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## Physical optics modeling of 2D dielectric lenses

Vladimir B. Yurchenko and Ayhan Altintas »View Author Affiliations

^{1,}

^{*}and Ayhan Altintas

^{2}

^{1}Institute of Radiophysics and Electronics, National Academy of Sciences of Ukraine, 12 Proskura St., 61085 Kharkov, Ukraine

^{2}Electrical and Electronics Engineering Department, Bilkent University, 06800 Bilkent, Ankara, Turkey

^{*}Corresponding author: v.yurchenko@nuim.ie

JOSA A, Vol. 26, Issue 2, pp. 305-312 (2009)

http://dx.doi.org/10.1364/JOSAA.26.000305

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### Abstract

We propose an advanced physical optics formulation for the accurate modeling of dielectric lenses used in quasi-optical systems of millimeter, submillimeter, and infrared wave applications. For comparison, we obtain an exact full-wave solution of a two-dimensional lens problem and use it as a benchmark for testing and validation of asymptotic models being considered.

© 2009 Optical Society of America

**OCIS Codes**

(080.3630) Geometric optics : Lenses

(220.3630) Optical design and fabrication : Lenses

(260.1960) Physical optics : Diffraction theory

(110.6795) Imaging systems : Terahertz imaging

**History**

Original Manuscript: August 20, 2008

Revised Manuscript: December 8, 2008

Manuscript Accepted: December 8, 2008

Published: January 27, 2009

**Citation**

Vladimir B. Yurchenko and Ayhan Altintas, "Physical optics modeling of 2D dielectric lenses," J. Opt. Soc. Am. A **26**, 305-312 (2009)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-26-2-305

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### References

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- M. N. O. Sadiku, Numerical Techniques in Electromagnetics (CRC, 1992).
- C. Muller, Foundations of the Mathematical Theory of Electromagnetic Waves (Springer-Verlag, 1969).
- D. W. Prather, M. S. Mirotznik, and J. N. Mait, “Boundary integral methods applied to the analysis of diffractive optical elements,” J. Opt. Soc. Am. A 14, 34-43 (1997). [CrossRef]
- G. Fikioris, “A note on the method of analytical regularization,” IEEE Antennas Propag. Mag. 43, 34-40 (2001). [CrossRef]
- S. V. Boriskina, P. Sewell, T. M. Benson, and A. I. Nosich, “Accurate simulation of two-dimensional optical microcavities with uniquely solvable boundary integral equations and trigonometric Galerkin discretization,” J. Opt. Soc. Am. A 21, 393-402 (2004). [CrossRef]
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- V. B. Yurchenko and A. Altintas, “Asymptotic wave-like modeling of dielectric lenses,” in Proceedings of the 6th International Conference on Antenna Theory and Techniques (ICATT 2007), 17-21 September 2007, Sevastopol, Ukraine, Y.S.Shifrin and N.N.Kolchigin, eds. (IEEE, 2007), pp. 93-98. [CrossRef]
- Y. Li and E. Wolf, “Focal shifts in diffracted converging spherical waves,” Opt. Commun. 39, 211-215 (1981). [CrossRef]

**Ade, P. A. R.**

- C. O'Sullivan, G. Cahill, J. A. Murphy, W. K. Gear, J. Harris, P. A. R. Ade, S. E. Church, K. L. Thompson, C. Pryke, J. Bock, M. Bowden, M. L. Brown, J. E. Carlstrom, P. G. Castro, T. Culverhouse, R. B. Friedman, K. M. Ganga, V. Haynes, J. R. Hinderks, J. Kovak, A. E. Lange, E. M. Leitch, O. E. Mallie, S. J. Melhuish, A. Orlando, L. Piccirillo, G. Pisano, N. Rajguru, B. A. Rusholme, R. Schwarz, A. N. Taylor, E. Y. S. Wu, and M. Zemcov, “The quasi-optical design of the QUaD telescope,” Infrared Phys. Technol. 51, 277-286 (2008).

**Altintas, A.**

- A. V. Boriskin, A. I. Nosich, S. V. Boriskina, T. M. Benson, P. Sewell, and A. Altintas, “Lens or resonator? Electromagnetic behavior of an extended hemielliptic lens for a submillimeter-wave receiver,” Microwave Opt. Technol. Lett. 43, 515-518 (2004). [CrossRef]
- V. B. Yurchenko and A. Altintas, “Asymptotic wave-like modeling of dielectric lenses,” in Proceedings of the 6th International Conference on Antenna Theory and Techniques (ICATT 2007), 17-21 September 2007, Sevastopol, Ukraine, Y.S.Shifrin and N.N.Kolchigin, eds. (IEEE, 2007), pp. 93-98. [CrossRef]

**Balanis, C. A.**

- C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, 1989).

**Benson, T. M.**

- S. V. Boriskina, P. Sewell, T. M. Benson, and A. I. Nosich, “Accurate simulation of two-dimensional optical microcavities with uniquely solvable boundary integral equations and trigonometric Galerkin discretization,” J. Opt. Soc. Am. A 21, 393-402 (2004). [CrossRef]
- A. V. Boriskin, A. I. Nosich, S. V. Boriskina, T. M. Benson, P. Sewell, and A. Altintas, “Lens or resonator? Electromagnetic behavior of an extended hemielliptic lens for a submillimeter-wave receiver,” Microwave Opt. Technol. Lett. 43, 515-518 (2004). [CrossRef]

**Bock, J.**

- C. O'Sullivan, G. Cahill, J. A. Murphy, W. K. Gear, J. Harris, P. A. R. Ade, S. E. Church, K. L. Thompson, C. Pryke, J. Bock, M. Bowden, M. L. Brown, J. E. Carlstrom, P. G. Castro, T. Culverhouse, R. B. Friedman, K. M. Ganga, V. Haynes, J. R. Hinderks, J. Kovak, A. E. Lange, E. M. Leitch, O. E. Mallie, S. J. Melhuish, A. Orlando, L. Piccirillo, G. Pisano, N. Rajguru, B. A. Rusholme, R. Schwarz, A. N. Taylor, E. Y. S. Wu, and M. Zemcov, “The quasi-optical design of the QUaD telescope,” Infrared Phys. Technol. 51, 277-286 (2008).

**Boriskin, A. V.**

**Boriskina, S. V.**

- S. V. Boriskina, P. Sewell, T. M. Benson, and A. I. Nosich, “Accurate simulation of two-dimensional optical microcavities with uniquely solvable boundary integral equations and trigonometric Galerkin discretization,” J. Opt. Soc. Am. A 21, 393-402 (2004). [CrossRef]

**Bowden, M.**

**Brown, M. L.**

**Cahill, G.**

**Carlstrom, J. E.**

**Castro, P. G.**

**Church, S. E.**

**Culverhouse, T.**

**Dong, B.-Z.**

- J.-S. Ye, B.-Y. Gu, B.-Z. Dong, and S.-T. Liu, “Application of improved first Rayleigh-Sommerfeld method to analyze the performance of cylindrical microlenses with different f-numbers,” J. Opt. Soc. Am. A 22, 862-869 (2005). [CrossRef]
- J.-S. Ye, B.-Z. Dong, B.-Y. Gu, G.-Z. Yang, and S.-T. Liu, “Analysis of a closed-boundary axilens with long focal depth and high transverse resolution based on rigorous electromagnetic theory,” J. Opt. Soc. Am. A 19, 2030-2035 (2002). [CrossRef]

**Duan, K.**

**Fan, S.**

- D. Feng, Y. Yan, G. Jin, and S. Fan, “Axial focusing characteristics of diffractive microlenses based on a rigorous electromagnetic theory,” J. Opt. A, Pure Appl. Opt. 6, 1067-1071 (2004). [CrossRef]

**Feng, D.**

- D. Feng, Y. Yan, G. Jin, and S. Fan, “Axial focusing characteristics of diffractive microlenses based on a rigorous electromagnetic theory,” J. Opt. A, Pure Appl. Opt. 6, 1067-1071 (2004). [CrossRef]

**Fikioris, G.**

- G. Fikioris, “A note on the method of analytical regularization,” IEEE Antennas Propag. Mag. 43, 34-40 (2001). [CrossRef]

**Friedman, R. B.**

**Ganga, K. M.**

**Gear, W. K.**

**Gu, B.-Y.**

- J.-S. Ye, B.-Y. Gu, B.-Z. Dong, and S.-T. Liu, “Application of improved first Rayleigh-Sommerfeld method to analyze the performance of cylindrical microlenses with different f-numbers,” J. Opt. Soc. Am. A 22, 862-869 (2005). [CrossRef]
- J.-S. Ye, B.-Z. Dong, B.-Y. Gu, G.-Z. Yang, and S.-T. Liu, “Analysis of a closed-boundary axilens with long focal depth and high transverse resolution based on rigorous electromagnetic theory,” J. Opt. Soc. Am. A 19, 2030-2035 (2002). [CrossRef]

**Harris, J.**

**Haynes, V.**

**Hinderks, J. R.**

**Jin, G.**

**Kovak, J.**

**Lange, A. E.**

**Leitch, E. M.**

**Li, Y.**

- Y. Li and E. Wolf, “Focal shifts in diffracted converging spherical waves,” Opt. Commun. 39, 211-215 (1981). [CrossRef]

**Liu, S.-T.**

**Lu, B.**

**Mait, J. N.**

**Mallie, O. E.**

**Melhuish, S. J.**

**Mirotznik, M. S.**

**Muller, C.**

- C. Muller, Foundations of the Mathematical Theory of Electromagnetic Waves (Springer-Verlag, 1969).

**Murphy, J. A.**

**Nosich, A. I.**

**Orlando, A.**

**O'Sullivan, C.**

**Piccirillo, L.**

**Pisano, G.**

**Prather, D. W.**

**Pryke, C.**

**Rajguru, N.**

**Rusholme, B. A.**

**Sadiku, M. N. O.**

- M. N. O. Sadiku, Numerical Techniques in Electromagnetics (CRC, 1992).

**Schneider, M.**

- P. Wenig, M. Schneider, and R. Weigel, “Performance analysis of a cylindric dielectric lens antenna for 77 GHz Automotive Radar,” in Proceedings of International Radar Symposium (IRS 2008), 21-23 May 2008, Wroclaw, Poland, A.Kawalec and P.Kaniewski, eds. (Institute of Radioelectronics, 2008), paper B1-1.

**Schwarz, R.**

**Sewell, P.**

**Taylor, A. N.**

**Thompson, K. L.**

**Walther, A.**

- A. Walther, The Ray and Wave Theory of Lenses (Cambridge U. Press, 2006).

**Weigel, R.**

- P. Wenig, M. Schneider, and R. Weigel, “Performance analysis of a cylindric dielectric lens antenna for 77 GHz Automotive Radar,” in Proceedings of International Radar Symposium (IRS 2008), 21-23 May 2008, Wroclaw, Poland, A.Kawalec and P.Kaniewski, eds. (Institute of Radioelectronics, 2008), paper B1-1.

**Wenig, P.**

**Wolf, E.**

- Y. Li and E. Wolf, “Focal shifts in diffracted converging spherical waves,” Opt. Commun. 39, 211-215 (1981). [CrossRef]

**Wu, E. Y. S.**

**Yan, Y.**

**Yang, G.-Z.**

**Ye, J.-S.**

**Yurchenko, V. B.**

- V. B. Yurchenko and A. Altintas, “Asymptotic wave-like modeling of dielectric lenses,” in Proceedings of the 6th International Conference on Antenna Theory and Techniques (ICATT 2007), 17-21 September 2007, Sevastopol, Ukraine, Y.S.Shifrin and N.N.Kolchigin, eds. (IEEE, 2007), pp. 93-98. [CrossRef]

**Zemcov, M.**

### IEEE Antennas Propag. Mag.

- G. Fikioris, “A note on the method of analytical regularization,” IEEE Antennas Propag. Mag. 43, 34-40 (2001). [CrossRef]

### Infrared Phys. Technol.

### J. Opt. A, Pure Appl. Opt.

### J. Opt. Soc. Am. A

- D. W. Prather, M. S. Mirotznik, and J. N. Mait, “Boundary integral methods applied to the analysis of diffractive optical elements,” J. Opt. Soc. Am. A 14, 34-43 (1997). [CrossRef]
- K. Duan and B. Lu, “Improved diffraction integral for studying the diffracted field of a spherical microlens,” J. Opt. Soc. Am. A 22, 2677-2681 (2005). [CrossRef]

### Microwave Opt. Technol. Lett.

### Opt. Commun.

### Other

- M. N. O. Sadiku, Numerical Techniques in Electromagnetics (CRC, 1992).
- C. Muller, Foundations of the Mathematical Theory of Electromagnetic Waves (Springer-Verlag, 1969).
- A. Walther, The Ray and Wave Theory of Lenses (Cambridge U. Press, 2006).
- C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, 1989).

**2008, O'Sullivan, Infrared Phys. Technol.**

**2005, Ye, J. Opt. Soc. Am. A**

**2005, Duan, J. Opt. Soc. Am. A**

**2004, Feng, J. Opt. A, Pure Appl. Opt.**

**2004, Boriskin, Microwave Opt. Technol. Lett.**

**2004, Boriskina, J. Opt. Soc. Am. A**

**2002, Ye, J. Opt. Soc. Am. A**

**2001, Fikioris, IEEE Antennas Propag. Mag.**

**1997, Prather, J. Opt. Soc. Am. A**

**1981, Li, Opt. Commun.**

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