A study of a phase formalism for calculating the cumulative density of states of one-dimensional photonic crystals |
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| Authors: | R A Abram A A Greshnov S Brand M A Kaliteevski |
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| Affiliation: | 1. Department of Physics, Durham University, Durham, UK.;2. Ioffe Physicotechnical Institute, St Petersburg, Russia.;3. ITMO University, St Petersburg, Russia.;4. St Petersburg Academic University, St Petersburg, Russia. |
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| Abstract: | We explore a phase formalism that underpins a method of calculation of the cumulative density of states of one-dimensional photonic crystals based on the node counting theorem. Node counting is achieved by considering the spatial dependence of a phase variable proportional to the logarithmic derivative of the electric field in the structure. The properties of the phase variable are considered for photonic crystals in general, and illustrative algebraic and numerical results are presented for the phase variable and cumulative density of states of a model crystal. It is also shown how a simple extension of the theory can facilitate the calculation of the reflectivity of finite samples. For a disordered model crystal, a differential equation for the distribution function of the phase variable is derived and then used to obtain a closed-form expression for the ensemble-averaged cumulative density of states and numerical results to illustrate band tailing in the photonic bandgap. |
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| Keywords: | Photonic crystal phase formalism node counting cumulative density of states disorder |
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