Abstract

In terms of the electromagnetic theory described in Part I of our current investigations [J. Opt. Soc. Am. A 24, 1776 (2007) ], the numerical method for and results of numerical computations corresponding to the electromagnetic theory of a waveguide multilayered optical memory are presented. Here the characteristics of the cross talk and the modulation contrast, the power of readout signals, the variation of the power of the readout signals with the scanning position along the track, and the distribution of the light intensity at the detector are investigated in detail. Results show that the polarization of the reading light, the feature sizes of bits, and the distances between the two adjacent tracks and the two adjacent bits on the same track have significant effects on the distribution of the light intensity at the detector, the power of the readout signals, the cross talk, and the modulation contrast. In addition, the optimal polarization of the reading light is also suggested.

© 2008 Optical Society of America

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References

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  1. Z. Liang, T. Yang, H. Ming, and J. Xie, “A novel 3D multilayered waveguide memory,” Proc. SPIE 4930, 134-137 (2002).
    [Crossref]
  2. Z. Liang, J. S. Chen, T. Yang, Y. Xie, J. Chen, and S. Zhuang, “Principles and experiments of the waveguide multilayered optical memory,” J. Optoelectron., Laser 15, 315-317 (2004) (in Chinese).
  3. T. Yang, Z. Liang, W. Qin, X. Cai, J. Chen, and S. Zhuang, “Side-scattering properties of a novel waveguide multilayer memory,” Opt. Eng. (Bellingham) 45, 095201 (2006).
    [Crossref]
  4. H. Guo, S. Zhuang, J. Chen, and Z. Liang, “Multilayered optical memory with bits stored as refractive index change. I. Electromagnetic theory,” J. Opt. Soc. Am. A 24, 1776-1785 (2007). Because of a printer's error, the term cos-3/2θ0 in Eq. (29b) should be cos-1/2θ0.
    [Crossref]
  5. M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, “Accurate and efficient computation of the Green's tensor for stratified media,” Phys. Rev. E 62, 5797-5807 (2000).
    [Crossref]
  6. T. J. Cui and W. C. Chew, “Fast evaluation of Sommerfeld integrals for EM scattering and radiation by three-dimensional buried objects,” IEEE Trans. Geosci. Remote Sens. 37, 887-900 (1999).
    [Crossref]
  7. T. Yu and W. Cai, “High-order window functions and fast algorithms for calculating dyadic electromagnetic Green's functions in multilayered media,” Radio Sci. 36, 559-569 (2001).
    [Crossref]
  8. L. Tsang, C. Ong, C. C. Huang, and V. Jandhyala, “Evaluation of the Green's function for the mixed potential integral equation (MPIE) method in the time domain for layered media,” IEEE Trans. Antennas Propag. 51, 1559-1571 (2003).
    [Crossref]
  9. M. Yuan, T. K. Sarkar, and M. Salazar-Palma, “A direct discrete complex image method from the closed-form Green's functions in multilayered media,” IEEE Trans. Microwave Theory Tech. 54, 1025-1031 (2006).
    [Crossref]
  10. E. Simsek, Q. H. Liu, and B. Wei, “Singularity subtraction for evaluation of Green's functions for multilayer media,” IEEE Trans. Microwave Theory Tech. 54, 216-224 (2006).
    [Crossref]
  11. H. Guo, S. Zhuang, J. Chen, and Z. Liang, “Imaging theory of an aplanatic system with a stratified medium based on the method for a vector coherent transfer function,” Opt. Lett. 31, 2978-2980 (2006).
    [Crossref] [PubMed]
  12. O. J. F. Martin, A. Dereux, and C. Girard, “Iterative scheme for computing exactly the total field propagating in dielectric structures of arbitrary shape,” J. Opt. Soc. Am. A 11, 1073-1080 (1994).
    [Crossref]
  13. L. B. Felsen and N. Marcuvitz, Radiation and Scattering of Waves (IEEE, 1994), pp. 455-456.
  14. Z. Cao, Y. Jiang, Q. Shen, X. Dou, and Y. Chen, “Exact analytical method for planar optical waveguides with arbitrary index profile,” J. Opt. Soc. Am. A 16, 2209-2212 (1999).
    [Crossref]
  15. H. Guo, J. Chen, and S. Zhuang, “Vector plane wave spectrum of an arbitrary polarized electromagnetic wave,” Opt. Express 14, 2095-2100 (2006).
    [Crossref] [PubMed]

2007 (1)

2006 (5)

M. Yuan, T. K. Sarkar, and M. Salazar-Palma, “A direct discrete complex image method from the closed-form Green's functions in multilayered media,” IEEE Trans. Microwave Theory Tech. 54, 1025-1031 (2006).
[Crossref]

E. Simsek, Q. H. Liu, and B. Wei, “Singularity subtraction for evaluation of Green's functions for multilayer media,” IEEE Trans. Microwave Theory Tech. 54, 216-224 (2006).
[Crossref]

H. Guo, S. Zhuang, J. Chen, and Z. Liang, “Imaging theory of an aplanatic system with a stratified medium based on the method for a vector coherent transfer function,” Opt. Lett. 31, 2978-2980 (2006).
[Crossref] [PubMed]

T. Yang, Z. Liang, W. Qin, X. Cai, J. Chen, and S. Zhuang, “Side-scattering properties of a novel waveguide multilayer memory,” Opt. Eng. (Bellingham) 45, 095201 (2006).
[Crossref]

H. Guo, J. Chen, and S. Zhuang, “Vector plane wave spectrum of an arbitrary polarized electromagnetic wave,” Opt. Express 14, 2095-2100 (2006).
[Crossref] [PubMed]

2004 (1)

Z. Liang, J. S. Chen, T. Yang, Y. Xie, J. Chen, and S. Zhuang, “Principles and experiments of the waveguide multilayered optical memory,” J. Optoelectron., Laser 15, 315-317 (2004) (in Chinese).

2003 (1)

L. Tsang, C. Ong, C. C. Huang, and V. Jandhyala, “Evaluation of the Green's function for the mixed potential integral equation (MPIE) method in the time domain for layered media,” IEEE Trans. Antennas Propag. 51, 1559-1571 (2003).
[Crossref]

2002 (1)

Z. Liang, T. Yang, H. Ming, and J. Xie, “A novel 3D multilayered waveguide memory,” Proc. SPIE 4930, 134-137 (2002).
[Crossref]

2001 (1)

T. Yu and W. Cai, “High-order window functions and fast algorithms for calculating dyadic electromagnetic Green's functions in multilayered media,” Radio Sci. 36, 559-569 (2001).
[Crossref]

2000 (1)

M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, “Accurate and efficient computation of the Green's tensor for stratified media,” Phys. Rev. E 62, 5797-5807 (2000).
[Crossref]

1999 (2)

T. J. Cui and W. C. Chew, “Fast evaluation of Sommerfeld integrals for EM scattering and radiation by three-dimensional buried objects,” IEEE Trans. Geosci. Remote Sens. 37, 887-900 (1999).
[Crossref]

Z. Cao, Y. Jiang, Q. Shen, X. Dou, and Y. Chen, “Exact analytical method for planar optical waveguides with arbitrary index profile,” J. Opt. Soc. Am. A 16, 2209-2212 (1999).
[Crossref]

1994 (2)

Cai, W.

T. Yu and W. Cai, “High-order window functions and fast algorithms for calculating dyadic electromagnetic Green's functions in multilayered media,” Radio Sci. 36, 559-569 (2001).
[Crossref]

Cai, X.

T. Yang, Z. Liang, W. Qin, X. Cai, J. Chen, and S. Zhuang, “Side-scattering properties of a novel waveguide multilayer memory,” Opt. Eng. (Bellingham) 45, 095201 (2006).
[Crossref]

Cao, Z.

Chen, J.

Chen, J. S.

Z. Liang, J. S. Chen, T. Yang, Y. Xie, J. Chen, and S. Zhuang, “Principles and experiments of the waveguide multilayered optical memory,” J. Optoelectron., Laser 15, 315-317 (2004) (in Chinese).

Chen, Y.

Chew, W. C.

T. J. Cui and W. C. Chew, “Fast evaluation of Sommerfeld integrals for EM scattering and radiation by three-dimensional buried objects,” IEEE Trans. Geosci. Remote Sens. 37, 887-900 (1999).
[Crossref]

Cui, T. J.

T. J. Cui and W. C. Chew, “Fast evaluation of Sommerfeld integrals for EM scattering and radiation by three-dimensional buried objects,” IEEE Trans. Geosci. Remote Sens. 37, 887-900 (1999).
[Crossref]

Dereux, A.

Dou, X.

Felsen, L. B.

L. B. Felsen and N. Marcuvitz, Radiation and Scattering of Waves (IEEE, 1994), pp. 455-456.

Gay-Balmaz, P.

M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, “Accurate and efficient computation of the Green's tensor for stratified media,” Phys. Rev. E 62, 5797-5807 (2000).
[Crossref]

Girard, C.

Guo, H.

Huang, C. C.

L. Tsang, C. Ong, C. C. Huang, and V. Jandhyala, “Evaluation of the Green's function for the mixed potential integral equation (MPIE) method in the time domain for layered media,” IEEE Trans. Antennas Propag. 51, 1559-1571 (2003).
[Crossref]

Jandhyala, V.

L. Tsang, C. Ong, C. C. Huang, and V. Jandhyala, “Evaluation of the Green's function for the mixed potential integral equation (MPIE) method in the time domain for layered media,” IEEE Trans. Antennas Propag. 51, 1559-1571 (2003).
[Crossref]

Jiang, Y.

Liang, Z.

H. Guo, S. Zhuang, J. Chen, and Z. Liang, “Multilayered optical memory with bits stored as refractive index change. I. Electromagnetic theory,” J. Opt. Soc. Am. A 24, 1776-1785 (2007). Because of a printer's error, the term cos-3/2θ0 in Eq. (29b) should be cos-1/2θ0.
[Crossref]

T. Yang, Z. Liang, W. Qin, X. Cai, J. Chen, and S. Zhuang, “Side-scattering properties of a novel waveguide multilayer memory,” Opt. Eng. (Bellingham) 45, 095201 (2006).
[Crossref]

H. Guo, S. Zhuang, J. Chen, and Z. Liang, “Imaging theory of an aplanatic system with a stratified medium based on the method for a vector coherent transfer function,” Opt. Lett. 31, 2978-2980 (2006).
[Crossref] [PubMed]

Z. Liang, J. S. Chen, T. Yang, Y. Xie, J. Chen, and S. Zhuang, “Principles and experiments of the waveguide multilayered optical memory,” J. Optoelectron., Laser 15, 315-317 (2004) (in Chinese).

Z. Liang, T. Yang, H. Ming, and J. Xie, “A novel 3D multilayered waveguide memory,” Proc. SPIE 4930, 134-137 (2002).
[Crossref]

Liu, Q. H.

E. Simsek, Q. H. Liu, and B. Wei, “Singularity subtraction for evaluation of Green's functions for multilayer media,” IEEE Trans. Microwave Theory Tech. 54, 216-224 (2006).
[Crossref]

Marcuvitz, N.

L. B. Felsen and N. Marcuvitz, Radiation and Scattering of Waves (IEEE, 1994), pp. 455-456.

Martin, O. J. F.

M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, “Accurate and efficient computation of the Green's tensor for stratified media,” Phys. Rev. E 62, 5797-5807 (2000).
[Crossref]

O. J. F. Martin, A. Dereux, and C. Girard, “Iterative scheme for computing exactly the total field propagating in dielectric structures of arbitrary shape,” J. Opt. Soc. Am. A 11, 1073-1080 (1994).
[Crossref]

Ming, H.

Z. Liang, T. Yang, H. Ming, and J. Xie, “A novel 3D multilayered waveguide memory,” Proc. SPIE 4930, 134-137 (2002).
[Crossref]

Ong, C.

L. Tsang, C. Ong, C. C. Huang, and V. Jandhyala, “Evaluation of the Green's function for the mixed potential integral equation (MPIE) method in the time domain for layered media,” IEEE Trans. Antennas Propag. 51, 1559-1571 (2003).
[Crossref]

Paulus, M.

M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, “Accurate and efficient computation of the Green's tensor for stratified media,” Phys. Rev. E 62, 5797-5807 (2000).
[Crossref]

Qin, W.

T. Yang, Z. Liang, W. Qin, X. Cai, J. Chen, and S. Zhuang, “Side-scattering properties of a novel waveguide multilayer memory,” Opt. Eng. (Bellingham) 45, 095201 (2006).
[Crossref]

Salazar-Palma, M.

M. Yuan, T. K. Sarkar, and M. Salazar-Palma, “A direct discrete complex image method from the closed-form Green's functions in multilayered media,” IEEE Trans. Microwave Theory Tech. 54, 1025-1031 (2006).
[Crossref]

Sarkar, T. K.

M. Yuan, T. K. Sarkar, and M. Salazar-Palma, “A direct discrete complex image method from the closed-form Green's functions in multilayered media,” IEEE Trans. Microwave Theory Tech. 54, 1025-1031 (2006).
[Crossref]

Shen, Q.

Simsek, E.

E. Simsek, Q. H. Liu, and B. Wei, “Singularity subtraction for evaluation of Green's functions for multilayer media,” IEEE Trans. Microwave Theory Tech. 54, 216-224 (2006).
[Crossref]

Tsang, L.

L. Tsang, C. Ong, C. C. Huang, and V. Jandhyala, “Evaluation of the Green's function for the mixed potential integral equation (MPIE) method in the time domain for layered media,” IEEE Trans. Antennas Propag. 51, 1559-1571 (2003).
[Crossref]

Wei, B.

E. Simsek, Q. H. Liu, and B. Wei, “Singularity subtraction for evaluation of Green's functions for multilayer media,” IEEE Trans. Microwave Theory Tech. 54, 216-224 (2006).
[Crossref]

Xie, J.

Z. Liang, T. Yang, H. Ming, and J. Xie, “A novel 3D multilayered waveguide memory,” Proc. SPIE 4930, 134-137 (2002).
[Crossref]

Xie, Y.

Z. Liang, J. S. Chen, T. Yang, Y. Xie, J. Chen, and S. Zhuang, “Principles and experiments of the waveguide multilayered optical memory,” J. Optoelectron., Laser 15, 315-317 (2004) (in Chinese).

Yang, T.

T. Yang, Z. Liang, W. Qin, X. Cai, J. Chen, and S. Zhuang, “Side-scattering properties of a novel waveguide multilayer memory,” Opt. Eng. (Bellingham) 45, 095201 (2006).
[Crossref]

Z. Liang, J. S. Chen, T. Yang, Y. Xie, J. Chen, and S. Zhuang, “Principles and experiments of the waveguide multilayered optical memory,” J. Optoelectron., Laser 15, 315-317 (2004) (in Chinese).

Z. Liang, T. Yang, H. Ming, and J. Xie, “A novel 3D multilayered waveguide memory,” Proc. SPIE 4930, 134-137 (2002).
[Crossref]

Yu, T.

T. Yu and W. Cai, “High-order window functions and fast algorithms for calculating dyadic electromagnetic Green's functions in multilayered media,” Radio Sci. 36, 559-569 (2001).
[Crossref]

Yuan, M.

M. Yuan, T. K. Sarkar, and M. Salazar-Palma, “A direct discrete complex image method from the closed-form Green's functions in multilayered media,” IEEE Trans. Microwave Theory Tech. 54, 1025-1031 (2006).
[Crossref]

Zhuang, S.

IEEE Trans. Antennas Propag. (1)

L. Tsang, C. Ong, C. C. Huang, and V. Jandhyala, “Evaluation of the Green's function for the mixed potential integral equation (MPIE) method in the time domain for layered media,” IEEE Trans. Antennas Propag. 51, 1559-1571 (2003).
[Crossref]

IEEE Trans. Geosci. Remote Sens. (1)

T. J. Cui and W. C. Chew, “Fast evaluation of Sommerfeld integrals for EM scattering and radiation by three-dimensional buried objects,” IEEE Trans. Geosci. Remote Sens. 37, 887-900 (1999).
[Crossref]

IEEE Trans. Microwave Theory Tech. (2)

M. Yuan, T. K. Sarkar, and M. Salazar-Palma, “A direct discrete complex image method from the closed-form Green's functions in multilayered media,” IEEE Trans. Microwave Theory Tech. 54, 1025-1031 (2006).
[Crossref]

E. Simsek, Q. H. Liu, and B. Wei, “Singularity subtraction for evaluation of Green's functions for multilayer media,” IEEE Trans. Microwave Theory Tech. 54, 216-224 (2006).
[Crossref]

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

J. Optoelectron., Laser (1)

Z. Liang, J. S. Chen, T. Yang, Y. Xie, J. Chen, and S. Zhuang, “Principles and experiments of the waveguide multilayered optical memory,” J. Optoelectron., Laser 15, 315-317 (2004) (in Chinese).

Opt. Eng. (Bellingham) (1)

T. Yang, Z. Liang, W. Qin, X. Cai, J. Chen, and S. Zhuang, “Side-scattering properties of a novel waveguide multilayer memory,” Opt. Eng. (Bellingham) 45, 095201 (2006).
[Crossref]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. E (1)

M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, “Accurate and efficient computation of the Green's tensor for stratified media,” Phys. Rev. E 62, 5797-5807 (2000).
[Crossref]

Proc. SPIE (1)

Z. Liang, T. Yang, H. Ming, and J. Xie, “A novel 3D multilayered waveguide memory,” Proc. SPIE 4930, 134-137 (2002).
[Crossref]

Radio Sci. (1)

T. Yu and W. Cai, “High-order window functions and fast algorithms for calculating dyadic electromagnetic Green's functions in multilayered media,” Radio Sci. 36, 559-569 (2001).
[Crossref]

Other (1)

L. B. Felsen and N. Marcuvitz, Radiation and Scattering of Waves (IEEE, 1994), pp. 455-456.

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Figures (16)

Fig. 1
Fig. 1

Schematic diagram of a waveguide multilayered optical memory.

Fig. 2
Fig. 2

Structures of a waveguide multilayered disc with the same cladding and substrate.

Fig. 3
Fig. 3

Integration path in the complex k ρ plane.

Fig. 4
Fig. 4

Distribution of bits and the position of the reading light spot.

Fig. 5
Fig. 5

Variation of the power of the readout signals with the scanning position along the track. Here the bits compose the binary code “0110111010.”

Fig. 6
Fig. 6

Distribution of the light intensity scattered by a single bit at the detector plane for various polarizations of the reading light: (a) mixed mode, (b) TE mode, (c) TM mode.

Fig. 7
Fig. 7

Relationship between the modulation contrast and the depth of bits in a case of a certain length and width of bits. Curves a, b, and c represent the mixed, TE, and TM modes, respectively.

Fig. 8
Fig. 8

Relationship between the modulation contrast and the width of bits in the case of a certain length and depth of bits. Curves a, b, and c represent the mixed, TE, and TM modes, respectively.

Fig. 9
Fig. 9

Relationship between the modulation contrast and the length of bits in the case of a certain width and depth of bits. Curves a, b, and c represent the mixed, TE, and TM modes, respectively.

Fig. 10
Fig. 10

Relationship between the modulation contrast and the thickness of the core.

Fig. 11
Fig. 11

Relationship between the cross talk and the depth of bits in the case of a certain length and width of bits. Curves a, b, and c represent the mixed, TE, and TM modes, respectively.

Fig. 12
Fig. 12

Relationship between the cross talk and the width of bits in the case of a certain length and depth of bits. Curves a, b, and c represent the mixed, TE, and TM modes, respectively.

Fig. 13
Fig. 13

Relationship between the cross talk and the length of bits in the case of a certain width and depth of bits. Curves a, b, and c represent the mixed, TE, and TM modes, respectively.

Fig. 14
Fig. 14

Relationship between the cross talk and the distance between the two adjacent tracks. Curves a, b, and c represent the mixed, TE, and TM modes, respectively.

Fig. 15
Fig. 15

Relationship between the cross talk and the distance between the two adjacent bits on the same track. Curves a, b, and c represent the mixed, TE, and TM modes, respectively.

Fig. 16
Fig. 16

Relationship between the power of the readout signals and the length of bits. Curves a, b, and c represent the mixed, TE, and TM modes, respectively.

Equations (48)

Equations on this page are rendered with MathJax. Learn more.

E ( r ) = E r ( r ) + D d r G ( r ; r ) V ( r ) E ( r ) ,
U 1 = 0 N m , n ( k ρ ) k ρ J 0 ( k ρ ρ ) d k ρ ,
U 2 = 2 ρ 1 0 N m , n ( k ρ ) J 1 ( k ρ ρ ) d k ρ U 1 ,
V 1 = 0 N m , n 1 ( k ρ ) k ρ J 0 ( k ρ ρ ) d k ρ ,
V 2 = 2 ρ 1 0 N m , n 1 ( k ρ ) J 1 ( k ρ ρ ) d k ρ V 1 ,
V 3 = 0 N m , n 2 ( k ρ ) k ρ 2 J 1 ( k ρ ρ ) d k ρ ,
V 4 = 0 N m , n 3 ( k ρ ) k ρ 2 J 1 ( k ρ ρ ) d k ρ ,
V 5 = 0 N m , n 4 ( k ρ ) k ρ J 0 ( k ρ ρ ) d k ρ ,
N m , n ( k ρ ) = 1 κ n Δ Υ m , n > exp [ j κ m ( z z m ) ] exp [ j κ n ( z z n ) ] × { 1 + R m > exp [ j 2 κ m ( z z m ) ] } { 1 + R n < exp [ j 2 κ n ( z z n 1 ) ] } ,
N m , n 1 ( k ρ ) = κ n k n 2 Δ Υ m , n > exp [ j κ m ( z z m ) ] exp [ j κ n ( z z n ) ] × { 1 + R m > exp [ j 2 κ m ( z z m ) ] } { 1 + R n < exp [ j 2 κ n ( z z n 1 ) ] } ,
N m , n 2 ( k ρ ) = 1 k n 2 Δ Υ m , n > exp [ j κ m ( z z m ) ] exp [ j κ n ( z z n ) ] × { 1 + R m > exp [ j 2 κ m ( z z m ) ] } { 1 R n < exp [ j 2 κ n ( z z n 1 ) ] } ,
N m , n 3 ( k ρ ) = κ n k n 2 κ m Δ Υ m , n > exp [ j κ m ( z z m ) ] exp [ j κ n ( z z n ) ] × { 1 R m > exp [ j 2 κ m ( z z m ) ] } { 1 + R n < exp [ j 2 κ n ( z z n 1 ) ] } ,
N m , n 4 ( k ρ ) = k t 2 k n 2 κ m Δ Υ m , n > exp [ j κ m ( z z m ) ] exp [ j κ n ( z z n ) ] × { 1 R m > exp [ j 2 κ m ( z z m ) ] } { 1 R n < exp [ j 2 κ n ( z z n 1 ) ] } ,
N m , n ( k ρ ) = 1 κ n Δ Υ m , n < exp [ j κ m ( z z m 1 ) ] exp [ j κ n ( z z n 1 ) ] × { 1 + R m > exp [ j 2 κ m ( z z m 1 ) ] } { 1 + R n > exp [ j 2 κ n ( z z n ) ] } ,
N m , n 1 ( k ρ ) = κ n k n 2 Δ Υ m , n < exp [ j κ m ( z z m 1 ) ] exp [ j κ n ( z z n 1 ) ] × { 1 + R m < exp [ j 2 κ m ( z z m 1 ) ] } { 1 + R n > exp [ j 2 κ n ( z z n ) ] } ,
N m , n 2 ( k ρ ) = 1 k n 2 Δ Υ m , n < exp [ j κ m ( z z m 1 ) ] exp [ j κ n ( z z n 1 ) ] × { 1 + R m < exp [ j 2 κ m ( z z m 1 ) ] } { 1 R n > exp [ j 2 κ n ( z z n ) ] } ,
N m , n 3 ( k ρ ) = κ n k n 2 κ m Δ Υ m , n < exp [ j κ m ( z z m 1 ) ] exp [ j κ n ( z z n 1 ) ] { 1 R m < exp [ j 2 κ m ( z z m 1 ) ] } { 1 + R n > exp [ j 2 κ n ( z z n ) ] } ,
N m , n 4 ( k ρ ) = k t 2 k n 2 κ m Δ Υ m , n < exp [ j κ m ( z z m 1 ) ] exp [ j κ n ( z z n 1 ) ] { 1 R m < exp [ j 2 κ m ( z z m 1 ) ] } { 1 R n > exp [ j 2 κ n ( z z n ) ] } ,
G m , n x x = ( j 8 π ) ( U 1 + U 2 cos 2 ϕ ) ,
G m , n x y = ( j 8 π ) U 2 sin 2 ϕ ,
G m , n y x = G m , n x y ,
G m , n y y = ( j 8 π ) ( U 1 U 2 cos 2 ϕ ) ,
G m , n x x = ( j 8 π ) ( V 1 V 2 cos 2 ϕ ) ,
G m , n x y = G m , n y x = ( j 8 π ) V 2 sin 2 ϕ ,
G m , n x z = ( 1 4 π ) V 3 cos ϕ ,
G m , n y y = ( j 8 π ) ( V 1 + V 2 cos 2 ϕ ) ,
G m , n y z = ( 1 4 π ) V 3 sin ϕ ,
G m , n z x = ( 1 4 π ) V 4 cos ϕ ,
G m , n z y = ( 1 4 π ) V 4 sin ϕ ,
G m , n z z = ( j 4 π ) V 5 .
Δ = [ 1 R n > ( z n ) R n < ( z n 1 ) exp ( j 2 κ n l n ) ] 1 ,
k 0 k a g ( k ρ ) d k ρ = C g ( k ρ ) d k ρ + j π i = 1 n Res ( k ρ i ) ,
W ( r ; r ) = 0 f ( k ρ ; r ; r ) m ( k ρ ) d k ρ ,
m ( k ρ ) = 1 R n > ( z n ) R n < ( z n 1 ) exp ( j 2 κ n l n ) ,
Res ( k ρ i ; r ; r ) = f ( k ρ i ; r ; r ) m ( k ρ i ) ,
d m ( k ρ ) d k ρ = ( j 2 l n R n > R n < d κ n d k ρ d R n > d k ρ R n < R n > d R n < d k ρ ) exp ( j 2 κ n l n ) ,
d R i > d k ρ = ( 1 + Γ i > R i + 1 > e j 2 κ i + 1 l i + 1 ) 2 { [ 1 ( R i + 1 > e j 2 κ i + 1 l i + 1 ) 2 ] d Γ i > d k ρ + ( 1 Γ i > Γ i > ) e j 2 κ i + 1 l i + 1 ( d R i + 1 > d k ρ j 2 l i + 1 R i + 1 > d κ i + 1 d k ρ ) } ,
d R i < d k ρ = ( 1 + Γ i < R i 1 < e j 2 κ i 1 l i 1 ) 2 { [ 1 ( R i 1 < e j 2 κ i 1 l i 1 ) 2 ] d Γ i < d k ρ + ( 1 Γ i < Γ i < ) e j 2 κ i 1 l i 1 ( d R i 1 < d k ρ j 2 l i 1 R i 1 < d κ i 1 d k ρ ) } .
d Γ i > d k ρ = 2 ( κ i + κ i + 1 ) 2 ( κ i + 1 d κ i d k ρ κ i d κ i + 1 d k ρ ) ,
d Γ i < d k ρ = 2 ( κ i + κ i 1 ) 2 ( κ i 1 d κ i d k ρ κ i d κ i 1 d k ρ ) .
d Γ i > d k ρ = 2 ϵ i + 1 ϵ i ( ϵ i κ i + 1 + ϵ i + 1 κ i ) 2 ( κ i d κ i + 1 d k ρ κ i + 1 d κ i d k ρ ) ,
d Γ i < d k ρ = 2 ϵ i 1 ϵ i ( ϵ i κ i 1 + ϵ i 1 κ i ) 2 ( κ i d κ i 1 d k ρ κ i 1 d κ i d k ρ ) .
d κ i d k ρ = { k ρ ( k i 2 k ρ 2 ) 1 2 0 k ρ k i j k ρ ( k ρ 2 k i 2 ) 1 2 k ρ > k i .
d R N > d k ρ = d Γ N > d k ρ .
d R 1 < d k ρ = d Γ 1 < d k ρ .
Cross talk = 20 log [ ( P d P A ) P A ] ,
Cross talk = ( P d P A ) P A .
Modulation Contrast = { ( P 1 P 0 ) P 1 for P 1 P 0 ( P 1 P 0 ) P 0 for P 1 < P 0 .

Metrics