Interplay between disorder and local field effects in photonic crystal waveguides

We introduce a theory to describe disorder-induced scattering in photonic crystal waveguides, specifically addressing the influence of local field effects and scattering within high-index-contrast perturbations. Local field effects are shown to increase the predicted disorder-induced scattering loss and result in significant resonance shifts of the waveguide mode. We demonstrate that two types of frequency shifts can be expected, a mean frequency shift and a RMS frequency shift, both acting in concert to blueshift and broaden the nominal band structure. For a representative waveguide, we predict substantial meV frequency shifts and band structure broadening for a telecommunications operating frequency, even for state of the art fabrication. The disorder-induced broadening is found to increase as the propagation frequency approaches the slow light regime (mode edge) due to restructuring of the electric field distribution. These findings have a dramatic impact on high-index-contrast nanoscale waveguides, and, for photonic crystal waveguides, suggest that the nominal slow-light mode edge may not even exist. Furthermore, our results shed new light on why it has hitherto been impossible to observe the very slow light regime for photonic crystal waveguides.Comment: 4 page lette

Coherent states, Path integral, and Semiclassical approximation

Using the generalized coherent states we argue that the path integral formulae for $SU(2)$ and $SU(1,1)$ (in the discrete series) are WKB exact,if the starting point is expressed as the trace of $e^{-iT\hat H}$ with $\hat H$ being given by a linear combination of generators. In our case,WKB approximation is achieved by taking a large ``spin'' limit: $J,K\rightarrow \infty$. The result is obtained directly by knowing that the each coefficient vanishes under the $J^{-1}$($K^{-1}$) expansion and is examined by another method to be legitimated. We also point out that the discretized form of path integral is indispensable, in other words, the continuum path integral expression leads us to a wrong result. Therefore a great care must be taken when some geometrical action would be adopted, even if it is so beautiful, as the starting ingredient of path integral.Comment: latex 33 pages and 2 figures(uuencoded postscript file), KYUSHU-HET-19 We have corrected the proof of the WKB-exactness in the section

Theory of disorder-induced multiple coherent scattering in photonic crystal waveguides

We introduce a theoretical formalism to describe disorder-induced extrinsic scattering in slow-light photonic crystal waveguides. This work details and extends the optical scattering theory used in a recent \emph{Physical Review Letter} [M. Patterson \emph{et al.}, \emph{Phys. Rev. Lett.} \textbf{102}, 103901 (2009)] to describe coherent scattering phenomena and successfully explain complex experimental measurements. Our presented theory, that combines Green function and coupled mode methods, allows one to self-consistently account for arbitrary multiple scattering for the propagating electric field and recover experimental features such as resonances near the band edge. The technique is fully three-dimensional and can calculate the effects of disorder on the propagating field over thousands of unit cells. As an application of this theory, we explore various sample lengths and disordered instances, and demonstrate the profound effect of multiple scattering in the waveguide transmission. The spectra yield rich features associated with disorder-induced localization and multiple scattering, which are shown to be exasperated in the slow light propagation regime

Current noise of a quantum dot p-i-n junction in a photonic crystal

The shot-noise spectrum of a quantum dot p-i-n junction embedded inside a three-dimensional photonic crystal is investigated. Radiative decay properties of quantum dot excitons can be obtained from the observation of the current noise. The characteristic of the photonic band gap is revealed in the current noise with discontinuous behavior. Applications of such a device in entanglement generation and emission of single photons are pointed out, and may be achieved with current technologies.Comment: 4 pages, 3 figures, to appear in Phys. Rev. B (2005

Sub-wavelength imaging at optical frequencies using canalization regime

Imaging with sub-wavelength resolution using a lens formed by periodic metal-dielectric layered structure is demonstrated. The lens operates in canalization regime as a transmission device and it does not involve negative refraction and amplification of evanescent modes. The thickness of the lens have to be an integer number of half-wavelengths and can be made as large as required for ceratin applications, in contrast to the other sub-wavelength lenses formed by metallic slabs which have to be much smaller than the wavelength. Resolution of $\lambda/20$ at 600 nm wavelength is confirmed by numerical simulation for a 300 nm thick structure formed by a periodic stack of 10 nm layers of glass with $\epsilon=2$ and 5 nm layers of metal-dielectric composite with $\epsilon=-1$. Resolution of $\lambda/60$ is predicted for a structure with same thickness, period and operating frequency, but formed by 7.76 nm layers of silicon with $\epsilon=15$ and 7.24 nm layers of silver with $\epsilon=-14$.Comment: 4 pages, 4 figures, submitted to PR