaxial bianisotropic media," Electromagnetics 19, 351-362 (1999).
[CrossRef]

J. Opt. Soc. Am. A (3)

Opt. Spectrosc. (1)

N. S. Averkiev and M. I. Dyakonov, "Electromagnetic waves localized at the interface of transparent anisotropic media," Opt. Spectrosc. 68, 653-655 (1990).

Sens. Actuators B (1)

J. Homola, S. Yee, and G. Gauglitz, "Surface plasmon resonance sensors: review," Sens. Actuators B 54, 3-15 (1999).
[CrossRef]

Sov. Phys. JETP (1)

M. I. D'yakonov, "New type of electromagnetic wave propogating at an interface," Sov. Phys. JETP 67, 714-716 (1988).

Other (2)

The right sides of Eqs. of have typographical errors. The correct versions are Eqs. of this paper.

Mineralogy Database, http://www.webmineral.com/ (20 April 2006).

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Figures (4)

Fig. 1
Fig. 1

Geometry of the biaxial bicrystalline interface. The optic ray axes in the region A ( z > 0 ) are parallel to the unit vectors c ̂ 1 A and c ̂ 2 A , while the corresponding unit vectors in region B ( z < 0 ) are c ̂ 1 B and c ̂ 2 B .

Fig. 2
Fig. 2

Normalized phase velocity of surface wave for ϵ ¯ = 1.6 and δ = 0 ° , 15°, 30°, 45°, 60°, and 75°.

Fig. 3
Fig. 3

Normalized transverse decay constant ¯ 1 for ϵ ¯ = 1.6 and δ = 0 ° , 15°, 30°, 45°, 60°, and 75°: (a) real part; (b) imaginary part. Note the symmetry between Figs. 3b, 4b.

Fig. 4
Fig. 4

Normalized transverse decay constant ¯ 2 for ϵ ¯ = 1.6 , and δ = 0 ° , 15°, 30°, 45°, 60° and 75°: (a) real part; (b) imaginary part.

Tables (1)

Tables Icon

Table 1 Parameters for Some Transparent Mineralogical Crystals

Equations (33)

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ϵ ͇ r A = [ α + β [ cos ( 2 δ ) cos ( 2 ξ ) ] β sin ( 2 ξ ) 0 β sin ( 2 ξ ) α + β [ cos ( 2 δ ) + cos ( 2 ξ ) ] 0 0 0 α ]
ϵ ͇ r B = [ α + β [ cos ( 2 δ ) cos ( 2 ξ ) ] β sin ( 2 ξ ) 0 β sin ( 2 ξ ) α + β [ cos ( 2 δ ) + cos ( 2 ξ ) ] 0 0 0 α ] ,
{ α = n b 2 , β = ( n c 2 n a 2 ) 2 , δ = cos 1 [ ( n c 2 n b 2 ) ( n c 2 n a 2 ) ] } .
k ̱ = κ x ̂ + i p z ̂ .
p 1 2 = A 1 + A 2 κ 2 + A 3 + A 4 κ 2 + A 5 κ 4
p 2 2 = A 1 + A 2 κ 2 A 3 + A 4 κ 2 + A 5 κ 4 ,
A 1 = k o 2 [ α + β cos ( 2 δ ) ] ,
A 2 = 2 α + β [ cos ( 2 δ ) cos ( 2 ξ ) ] 2 α ,
A 3 = k o 4 β 2 ,
A 4 = k o 2 β 2 [ cos ( 2 δ ) cos ( 2 ξ ) 1 α ] ,
A 5 = { β [ cos ( 2 δ ) cos ( 2 ξ ) ] 2 α } 2 ,
0 = { ( p 1 p 2 ) 2 ( p 1 2 + p 1 p 2 + p 2 2 + k o 2 α κ 2 + k o 2 β [ cos ( 2 δ ) + cos ( 2 ξ ) ] ) ( p 1 p 2 k o 2 α + κ 2 k o 2 β [ cos ( 2 δ ) + cos ( 2 ξ ) ] ) } { sin 2 ( 2 ξ ) ( k o 2 α κ 2 ) 3 } .
( p 1 p 2 ) 2 = 0 ,
p 1 2 + p 1 p 2 + p 2 2 + k o 2 α κ 2 + k o 2 β [ cos ( 2 δ ) + cos ( 2 ξ ) ] = 0 ,
p 1 p 2 k o 2 α + κ 2 k o 2 β [ cos ( 2 δ ) + cos ( 2 ξ ) ] = 0 .
p 1 2 p 2 2 k o 2 α + κ 2 k o 2 β [ cos ( 2 δ ) + cos ( 2 ξ ) ] = p 1 p 2 ,
k o 2 α κ 2 + k o 2 β [ cos ( 2 δ ) + cos ( 2 ξ ) ] = p 1 p 2 ,
p 1 2 p 2 2 k o 2 α + κ 2 k o 2 β [ cos ( 2 δ ) + cos ( 2 ξ ) ] = p 1 p 2
k o 2 α κ 2 + k o 2 β [ cos ( 2 δ ) + cos ( 2 ξ ) ] = p 1 p 2
κ 2 = k o 2 C 0 12 α cos ( 2 ξ ) + C 1 + C 2 cos ( 2 ξ ) + C 3 cos ( 4 ξ ) + C 4 cos ( 6 ξ ) 8 [ cos ( 2 δ ) cos ( 2 ξ ) ] ,
C 0 = 4 α cos ( 2 δ ) 4 β sin 2 ( 2 δ ) ,
C 1 = 16 α 2 + 6 β 2 + 24 α β cos ( 2 δ ) + 8 ( α 2 β 2 ) cos ( 4 δ ) + 8 α β cos ( 6 δ ) + 2 β 2 cos ( 8 δ ) ,
C 2 = 32 α 2 cos ( 2 δ ) + 16 α β cos ( 4 δ ) ,
C 3 = 8 α 2 32 α β cos ( 2 δ ) ,
C 4 = 16 α β .
p 1 k o 2 β [ α β + β cos ( 2 δ ) ] cos 2 δ α ,
p 2 2 k o 2 α β 3 sec 2 δ [ α β + β cos ( 2 δ ) ] 3 ξ 2 .
{ ¯ 1 p 1 ( k o n a ) ¯ 2 p 2 ( k o n a ) } ,
ϵ ¯ = ( n c n a ) 2 .
v ¯ = v min { v + , v } .
sin ( 2 ξ ) = 0
k o 2 α κ 2 = 0 .
κ 2 = k o 2 α [ 4 α cos ( 2 δ ) + β ( 5 + 3 cos ( 4 δ ) ) ] 4 α cos ( 2 δ ) + 2 β sin 2 ( 2 δ ) .

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