Abstract
We examine defect modes in four-section helical hotonic crystals (HPCs) that comprise three twist defects located at the intersections. The three twist defects are introduced by a single angle phit , but they are quantified differently by the jump angles across the successive sections. The two defect modes are localized at the different defect sites and can be either coupled or uncoupled to each other, depending on the value of phit . The two defect modes are excited by normally incident plane waves of different circular polarization states as the HPC thickness increases. When the two defect modes are uncoupled to each other, two co-handed reflection holes are present in the Bragg regime for small thickness, but they evolve into two stable cross-handed transmission holes for sufficiently large thickness. When the two defect modes are coupled to each other, however, three co-handed reflection holes appear around the center of the Bragg regime for small thickness, and they evolve into three cross-handed transmission holes as thickness increases, and eventually all three co-handed transmission holes coalesce into one stable cross-handed transmission hole for sufficiently large thickness. Finally, the simultaneous occurrence of the two types of spectral holes at a single resonance wavelength can be realized for specific values of sample thickness when the two defect modes are uncoupled to each other.
Highlights
Periodic structurally chiral materials have been extensively studied during the last century due to the unique properties and applications of self–organized cholesteric liquid crystals (CLCs) [1, 2]
We present the characteristics of two circularly polarized (CP) defect modes in a four–section helical photonic crystals (HPCs) which has three intersectional twist defects, all described by an angle φt
An exceptional case is that the energy density for the co–handed incidence case can reach the peaks at the two φt –twist defect sites that are significantly larger than the saturated peak of the energy density for the cross–handed case, as shown in Fig. 4(a 3) for νD = 40. This implies that the defect mode coupled with the φt –twist defect can be excited by both the co– handed and the cross–handed CP plane waves for the specific values of ν D; the two types of spectral holes simultaneously appear at the resonance wavelength λ 02, as demonstrated by Fig. 2(c)
Summary
Periodic structurally chiral materials have been extensively studied during the last century due to the unique properties and applications of self–organized cholesteric liquid crystals (CLCs) [1, 2]. The defect mode is localized to the defect site and can be excited by a normally incident CP plane wave of either the co–handed type or the cross–handed type — depending on the thickness of the HPC. The width of the photonic band gap is tiny but stable for large thickness of the HPC, because the electromagnetic energy density at the defect site saturates instead of scaling exponentially with respect to the thickness [11] This defect mode can be harnessed for new optical devices, such as low threshold lasers [17], chiral filters [10], and chiral fibers [18], provided that dissipation in the HPC is small enough to be ignored [12].
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