Optimization of optical communication window mesh through full-wave analysis of periodic mesh

Optics Communications 281 (2008) 4835–4839

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Optimization of optical communication window mesh through full-wave analysis of periodic mesh Jiubin Tan, Yongmeng Liu * Harbin Institute of Technology, Ultra-precision Optical and Electronic Instrument Engineering Center, P.O. Box 3016, Harbin 150001, PR China

a r t i c l e

i n f o

Article history: Received 26 April 2008 Received in revised form 20 June 2008 Accepted 21 June 2008

Keywords: Optimization Optical communication window mesh Optical transmittance Shielding effectiveness Zeroth order diffraction

a b s t r a c t In order to develop an optical communication window mesh with good optical transmittance and shielding effectiveness at the same time, models were established for the shielding effectiveness and optical transmittance of optical communication window mesh, verified through experiments, and used to run full-wave analyses. The effect of period and linewidth of mesh on the shielding effectiveness and optical transmittance of optical communication window mesh was investigated through simulation. Simulation results indicated that better optical transmittance can be achieved using optical communication window mesh with high porosity and finer linewidth while the given shielding effectiveness requirement is satisfied. Crown Copyright Ó 2008 Published by Elsevier B.V. All rights reserved.

1. Introduction Much work has been done on metal meshes [1–4], and reflective mesh dishes have been extensively used in microwave community for quite sometime [5–9]. As a very good example of the work done on entire transmittance, Möller et al. deal with filtering effects of IR meshes. Although the meshes they used and the meshes we used for the present study are optical filters used for optical communication, the meshes they used was a type of an infrared bandpass filter used in the astrophysical community; and the meshes we used for the present study was a type of filter which functions as both a highpass filter for optical signals (visible, near to far IR) and a low-cut filter for microwave interference signals [10–14]. In order to achieve better optical transmittance in optical communication window mesh while the given shielding effectiveness requirement is satisfied, it is important to further study the effect of period and linewidth of mesh on the optical transmittance and shielding effectiveness of optical communication window mesh. However, to the best of our knowledge, not much work has been done on the use of zeroth order microwave diffraction to calculate the shielding effectiveness of optical communication window mesh in the microwave interference waveband. Interference microwave wavelength is much greater than the mesh period, so all the high-order diffractions are in the evanescent mode to attenuate soon off the near-field, and only zeroth or* Corresponding author. Tel.: +86 451 86412041; fax: +86 451 86402258. E-mail address: [email protected] (Y. Liu).

der diffraction is in propagating mode to transmit into the far-field. The shielding effectiveness of such optical communication window mesh can thus be evaluated by calculating and measuring the zeroth order diffraction energy in the far-field only. So we modeled the optical transmittance and shielding effectiveness of optical communication mesh window, verified these models through simulations and experiments, and used them to run full-wave analyses. We investigated the effect of period and linewidth of mesh on the shielding effectiveness and optical transmittance of optical communication window mesh through simulation. Simulation results indicated that better optical transmittance can be achieved in an optical communication mesh window optimized through full-wave analysis by using periodic mesh with high porosity and finer linewidth while the given shielding effectiveness requirement is satisfied. 2. Modeling shielding effectiveness and optical transmittance of optical communication window mesh 2.1. Shielding effectiveness of optical communication window mesh Shielding effectiveness means reduction in transmittance of electromagnetic interference, and it is defined as the ratio of transmitted wave intensity to incident intensity [15]. As shown in Fig. 1, the optical communication window mesh consists of sub-wavelength square apertures and fine metal grids. The period of window mesh is defined as g, and its fine linewidth is defined as 2a. Incident plane wave vector kinc is at angle h from axis z and angle u from axis x.

0030-4018/$ - see front matter Crown Copyright Ó 2008 Published by Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2008.06.044

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J. Tan, Y. Liu / Optics Communications 281 (2008) 4835–4839

These values are associated with the Floquet harmonics for the doubly periodic mesh. The explicit expressions for am and bn are as follows [18]:

am ¼ 2pm=g þ k0 sin h cos u

ð4Þ

bn ¼ 2pn=g þ k0 sin h sin u

ð5Þ

The spectral wave vector propagating along axis z can be expressed as

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 k  ða2m þ b2n Þ vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi " u 2  2 # u k k t m þ sin h cos u þ n þ sin h sin u ¼k 1 g g

cmn ¼

Fig. 1. Optical communication window mesh and incident plane wave vector.

The optical communication window mesh is produced using photolithographic technique on the inner surface of window to improve its strength. According to Floquet’s theorem, the scattered field integral equation for periodic mesh can be transformed into the scattered field integral equation for a single unit cell only. As shown in Fig. 2, the full-wave analysis model used for a single unit cell is surrounded by periodic boundaries, and Y0 and Y1 are the characteristic admittances of air and window substrate, respectively. According to Floquet’s theorem, the induced magnetic current in metal mesh arrays is a periodic function which can be represented by two dimensional summations of all its Fourier components as shown below [16]. m¼1 X

~ a; bÞ ¼ Mð

n¼1 X

~ mn ejam x ejbn y M

ð1Þ

m¼1 n¼1

The scattered magnetic field at the mesh and air interfaces can be expressed as a product between the composite Green’s function and the spectral magnetic current in the spectral domain as shown below [17].

"

~s H x ~ Hs

#

y

¼

m¼1 X

nX ¼1

m¼1 n¼1

"

~ xx G ~ yx G

~ xy G ~ yy G

#"

# ~ x ðam ; b Þ M n ejðam xþbn yÞ ~ y ðam ; b Þ M

ð2Þ

n

With the input admittance of window substrate taken into account the composite Green’s function can be obtained using spectral-domain immittance approach.

"

~ xx G ~ yx G

~ xy G ~ yy G

# ¼

1

a2m þ b2n

"

Y~ s a2m þ Y~ p b2n ðY~ s  Y~ p Þam b

n

ðY~ s  Y~ p Þam bn Y~ s b2 þ Y~ p a2 n

Because interference microwave wavelength is much greater than window mesh period (k » g), only m = n = 0 satisfies the propagating modes condition (c00 is positive real), and high-order diffractions (cmn is negative imaginary) are the evanescent modes and attenuate soon off the near-field, so only the zeroth order diffraction energy of such optical communication window mesh can transmit into the far-field. The shielding effectiveness of optical communication window mesh can therefore be calculated and measured by assessing the zeroth order diffraction energy in the far-field. And shielding effectiveness (SE) can be given by [15]

SEðdBÞ ¼ 10 log

ð3Þ

~ s and Y ~ p denote perpendicular and parallel polarization input Y admittances of window substrate, respectively. The Fourier transform of the induced magnetic current is nonzero only for an infinite set of discrete values of spectral variables am and bn because the window mesh is infinitely doubly periodic.

  Ht  It ¼ 20 log   Ii Hi

ð7Þ

The spectral domain equation of full-wave analysis model Eq. (2) can be solved by transforming it into an algebraic matrix equation using spectral Galerkin’s moment method to avoid the division of a large number of computational grids [19,20]. And the shielding effectiveness can be thus easily obtained by calculating the zeroth diffraction energy. 2.2. Optical transmittance of optical communication window mesh Optical communication window mesh behaves as optical gratings and diffracts many higher orders at the visible and infrared waveband. The optical point spread function (PSF) of optical communication window mesh can be given by the following expression [11]:

Iðm; nÞ ¼

#

m

ð6Þ

    ðg  2aÞ4 2 mðg  2aÞ 2 nðg  2aÞ sin c sin c g g g4

ð8Þ

Only the zeroth order diffracted energy is useful for optical imaging, and all the others higher orders increase the system stray light level and degrade the optical imaging performance of optical communication system. The zeroth order transmittance of PSF can be given by

Ið0; 0Þ ¼

ðg  2aÞ4 ¼ g4

 4 2a 1 g

ð9Þ

3. Optimization of optical communication window mesh 3.1. Simulation of shielding effectiveness and experimental verification

Fig. 2. Unit cell of optical communication window mesh and its full-wave model.

In order to analyze the frequency characteristic of shielding effectiveness of window mesh and verify the validity of the fullwave analysis method, two optical communication window mesh samples A with g of 320 lm and 2a of 4.5 lm and B with g of 160 lm and 2a of 5.5 lm were fabricated on quartz window glass using UV photolithographic technique. The shielding effectiveness of the samples was measured in the microwave interference

J. Tan, Y. Liu / Optics Communications 281 (2008) 4835–4839

waveband from 12 to 18 GHz using a shielding effectiveness measurement system as shown in Fig. 3 below. The shielding effectiveness measurement system consists of an Agilent E8363B PNA series network analyzer, a transmitter lens antenna, and a receiver lens antenna. The spherical wave transmitted by the transmitter antenna is collimated into the plane wave through the convergent lens of the transmitter lens antenna, the plane wave diffracts through the mesh windows into the zeroth order transmittance wave, which passes the convergent lens of the receiver lens antenna and converges into the receiver antenna in the far-field. The measurement system was calibrated before use and its measurement error was less than ±1 dB. The measurement procedure is as follows: firstly, adjust the output energy intensity of the transmitter lens antenna to ensure that the outputs of Agilent E8363B PNA series network analyzer are zero without mesh window sample put between the transmitter lens antenna and the receiver lens antenna; then put the mesh window sample between these two antennas, the outputs of Agilent E8363B PNA series network analyzer are the shielding effectiveness measurement value.

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The measurements and experimental simulation of sample A and B are shown in Fig. 4a and b below. It can be seen from Fig. 4 above that the shielding effectiveness of optical communication window mesh rapidly decreases as the frequency increases, i.e., the shielding effectiveness at a higher frequency is lower than that at a lower frequency; and the effectiveness of full-wave analysis method is verified by comparison measurements with simulation results. So, the optimization of optical window mesh was done at 18 GHz in the following subsection because its shielding effectiveness at a higher frequency was lower than that at a lower frequency. 3.2. Effect of period and linewidth of mesh on shielding effectiveness and optical transmittance of mesh The shielding effectiveness and optical transmittance of optical communication window mesh are mainly determined by the period and linewidth of mesh. With the period of mesh varying from 100 lm to 500 lm and the linewidth of mesh varying from 1 lm

Fig. 3. Photograph of shielding effectiveness measurement system.

Fig. 4. Comparison of actual measurements with simulation results of sample A (a) and B (b) at 0° incidence.

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to 10 lm, the shielding effectiveness of window mesh was calculated at 18 GHz as shown in Fig. 5a and the zeroth order transmittance of mesh was calculated using Eq. (9) as shown in Fig. 5b. It can be seen from Fig. 5a that the shielding effectiveness of optical communication window mesh slowly increases as the linewidth of mesh increases, and rapidly increases as the period of mesh decreases. It can therefore be concluded that the shielding effectiveness of mesh is mainly determined by the period of mesh. On the other hand, it can be seen from Fig. 5b that the zeroth order transmittance of optical communication window mesh rapidly decreases as the linewidth of mesh increases and/or as the period of mesh decreases. It can be seen from above that as the linewidth of mesh increases, the shielding effectiveness increases but the optical transmittance of mesh decreases; as the period of mesh increases, the optical transmittance of mesh increases but the shielding effectiveness of mesh decreases. It can therefore be concluded that the shielding effectiveness and the optical transmittance of mesh are a pair of inherent conflicts. It is the key to the optimization of mesh period and linewidth to strike a good balance between them. 3.3. Optimization of porosity and linewidth of optical communication window mesh For the design of a particular optical communication window mesh, there is always a specified shielding effectiveness requirement. It can be seen from Fig. 5a and b that different combinations

of period and linewidth of mesh can be used to achieve different optical transmittances of mesh while the shielding effectiveness requirement is satisfied. And a better transmittance can be achieved by optimizing the combination of mesh period and linewidth. For example, as shown in Fig. 6a, a specified shielding effectiveness requirement of 14 dB can be achieved at 18 GHz using combination A of 2a/g of 0.008 and g of 320 lm, or B of 2a/g of 0.014 and 2a of 5 lm. However, as shown in Fig. 6b, the zeroth order transmittance of optical communication window mesh is 2.3% higher with combination A than that with combination B. A higher optical transmittance can therefore be achieved using optical communication window mesh with higher porosity. As shown in Fig. 5a and b, ten combinations of mesh period and linewidth can be used to optimize optical communication window mesh, and they are selected from the combinations used to satisfy the shielding effectiveness requirement of 14 dB and the corresponding zeroth order transmittances. It can be seen from Table 1 that the zeroth order transmittance of optical communication window mesh with a linewidth of 1 lm is 7.8% higher than that with a linewidth of 10 lm for the shielding effectiveness requirement of 14 dB. As shown in Fig. 7, the zeroth order transmittance rapidly decreases as the linewidth of mesh increases, and so, better optical transmittance can be achieved using optical communication window mesh with high porosity and finer linewidth while the given shielding effectiveness requirement is satisfied .

Fig. 5. Shielding effectiveness at 18 GHz (a) and zeroth order transmittance (b) versus the period and linewidth of mesh.

Fig. 6. Shielding effectiveness at 18 GHz (a) and zeroth order transmittance (b) versus 2a/g.

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J. Tan, Y. Liu / Optics Communications 281 (2008) 4835–4839 Table 1 Combinations of mesh period and linewidth and their corresponding zero order optical transmittance Combination

1

2

3

4

5

6

7

8

9

10

Linewidth (lm) Period (lm) Transmittance (%)

1 256 98.5

2 293 97.3

3 320 96.3

4 342 95.4

5 356 94.5

6 372 93.7

7 381 92.9

8 393 92.1

9 405 91.4

10 415 90.7

Used to achieve given shielding effectiveness requirement of 14 dB at 18 GHz.

nication window mesh with high porosity and finer linewidth while the given shielding effectiveness requirement is satisfied. Acknowledgments We thank National Natural Science Foundation of China (Grant No. 50675052) and ‘‘211 Projects” Foundation from Ministry of Education of China for their financial support. Our special thanks go to Prof. Dacheng Zhang and Dr. Ting Li for fabrication of metal mesh samples, and Prof. Zengming Cao for measurement of electromagnetic shielding effectiveness. References

Fig. 7. Zeroth order transmittance versus the linewidth at a given shielding effectiveness requirement of 14 dB.

4. Conclusion It can be seen from the presentation above that in order to develop an optical communication window mesh with good optical transmittance and shielding effectiveness at the same time, models were established for the shielding effectiveness and optical transmittance of optical communication window mesh, verified through experiments, and used to run full-wave analyses. The effect of period and linewidth of mesh on the shielding effectiveness and optical transmittance of optical communication window mesh was investigated through simulation. Simulation results indicated that better optical transmittance can be achieved using optical commu-

[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20]

K.D. Möller, O. Sternberg, H. Grebel, K.P. Stewart, Appl. Opt. 41 (2002) 1942. R. Ulrich, Infrared Phys. 7 (1967) 37. R.A. Wood, N. Brignall, C.R. Pidgeon, F.A. Berkdar, Opt. Commun. 14 (1975) 301. J.L. Bruneau, P. Belland, D. Véron, Opt. Commun. 24 (1978) 259. F. O’Nians, J. Matson, U.S. Patent 3231892, (1966). V.D. Agrawal, W.A. Imbriale, IEEE Trans. Antenna Propag. 27 (1979) 466. Y.R. Samii, S.W. Lee, IEEE Trans. Antenna Propag. 33 (1985) 76. M.S. Harada, M. Watanabe, Acta Astronaut. 53 (2003) 899. A. Miura, Y.R. Samii, IEEE Trans. Antennas Propag. 55 (2007) 1022. J.B. Tan, Z.G. Lu, Opt. Express 15 (2007) 790. M. Kohin, S.J. Wein, J.D. Traylor, R.C. Chase, J.E. Chapman, Opt. Eng. 32 (1993) 911. C.I. Bright, SPIE 2286 (1994) 388. J.C. Kirsch, W.R. Lindberg, D.C. Harris, M.J. Adcock, T.P. Li, E.A. Welsh, R.D. Akins, SPIE 5786 (2005) 33. S.S. Bayya, G.D. Chin, G. Villalobos, J.S. Sanghera, I.D. Aggarwal, SPIE 5786 (2005) 262. C.R. Paul, Introduction to Electromagnetic Compatibility, Wiley, New York, 2006. T. Itoh, IEEE Microwave Theory Tech. 28 (1980) 733. R. Mittra, C.H. Chan, T. Cwik, Proc. IEEE 76 (1988) 1593. T.K. WU, Frequency Selective Surface and Grid Array, Wiley, New York, 1995. C. Ciminelli, F. Peluso, M. Armen, Opt. Express 13 (2005) 9729. S. Guo, S. Albin, R. Rogowski, Opt. Express 12 (2004) 198.