Abstract

We use the plane-wave (PW) method to calculate the superlens frequency of photonic crystals with various material compositions. At this frequency, photonic crystal behaves like a medium with isotropic negative index equal to −1. The relationship between the frequency and material compositions is derived from the calculated data. For the TE and TM modes, the relationship has the same format. From the relationship, a case has been chosen and, under these conditions, the wave-propagating field through the photonic crystal has been calculated by the finite-difference time-domain method. A good agreement is obtained between the results from the PW method and the finite-difference time-domain calculation. This is very useful for fabricating photonic crystal superlens material at an appropriate frequency.

© 2008 Optical Society of America

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References

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  1. V. G. Veselago, “Electrodynamics of substances with simultaneously negative electrical and magnetic permeabilities,” Usp. Fiz. Nauk 92, 517-526 (1967).
  2. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of epsi and μ,” Sov. Phys. Usp. 10, 509-514 (1968).
    [CrossRef]
  3. V. G. Veselago, “Electrodynamics of materials with negative index of refraction,” Usp. Fiz. Nauk 173, 790-794 (2003).
    [CrossRef]
  4. J. B. Pendry and D. R. Smith, “Reversing light with negative refraction,” Phys. Today 57, 37-43 (2004).
    [CrossRef]
  5. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
    [CrossRef]
  6. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77-79 (2001).
    [CrossRef] [PubMed]
  7. R. Gajic, R. Meisels, F. Kuchar, and K. Hingerl, “Refraction and rightness in photonic crystals,” Opt. Express 13, 8596-8604 (2005).
    [CrossRef] [PubMed]
  8. C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refractive without negative effective index,” Phys. Rev. B 65, 201104(R) (2002).
    [CrossRef]
  9. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966-3969 (2000).
    [CrossRef] [PubMed]
  10. M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: refractionlike behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62, 10696 (2000).
    [CrossRef]
  11. S. Foteinopoulou and C. M. Soukoulis, “Negative refraction and left-handed behavior in two-dimensional photonic crystals,” Phys. Rev. B 67, 235107 (2003).
    [CrossRef]
  12. R. Gajic, R. Meisels, F. Kuchar, and K. Hingerl, “All-angle left-handed negative refraction in Kagome and honeycomb lattice photonic crystals,” Phys. Rev. B 73, 165310 (2006).
    [CrossRef]
  13. S. P. Guo and S. Albin, “Simple plane wave implementation for photonic crystal calculations,” Opt. Express 11, 167-175 (2003).
    [CrossRef] [PubMed]
  14. M. Qiu, “Effective index method in heterostructure slab waveguide based two-dimensional photonic crystals,” Appl. Phys. Lett. 81, 1163-1165 (2002).
    [CrossRef]
  15. M. Qiu, B. Jaskorzynska, M. Swillo, and H. Benisty, “Time-domain 2D modeling of slab-waveguide based photonic-crystal devices in the presence of out-of-plane radiation losses,” Microwave Opt. Technol. Lett. 34, 387-393 (2002).
    [CrossRef]
  16. M. Qiu, F2P: Finite-difference time-domain 2D simulator for Photonic devices, http://www.imit.kth.se/info/FOFU/PC/F2P/.
  17. M. Plihal and A. A. Maradudin, “Photonic band structure of two-dimensional systems: the triangular lattice,” Phys. Rev. B 44, 8565-8571 (1991).
    [CrossRef]

2006 (1)

R. Gajic, R. Meisels, F. Kuchar, and K. Hingerl, “All-angle left-handed negative refraction in Kagome and honeycomb lattice photonic crystals,” Phys. Rev. B 73, 165310 (2006).
[CrossRef]

2005 (1)

2004 (1)

J. B. Pendry and D. R. Smith, “Reversing light with negative refraction,” Phys. Today 57, 37-43 (2004).
[CrossRef]

2003 (3)

V. G. Veselago, “Electrodynamics of materials with negative index of refraction,” Usp. Fiz. Nauk 173, 790-794 (2003).
[CrossRef]

S. Foteinopoulou and C. M. Soukoulis, “Negative refraction and left-handed behavior in two-dimensional photonic crystals,” Phys. Rev. B 67, 235107 (2003).
[CrossRef]

S. P. Guo and S. Albin, “Simple plane wave implementation for photonic crystal calculations,” Opt. Express 11, 167-175 (2003).
[CrossRef] [PubMed]

2002 (3)

M. Qiu, “Effective index method in heterostructure slab waveguide based two-dimensional photonic crystals,” Appl. Phys. Lett. 81, 1163-1165 (2002).
[CrossRef]

M. Qiu, B. Jaskorzynska, M. Swillo, and H. Benisty, “Time-domain 2D modeling of slab-waveguide based photonic-crystal devices in the presence of out-of-plane radiation losses,” Microwave Opt. Technol. Lett. 34, 387-393 (2002).
[CrossRef]

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refractive without negative effective index,” Phys. Rev. B 65, 201104(R) (2002).
[CrossRef]

2001 (1)

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77-79 (2001).
[CrossRef] [PubMed]

2000 (2)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: refractionlike behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62, 10696 (2000).
[CrossRef]

1999 (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

1991 (1)

M. Plihal and A. A. Maradudin, “Photonic band structure of two-dimensional systems: the triangular lattice,” Phys. Rev. B 44, 8565-8571 (1991).
[CrossRef]

1968 (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of epsi and μ,” Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

1967 (1)

V. G. Veselago, “Electrodynamics of substances with simultaneously negative electrical and magnetic permeabilities,” Usp. Fiz. Nauk 92, 517-526 (1967).

Appl. Phys. Lett. (1)

M. Qiu, “Effective index method in heterostructure slab waveguide based two-dimensional photonic crystals,” Appl. Phys. Lett. 81, 1163-1165 (2002).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Microwave Opt. Technol. Lett. (1)

M. Qiu, B. Jaskorzynska, M. Swillo, and H. Benisty, “Time-domain 2D modeling of slab-waveguide based photonic-crystal devices in the presence of out-of-plane radiation losses,” Microwave Opt. Technol. Lett. 34, 387-393 (2002).
[CrossRef]

Opt. Express (2)

Phys. Rev. B (5)

M. Plihal and A. A. Maradudin, “Photonic band structure of two-dimensional systems: the triangular lattice,” Phys. Rev. B 44, 8565-8571 (1991).
[CrossRef]

M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: refractionlike behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62, 10696 (2000).
[CrossRef]

S. Foteinopoulou and C. M. Soukoulis, “Negative refraction and left-handed behavior in two-dimensional photonic crystals,” Phys. Rev. B 67, 235107 (2003).
[CrossRef]

R. Gajic, R. Meisels, F. Kuchar, and K. Hingerl, “All-angle left-handed negative refraction in Kagome and honeycomb lattice photonic crystals,” Phys. Rev. B 73, 165310 (2006).
[CrossRef]

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refractive without negative effective index,” Phys. Rev. B 65, 201104(R) (2002).
[CrossRef]

Phys. Rev. Lett. (1)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

Phys. Today (1)

J. B. Pendry and D. R. Smith, “Reversing light with negative refraction,” Phys. Today 57, 37-43 (2004).
[CrossRef]

Science (1)

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Sov. Phys. Usp. (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of epsi and μ,” Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Usp. Fiz. Nauk (2)

V. G. Veselago, “Electrodynamics of materials with negative index of refraction,” Usp. Fiz. Nauk 173, 790-794 (2003).
[CrossRef]

V. G. Veselago, “Electrodynamics of substances with simultaneously negative electrical and magnetic permeabilities,” Usp. Fiz. Nauk 92, 517-526 (1967).

Other (1)

M. Qiu, F2P: Finite-difference time-domain 2D simulator for Photonic devices, http://www.imit.kth.se/info/FOFU/PC/F2P/.

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Figures (8)

Fig. 1
Fig. 1

TM band structure of a 2D PhC with a filling factor f = 0.8358 , ε a = 1 , and ε b = 7 in the first Brillouin zone.

Fig. 2
Fig. 2

Equifrequency contours of band 2 with a filling factor f = 0.8358 , ε a = 1 , and ε b = 7 in the first Brillouin zone; circle with the blue dashed line shows ω ¯ = 0.564 in air.

Fig. 3
Fig. 3

Effective refractive index versus normalized frequency in band 2 with a filling factor f = 0.8358 , ε a = 1 and ε b = 7 . Squares indicate the calculated results.

Fig. 4
Fig. 4

Effective refractive index versus normalized frequency at filling factor (a) 0.58 ( R = 0.4 a ) , (b) 0.444 ( R = 0.35 a ) , (c) 0.326 ( R = 0.3 a ) , and (d) 0.145 ( R = 0.2 a ) . Squares indicate the calculated results.

Fig. 5
Fig. 5

AANR frequency versus filling factor with ε b ε a = 7 . Squares indicate the calculated results.

Fig. 6
Fig. 6

AALNR frequency of TM mode as a function of RDC and filling factor. The dots and meshed surface represent the calculated and fitted result, respectively.

Fig. 7
Fig. 7

(a) PhC structure and the (b) wave pattern of ω ¯ = 0.434 TM electromagnetic wave propagating through the PhC as an incident angle 20 ° to the Γ M surface.

Fig. 8
Fig. 8

AALNR frequency of TE mode as a function of RDC and filling factor. The dots and meshed surface represent the calculated and fitted result, respectively.

Tables (2)

Tables Icon

Table 1 Coefficients in Regression Equation (2) for AALNR Frequencies of TM Mode

Tables Icon

Table 2 Coefficients in Regression Equation (2) for AALNR Frequencies of TE Mode

Equations (2)

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y = 0.3814 0.08111 x + 0.56191 x 2 0.9229 x 3 + 0.75157 x 4 ,
z ( x , y ) = i = 0 3 j = 0 3 a i j x i y j .

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