Photonic crystals often large air spaces between the periodic elements which cannot provide support for the suspension of the metallic elements of either the radiating element, connecting transmission line or other parts of an antenna system. The fabrication of an antenna system, including the mixer, local oscillator and all other peripheral circuitry onto a thin, low-loss, dielectric membrane allows both support for the structure and continued repositioning of the antenna on a PBG substrate. This allows investigation into the effects of antenna orientation due to the interaction with the underlying photonic crystal[1,2]. The transfer matrix technique [3] is used to theoretically investigate the effect of placing a membrane on the surface of finite thickness 2-dimensional periodic photonic crystals, experimental data is presented to verify the findings. The study of the transmission coefficients of electromagnetic waves through a photonic crystal with and without a membrane is presented. A difference in performance is observed even for a membrane thickness that is unable to support guided substrate modes through total internal reflection. The transmittance has been investigated for two crystal orientations, Figure 1, for normally incident external plane waves.
Two membranes have been studied, 100••••m silicon • silicon =11.7, and 25••••m kapton, kapton =3.7. The photonic crystals studied have a lattice constant and for the 2D lattices discussed and are made from silicon bars. The bars have dimensions in the x,z directions respectively. We define TE or E- (TM or H-) polarised waves as those which have their E- (H-) field confined to the xz plane, that is to say the H- (E-) field is parallel to the y-axis, see Figure 1. The influence of the membrane has been studied between 67-110GHz, the limit of the W-band analyser. Figure 2 shows the TM transmittance for three crystal thicknesses, L=2h, 4h and 8h for the perfect crystal and both membranes for the • X direction. Figure 1 2D crystal orientation, Where a is the periodic spacing of the bars in the x-direction, h is the mid point-point separation of the bars in the z-direction. The membranes have been applied only to the first layer of bars in both lattice configurations.
•• • •X and •• • •M.
a 1275••••m =
h 780••••m =
340x390••••m
The application of a membrane onto the surface of a 2D photonic crystal, while interacting with the underlying crystal, does not seriously perturb the transmission response of a thick PBG substrate. For the regions studied the application of a membrane actually has helped to steepen the gradient of the lower band edge cut-off frequency aiding the PBG performance of the crystal. However the upper frequency range of the experimental set up was incapable of measuring the effect on the membrane on the upper band edge of the crystal. The membranes studied, Silicon and Kapton, are unable to support T.I.R. guided modes at the frequency of the PBG. Theoretical and experimental work has demonstrated that these membranes are good candidates for substrates onto which an antenna system can be fabricated before integration onto the surface of a photonic crystal.
References:
1 LEUNG,W.Y., BISWAS,R., CHENG,S., SIGALAS,M.M. McCALMONT,J.S.,
TUTTLE,G., HO,K.M., ‘Slot antennas on Photonic Band Gap
Crystals’, IEEE Trans. A&P, 1997, 45 (10), pp 1569-1570.
2 SIGALAS, M.M., BISWAS, R., HO, K.M., LEUNG,W. TUTTLE,G., CROUCH,
D.D., ‘The effect of photonic crystals on dipole antennas’,
Electromagnetics, 1999, 19, pp291-303
3 BELL, P.M., PENDRY, J. B., MARTIN MORENO, L., WARD, A.J.,: ‘A
program for calculating photonic band structures and transmission
coefficients of complex structures,’ Computer Physics
Communications, 1995, 85, pp. 307-322
Figure 2 • X Lattice: Measured and Theoretical TM Response.
Top, middle and bottom plots correspond to the TM transmission response for a crystal thickness’s L=2h, 4h and 8h thick. Plots on the left, red, green and black correspond to the no membrane case, 25um Kapton membrane and 100um Silicon membrane respectively. Plots on the right, solid, dot, dash correspond to the theoretical response for the no membrane case, 25um Kapton membrane and 100um Silicon membrane.
100••••m 25••••m