OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 4 — Feb. 25, 2013
  • pp: 4228–4234
« Show journal navigation

Experimental study on a resonance mesh coating fabricated using a UV-lithography technique

Yongmeng Liu and Jiubin Tan  »View Author Affiliations


Optics Express, Vol. 21, Issue 4, pp. 4228-4234 (2013)
http://dx.doi.org/10.1364/OE.21.004228


View Full Text Article

Acrobat PDF (1604 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

In order to achieve high optical transparency and Ka-band bandpass filtering simultaneously, a resonance mesh coating sample is fabricated using a UV-lithography technique. Optical transmission is measured using an Ocean Optics QE65000 spectrometer. And Ka-band bandpass filtering is measured using an Agilent E8363B PNA series network analyzer. Experimental results indicate that the optical transmission of the resonance mesh coating is 63.4% higher than that of non-meshed Frequency Selective Surfaces (FSS) with equivalent aperture parameters, and the transmittance loss of the coating is lower than 0.21 dB while the coating has a Ka-band resonance frequency of 32 GHz. It can therefore be concluded that the resonance mesh coating can be used as a dual-mode spatial filter to achieve high optical transparency and Ka-band bandpass filtering.

© 2013 OSA

1. Introduction

Electromagnetic interference (EMI) is a very strong consideration in designing windows and domes for space observation and communication [1

1. J. C. Kirsch, W. R. Lindberg, D. C. Harris, M. J. Adcock, T. P. Li, E. A. Welsh, and R. D. Adkins, “Tri-mode seeker dome considerations,” Proc. SPIE 5786, 33–40 (2005). [CrossRef]

]. Electromagnetic shielding is done for optical sensors using conductive metal meshes [2

2. M. Kohin, S. J. Wein, J. D. Traylor, R. C. Chase, and J. E. Chapman, “Analysis and design of transparent conductive coatings and filters,” Opt. Eng. 32(5), 911–925 (1993). [CrossRef]

5

5. J. I. Halman, K. A. Ramsey, M. Thomas, and A. Griffin, “Predicted and measured transmission and diffraction by a metallic mesh coating,” Proc. SPIE 7302, 73020Y1 (2009).

]. Electromagnetic shielding of microwave sensors is provided by bandpass Frequency Selective Surfaces (FSS) which block all but a pass band around the frequency of interest [6

6. S. A. Kuznetsov, M. Navarro-Cía, V. V. Kubarev, A. V. Gelfand, M. Beruete, I. Campillo, and M. Sorolla, “Regular and anomalous extraordinary optical transmission at the THz-gap,” Opt. Express 17(14), 11730–11738 (2009). [CrossRef] [PubMed]

,7

7. B. A. Munk, Frequency Selective Surfaces: Theory and Design (John Wiley and Sons, 2000).

]. None of these approaches can be easily applied to these optics/microwave dual-mode detection windows to achieve high optical transparency and microwave bandpass filtering and to provide shielding at out-of-band microwave/radio frequencies because metal meshes block the microwave signal and FSS cause very low optical transmittance. It is therefore of great significance to develop a conductive coating which can be used to achieve high optical transmission and stable microwave bandpass.

This problem can be resolved by creating a resonance cavity coating. This coating is a periodic array of apertures removed from high optical transparent conductive meshes [8

8. H. X. Zhu, X. G. Feng, J. L. Zhao, F. C. Liang, Y. S. Wang, X. Chen, and J. S. Gao “Design of antireflection and bandpass frequency selective surface combining coatings for ZnS optical window,” Acta Opt. Sin. 30(9), 2766–2770 (2010). [CrossRef]

]. And it behaves like a bandpass filter. This coating can be tuned to cover the frequencies for Ka-band (26-40GHz), but it does not degrade the optical transparency of an optical window. So a resonance mesh coating is developed by combining metallic meshes with bandpass FSS as a dual-mode spatial filter. A resonance mesh sample is fabricated using a UV-lithography technique, and an experimental study is done with the sample.

2. Structural description and fabrication of a resonance mesh coating

As shown in Fig. 1
Fig. 1 Unit cell of transparency conductive resonance mesh coating.
, the resonance mesh coating is a periodic array with square-loop apertures removed from transparent conductive metal meshes consisting of periodic sub-millimetric square apertures and fine metal grids. The period and linewidth of transparent conductive metal meshes are g and 2a, and the FSS period, outer and inner side lengths of the square-loop aperture are m1g, m2g and m3g respectively.

The square-loop aperture FSS resonates when its average circumference equals a multiple of the vacuum wavelength, so the outer side length and inner side length of square-loop apertures are 3 mm and 2 mm respectively.

As shown in Fig. 2
Fig. 2 Micrograph of transparency conductive resonance mesh sample.
, the resonance mesh sample consists of a titanium bonding layer of 50 nm thick and an aluminum layer of 950 nm thick and a quartz glass window substrate with an antireflective coating. The metal mesh has a period of 250 μm and a linewidth of 10 μm, FSS has a period of 4 mm and outer and inner side lengths of square-loop aperture of 3 mm and 2 mm respectively.

3. Theoretical modeling and experimental validity

3.1 Optical transmission analysis and experiments

Metal meshes behave as diffractive gratings at optical frequencies, and so, they produce diffracted orders. The effect of metal losses is negligible because the induced current of mesh coating is very slight. The optical diffraction and transmission of a resonance mesh coating is modeled and predicted using scalar optical diffraction theory. The optical point spread function (PSF) of an optical system is given by the modulus squared of the Fourier transform of a pupil function. The pupil transmittance functions for an optical system with conversation square-loop aperture FSS t1(x, y), periodic metal meshes t2(x, y) and a resonance mesh coating t3(x, y) in the pupil can be obtained using Eqs. (1), (2) and (3) respectively.
t1(x,y)=rect(xm2g,ym2g)rect(xm3g,ym3g),
(1)
t2(x,y)=rect(xg2a,yg2a)**m1n1δ(xm1g,yn1g),
(2)
t3(x,y)=t1(x,y)+t2(x,y,m1)t2(x,y,m2)+t2(x,y,m3),
(3)
where ** is a two dimensional convolution, and rect(x,y) is a two dimensional rectangular transmittance function [9

9. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill Companies Inc., 1996).

].

To find the performance degradation caused by the use of conventional square-loop aperture FSS, periodic metal meshes and a resonance mesh coating, the irradiance distribution of PSFs is normalized to the peak irradiance of the PSF with a square aperture entrance pupil with an area of (m1g)2 in the optical imaging system. Then the normalized diffraction distribution of PSF for the system with conventional square-loop aperture FSS, periodic metal meshes and a resonance mesh coating can be obtained using Eqs. (4), (5) and (6) respectively.
I1(θx,θy)=(m2m1)4sinc2(πm2gθxλ)sinc2(πm2gθyλ)(m3m1)4sinc2(πm3gθxλ)sinc2(πm3gθyλF),
(4)
I2(θx,θy)=(g2a)4g4m=1m1n=1m1sinc2[m(g2a)g]sinc2[n(g2a)g]×sinc2[m1gλ(θxmλg)]sinc2[m1gλ(θynλg)],
(5)
I3(θx,θy)=I1(θx,θy)+I2(θx,θy,m1)I2(θx,θy,m2)+I2(θx,θy,m3),
(6)
where θx and θy are the Fourier frequencies along axis x and y respectively, and λ is the optical wavelength and λ = 0.6328 μm. The normalized PSF of a resonance mesh coating is simulated and shown in Fig. 3
Fig. 3 Normalized PSF of transparency conductive resonance mesh coating.
using the analytical models above.

Figure 3 shows that the conductive resonance mesh coating generates multiple diffracted orders at angles θx and θy, and the shape of each diffracted order is similar to that of the PSF of non-meshed FSS. For imaging quality, only the zero-order optical diffracted energy of a mesh coating is useful, and all the others higher-order energies will increase the level of stray light and degrade the optical imaging. So we compare the improvement of the zero-order optical transmission in Fig. 4
Fig. 4 Comparison of zero-order optical transmission of resonance mesh coating and bandpass FSS with equivalent aperture parameters.
.

It can be seen from Fig. 4 that the zero-order optical transmittance of the resonance mesh coating has been remarkable improved. The zero-order optical transmission of the non-meshed FSS is 25.4%, and that of the resonance mesh coating proposed with equivalent aperture parameters is 88.8%, there is an increase of 63.4%, which is equivalent to the square of the increased open areas of metallic grids. So the enhancement in the zero-order optical transmission results from the increase in the open areas of metallic grids. The zero-order optical transmittance increases as the linewidth of mesh decreases and/or as the period of mesh increases. In other words, the zero-order optical transmission increases as the ratio between open areas and metallic line areas increases.

The optical transmittance of the resonance mesh sample is measured using an optical transmittance measurement system in an optical waveband ranging from 400 nm to 900 nm to verify the feasibility of high optical transparency and the validity of the analytical models above. The optical transmittance measurement setup consists of an Ocean Optics QE65000 spectrometer with a quantum efficiency of 90% and a signal-to-noise ratio of 1000:1, an optical source of D3100 Tritium Tungsten Lamp and a collimating objective lens. The measurements are as shown in Fig. 5
Fig. 5 Measurement results of optical transmittance of resonance mesh sample.
below.

It can be seen from Fig. 5 that the measurement results of optical transmission of the resonance mesh coating sample are between 88.5% and 89.1%. So the measurement results agree well with the simulation results, which verify the feasibility of high optical transparency and the validity of the optical transmittance analytical models.

3.2 Ka-band bandpass filtering performance analysis and experiments

A resonance mesh coating behaves like a bandpass filter in Ka-band radar frequency band [10

10. R. Ulrich, “Far-infrared properties of metallic mesh and its complementary structure,” Infrared Phys. 7(1), 37–55 (1967). [CrossRef]

12

12. K. T. Jacoby, M. W. Pieratt, J. I. Halman, and K. A. Ramsey, “Predicted and measured EMI shielding effectiveness of a metallic mesh coating on a sapphire window over a broad frequency range,” Proc. SPIE 7302,73020X1 (2009).

]. In order to study the difference of Ka-band transmittance and resonance frequency, the Ka-band bandpass filtering characteristics of the non-meshed FSS and the resonance mesh coating sample are analyzed using finite element method. Firstly, the periodic structure of a bandpass FSS is reduced to a unit cell using linked boundary conditions to replicate the infinite lattice; then the incoming plane is set up under normal incidence, and the polarization direction of the incoming wave is parallel to axis x; and the perfectly matched layer is set up under the FSS layer to absorb reflected waves but allow incident waves through.

Figure 6
Fig. 6 Surface induced current distribution maps at resonance frequency of non-meshed FSS (a) and conductive resonant mesh coating (b) with equivalent aperture parameters.
shows that the induced current of non-meshed FSS has a gradient distribution along the incidence direction of axis x. The maximum current is induced on the metal edge around the square-loop aperture. The maximum current of the conductive resonance mesh coating is induced on the metal lines around the square-loop aperture. And the induced electron density in a unit cell of the conductive resonance mesh coating is lower than that of the non-meshed FSS with equivalent aperture parameters. So the resonance frequency of the conductive resonance mesh coating is shifted downwards to a lower frequency due to the reduction of the induced electron density in a unit cell from the view point of plasma frequency [13

13. J. F. Zhang, J. Y. Ou, N. Papasimakis, Y. F. Chen, K. F. Macdonald, and N. I. Zheludev, “Continuous metal plasmonic frequency selective surfaces,” Opt. Express 19(23), 23279–23285 (2011). [CrossRef] [PubMed]

, 14

14. L. K. Sun, H. F. Cheng, Y. J. Zhou, and J. Wang, “Broadband metamaterial absorber based on coupling resistive frequency selective surface,” Opt. Express 20(4), 4675–4680 (2012). [CrossRef] [PubMed]

].

The simulation results of transmittance in a frequency band ranging from 6 to 40 GHz are as shown in Fig. 7(a)
Fig. 7 Simulations (a) and measurements (b) of Ka-band transmittance of resonance mesh coating and non-meshed FSS with equivalent aperture parameters.
. And we measured the Ka-band bandpass filtering characteristics of the resonance mesh sample using a microwave transmittance measurement system to verify the feasibility of Ka-band bandpass filtering and the validity of the simulation results. The microwave transmittance measurement system consists of an Agilent E8363B PNA series network analyzer, a transmitter antenna, and a receiver antenna. The measurement system was calibrated before use and its measurement error was less than ± 1 dB. The measurements are as shown in Fig. 7(b) below.

It can be seen from Fig. 7 that the resonance frequency of the conductive resonance mesh sample is 32 GHz, and its corresponding transmission loss is 0.21 dB. Meanwhile, the resonance frequency of the non-meshed FSS with equivalent aperture parameters is 32.5 GHz, and its corresponding transmission loss is 0.17 dB. The shift in resonance frequency and the attenuation of Ka-band transmission are 0.5 GHz and 0.04 dB respectively, and the difference of resonance frequency and Ka-band transmission between the resonance mesh coating and the non-meshed FSS is slight. And the measurement results agree well with the simulation results, which verify the feasibility of Ka-band bandpass filtering and the validity of the simulation results.

From the view point of transmission line model of FSS, the lumped circuit models of a non-meshed bandpass FSS is shown in Fig. 8(a)
Fig. 8 Lumped circuit models of non-meshed bandpass FSS (a) and resonance mesh coating (b).
, and LF, CF and RF are the corresponding equivalent inductor, capacitor and sheet resistance respectively. In a first approximation, the Ka-band transmission is dominated by sheet impedance, and the resonance frequency fr is dominated by a LFCF tank, whereas the losses by RF sheet resistance [15

15. P. E. Ciddor and L. B. Whitbourn, “Equivalent thin film of a periodic metal grid,” Appl. Opt. 28(6), 1228–1230 (1989). [CrossRef] [PubMed]

18

18. C. S. R. Kaipa, A. B. Yakovlev, F. Medina, F. Mesa, C. A. M. Butler, and A. P. Hibbins, “Circuit modeling of the transmissivity of stacked two-dimensional metallic meshes,” Opt. Express 18(13), 13309–13320 (2010). [CrossRef] [PubMed]

]. As shown in Fig. 8(b), therefore, capacitance CM and resistor RM are incorporated into the lumped circuit model of the resonance mesh coating consideration for the meshing and the discontinuity of metal film and the increase in open area.

As shown in Fig. 8, the increase in equivalent capacitance from CF to (CF + CM) causes the shift of the resonant frequency, and the increase in equivalent sheet resistor from RF to (RF + RM) causes the losses and attenuation of the Ka-band transmission of the resonance mesh coating. So the resonance frequency shifts from 32.5 GHz downwards to 32GHz and the Ka-band transmission loss at resonance frequency increases from 0.17 dB to 0.21dB.

4. Conclusion

In conclusion, a conductive resonance mesh coating is fabricated by combining bandpass FSS with metallic meshes as a dual-mode spatial filter to achieve high optical transparency and Ka-band bandpass filtering simultaneously. Simulation and measurement results indicate that optical transmission of the resonance mesh coating is 63.4% higher than that of non-meshed FSS with equivalent aperture parameters, and the transmittance loss of the coating is lower than 0.21dB while the coating has a Ka-band resonance frequency of 32 GHz. It can therefore be concluded that the resonance mesh coating can be used as a dual-mode spatial filter to achieve high optical throughput and Ka-band bandpass filtering in a dual-mode detection system.

Acknowledgments

This work is funded by National Natural Science Foundation of China (Grant Nos. 61108052 and 61078049), China Postdoctoral Science Foundation (Grant No.20100481011) and special grade of the financial support from China Postdoctoral Science Foundation (Grant No.201104417), Hei Long Jiang Postdoctoral Foundation (Grant No. LBH-Z10123) and Fundamental Research Funds for the Central Universities (Grant No. HIT. NSRIF. 2010106).

References and links

1.

J. C. Kirsch, W. R. Lindberg, D. C. Harris, M. J. Adcock, T. P. Li, E. A. Welsh, and R. D. Adkins, “Tri-mode seeker dome considerations,” Proc. SPIE 5786, 33–40 (2005). [CrossRef]

2.

M. Kohin, S. J. Wein, J. D. Traylor, R. C. Chase, and J. E. Chapman, “Analysis and design of transparent conductive coatings and filters,” Opt. Eng. 32(5), 911–925 (1993). [CrossRef]

3.

C. I. Bright, “Electromagnetic shielding for electro-optical windows and domes,” Proc. SPIE 2286, 388–396 (1994). [CrossRef]

4.

J. B. Tan and Z. G. Lu, “Contiguous metallic rings: an inductive mesh with high transmissivity, strong electromagnetic shielding, and uniformly distributed stray light,” Opt. Express 15(3), 790–796 (2007). [CrossRef] [PubMed]

5.

J. I. Halman, K. A. Ramsey, M. Thomas, and A. Griffin, “Predicted and measured transmission and diffraction by a metallic mesh coating,” Proc. SPIE 7302, 73020Y1 (2009).

6.

S. A. Kuznetsov, M. Navarro-Cía, V. V. Kubarev, A. V. Gelfand, M. Beruete, I. Campillo, and M. Sorolla, “Regular and anomalous extraordinary optical transmission at the THz-gap,” Opt. Express 17(14), 11730–11738 (2009). [CrossRef] [PubMed]

7.

B. A. Munk, Frequency Selective Surfaces: Theory and Design (John Wiley and Sons, 2000).

8.

H. X. Zhu, X. G. Feng, J. L. Zhao, F. C. Liang, Y. S. Wang, X. Chen, and J. S. Gao “Design of antireflection and bandpass frequency selective surface combining coatings for ZnS optical window,” Acta Opt. Sin. 30(9), 2766–2770 (2010). [CrossRef]

9.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill Companies Inc., 1996).

10.

R. Ulrich, “Far-infrared properties of metallic mesh and its complementary structure,” Infrared Phys. 7(1), 37–55 (1967). [CrossRef]

11.

L. B. Whitbourn and R. C. Compton, “Equivalent-circuit formulas for metal grid reflectors at a dielectric boundary,” Appl. Opt. 24(2), 217–220 (1985). [CrossRef] [PubMed]

12.

K. T. Jacoby, M. W. Pieratt, J. I. Halman, and K. A. Ramsey, “Predicted and measured EMI shielding effectiveness of a metallic mesh coating on a sapphire window over a broad frequency range,” Proc. SPIE 7302,73020X1 (2009).

13.

J. F. Zhang, J. Y. Ou, N. Papasimakis, Y. F. Chen, K. F. Macdonald, and N. I. Zheludev, “Continuous metal plasmonic frequency selective surfaces,” Opt. Express 19(23), 23279–23285 (2011). [CrossRef] [PubMed]

14.

L. K. Sun, H. F. Cheng, Y. J. Zhou, and J. Wang, “Broadband metamaterial absorber based on coupling resistive frequency selective surface,” Opt. Express 20(4), 4675–4680 (2012). [CrossRef] [PubMed]

15.

P. E. Ciddor and L. B. Whitbourn, “Equivalent thin film of a periodic metal grid,” Appl. Opt. 28(6), 1228–1230 (1989). [CrossRef] [PubMed]

16.

H. E. Went, A. P. Hibbins, J. R. Sambles, C. R. Lawrence, and A. P. Crick, “Selective transmission through very deep zero-order metallic gratings at microwave frequencies,” Appl. Phys. Lett. 77(18), 2789–2791 (2000). [CrossRef]

17.

J. B. Tan and Y. M. Liu, “Optimization of optical communication window mesh through full wave analysis of periodic mesh,” Opt. Commun. 281(19), 4835–4839 (2008). [CrossRef]

18.

C. S. R. Kaipa, A. B. Yakovlev, F. Medina, F. Mesa, C. A. M. Butler, and A. P. Hibbins, “Circuit modeling of the transmissivity of stacked two-dimensional metallic meshes,” Opt. Express 18(13), 13309–13320 (2010). [CrossRef] [PubMed]

OCIS Codes
(050.1220) Diffraction and gratings : Apertures
(350.2460) Other areas of optics : Filters, interference
(050.6624) Diffraction and gratings : Subwavelength structures
(310.7005) Thin films : Transparent conductive coatings

ToC Category:
Diffraction and Gratings

History
Original Manuscript: October 25, 2012
Revised Manuscript: November 24, 2012
Manuscript Accepted: November 28, 2012
Published: February 12, 2013

Citation
Yongmeng Liu and Jiubin Tan, "Experimental study on a resonance mesh coating fabricated using a UV-lithography technique," Opt. Express 21, 4228-4234 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-4-4228


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. J. C. Kirsch, W. R. Lindberg, D. C. Harris, M. J. Adcock, T. P. Li, E. A. Welsh, and R. D. Adkins, “Tri-mode seeker dome considerations,” Proc. SPIE5786, 33–40 (2005). [CrossRef]
  2. M. Kohin, S. J. Wein, J. D. Traylor, R. C. Chase, and J. E. Chapman, “Analysis and design of transparent conductive coatings and filters,” Opt. Eng.32(5), 911–925 (1993). [CrossRef]
  3. C. I. Bright, “Electromagnetic shielding for electro-optical windows and domes,” Proc. SPIE2286, 388–396 (1994). [CrossRef]
  4. J. B. Tan and Z. G. Lu, “Contiguous metallic rings: an inductive mesh with high transmissivity, strong electromagnetic shielding, and uniformly distributed stray light,” Opt. Express15(3), 790–796 (2007). [CrossRef] [PubMed]
  5. J. I. Halman, K. A. Ramsey, M. Thomas, and A. Griffin, “Predicted and measured transmission and diffraction by a metallic mesh coating,” Proc. SPIE 7302, 73020Y1 (2009).
  6. S. A. Kuznetsov, M. Navarro-Cía, V. V. Kubarev, A. V. Gelfand, M. Beruete, I. Campillo, and M. Sorolla, “Regular and anomalous extraordinary optical transmission at the THz-gap,” Opt. Express17(14), 11730–11738 (2009). [CrossRef] [PubMed]
  7. B. A. Munk, Frequency Selective Surfaces: Theory and Design (John Wiley and Sons, 2000).
  8. H. X. Zhu, X. G. Feng, J. L. Zhao, F. C. Liang, Y. S. Wang, X. Chen, and J. S. Gao “Design of antireflection and bandpass frequency selective surface combining coatings for ZnS optical window,” Acta Opt. Sin.30(9), 2766–2770 (2010). [CrossRef]
  9. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill Companies Inc., 1996).
  10. R. Ulrich, “Far-infrared properties of metallic mesh and its complementary structure,” Infrared Phys.7(1), 37–55 (1967). [CrossRef]
  11. L. B. Whitbourn and R. C. Compton, “Equivalent-circuit formulas for metal grid reflectors at a dielectric boundary,” Appl. Opt.24(2), 217–220 (1985). [CrossRef] [PubMed]
  12. K. T. Jacoby, M. W. Pieratt, J. I. Halman, and K. A. Ramsey, “Predicted and measured EMI shielding effectiveness of a metallic mesh coating on a sapphire window over a broad frequency range,” Proc. SPIE 7302,73020X1 (2009).
  13. J. F. Zhang, J. Y. Ou, N. Papasimakis, Y. F. Chen, K. F. Macdonald, and N. I. Zheludev, “Continuous metal plasmonic frequency selective surfaces,” Opt. Express19(23), 23279–23285 (2011). [CrossRef] [PubMed]
  14. L. K. Sun, H. F. Cheng, Y. J. Zhou, and J. Wang, “Broadband metamaterial absorber based on coupling resistive frequency selective surface,” Opt. Express20(4), 4675–4680 (2012). [CrossRef] [PubMed]
  15. P. E. Ciddor and L. B. Whitbourn, “Equivalent thin film of a periodic metal grid,” Appl. Opt.28(6), 1228–1230 (1989). [CrossRef] [PubMed]
  16. H. E. Went, A. P. Hibbins, J. R. Sambles, C. R. Lawrence, and A. P. Crick, “Selective transmission through very deep zero-order metallic gratings at microwave frequencies,” Appl. Phys. Lett.77(18), 2789–2791 (2000). [CrossRef]
  17. J. B. Tan and Y. M. Liu, “Optimization of optical communication window mesh through full wave analysis of periodic mesh,” Opt. Commun.281(19), 4835–4839 (2008). [CrossRef]
  18. C. S. R. Kaipa, A. B. Yakovlev, F. Medina, F. Mesa, C. A. M. Butler, and A. P. Hibbins, “Circuit modeling of the transmissivity of stacked two-dimensional metallic meshes,” Opt. Express18(13), 13309–13320 (2010). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited