Evidence of Bloch wave propagation within photonic crystal waveguides

We report in this paper results obtained from characterizations of photonic band gap waveguide, using near field optical microscopy. We will show evidence of a Bloch wave propagating within our W1 photonic crystal waveguides (PCWs) structure, using a 2D Fourier transform approach. The processed image will then be compared to simulations obtained from plane wave method. This comparison exhibits that near-field measurements, using tapered optical fibers as probes, are mainly sensitive to the electric field propagating within the structure. PACS 42.25.-p; 42.30.Va; 42.770.-Qs; 42.82.-Et     

Real-space observation of ultraslow light in photonic crystal waveguides

We show the real-space observation of fast and slow pulses propagating inside a photonic crystal waveguide by time-resolved near-field scanning optical microscopy. Local phase and group velocities of modes are measured. For a specific optical frequency we observe a localized pattern associated with a flat band in the dispersion diagram. During at least 3 ps, movement of this field is hardly discernible: its group velocity would be at most c/1000. The huge trapping times without the use of a cavity reveal new perspectives for dispersion and time control within photonic crystals.     

Experimental observation of strong photon localization in disordered photonic crystal waveguides

We demonstrate experimentally that structural perturbations imposed on highly dispersive photonic crystal-based waveguides give rise to spectral features that bear signatures of Anderson localization. Sharp resonances with effective Q's of over 30 000 are found in scattering spectra of disordered waveguides. The resonances are observed in a approximately 20-nm bandwidth centered at the cutoff of slowly guided Bloch modes. The origin of the spectral features can be explained by the interference of coherently scattered electromagnetic waves which results in the formation of a narrow impurity (or localization) band populated with spectrally distinct quasistates. Standard photon localization criteria are fulfilled in the localization band.     

Packing density of conventional waveguides and photonic crystal waveguides

We compare coupling between parallel waveguides within one-dimensional photonic crystals and coupling between conventional waveguides. We consider the situation in which coupling between the waveguides is minimized, so that light in the waveguides propagates essentially independently. Subject to this condition, we compare the minimum mutual distance between conventional planar waveguides and waveguides in one-dimensional photonic crystals. We find that the packing densities of the conventional and periodic structures are comparable.     

Silicon-based two-dimensional photonic crystal waveguides

A review of the properties of silicon-based two-dimensional (2D) photonic crystals is given, essentially infinite 2D photonic crystals made from macroporous silicon and photonic crystal slabs based on silicon-on-insulator basis. We discuss the bulk photonic crystal properties with particular attention to the light cone and its impact on the band structure. The application for wave guiding is discussed for both material systems, and compared to classical waveguides based on index-guiding. Losses of resonant waveguide modes above the light line are discussed in detail.     

Optical trirefringence in photonic crystal waveguides

We demonstrate that 2D photonic crystals can possess optical trirefringence in which there are six field orientations for which linear incident light is not perturbed on reflection or transmission. Such a property is rigorously forbidden in homogeneous nonmagnetic dielectrics which can possess only optical birefringence. We experimentally demonstrate this phenomena in silicon-based mesostructures formed from photonic crystal waveguides embedded in a Fabry-Perot cavity. Multirefringence is controlled by the presence of submicron dielectric patterning and is well explained by an exact scattering matrix theory.     

Modes of coupled photonic crystal waveguides

We consider the modes of coupled photonic crystal waveguides. We find that the fundamental modes of these structures can be either even or odd, in contrast with the behavior in coupled conventional waveguides, in which the fundamental mode is always even. We explain this finding using an asymptotic model that is valid for long wavelengths.     

Antiresonant reflecting photonic crystal optical waveguides

We propose a simple analytical theory for low-index core photonic bandgap optical waveguides based on an antiresonant reflecting guidance mechanism. We identify a new regime of guidance in which the spectral properties of these structures are largely determined by the thickness of the high-index layers and the refractive-index contrast and are not particularly sensitive to the period of the cladding layers. The attenuation properties are controlled by the number of high/low-index cladding layers. Numerical simulations with the beam propagation method confirm the predictions of the analytical model. We discuss the implications of the results for photonic bandgap fibers.     

Anomalous propagation loss in photonic crystal waveguides

Propagation loss can occur in photonic crystal waveguides without complete optical confinement. We employ a highly efficient transfer-matrix method which allows for accurate and reliable extraction of the propagation loss even at an extremely low level. The results for a two-dimensional photonic crystal waveguide shows that the loss exponentially decays via the waveguide wall thickness. An anomalous phenomenon is found where the loss for guided modes near the upper band gap edge can be several orders of magnitude smaller than that for modes in the middle of the band gap. This anomaly can be well explained by the localization degree of guided modes at different frequency domains.     

Coupling into slow-mode photonic crystal waveguides

We study efficient injectors for coupling light from z-invariant ridge waveguides into slow Bloch modes of single-row defect photonic crystal waveguides. Two-dimensional vectorial computations performed with a Bloch mode theory approach predict that very high efficiencies (>90%) can be achieved for injector lengths of only a few wavelengths in length, even for small group velocities in the range of c/100-c/400. This result suggests that photonic crystal devices operating with slow waves can be interfaced with classical waveguides without sacrificing compactness.     

Efficient couplers for photonic crystal waveguides

We use two-dimensional simulations to study the design of tapers to provide efficient, low reflection coupling between a waveguide in a two-dimensional photonic crystal (PC) and free space. We find that, largely independent of the PC parameters, or of the length and width of the tapered region, the same type of concave, horn-shaped tapering profile is optimal for coupling from the waveguide into free space, and significantly out-performs the widely used linear taper. We also find that optimal tapers can radiate nearly Gaussian beams, and therefore they can also provide efficient coupling of Gaussian beams from free space into the PC waveguide. These properties are better exhibited by rod-type PCs with E_z polarization than by hole-type PCs with H_z polarization. This study of taper couplers exemplifies a design strategy for photonic circuits which optimizes positioning of the cylinders immediately surrounding the light path, and then builds the rest of the crystal structure around these cylinders.     

Advanced impedance matching in photonic crystal waveguides

We demonstrate that the dispersion of guided propagating modes in certain Photonic Crystal Waveguides (PCWGs) can be kept constant when the waveguide’s structure changes along the propagation direction. This suggests that the principle of constant group velocity matching may be utilized to improve impedance matching between different types of PCWGs while at the same time providing significant design flexibility. We illustrate this principle through the design of several efficient coupling structures between two different PCWGs via a local density of states and Fourier transform analysis of the associate electromagnetic fields. The couplers consist of heterostructures whose individual sections exhibit rather distinct structural parameters. Furthermore, we compare these structures to an adiabatic coupler.     

Experimental observation of evanescent modes at the interface to slow-light photonic crystal waveguides

We experimentally study the fields close to an interface between two photonic crystal waveguides that have different dispersion properties. After the transition from a waveguide in which the group velocity of light is v(g) ~ c/10 to a waveguide in which it is v(g) ~ c/100, we observe a gradual increase in the field intensity and the lateral spreading of the mode. We attribute this evolution to the existence of a weakly evanescent mode that exponentially decays away from the interface. We compare this to the situation where the transition between the waveguides only leads to a minor change in group velocity and show that, in that case, the evolution is absent. Furthermore, we apply novel numerical mode extraction techniques to confirm experimental results.     

Development of curved two-dimensional photonic crystal waveguides

A two-dimensional photonic crystal waveguide with a novel geometry is introduced. The center line of this waveguide is bent along a free-curve such that the direction of the propagating light can be changed without scattering or reflection losses. The design method is described for a triangular lattice, its optical properties such as transmission spectrum and dispersion relation are calculated, and actual devices are then fabricated and demonstrated that they worked as optical waveguides.     

Diffraction engineering in arrays of photonic crystal waveguides

Light propagation in uniform arrays of photonic crystal waveguides is studied. We demonstrate that, in stark contrast to the case of conventional waveguide arrays, diffraction can be tailored both in magnitude and sign by varying only the spacing between adjacent waveguides. Diffraction management in ultracompact arrays of straight photonic crystal waveguides is demonstrated by solving Maxwell's equations through the time-domain finite-element method.     

Tight-binding method modelling of photonic crystal waveguides

We present here a tight-binding-like modelling of two-dimensional (2D) photonic crystals (PCs). Adopted from solid-state physics, the concept of generalized Wannier functions is used to construct a localized state basis that allows a parameter-free ab initio study of defects in PCs. We demonstrate here for a 2D triangular lattice of dielectric rods in air, the existence of this localized basis and the possibility to study large scale complex dielectric structures deviating from periodicity. Specific numerical simulations on a split waveguide embedded in this triangular lattice are performed, and they demonstrate the superiority of this method over plane wave based techniques.     

Tight-binding method modelling of photonic crystal waveguides

We present here a tight-binding-like modelling of two-dimensional (2D) photonic crystals (PCs). Adopted from solid-state physics, the concept of generalized Wannier functions is used to construct a localized state basis that allows a parameter-free ab initio study of defects in PCs. We demonstrate here for a 2D triangular lattice of dielectric rods in air, the existence of this localized basis and the possibility to study large scale complex dielectric structures deviating from periodicity. Specific numerical simulations on a split waveguide embedded in this triangular lattice are performed, and they demonstrate the superiority of this method over plane wave based techniques.     

Improved Y-splitter photonic crystal waveguides in terahertz regime

Using the finite-difference time-domain method, the electromagnetic field distribution of terahertz waves in different photonic crystals Y-splitters were simulated. By continuous wave excitation of the guided mode, the simulation results show that those different Y-splitters can divide the power in an input wave guide equally between two output waveguides. By pulse excitation of a Gaussian envelope in time, the different Y-splitters have large different amplitude-frequency characteristics. The improved Y-splitter with a rod in the junction and without rods in the corners has widest −3-dB bandwidth 0.224 THz, and the amplitude reaches 0.616. The improved Y-splitter has better performance than other Y-splitters. These results provide a useful guide and a theoretical basis for the developments of terahertz functional components.     

Beaming effect from increased-index photonic crystal waveguides

We study the beaming effect of light for the case of increased-index photonic crystal (PhC) waveguides, formed through the omission of low-dielectric media in the waveguide region. We employ the finite-difference time-domain numerical method for characterizing the beaming effect and determining the mechanisms of loss and the overall efficiency of the directional emission. We find that, while this type of PhC waveguide is capable of producing a highly collimated emission as was demonstrated experimentally, the inherent characteristics of the structure result in a restrictively low efficiency in the coupling of light into the collimated beam of light.