Abstract

Diffractive optical element design is an important problem for many applications and is usually achieved by the Gerchberg–Saxton or the Yang–Gu algorithm. These algorithms are formulated on the basis of monochromatic wave propagation and the far-field assumption, because the Fourier transform is used to model the wave propagation. We propose an iterative algorithm (based on rigorous coupled-wave analysis) for the design of a diffractive optical element. Since rigorous coupled-wave analysis (instead of Fourier transformation) is used to calculate the light-field distribution behind the optical element, the diffractive optical element can thus be better designed. Simulation results are provided to verify the proposed algorithm for designing a converging lens. Compared with the well-known Gerchberg–Saxton and Yang–Gu algorithms, our method provides 7.8% and 10.8%, respectively, improvement in converging the light amplitude when a microlens is desired. In addition, the proposed algorithm provides a solution that is very close to the solution obtained by the simulated annealing method (within 1.89% error).

© 2001 Optical Society of America

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References

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  1. M. Born, E. Wolf, Principles of Optics (Pergamon, Cambridge, UK, 1997).
  2. C. Chang, J. Harbison, C. Zah, M. Maeda, L. Stoffel, T. Lee, “Multiple wavelength tunable surface-emitting laser arrays,” IEEE J. Quantum Electron. 27, 1368–1376 (1991).
    [CrossRef]
  3. L. Eng, K. Bacher, W. Yuen, J. Harris, C. C. Hasnain, “Multiple-wavelength vertical cavity laser arrays on patterned substrates,” IEEE J. Quantum Electron. 12, 624–628 (1995).
    [CrossRef]
  4. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  5. F. Koyama, Y. Hayashi, N. Ohnoki, N. Hatori, K. Iga, “Two-dimensional multiwavelength surface emitting laserarrays fabricated by nonplanar MOCVD,” Electron. Lett. 30, 1947–1948 (1994).
    [CrossRef]
  6. R. Nordin, A. Levi, R. Nottenburg, J. T. Ek, R. Logan, “A system perspective on digital interconnection technology,” IEEE J. Lightwave Technol. 10, 811–827 (1992).
    [CrossRef]
  7. W. Yuen, G. Li, C. C. Hasnain, “Multiple-wavelength vertical-cavity surface-emitting laser arrays with a record wavelength span,” IEEE Photon. Technol. Lett. 8, 4–6 (1996).
    [CrossRef]
  8. W. Dasher, P. Long, R. Stein, “Cost-effective mass fabrication of multilevel diffractive optical elements by use of signal optical exposure with a gray-scale mask on high-energy beam-sensitive glass,” Appl. Opt. 36, 4675–4680 (1997).
    [CrossRef]
  9. G. Strang, Introduction to Applied Mathematics (Wellesley-Cambridge, Wellesley, Mass., 1986).
  10. R. W. Gerchberg, W. O. Saxton, “Phase determination for image and diffraction plane pictures in the electron microscope,” Optik 34, 275–284 (1971).
  11. R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 227–246 (1972).
  12. B. Gu, G. Yang, “On the phase retrieval problem in optical and electronic microscopy,” Acta Opt. Sin. 1, 517–522 (1981).
  13. B. Gu, G. Yang, B. Dong, “General theory for performing an optical transform,” Appl. Opt. 25, 3197–3206 (1986).
    [CrossRef] [PubMed]
  14. G. Yang, B. Gu, “On the amplitude-phase retrieval problem in the optical system,” Acta Phys. Sin. 30, 410–413 (1981).
  15. L. Li, “Use of Fourier series in the analysis of discontinous periodic structures,” J. Opt. Soc. Am. A 13, 1870–1876 (1996).
    [CrossRef]
  16. L. Li, “New formulation of the Fourier modal method for crossed surface-relief gratings,” J. Opt. Soc. Am. A 14, 2758–2767 (1997).
    [CrossRef]
  17. S. T. Han, Y. L. Tsao, R. M. Walser, M. F. Becker, “Electromagnetic scattering of two-dimensional surface-relief dielectric gratings,” Appl. Opt. 31, 2343–2352 (1992).
    [CrossRef] [PubMed]
  18. M. G. Moharam, T. K. Gaylord, “Rigorous coupled-wave analysis of planar grating diffraction,” J. Opt. Soc. Am. 71, 811–818 (1981).
    [CrossRef]
  19. M. G. Moharam, T. K. Gaylord, “Chain-matrix analysis of arbitrary-thickness dielectric reflection gratings,” J. Opt. Soc. Am. 72, 187–190 (1982).
    [CrossRef]
  20. M. G. Moharam, T. K. Gaylord, “Planar dielectric grating diffraction theories,” Appl. Phys. B 28, 1–14 (1982).
    [CrossRef]
  21. M. G. Moharam, T. K. Gaylord, “Diffraction analysis of dielectric surface-relief grating,” J. Opt. Soc. Am. 72, 1385–1392 (1982).
    [CrossRef]
  22. M. G. Moharam, T. K. Gaylord, “Three-dimensional vector coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 73, 1105–1112 (1983).
    [CrossRef]
  23. M. G. Moharam, E. B. Grann, D. A. Pommet, “Formulation for stable and efficient implementation of the rigor-ous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 3, 1780–1787 (1996).
    [CrossRef]
  24. M. S. Kim, C. C. Guest, “Simulated annealing algorithm for binary phase-only filters in pattern classification,” Appl. Opt. 29, 1203–1208 (1990).
    [CrossRef] [PubMed]
  25. S. Kirkpartick, C. D. Gellatt, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
    [CrossRef]
  26. N. Yoshikawa, T. Yatagai, “Phase optimization of a ki-noform by simulated annealing,” Appl. Opt. 33, 863–868 (1994).
    [CrossRef] [PubMed]
  27. E. Noponen, “Eigenmode method for electromagnetic syn-thesis of diffractive elements with three-dimensional profiles,” J. Opt. Soc. Am. A 11, 2494–2502 (1994).
    [CrossRef]
  28. Please note that the DOE’s phase transmittance (before quantization) is different between the last two iterations of our algorithm and that the largest difference between the last two iterations is 2.87×10-3.However, our algorithm still converges, because the phases after quantization become identical.

1997 (2)

1996 (3)

1995 (1)

L. Eng, K. Bacher, W. Yuen, J. Harris, C. C. Hasnain, “Multiple-wavelength vertical cavity laser arrays on patterned substrates,” IEEE J. Quantum Electron. 12, 624–628 (1995).
[CrossRef]

1994 (3)

1992 (2)

S. T. Han, Y. L. Tsao, R. M. Walser, M. F. Becker, “Electromagnetic scattering of two-dimensional surface-relief dielectric gratings,” Appl. Opt. 31, 2343–2352 (1992).
[CrossRef] [PubMed]

R. Nordin, A. Levi, R. Nottenburg, J. T. Ek, R. Logan, “A system perspective on digital interconnection technology,” IEEE J. Lightwave Technol. 10, 811–827 (1992).
[CrossRef]

1991 (1)

C. Chang, J. Harbison, C. Zah, M. Maeda, L. Stoffel, T. Lee, “Multiple wavelength tunable surface-emitting laser arrays,” IEEE J. Quantum Electron. 27, 1368–1376 (1991).
[CrossRef]

1990 (1)

1986 (1)

1983 (2)

1982 (3)

1981 (3)

B. Gu, G. Yang, “On the phase retrieval problem in optical and electronic microscopy,” Acta Opt. Sin. 1, 517–522 (1981).

G. Yang, B. Gu, “On the amplitude-phase retrieval problem in the optical system,” Acta Phys. Sin. 30, 410–413 (1981).

M. G. Moharam, T. K. Gaylord, “Rigorous coupled-wave analysis of planar grating diffraction,” J. Opt. Soc. Am. 71, 811–818 (1981).
[CrossRef]

1972 (1)

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 227–246 (1972).

1971 (1)

R. W. Gerchberg, W. O. Saxton, “Phase determination for image and diffraction plane pictures in the electron microscope,” Optik 34, 275–284 (1971).

Bacher, K.

L. Eng, K. Bacher, W. Yuen, J. Harris, C. C. Hasnain, “Multiple-wavelength vertical cavity laser arrays on patterned substrates,” IEEE J. Quantum Electron. 12, 624–628 (1995).
[CrossRef]

Becker, M. F.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Cambridge, UK, 1997).

Chang, C.

C. Chang, J. Harbison, C. Zah, M. Maeda, L. Stoffel, T. Lee, “Multiple wavelength tunable surface-emitting laser arrays,” IEEE J. Quantum Electron. 27, 1368–1376 (1991).
[CrossRef]

Dasher, W.

Dong, B.

Ek, J. T.

R. Nordin, A. Levi, R. Nottenburg, J. T. Ek, R. Logan, “A system perspective on digital interconnection technology,” IEEE J. Lightwave Technol. 10, 811–827 (1992).
[CrossRef]

Eng, L.

L. Eng, K. Bacher, W. Yuen, J. Harris, C. C. Hasnain, “Multiple-wavelength vertical cavity laser arrays on patterned substrates,” IEEE J. Quantum Electron. 12, 624–628 (1995).
[CrossRef]

Gaylord, T. K.

Gellatt, C. D.

S. Kirkpartick, C. D. Gellatt, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef]

Gerchberg, R. W.

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 227–246 (1972).

R. W. Gerchberg, W. O. Saxton, “Phase determination for image and diffraction plane pictures in the electron microscope,” Optik 34, 275–284 (1971).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Grann, E. B.

Gu, B.

B. Gu, G. Yang, B. Dong, “General theory for performing an optical transform,” Appl. Opt. 25, 3197–3206 (1986).
[CrossRef] [PubMed]

G. Yang, B. Gu, “On the amplitude-phase retrieval problem in the optical system,” Acta Phys. Sin. 30, 410–413 (1981).

B. Gu, G. Yang, “On the phase retrieval problem in optical and electronic microscopy,” Acta Opt. Sin. 1, 517–522 (1981).

Guest, C. C.

Han, S. T.

Harbison, J.

C. Chang, J. Harbison, C. Zah, M. Maeda, L. Stoffel, T. Lee, “Multiple wavelength tunable surface-emitting laser arrays,” IEEE J. Quantum Electron. 27, 1368–1376 (1991).
[CrossRef]

Harris, J.

L. Eng, K. Bacher, W. Yuen, J. Harris, C. C. Hasnain, “Multiple-wavelength vertical cavity laser arrays on patterned substrates,” IEEE J. Quantum Electron. 12, 624–628 (1995).
[CrossRef]

Hasnain, C. C.

W. Yuen, G. Li, C. C. Hasnain, “Multiple-wavelength vertical-cavity surface-emitting laser arrays with a record wavelength span,” IEEE Photon. Technol. Lett. 8, 4–6 (1996).
[CrossRef]

L. Eng, K. Bacher, W. Yuen, J. Harris, C. C. Hasnain, “Multiple-wavelength vertical cavity laser arrays on patterned substrates,” IEEE J. Quantum Electron. 12, 624–628 (1995).
[CrossRef]

Hatori, N.

F. Koyama, Y. Hayashi, N. Ohnoki, N. Hatori, K. Iga, “Two-dimensional multiwavelength surface emitting laserarrays fabricated by nonplanar MOCVD,” Electron. Lett. 30, 1947–1948 (1994).
[CrossRef]

Hayashi, Y.

F. Koyama, Y. Hayashi, N. Ohnoki, N. Hatori, K. Iga, “Two-dimensional multiwavelength surface emitting laserarrays fabricated by nonplanar MOCVD,” Electron. Lett. 30, 1947–1948 (1994).
[CrossRef]

Iga, K.

F. Koyama, Y. Hayashi, N. Ohnoki, N. Hatori, K. Iga, “Two-dimensional multiwavelength surface emitting laserarrays fabricated by nonplanar MOCVD,” Electron. Lett. 30, 1947–1948 (1994).
[CrossRef]

Kim, M. S.

Kirkpartick, S.

S. Kirkpartick, C. D. Gellatt, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef]

Koyama, F.

F. Koyama, Y. Hayashi, N. Ohnoki, N. Hatori, K. Iga, “Two-dimensional multiwavelength surface emitting laserarrays fabricated by nonplanar MOCVD,” Electron. Lett. 30, 1947–1948 (1994).
[CrossRef]

Lee, T.

C. Chang, J. Harbison, C. Zah, M. Maeda, L. Stoffel, T. Lee, “Multiple wavelength tunable surface-emitting laser arrays,” IEEE J. Quantum Electron. 27, 1368–1376 (1991).
[CrossRef]

Levi, A.

R. Nordin, A. Levi, R. Nottenburg, J. T. Ek, R. Logan, “A system perspective on digital interconnection technology,” IEEE J. Lightwave Technol. 10, 811–827 (1992).
[CrossRef]

Li, G.

W. Yuen, G. Li, C. C. Hasnain, “Multiple-wavelength vertical-cavity surface-emitting laser arrays with a record wavelength span,” IEEE Photon. Technol. Lett. 8, 4–6 (1996).
[CrossRef]

Li, L.

Logan, R.

R. Nordin, A. Levi, R. Nottenburg, J. T. Ek, R. Logan, “A system perspective on digital interconnection technology,” IEEE J. Lightwave Technol. 10, 811–827 (1992).
[CrossRef]

Long, P.

Maeda, M.

C. Chang, J. Harbison, C. Zah, M. Maeda, L. Stoffel, T. Lee, “Multiple wavelength tunable surface-emitting laser arrays,” IEEE J. Quantum Electron. 27, 1368–1376 (1991).
[CrossRef]

Moharam, M. G.

Noponen, E.

Nordin, R.

R. Nordin, A. Levi, R. Nottenburg, J. T. Ek, R. Logan, “A system perspective on digital interconnection technology,” IEEE J. Lightwave Technol. 10, 811–827 (1992).
[CrossRef]

Nottenburg, R.

R. Nordin, A. Levi, R. Nottenburg, J. T. Ek, R. Logan, “A system perspective on digital interconnection technology,” IEEE J. Lightwave Technol. 10, 811–827 (1992).
[CrossRef]

Ohnoki, N.

F. Koyama, Y. Hayashi, N. Ohnoki, N. Hatori, K. Iga, “Two-dimensional multiwavelength surface emitting laserarrays fabricated by nonplanar MOCVD,” Electron. Lett. 30, 1947–1948 (1994).
[CrossRef]

Pommet, D. A.

Saxton, W. O.

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 227–246 (1972).

R. W. Gerchberg, W. O. Saxton, “Phase determination for image and diffraction plane pictures in the electron microscope,” Optik 34, 275–284 (1971).

Stein, R.

Stoffel, L.

C. Chang, J. Harbison, C. Zah, M. Maeda, L. Stoffel, T. Lee, “Multiple wavelength tunable surface-emitting laser arrays,” IEEE J. Quantum Electron. 27, 1368–1376 (1991).
[CrossRef]

Strang, G.

G. Strang, Introduction to Applied Mathematics (Wellesley-Cambridge, Wellesley, Mass., 1986).

Tsao, Y. L.

Walser, R. M.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Cambridge, UK, 1997).

Yang, G.

B. Gu, G. Yang, B. Dong, “General theory for performing an optical transform,” Appl. Opt. 25, 3197–3206 (1986).
[CrossRef] [PubMed]

G. Yang, B. Gu, “On the amplitude-phase retrieval problem in the optical system,” Acta Phys. Sin. 30, 410–413 (1981).

B. Gu, G. Yang, “On the phase retrieval problem in optical and electronic microscopy,” Acta Opt. Sin. 1, 517–522 (1981).

Yatagai, T.

Yoshikawa, N.

Yuen, W.

W. Yuen, G. Li, C. C. Hasnain, “Multiple-wavelength vertical-cavity surface-emitting laser arrays with a record wavelength span,” IEEE Photon. Technol. Lett. 8, 4–6 (1996).
[CrossRef]

L. Eng, K. Bacher, W. Yuen, J. Harris, C. C. Hasnain, “Multiple-wavelength vertical cavity laser arrays on patterned substrates,” IEEE J. Quantum Electron. 12, 624–628 (1995).
[CrossRef]

Zah, C.

C. Chang, J. Harbison, C. Zah, M. Maeda, L. Stoffel, T. Lee, “Multiple wavelength tunable surface-emitting laser arrays,” IEEE J. Quantum Electron. 27, 1368–1376 (1991).
[CrossRef]

Acta Opt. Sin. (1)

B. Gu, G. Yang, “On the phase retrieval problem in optical and electronic microscopy,” Acta Opt. Sin. 1, 517–522 (1981).

Acta Phys. Sin. (1)

G. Yang, B. Gu, “On the amplitude-phase retrieval problem in the optical system,” Acta Phys. Sin. 30, 410–413 (1981).

Appl. Opt. (5)

Appl. Phys. B (1)

M. G. Moharam, T. K. Gaylord, “Planar dielectric grating diffraction theories,” Appl. Phys. B 28, 1–14 (1982).
[CrossRef]

Electron. Lett. (1)

F. Koyama, Y. Hayashi, N. Ohnoki, N. Hatori, K. Iga, “Two-dimensional multiwavelength surface emitting laserarrays fabricated by nonplanar MOCVD,” Electron. Lett. 30, 1947–1948 (1994).
[CrossRef]

IEEE J. Lightwave Technol. (1)

R. Nordin, A. Levi, R. Nottenburg, J. T. Ek, R. Logan, “A system perspective on digital interconnection technology,” IEEE J. Lightwave Technol. 10, 811–827 (1992).
[CrossRef]

IEEE J. Quantum Electron. (2)

C. Chang, J. Harbison, C. Zah, M. Maeda, L. Stoffel, T. Lee, “Multiple wavelength tunable surface-emitting laser arrays,” IEEE J. Quantum Electron. 27, 1368–1376 (1991).
[CrossRef]

L. Eng, K. Bacher, W. Yuen, J. Harris, C. C. Hasnain, “Multiple-wavelength vertical cavity laser arrays on patterned substrates,” IEEE J. Quantum Electron. 12, 624–628 (1995).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

W. Yuen, G. Li, C. C. Hasnain, “Multiple-wavelength vertical-cavity surface-emitting laser arrays with a record wavelength span,” IEEE Photon. Technol. Lett. 8, 4–6 (1996).
[CrossRef]

J. Opt. Soc. Am. (4)

J. Opt. Soc. Am. A (4)

Optik (2)

R. W. Gerchberg, W. O. Saxton, “Phase determination for image and diffraction plane pictures in the electron microscope,” Optik 34, 275–284 (1971).

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 227–246 (1972).

Science (1)

S. Kirkpartick, C. D. Gellatt, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef]

Other (4)

Please note that the DOE’s phase transmittance (before quantization) is different between the last two iterations of our algorithm and that the largest difference between the last two iterations is 2.87×10-3.However, our algorithm still converges, because the phases after quantization become identical.

M. Born, E. Wolf, Principles of Optics (Pergamon, Cambridge, UK, 1997).

G. Strang, Introduction to Applied Mathematics (Wellesley-Cambridge, Wellesley, Mass., 1986).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

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Figures (12)

Fig. 1
Fig. 1

Schematic diagram of the optical system being considered.

Fig. 2
Fig. 2

Geometry of the 1-D DOE diffraction problem.

Fig. 3
Fig. 3

Geometry of the 2-D DOE diffraction problem.

Fig. 4
Fig. 4

Actual structure of the lens.

Fig. 5
Fig. 5

Relationship between the number of diffraction order and the (0,0)th transmitted order’s diffraction efficiency in (a) 3-D and (b) 2-D.

Fig. 6
Fig. 6

Convergence behavior of the diffraction order in RCWA algorithm in (a) 3-D and (b) 2-D.

Fig. 7
Fig. 7

Convergence behavior in (a) the (0,-1)st transmitted order and (b) (1,1)th reflected order.

Fig. 8
Fig. 8

Output-diffraction pattern of the designed DOE (with 128×128 pixels and eight phase levels) from (a) G–S, (b) Y–G and (c) RCWA-based algorithms (uniform beam case).

Fig. 9
Fig. 9

Correlation between diffraction patterns from different DOE-design algorithms as a function of distance L (uniform input-beam case).

Fig. 10
Fig. 10

Output diffraction pattern of the designed DOE (with 128×128 pixels and eight phase levels) from (a) G–S, (b) Y–G and (c) RCWA-based algorithms (Gaussian input-beam case).

Fig. 11
Fig. 11

Correlation between diffraction patterns from different DOE-design algorithms as a function of distance L (Gaussian input-beam case).

Fig. 12
Fig. 12

Results of the SA-RCWA algorithm in terms of iteration number. (Result of the RCWA-based algorithm is shown for comparison.)

Tables (2)

Tables Icon

Table 1 Simulation Results for the Case of a Uniform Input Beam

Tables Icon

Table 2 Simulation Results for the Case of a Gaussian Input Beam

Equations (32)

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

U1(x, y)=A1(x, y)exp[jϕ1(x, y)],
U2(fx, fy)=A2(fx, fy)exp[jϕ2(fx, fy)].
(x, z)=(x+Λ, z)=pp(z)exp(jpKx),
E1=exp[-j(kx0x+kz0z)]+iRi exp[-j(kxix+kzi1z),
E3=iTi exp{-j[kxix+kzi3(z-d)]},
E2=iSi exp[-j(kxix+kzi2z)],
2E2+k2(x, z)E2=0.
d2Si(z)dz2-2jkz0dSi(z)dz=(kxi2+kx02)Si(z)-k2pp(z)Si-p(z),
Si(z)=m=-Cmωim exp(λmz)m=-MMCmωim exp(λmz),
δi0+Ri=m=-Cmωimm=-MMCmωim,
(δi0-Ri)κzi=m=-Cmωim(κz0+jλm)m=-MMCmωim(κz0+jλm),
Ti=m=-Cmωim exp(λmd)m=-MMCmωim exp(λmd),
Tiκzi3=m=-Cmωim(κz0+jλm)exp(λmd)m=-MMCmωim(κz0+jλm)exp(λmd).
(x, y)=g,hgh exp[j(gKxx+hKyy)],
E1=Einc+m,nRmn exp[-jk1mn·r],
E3=m,nexp[-jk3mn·(r-p)],
E2=E2xxˆ+E2yyˆ=m,n[Sxmn(z)xˆ+Symn(z)yˆ]×exp(-jσmn·r),
Sxmn(z)=m=-n=-Cxmnωxmn exp(λxmnz)m=-MMn=-NNCxmnωxmn exp(λxmnz),
Symn(z)=m=-n=-Cymnωymn exp(λymnz)m=-MMn=-NNCymnωymn exp(λymnz).
uxδm0δn0+Rxmn=Sxmn(0),
uyδm0δn0+Rymn=Symn(0),
δm0δn0(ky0ux-k1 cos θuy)-kz1mnRymn+kynRzmn=ky0Uxmn(0),
δm0δn0(k1 cos θux-kzuz)+kz1mnRxmn-kxmRzmn=k0Uymn(0),
Txmn=Sxmn(d),
Tymn=Symn(d),
-kx3mnTymn+kynTzmn=k0Uxmn(d),
kx3mnTxmn-kxmTZmn=k0Uymn(d),
H=[j/(ωμ0)]×E.
U2(fx, fy)=U2(fx, fy)+εifU2(fx, fy)>U2(fx, fy)+εU2(fx, fy)-εifU2(fx, fy)<U2(fx, fy)-εU2(fx, yy)otherwise.
cost=|U2(fx, fy)-U2(fx, fy)|,
P(Δcost)=exp(-Δcost/T)
T=T0/(1+t),

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