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ABSTRACT: Using a novel numerical method we calculate the energy absorption of a silicon nanowire array, for photovoltaics. We show that dilute arrays deliver optimal integrated absorption on a per-silicon-volume basis, and identify the enhancement mechanism.
Lasers and Electro-Optics (CLEO), 2011 Conference on; 06/2011
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ABSTRACT: We investigate the formation of photonic crystal waveguide (PCW) modes within the framework of perturbation theory. We derive a differential equation governing the envelope of PCW modes constructed from weak perturbations using an effective mass formulation based on the Luttinger-Kohn method from solid-state physics. The solution of this equation gives the frequency of the mode and its field. The differential equation lends itself to simple analytic approximations which reduce the problem to that of solving slab waveguide modes. By using this model, we demonstrate that the nature of the projected band structure and corresponding Bloch functions are central to the behaviour of PCW modes. With this understanding, we explain why the odd mode in a hexagonal PCW spans the entire Brillouin zone while the even mode is cut off.
Optics Express 10/2009; 17(22):19629-43. · 3.59 Impact Factor
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ABSTRACT: We show that efficient coupling between fast and slow photonic crystal waveguide modes is possible, provided that there exist strong evanescent modes to match the waveguide fields across the interface. Evanescent modes are required when the propagating modes have substantially different modal fields, which occurs, for example, when coupling an index-guided mode and a gap-guided mode.
Optics Express 09/2009; 17(20):17338-43. · 3.59 Impact Factor
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ABSTRACT: We consider the coupling into a slow mode that appears near an inflection point in the band structure of a photonic crystal waveguide. Remarkably, the coupling into this slow mode, which has a group index ng>1000, can be essentially perfect without any transition region. We show that this efficient coupling occurs thanks to an evanescent mode in the slow medium, which has appreciable amplitude and helps satisfy the boundary conditions but does not transport any energy.
Optics Letters 11/2008; 33(22):2644-6. · 3.40 Impact Factor
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ABSTRACT: We suggest a novel and general approach to the design of photonic-crystal directional couplers operating in the slow-light regime. We predict, based on a general symmetry analysis, that robust tunneling of slow-light pulses is possible between antisymmetrically coupled photonic crystal waveguides. We demonstrate, through Bloch mode frequency-domain and finite-difference time-domain (FDTD) simulations that, for all pulses with strongly reduced group velocities at the photonic band-gap edge, complete switching occurs at a fixed coupling length of just a few unit cells of the photonic crystal.
Optics Express. 01/2008; 16:1104--14.
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ABSTRACT: We present an exact method for modelling modes of general defects with infinite cladding. It handles the pathological case of highly extended modes and establishes the fundamental mode of a conventional PCF has no cut-off.
Optical Internet, 2007 and the 2007 32nd Australian Conference on Optical Fibre Technology. COIN-ACOFT 2007. Joint International Conference on; 07/2007
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ABSTRACT: We consider defect modes created in complete gaps of 2D photonic crystals by perturbing the dielectric constant in some region. We study their evolution from a band edge with increasing perturbation using an asymptotic method that approximates the Green function by its dominant component which is associated with the bulk mode at the band edge. From this, we derive a simple exponential law which links the frequency difference between the defect mode and the band edge to the relative change in the electric energy. We present numerical results which demonstrate the accuracy of the exponential law, for TE and TM polarizations, hexagonal and square arrays, and in each of the first and second band gaps.
Optics Express 05/2007; 15(8):4753-62. · 3.59 Impact Factor
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ABSTRACT: We investigate localized defect states near the edge of a band gap in a two-dimensional photonic crystal. An asymptotic approach based on Green’s functions leads to analytical results both for the frequency and for the spatial behavior of the defect states. In particular, we find a simple exponential law which relates the change in frequency of the defect states to the relative change in electrical energy of the Bloch modes on the band edge, and to the density of states in the photonic crystal. We find that the symmetries of the Bloch modes at band extrema play an important role in the manifestation and evolution of defect states. We confirm the analysis with numerical simulations based on the fictitious source superposition method.
Phys. Rev. A. 77(6).
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ABSTRACT: An exact theory for modelling modes of generalised defects in 2D photonic crystals (PCs) with a genuinely infinite cladding is presented. The approach builds on our fictitious source superposition method for simple defects and permits an elegant extension allowing the modelling of arbitrary defects. Numerical results that demonstrate the accuracy and efficiency of the extended method are presented. We also use the method to study the evolution of the mode generated by varying the refractive index of a single defect cylinder and find significant differences between the behaviour of defects in rod-type and hole-type PCs.
Physica B: Condensed Matter.
