Electromagnetic crystals (EC) in microstrip technology have been recently proposed as efficient Bragg reflectors. They are implemented by etching the ground plane or by drilling the substrate following a periodic pattern. In this paper we propose a simple and fast fibre Bragg grating (FBG)-based model for the synthesis and analysis of these microstrip ECs with sinusoidal patterns. The method rests on the analogy found between the frequency responses of a microstrip EC and a FBG. Based on this analogy, an equivalence relationship between the physical parameters of a microstrip EC and those of an equivalent FBG has been established. The equivalence assures that the frequency response of the microstrip EC is a down-shifted replica of the one corresponding to its equivalent FBG. This model avoids the use of the time-consuming electromagnetic calculations involved in the analysis of the microstrip ECs as well as the trial method employed until now in the synthesis, since a FBG response arises immediately from coupled-mode theory. At the same time the theoretical difficulties encountered in the formal derivation of coupled-mode theory for microstrip ECs are also avoided by the equivalence relationship found.
[1]
Tatsuo Itoh,et al.
Novel architectures for high-efficiency amplifiers for wireless applications
,
1998
.
[2]
Steven G. Johnson,et al.
Photonic Crystals: Molding the Flow of Light
,
1995
.
[3]
Txema Lopetegi,et al.
1‐D and 2‐D photonic bandgap microstrip structures
,
1999
.
[4]
M. Adams,et al.
Optical waves in crystals
,
1984,
IEEE Journal of Quantum Electronics.
[5]
Txema Lopetegi,et al.
Multiple-frequency-tuned photonic bandgap microstrip structures
,
2000
.
[6]
T. Itoh.
Analysis of Microstrip Resonators
,
1974
.
[7]
Txema Lopetegi,et al.
Novel photonic bandgap microstrip structures using network topology
,
2000
.