Perturbation approach for the control of the quality factor in photonic crystal membranes: Application to selective absorbers

Above the light line, guided modes cannot be perpetually sustained into a photonic crystal membrane owing to its periodic modulation. The resulting leaky waves are nowadays largely exploited in the context of integrated optics. We develop here a model affording insight into the mechanism that allows the obtention of resonances endowed with extremely high quality factors. As a matter of fact, the model indicates that the quality factor can take arbitrarily high values and that this phenomenon results from the coupling between guided and radiated modes. The obtained tight control over the emission spectrum of a photonic crystal membrane is employed to design a spectrally and spatially selective absorber.

Figure 1

A PCM surrounded by two semi-infinite media

Figure 2

(a) Radiation losses in terms of the ratio $d/\lambda$ of a silicon membrane embedded in silica (we have assumed that $n_{\mathrm{Si}}=3.481$ and $n_{{\mathrm{SiO}}_2}=1.528)$. The curve has been normalized to the maximum value of $\mathrm{Re}\left(h_1\right)$. (b) Enlargement of the radiation losses and comparison with the inverse of the $Q$ factor calculated by FDTD simulations. Gray (dark) curve: perturbation approach. Orange (light) curve: numerical calculation of $1/Q$.

Figure 3

The optical thickness $\left(d{n}_2/\lambda \right)$ of the membrane that leads to infinite photons lifetime is universal.

Figure 4

Quality factor in terms of $\theta$. For the PCM under consideration, $Q$ is reduced by four orders of magnitude when the angle is varied from 0 to 10.

Figure 5

Reflection, transmission, and absorption coefficients as functions of (a) $\theta$ at $\lambda =1.5\mu \mathrm{m}$ and (b) $\lambda$ at $\theta =0$. (c) Mapping of the absorption coefficient in terms of $\lambda$ and $\theta$.