Omnidirectional Single-negative Gap and in Fibonacci Sequences Composed of Single-negative Materials
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Omnidirectional Single-negative Gap and in Fibonacci Sequences Composed of Single-negative Materials Ting-yi Shang & Hui-yun Zhang & Yu-ping Zhang & Peng Wang & Jian-quan Yao
Received: 2 August 2006 / Accepted: 27 April 2007 / Published online: 24 May 2007 # Springer Science + Business Media, LLC 2007
Abstract The band structures of Fibonacci sequence composed of single-negative materials are studied with a transfer matrix method. A new type of omnidirectional single-negative gaps is found in the Fibonacci sequence. In contrast to the Bragg gaps, such an omnidirectional single-negative gap is insensitive to the incident angles and polarization, and is invariant upon the change of the ratio of the thicknesses of two media. It is found that omnidirectional single-negative gap exists in the other Fibonacci sequence, and it is rather stable and independence of the structure sequence. Keywords Photonic crystals . Negative refractive index materials . Omnidirectional single-negative gaps . Fibonacci sequences
1 Introduction Recently, the so-called negative refractive index materials or double-negative (DNG) materials with negative permeability ɛ and permittivity μ have received renewed attention due to their novel properties such as negative refraction index, antiparallel group, and phase velocities [1–7]. Negative index materials (NIMs) which were first predicted by Veselago [11] in 1968. The existence of such materials with a negative refractive index was demonstrated experimentally in recent years [2, 8, 9] and negative index materials have become a new research topic. Besides DNG materials, the materials in which only one of the material parameters has negative value have attracted people’s interest [10, 11]. They are called single negative (SNG) materials which include the epsilon-negative (ENG) media T.-y. Shang College of information technology, HLJ August First Land Reclamation University, Daqing Heilongjiang 163319, China H.-y. Zhang (*) : Y.-p. Zhang : P. Wang : J.-q. Yao College of Precision Instrument and Optoelectronics Engineering, Institute of Laser and Optoelectronics, Tianjin University, Tianjin 300072, China e-mail: [email protected]
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Int J Infrared Milli Waves (2007) 28:671–676
with negative permittivity but positive permeability and the mu-negative (MNG) media with negative permeability but positive permittivity. It has been demonstrated that the periodic stacking of alternating layers of positive and negative index materials (including DNG and SNG materials) have exhibited special features [5–7]. It is found that the periodic stacking of alternating layers of positive and negative index material leads to a zero n gap where the average refractive index for the stacking is close to zero. The zero n gap is insensitive to the incident angle comparing with the ordinary Bragg gap [3, 5, 6]. The similar properties have also been investigated for Fibonacci sequence(FS) with DNG materials [12–14]. To the best of our knowledge, there is no one to study the bandgap properties of the FS st
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