Abstract

In this paper, we present an optimal shape design method for a dielectric microlens which is used to focus an incoming infrared plane wave in wideband, by exploiting the finite difference time domain (FDTD) technique and the topology optimization technique. Topology optimization is a scheme to search an optimal shape by adjusting the material properties, which are design variables, within the design space. And by introducing the adjoint variable method, we can effectively calculate a derivative of the objective function with respect to the design variable. To verify the proposed method, a shape design problem of a dielectric microlens is tested when illuminated by a transverse electric (TE)-polarized infrared plane wave. In this problem, the design variable is the dielectric constant within the design space of a dielectric microlens. The design objective is to maximally focus the incoming magnetic field at a specific point in wideband.

© 2009 Optical Society of Korea

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  1. E. J. Haug, K. K. Choi, and V. Komkov, Design Sensitivity Analysis of Structural System (Academic Press, New York, USA, 1986)
  2. Y. S. Chung, C. Cheon, I. H. Park, and S. Y. Hahn, "Optimal design method for microwave device using FDTD and design sensitivity analysis," IEEE Trans. MTT. 48, 2289-2296 (2000)
    [CrossRef]
  3. Y. S. Chung, J. Ryu, C. Cheon, I. H. Park, and S. Y. Hahn, "Optimal design method for microwave device using time domain method and design sensitivity analysis : I. FETD case," IEEE Trans. Magn. 37, 3289-3293 (2001)
    [CrossRef]
  4. Y. S. Chung, C. Cheon, I. H. Park, and S. Y. Hahn, "Optimal design method for microwave device using time domain method and design sensitivity analysis : II. FDTD case," IEEE Trans. Magn. 37, 3255-3259 (2001)
    [CrossRef]
  5. M. P. Bendsoe and N. Kikuchi, "Generating optimal topologies in structural design using a homogenization method," Computer Methods in Applied Mechanics and Engineering 71, 197-224 (1988)
    [CrossRef]
  6. M. P. Bendsoe, "Optimal shape design as a material distribution problem," Structural Optimization 1, 193-202 (1989)
    [CrossRef]
  7. K. Suzuki and N. Kikuchi, "A homogenization method for shape and topology optimization," Computer Methods in Applied Mechanics and Engineering 93, 291-318 (1991)
    [CrossRef]
  8. H. P. Mlejnek and R. Schirrmacher, "An engineer"s approach to optimal material distribution and shape finding," Computer Methods in Applied Mechanics and Engineering 106, 1-26 (1993)
    [CrossRef]
  9. R. J. Yang, "Multidiscipline topology optimization," Computer & Structures 63, 1205-1212 (1997)
    [CrossRef]
  10. D. N. Dyck and D. A. Lawther, "Automated design of magnetic devices by optimizing material distribution," IEEE Trans. Magn. 32, 1188-1193 (1996)
    [CrossRef]
  11. H. Lee, "Computer aided optimal design methods for waveguide structures," Ph.D. Dissertation, Seoul National University (1995)
  12. D. S. Katz, "FDTD modeling of dielectric lens," http://pat.jpl.nara.gov/public/dsk/FDTD (1998)
  13. J. Choi, J. Jung, S. Park, and T. Kwon, "The compound refractive lens for hard X-ray focusing," J. Opt. Soc. Korea 11, 76-81 (2007)
    [CrossRef]
  14. G. Kweon, Y. Choi, and M. Laikin, "Fisheye lens for image processing application," J. Opt. Soc. Korea 12, 79-87 (2008)
    [CrossRef]
  15. A. Taflove, Computational Electrodynamics: The Finite-Difference Time-domain Method (Artech House, Boston, USA, 1995)
  16. K. Demarest, R. Plumb, and Z. Huang, "FDTD modeling of scatterers in stratified media," IEEE Trans. Antennas Propag. 43, 1164-1168 (1995)
    [CrossRef]
  17. P. B. Wong, G. L. Tyler, J. E. Baron, E. M. Gurrola, and R. A. Simpson, "A three-wave FDTD approach to surface scattering with applications to remote sensing of geophysical surfaces," IEEE Trans. Antennas Propag. 44, 504-514 (1996)
    [CrossRef]
  18. J. B. Schneider, C. L. Wagner, and O. M. Ramahi, "Implementation of transparent sources in FDTD simulation," IEEE Trans. Antennas Propag. 46, 1159-1168 (1998)
    [CrossRef]
  19. C. A Balanis, Antenna Theory: Analysis and Design (John Wiley & Sons, Singapore, 1982)
  20. H. Jasik, Antenna Engineering Handbook (McGraw- Hill, New York, USA, 1961)

2008 (1)

G. Kweon, Y. Choi, and M. Laikin, "Fisheye lens for image processing application," J. Opt. Soc. Korea 12, 79-87 (2008)
[CrossRef]

2007 (1)

J. Choi, J. Jung, S. Park, and T. Kwon, "The compound refractive lens for hard X-ray focusing," J. Opt. Soc. Korea 11, 76-81 (2007)
[CrossRef]

2001 (2)

Y. S. Chung, J. Ryu, C. Cheon, I. H. Park, and S. Y. Hahn, "Optimal design method for microwave device using time domain method and design sensitivity analysis : I. FETD case," IEEE Trans. Magn. 37, 3289-3293 (2001)
[CrossRef]

Y. S. Chung, C. Cheon, I. H. Park, and S. Y. Hahn, "Optimal design method for microwave device using time domain method and design sensitivity analysis : II. FDTD case," IEEE Trans. Magn. 37, 3255-3259 (2001)
[CrossRef]

2000 (1)

Y. S. Chung, C. Cheon, I. H. Park, and S. Y. Hahn, "Optimal design method for microwave device using FDTD and design sensitivity analysis," IEEE Trans. MTT. 48, 2289-2296 (2000)
[CrossRef]

1998 (2)

J. B. Schneider, C. L. Wagner, and O. M. Ramahi, "Implementation of transparent sources in FDTD simulation," IEEE Trans. Antennas Propag. 46, 1159-1168 (1998)
[CrossRef]

D. S. Katz, "FDTD modeling of dielectric lens," http://pat.jpl.nara.gov/public/dsk/FDTD (1998)

1997 (1)

R. J. Yang, "Multidiscipline topology optimization," Computer & Structures 63, 1205-1212 (1997)
[CrossRef]

1996 (2)

D. N. Dyck and D. A. Lawther, "Automated design of magnetic devices by optimizing material distribution," IEEE Trans. Magn. 32, 1188-1193 (1996)
[CrossRef]

P. B. Wong, G. L. Tyler, J. E. Baron, E. M. Gurrola, and R. A. Simpson, "A three-wave FDTD approach to surface scattering with applications to remote sensing of geophysical surfaces," IEEE Trans. Antennas Propag. 44, 504-514 (1996)
[CrossRef]

1995 (3)

A. Taflove, Computational Electrodynamics: The Finite-Difference Time-domain Method (Artech House, Boston, USA, 1995)

K. Demarest, R. Plumb, and Z. Huang, "FDTD modeling of scatterers in stratified media," IEEE Trans. Antennas Propag. 43, 1164-1168 (1995)
[CrossRef]

H. Lee, "Computer aided optimal design methods for waveguide structures," Ph.D. Dissertation, Seoul National University (1995)

1993 (1)

H. P. Mlejnek and R. Schirrmacher, "An engineer"s approach to optimal material distribution and shape finding," Computer Methods in Applied Mechanics and Engineering 106, 1-26 (1993)
[CrossRef]

1991 (1)

K. Suzuki and N. Kikuchi, "A homogenization method for shape and topology optimization," Computer Methods in Applied Mechanics and Engineering 93, 291-318 (1991)
[CrossRef]

1989 (1)

M. P. Bendsoe, "Optimal shape design as a material distribution problem," Structural Optimization 1, 193-202 (1989)
[CrossRef]

1988 (1)

M. P. Bendsoe and N. Kikuchi, "Generating optimal topologies in structural design using a homogenization method," Computer Methods in Applied Mechanics and Engineering 71, 197-224 (1988)
[CrossRef]

1986 (1)

E. J. Haug, K. K. Choi, and V. Komkov, Design Sensitivity Analysis of Structural System (Academic Press, New York, USA, 1986)

1982 (1)

C. A Balanis, Antenna Theory: Analysis and Design (John Wiley & Sons, Singapore, 1982)

1961 (1)

H. Jasik, Antenna Engineering Handbook (McGraw- Hill, New York, USA, 1961)

Antennas and Propagation, IEEE Transactions on (2)

K. Demarest, R. Plumb, and Z. Huang, "FDTD modeling of scatterers in stratified media," IEEE Trans. Antennas Propag. 43, 1164-1168 (1995)
[CrossRef]

J. B. Schneider, C. L. Wagner, and O. M. Ramahi, "Implementation of transparent sources in FDTD simulation," IEEE Trans. Antennas Propag. 46, 1159-1168 (1998)
[CrossRef]

Computer Methods in Applied Mechanics and Engineering (3)

M. P. Bendsoe and N. Kikuchi, "Generating optimal topologies in structural design using a homogenization method," Computer Methods in Applied Mechanics and Engineering 71, 197-224 (1988)
[CrossRef]

K. Suzuki and N. Kikuchi, "A homogenization method for shape and topology optimization," Computer Methods in Applied Mechanics and Engineering 93, 291-318 (1991)
[CrossRef]

H. P. Mlejnek and R. Schirrmacher, "An engineer"s approach to optimal material distribution and shape finding," Computer Methods in Applied Mechanics and Engineering 106, 1-26 (1993)
[CrossRef]

Computers & Structures (1)

R. J. Yang, "Multidiscipline topology optimization," Computer & Structures 63, 1205-1212 (1997)
[CrossRef]

IEEE Trans. Antennas Propag. (1)

P. B. Wong, G. L. Tyler, J. E. Baron, E. M. Gurrola, and R. A. Simpson, "A three-wave FDTD approach to surface scattering with applications to remote sensing of geophysical surfaces," IEEE Trans. Antennas Propag. 44, 504-514 (1996)
[CrossRef]

Journal of the Optical Society of Korea (2)

J. Choi, J. Jung, S. Park, and T. Kwon, "The compound refractive lens for hard X-ray focusing," J. Opt. Soc. Korea 11, 76-81 (2007)
[CrossRef]

G. Kweon, Y. Choi, and M. Laikin, "Fisheye lens for image processing application," J. Opt. Soc. Korea 12, 79-87 (2008)
[CrossRef]

Magnetics, IEEE Transactions on (3)

D. N. Dyck and D. A. Lawther, "Automated design of magnetic devices by optimizing material distribution," IEEE Trans. Magn. 32, 1188-1193 (1996)
[CrossRef]

Y. S. Chung, J. Ryu, C. Cheon, I. H. Park, and S. Y. Hahn, "Optimal design method for microwave device using time domain method and design sensitivity analysis : I. FETD case," IEEE Trans. Magn. 37, 3289-3293 (2001)
[CrossRef]

Y. S. Chung, C. Cheon, I. H. Park, and S. Y. Hahn, "Optimal design method for microwave device using time domain method and design sensitivity analysis : II. FDTD case," IEEE Trans. Magn. 37, 3255-3259 (2001)
[CrossRef]

Microwave Theory and Techniques, IEEE Transactions on (1)

Y. S. Chung, C. Cheon, I. H. Park, and S. Y. Hahn, "Optimal design method for microwave device using FDTD and design sensitivity analysis," IEEE Trans. MTT. 48, 2289-2296 (2000)
[CrossRef]

Structural and Multidisciplinary Optimization (1)

M. P. Bendsoe, "Optimal shape design as a material distribution problem," Structural Optimization 1, 193-202 (1989)
[CrossRef]

Other (6)

A. Taflove, Computational Electrodynamics: The Finite-Difference Time-domain Method (Artech House, Boston, USA, 1995)

C. A Balanis, Antenna Theory: Analysis and Design (John Wiley & Sons, Singapore, 1982)

H. Jasik, Antenna Engineering Handbook (McGraw- Hill, New York, USA, 1961)

E. J. Haug, K. K. Choi, and V. Komkov, Design Sensitivity Analysis of Structural System (Academic Press, New York, USA, 1986)

H. Lee, "Computer aided optimal design methods for waveguide structures," Ph.D. Dissertation, Seoul National University (1995)

D. S. Katz, "FDTD modeling of dielectric lens," http://pat.jpl.nara.gov/public/dsk/FDTD (1998)

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