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Wideband and low dispersion slow light by chirped photonic crystal coupled waveguide

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Abstract

Previously, we discussed an optical delay device consisting of a directional coupler of two different photonic crystal (PC) waveguides. It generates wideband and low dispersion slow light. However, it is easily degraded by a large reflection loss for a small imperfection of the coupling condition. In this paper, we propose and theoretically discuss a PC coupled waveguide, which allows more robust slow light with lower loss. For this device, unique photonic bands with a zero or negative group velocity at the inflection point can be designed by the structural tuning. Finite difference time domain simulation demonstrates the stopping and/or back and forth motion of an ultrashort optical pulse in the device combined with the chirped structure. For a signal bandwidth of 40 GHz, the average group index of the slow light will be 450, which gives a 1 ns delay for a device length of 670 μm. The theoretical total insertion loss at the device and input/output structures is as low as 0.11 dB.

©2005 Optical Society of America

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Supplementary Material (2)

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Media 2: MOV (2353 KB)     

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Figures (10)

Fig. 1.
Fig. 1. Schematic of ideal band shifted by chirping against the frequency of incident light (dashed line).
Fig. 2.
Fig. 2. Schematic of PC directional coupler with coupled mode profiles and corresponding bands.
Fig. 3.
Fig. 3. Real structures of PC coupled waveguides and corresponding bands. Thick and thin lines indicate bands of the even mode and other modes, respectively. Light gray and dark gray regions show the light cone above the air light line and slab mode regions, respectively. For the band of (a), airhole shift d is set to be 0.25a.
Fig. 4.
Fig. 4. Dependence of band for the structure of Fig. 3(a) on background index n, where d = 0.25a is assumed.
Fig. 5.
Fig. 5. Dependence of band for the structure of Fig. 3(a) on airhole shift d, where n = 2.963 is assumed.
Fig. 6.
Fig. 6. Light intensity profile for each time frame and pulse waveforms of light power toward the right side. (a) and (b) are those for structures of Fig. 3(a) with d = 0.25a and 0.10a, respectively. Line in each figure shows corresponding photonic band. Animations show the light propagation (Hz field) for each structure, where red, yellow, green, light blue and dark blue show intensities from plus to minus. [Media 1] [Media 2]
Fig. 7.
Fig. 7. Schematic band diagram in the repeated zone scheme for the explanation of back and forth motion in Fig. 6(b).
Fig. 8.
Fig. 8. Upper limit values of g and g ∆ωs/ω for bands of Fig. 5 calculated with ∆ωs/ω, where d is used as a parameter.
Fig. 9.
Fig. 9. I/O structure for the structure of Fig. 3(a) with photonic wire waveguides. (a) Half elliptical taper used with bend waveguide type branch. (b) Half circular funnel taper as a confluence.
Fig. 10.
Fig. 10. I/O structure for the structure of Fig. 3(a) with PC single line defect waveguides. (a) Branch. (b) Confluence.

Equations (5)

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Δ T = 0 Δ L d x υ g ( x ) = 0 Δ L n g ( x ) c d x .
n ͂ g = c υ ͂ g = c Δ L Δ T = 0 Δ L n g ( x ) d x Δ L .
n ͂ g ω 0 ω 0 + Δ ω n g ( ω ) d ω / Δ ω = ω 0 ω 0 + Δ ω c d k d ω d ω / Δ ω = k 0 k 0 + Δ k c d k / Δ ω = c Δ k Δ ω
n ͂ g Δ ω s ω n ͂ g Δ ω 2 ω = Δ k 2 k .
n ͂ g Δ ω s ω n ͂ g Δ ω Δ ω p 2 ω = Δ k 2 k ( 1 Δ ω p Δ ω )
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