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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 2 — Jan. 19, 2009
  • pp: 598–602
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Polarization dependent devices realized by using asymmetrical hole array on a metallic film

Shaoyun Yin, Chongxi Zhou, Xiaochun Dong, and Chunlei Du  »View Author Affiliations


Optics Express, Vol. 17, Issue 2, pp. 598-602 (2009)
http://dx.doi.org/10.1364/OE.17.000598


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Abstract

A method is brought forward for realizing polarization dependent devices by employing sub-wavelength asymmetrical hole array on a metallic film. Based on the fundamental mode approximation, the phase retardations of rectangular hole for two orthogonal polarization incident waves are analyzed and calculated. Using rectangular hole array, a bifocal-polarization lens for the infrared radiation with 10.6μm wavelength is designed. Its focal lengths for x- and y- polarized incident wave are examined by the finite difference time domain (FDTD) method and the Rayleigh-Sommerfeld diffraction integrals and the obtained results agree well with the designed values.

© 2009 Optical Society of America

1. Introduction

Polarization technology is an important branch of optical technology. Polarization dependent devices such as polarizer, beam splitter and phase retarder are widely used in the fields of optical detecting [1

1. F. Cremer, W. de Jong, and K. Schutte, “Infrared polarization measurements and modeling applied to surface-laid antipersonnel landmines,” Opt. Eng. 41, 1021–1032 (2002). [CrossRef]

], beam shaping [2

2. B. Hao and J. Leger, “Polarization beam shaping,” App. Opt. 46, 8211–8217 (2007). [CrossRef]

] and information reading-writing [3

3. G. Martinez-Ponce, T. Petrova, N. Tomova, V. Dragostnova, T. Todorov, and L. Nikolova, “Bifocal-polarization holographic lens,” Opt. Lett. 29, 1001–1003 (2004). [CrossRef] [PubMed]

]. However, traditional polarization dependent devices have several deficiencies. First of all, the devices employing the double refraction effect of birefringent crystals are usually big and relatively heavy [4

4. K. Takano, M. Saito, and M. Miyagi, “Cube polarizers by the use of metal particles in anodic alumina films,” App. Opt. 33, 3507–3512 (1994). [CrossRef]

]. Secondly, in region of the infrared radiation, it is difficult to find suitable birefringent crystal. Except a kind of line grid polarizer has been used extensively for a long time [5

5. G. R. Bird and M. Parrish Jr., “The wire grid as a near-infrared polarizer,” J. Opt. Soc. Am. , 50, 886–891 (1960). [CrossRef]

], other polarization dependent devices are rarely reported.

2. Design method

The polarization characters of a rectangular hole can be determined by solving the Helmholtz equation. Considering a rectangular hole with sides ax and ay perforated on the metallic film with thickness h, if h>λo, and λo/2<ax, ay.<λo, (here, λo is the incident wavelength) the first order TE guide mode will dominate the transmitted energy [8

8. J. M. Brok and H. P. Urbach, “Extraordinary transmission through 1, 2 and 3 holes in a perfect conductor, modelled by a mode expansion technique,” Opt. Express. 14, 2552–2572 (2006). [CrossRef] [PubMed]

]. In this paper, metals are treated within the perfect conductor approximation (PCA), so our results are qualitatively accurate in the far-infrared to microwave frequency regime [9–11

9. L. Martin-Moreno and F. J. Garcia-Vidal, “Optical transmission through circular hole arrays in optically thick metal films,” Opt. Express. 12, 3619–3628 (2004). [CrossRef]

]. Combining the Helmholtz equation with the PCA, the electric field in the hole can be derived and expressed as:

E(x,y.z)=Axx̂0sin(πy/ay)exp(izk02π2/ay2)+Ayŷ0sin(πx/ax)exp(izk02π2/ax2)
(1)

Where ko is the wave vector of the incident wave, xo, yo are the unit vectors of x, y directions, and Ax, Ay are the magnitudes of the TE01 and TE10 guide modes in the rectangular hole. From Eq. (1), the phase retardations for these two guide modes after they get through the hole can be obtained as:

φx=hk02π2/ay2
(2)
φy=hk02π2/ax2
(3)

These two equations indicate that the phase of the transmitted electric field can be modulated by varying the sides or depth of the hole. Based on the design regulation of traditional diffractive optical devices, when the phase modulated scope can cover the range of 2π, the considered structures will be suitable for realizing phase modulation devices. Figure 1 gives the phase retardation as a function of the side for different film thicknesses obtained from Eqs. (2) and (3). In order to guarantee the 2π phase modulation ability, it can be seen that the hole should be deeper than 2/√3 λ 0. The figure also shows that the phase retardation is quite sensitive to the sides of the hole when the hole’s sides are close to 0.5λo, which is disadvantageous for the practical structure fabrication since it would require a rigorous fabrication tolerance. By this consideration, the minimum side is selected being larger than 0.5λo in our design.

Fig. 1. The phase retardation of the first order TE mode varies as a function of its related side a for a rectangular hole on the metallic film with various thicknesses.

3. Design example

A bifocal lens with two focal planes for different polarizations of the incident light was designed as an example by our approach. The incident light is in the infrared range with wavelength of 10.6μm. As we know, the perfect conductor approximation will invalidate if the dimensions of the structure can compare to the skin depth [20

20. J. R. Sucklinget al, “Finite conductance governs the resonance transmission of thin metal slits at Microwave Frequencies,” Phys. Rev. Lett. 92, 147201 (2004). [CrossRef]

]. In our case, the refractive index of a typical metal Au is about 12.5+55i at the wavelength of 10.6μm[21

21. D. W. Lynch and W. R. Hunter, Handbook of Optical constants of solids, (Academic Press, Palik, E. D., ed., New York, 1985).

], the calculated skin depth is only 0.064μm which is very small comparing to the dimension of the hole-structure. Therefore, it is reasonable to take the metal film as a perfect conductor. The lens consists of square latticed rectangular holes with period of λo on the metallic film with thickness of 1.8 λo. Its aperture is 280μm and its focal length for the x-polarized incident plane wave is 200 μm, for the y-polarized incident plane wave is 150μm. The structure of this bifocal lens and the definition of coordinate are shown as Fig. 2(a).

Fig. 2. (a). Diagram of the metallic bifocal-polarization lens; (b) the corresponding phase retardation functions for y- and x- polarized incidence of the holes in the frame formed by white-dotted line in Fig. 2(a).

For the lens with focal length f, the phase difference φ(r) between the center of the structure and the location r away from the center can be determined by the following expression:

φ(r)=2mπ+2π(r2+f2f)/λ0
(4)

Here an integer m is properly set to guarantee the phase modulation scope being in the range (π, 3π) (see Fig. 1). When 3π phase retardation is taken in the center of the designed bifocal lens, the obtained sides of the rectangular hole is in the range (0.52λo, 0.905 λo). Figure 2(b) shows the phase retardation for the holes at the line crossing through the lens’ center parallel to x axis. In this figure the continuous curve represents the phase distribution of an ideal lens with equivalent focal length; each red point on the curve is the phase corresponding to a rectangular hole. The abscissa represents its location and the ordinate of it represents its phase retardation. It should be noticed that the sketch map Fig. 2(a) shows only part of the holes in the designed bifocal lens.

After all the parameters were determined, we calculated the intensity distribution of the electric field behind the lens by carrying out the following two steps: Firstly, the electric field on the plane 1 μm away from the metallic film was obtained by finite difference time domain (FDTD) method. Then the electric field behind this plane was calculated by Rayleigh-Sommerfeld diffraction integrals. In the FDTD simulation, the incident is the plane wave with unit amplitude. Considering the difference in the side lengths among the holes generally being larger than 0.1 μm, the grids in xy plane are specified to be 0.1 μm; while in the z direction, since the thickness is constant, the grid length is specified to be 0.4μm. Figure 3 gives the intensity distribution of the electric field behind the bifocal lens for x- and y- polarized incident plane wave respectively. If we define the location of the brightest point on the z axis as the location of the focus, the focal length for x polarization will be 195μm, the relative error is -2.5%; for y polarization, 146μm, corresponding to relative error -2.7%. This discrepancy is consistent with the precision of our FDTD calculation and the near-far field transformation.

Fig. 3. The intensity (E 2) distribution of electric field behind the bifocal lens for x- and y-polarized incident plane wave respectively. (a) and (c) are the intensity for y=0 and z from 100μm to 250μm; (b) and (d) are the intensity distribution on the optical axis for z from 100μm to 250μm;

The spot size in the focal plane (z=200μm for x polarization and z=150μm for y polarization) can be obtained from Fig. 3. The results indicate that for x-polarization, the full-width of half-maximum (FWHM) of the focus is 10.1 μm; for y-polarization, the FWHM of the focus is about 8.5μm. While the radius of the Airy disk of traditional lenses with the same aperture and focal lengths are 9.2μm and 6.9μm. We can see that the spot sizes are close to the diffractive limitation.

The calculation results show good consistence with the designed values. For the reason that this kind of devices is formed by sub-wavelength hole array on thin metal film and by using only one piece of it complex phase modulation functions can be realized. Equipments using it will naturally owe the virtues of light weight and high compactness. Moreover, its design and manufacture are simple than the traditional polarization sensitive optical devices, and it is suitable for infrared regime where the polarization sensitive devices is hard to be achieved due to the lack of usable birefringent crystals. All of these make us believe that this kind of devices will provide great potential for polarization involved applications.

4. Conclusion

In conclusion, a method has been introduced to achieve polarization dependent devices by using asymmetrical hole arrays on metallic film. In order to testify this method, we designed a bifocal lens used for 10.6μm incident wavelength and the phase modulation ability of it was studied by using numerical method. The calculation results show that this device not only possesses the designed polarization properties, it also bears the perfect focusing properties for the focus sizes on both focal planes are close to the diffraction limitation. Hence this method opens an avenue to realize various polarization dependent devices with light weight and high compactness.

This work was supported by 863 Program(2007AA03Z332),973Program (2006CB302900) of China and the Chinese Nature Science Grant (60678035, 60727006). The authors thank Haofei Shi, Lifang Shi and Qiling Deng for their kind contributions to the work.

References and links

1.

F. Cremer, W. de Jong, and K. Schutte, “Infrared polarization measurements and modeling applied to surface-laid antipersonnel landmines,” Opt. Eng. 41, 1021–1032 (2002). [CrossRef]

2.

B. Hao and J. Leger, “Polarization beam shaping,” App. Opt. 46, 8211–8217 (2007). [CrossRef]

3.

G. Martinez-Ponce, T. Petrova, N. Tomova, V. Dragostnova, T. Todorov, and L. Nikolova, “Bifocal-polarization holographic lens,” Opt. Lett. 29, 1001–1003 (2004). [CrossRef] [PubMed]

4.

K. Takano, M. Saito, and M. Miyagi, “Cube polarizers by the use of metal particles in anodic alumina films,” App. Opt. 33, 3507–3512 (1994). [CrossRef]

5.

G. R. Bird and M. Parrish Jr., “The wire grid as a near-infrared polarizer,” J. Opt. Soc. Am. , 50, 886–891 (1960). [CrossRef]

6.

Y. Chen, C. Zhou, X. Luo, and C. Du, “Structured lens formed by a 2D square hole array in a metallic film,” Opt. Lett. 33, 753–755 (2008). [CrossRef] [PubMed]

7.

S. Yin, C. Zhou, X. Luo, and C. Du, “Imaging by a sub-wavelength metallic lens with large field of view,” Opt. Express. 16, 2578–2583 (2008). [CrossRef] [PubMed]

8.

J. M. Brok and H. P. Urbach, “Extraordinary transmission through 1, 2 and 3 holes in a perfect conductor, modelled by a mode expansion technique,” Opt. Express. 14, 2552–2572 (2006). [CrossRef] [PubMed]

9.

L. Martin-Moreno and F. J. Garcia-Vidal, “Optical transmission through circular hole arrays in optically thick metal films,” Opt. Express. 12, 3619–3628 (2004). [CrossRef]

10.

Z. Wang, C. T. Chan, W. Zhang, N. Ming, and P. Sheng, “Three-dimensional self-assembly of metal nanoparticles: possible photonic crystal with a complete gap below the plasma frequency,” Phys. Rev. B 64, 113108 (2001). [CrossRef]

11.

G. Shvets, S. Trendafilov, J. B. Pendry, and A. Sarychev, “Guiding, focusing and sensing on the subwavelength scale using metallic wire arrays,” Phys. Rev. Lett. 99, 053903 (2007). [CrossRef] [PubMed]

12.

H. M. Barlow and A. L. Cullen, “Surface waves,” Proc. IEE 100, 329–347 (1953).

13.

R. Collin, Field Theory of Guided Waves (Wiley, New York, ed. 2, 1990). [CrossRef]

14.

A. P. Hibbins, B. R. Evans, and J. R. Sambles, “Experimental verification of designer surface plasmons,” Sci. 308, 670–672 (2005). [CrossRef]

15.

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Sci. 305, 847–848 (2004). [CrossRef]

16.

M. Beruete, M. Sorolla, I. Campillo, J. S. Dolado, and L. Martin-Moreno, “Enhanced millimeter-wave transmission through subwavelength hole arrays,” Opt. Lett. 29, 2500–2502 (2004). [CrossRef] [PubMed]

17.

F. J. Garcia de Abajo, J. J. Saenz, I. Campillo, and J. S. Dolado, “Site and lattice resonances in metallic hole arrays,” Opt. Express. 14, 7–18 (2006). [CrossRef] [PubMed]

18.

H. Cao and A. Nahata, “Resonantly enhanced transmission of terahertz radiation through a periodic array of subwavelength apertures,” Opt. Express. 12, 1004–1010 (2004). [CrossRef] [PubMed]

19.

F. J. Garcia De Abajo, R. Gomez-Medina, and J. J. Saenz, “Full transmission through perfect-conductor subwavelength hole arrays,” Phys. Rev. E 72, 016608 (2005). [CrossRef]

20.

J. R. Sucklinget al, “Finite conductance governs the resonance transmission of thin metal slits at Microwave Frequencies,” Phys. Rev. Lett. 92, 147201 (2004). [CrossRef]

21.

D. W. Lynch and W. R. Hunter, Handbook of Optical constants of solids, (Academic Press, Palik, E. D., ed., New York, 1985).

OCIS Codes
(050.1970) Diffraction and gratings : Diffractive optics
(260.3060) Physical optics : Infrared
(260.3910) Physical optics : Metal optics
(260.5430) Physical optics : Polarization
(310.0310) Thin films : Thin films

ToC Category:
Physical Optics

History
Original Manuscript: November 11, 2008
Revised Manuscript: December 15, 2008
Manuscript Accepted: December 20, 2008
Published: January 7, 2009

Citation
Shaoyun Yin, Congxi Zhou, Xiaochun Dong, and Chunlei Du, "Polarization dependent devices realized by using asymmetrical hole array on a metallic film," Opt. Express 17, 598-602 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-2-598


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References

  1. F. Cremer, W. de Jong, and K. Schutte, "Infrared polarization measurements and modeling applied to surface-laid antipersonnel landmines," Opt. Eng. 41, 1021-1032 (2002). [CrossRef]
  2. B. Hao and J. Leger, "Polarization beam shaping," App. Opt. 46, 8211-8217 (2007). [CrossRef]
  3. G. Martinez-Ponce, T. Petrova, N. Tomova, V. Dragostnova, T. Todorov, and L. Nikolova, "Bifocal-polarization holographic lens," Opt. Lett. 29, 1001-1003 (2004). [CrossRef] [PubMed]
  4. K. Takano, M. Saito, and M. Miyagi, "Cube polarizers by the use of metal particles in anodic alumina films," App. Opt. 33, 3507-3512 (1994). [CrossRef]
  5. G. R. Bird and M. ParrishJr., "The wire grid as a near-infrared polarizer," J. Opt. Soc. Am. 50, 886-891 (1960). [CrossRef]
  6. Y. Chen, C. Zhou, X. Luo, and C. Du, "Structured lens formed by a 2D square hole array in a metallic film," Opt. Lett. 33, 753-755 (2008). [CrossRef] [PubMed]
  7. S. Yin, C. Zhou, X. Luo, and C. Du, "Imaging by a sub-wavelength metallic lens with large field of view," Opt. Express. 16, 2578-2583 (2008). [CrossRef] [PubMed]
  8. J. M. Brok and H. P. Urbach, "Extraordinary transmission through 1, 2 and 3 holes in a perfect conductor, modelled by a mode expansion technique," Opt. Express. 14, 2552-2572 (2006). [CrossRef] [PubMed]
  9. L. Martin-Moreno and F. J. Garcia-Vidal, "Optical transmission through circular hole arrays in optically thick metal films," Opt. Express. 12, 3619-3628 (2004). [CrossRef]
  10. Z. Wang, C. T. Chan, W. Zhang, N. Ming, and P. Sheng, "Three-dimensional self-assembly of metal nanoparticles: possible photonic crystal with a complete gap below the plasma frequency," Phys. Rev. B 64, 113108 (2001). [CrossRef]
  11. G. Shvets, S. Trendafilov, J. B. Pendry, and A. Sarychev, "Guiding, focusing and sensing on the subwavelength scale using metallic wire arrays," Phys. Rev. Lett. 99, 053903 (2007). [CrossRef] [PubMed]
  12. H. M. Barlow and A. L. Cullen, "Surface waves," Proc. IEE 100, 329-347 (1953).
  13. R. Collin, Field Theory of Guided Waves (Wiley, New York, ed. 2, 1990). [CrossRef]
  14. A. P. Hibbins, B. R. Evans, and J. R. Sambles, "Experimental verification of designer surface plasmons," Science 308, 670-672 (2005). [CrossRef]
  15. J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, "Mimicking surface plasmons with structured surfaces," Science 305, 847-848 (2004). [CrossRef]
  16. M. Beruete, M. Sorolla, I. Campillo, J. S. Dolado and L. Martin-Moreno, "Enhanced millimeter-wave transmission through subwavelength hole arrays," Opt. Lett. 29, 2500-2502 (2004). [CrossRef] [PubMed]
  17. F. J. Garcia de Abajo, J. J. Saenz, I. Campillo, and J. S. Dolado, "Site and lattice resonances in metallic hole arrays," Opt. Express. 14, 7-18 (2006). [CrossRef] [PubMed]
  18. H. Cao and A. Nahata, "Resonantly enhanced transmission of terahertz radiation through a periodic array of subwavelength apertures," Opt. Express. 12, 1004-1010 (2004). [CrossRef] [PubMed]
  19. F. J. Garcia De Abajo, R. Gomez-Medina, and J. J. Saenz, "Full transmission through perfect-conductor subwavelength hole arrays," Phys. Rev. E 72, 016608 (2005). [CrossRef]
  20. J. R. Suckling et al, "Finite conductance governs the resonance transmission of thin metal slits at Microwave Frequencies," Phys. Rev. Lett. 92, 147201 (2004). [CrossRef]
  21. D. W. Lynch and W. R. Hunter, Handbook of Optical constants of solids (Academic Press, Palik, E. D., ed., New York, 1985).

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