Surface wave effect on light scattering from one-dimensional photonic crystals

Light scattering and reflection measurements using attenuated total reflection technique for s polarization of the incident light on a finite one-dimensional photonic crystal are reported. Angular specular reflection was measured experimentally to determine, the optimum thickness, the angular position of the surface mode, and the number of bi-layers of the system. It was demonstrated that the position of the surface mode inside the last film is close to the asymptotic value when the number of periods is increased. Spectral reflection measurements were made to determine experimentally the band gap width and measure the dispersion relation of the surface mode inside this band. The corresponding field amplitude was calculated (∣E∣²) showing that in resonant conditions it has a maximum near the surface. The angular dependence of the scattered light measured displays a peak caused by singles cattering and located approximately at the excitation angle of the surface electromagnetic mode. When the incident light is in resonance with the surface electromagnetic wave, it is found experimentally that the scattering of light is enhanced overall by approximately one order of magnitude in comparison with the off-resonance case.     

Analytical and numerical study on grating depth effects in grating coupled waveguide sensors

The in-coupling process for grating-coupled planar optical waveguide sensors is investigated in the case of TE waves. A simple analytical model based on the Rayleigh–Fourier–Kiselev method is applied to take into account the depth of the grating coupler, which is usually neglected in the modeling. Analytical expressions are derived both for the position and width of the in-coupling peaks to illustrate the effects of grating depth on the guided mode resonances in grating coupled waveguide sensors. Numerical computations verify the model for shallow gratings both in terms of peak shape and position and provide the limitations for the analytical formulas.     

Flexible Control of Light Propagation Using a Novel Photonic Crystal Hetero-Waveguide Based on Silicon-on-Insulator Slab

We demonstrate a photonic crystal hetero-waveguide based on silicon-on-insulator (SOI) slab, consisting of two serially connected width-reduced photonic crystal waveguides with different radii of the air holes adjacent to the waveguide. We show theoretically that the transmission window of the structure corresponds to the transmission range common to both waveguides and it is in inverse proportion to the discrepancy between the two waveguides. Also the group velocity of guided mode can be changed from low to high or high to low, depending on which port of the structure the signal is input from just in the same device, and the variation is proportional to the discrepancy between the two waveguides. Using this novel structure, we realize flexible control of transmission window and group velocity of guided mode simultaneously.     

Efficient omnidirectional couplers achieved by anisotropic photonic crystal waveguides

Photonic crystals (PCs) have many potential applications because of their ability to control light-wave propagation. We have investigated omnidirectional couplers in two-dimensional anisotropic PC structures. The anisotropic PC coupler composed of an anisotropic-dielectric cylinder in air is studied by solving Maxwell's equations using the plane wave expansion method and finite-difference time-domain method. The photonic band structures are found to exhibit absolute bandgaps for the square lattices. Numerical simulations show that the incident light-waves at both transverse electric and transverse magnetic modes have efficient coupling in anisotropic PC coupler with square lattices. The guided modes and coupling length are analyzed by considering various line defect anisotropic PC waveguides and interaction regions of couplers. Such a mechanism of omnidirectional coupling should open up a new application for designing components in photonic integrated circuits.     

Photonic crystal waveguides and their applicationsInvited Paper

Two-dimensional (2D) slab photonic crystal waveguides (PCWGs) on silicon-on-insulator (SOI) wafer were designed and fabricated. Full photonic band gap, band gap guided mode, and index guided mode were observed by measuring the transmission spectra. Mini-stop-bands in the PCWG were simulated with different structure parameters. Coupling characteristics of PCWG were investigated theoretically considering the imperfections during the fabrication process. It was found that suppressing power reservation effect can realize both short coupling length and high coupling efficiency.     

Flat-topped beam output from a double-clad rectangular dielectric waveguide laser with a high-index inner cladding

A novel method to produce a flat-topped laser beam by using a double-clad rectangular waveguide laser with high-index inner cladding is presented. The waveguide dispersion equation for cosine mode was deduced, the condition for the flattened mode was given out, relative gains for guided modes were calculated numerically and analyzed. Results indicate that a gain advantage for the flattened mode is clear, a flat-topped laser beam can be achieved when the optical confinement factor, the gain intensity and the output coupler are chosen suitably.     

Multi-layer cladding leaky planar waveguide for high-power applications

We design a multi-layer cladding large-core planar waveguide that supports a single guided mode. The waveguide works on the principle of higher-order mode discrimination. The cladding of the waveguide is formed by alternate low- and high- index regions, which helps leaking out of higher-order modes while retaining the fundamental mode over the entire length of the waveguide. The structure is analyzed by the transfer-matrix method and the leakage losses of the modes have been calculated. We show that a waveguide formed in silica with numerical aperture 0.24 and core width 10 μm can be designed to exhibit single-mode operation at 1550-nm wavelength. Such a structure should find applications in high-power planar waveguide lasers and amplifiers.     

Wave propagation in uniaxial graded-index optical waveguides

Propagation of guided-modes in uniaxial optical waveguides is investigated. When the optical axis lies in the plane of the waveguide, a coupling between TE and TM modes takes place. Based on the coupled-mode theory, the propagating constants of the hybrid modes, the coupling coefficient and the interaction length are determined. A simple model is proposed to describe the guided mode behaviour. The results are illustrated for the case of Ti-diffused LiNbO₃ waveguide.     

A novel compact wavelength-division multiplexer using highly dispersive waveguide-to-waveguide coupling

A novel compact wavelength-division multiplexer using highly dispersive waveguide-to-waveguide coupling is designed, simulated and analyzed. The device consists of two very close single-moded waveguides that are periodically connected to form a mode-dependent dispersive grating. It is demonstrated that the wavelengths over the edges of the photonic band gap contributed by the grating can be separated in a very short propagation distance. Using the finite-difference time-domain method, the result shows that the wavelengths of 1570 and 1530 nm are separated by the grating in a coupler length of 57 μm which is much shorter than the required length of about 340 μm without grating assistance. The channel contrast of 20 dB and the insertion loss about 2 dB are achieved.     

Planar Er- and Yb-doped amplifiers and lasers

New results in erbium-doped planar waveguide amplifiers and lasers are presented. The waveguides are produced in silica-on-silicon technology using plasma-enhanced chemical vapor deposition. Waveguide propagation losses outside the erbium absorption band are improved to values below 0.05 dB/cm for a core–cladding index step of around 1.4%. Amplifier arrays show a net gain of more than 12 dB over the entire C-band. Received: 13 June 2001 / Published online: 23 October 2001     

Propagation of light through localized coupled-cavity modes in one-dimensional photonic band-gap structures

We report on the observation of a new type of propagation mechanism through evanescent coupled optical cavity modes in one-dimensional photonic crystals. The crystal is fabricated from alternating silicon-oxide/silicon-nitride pairs with silicon-oxide cavity layers. We achieved nearly full transmission throughout the guiding band of the periodic coupled cavities within the photonic band gap. The tight-binding (TB) parameter κ is determined from experimental results, and the dispersion relation, group velocity and photon lifetime corresponding to the coupled-cavity structures are analyzed within the TB approximation. The measurements are in good agreement with transfer-matrix-method simulations and predictions of the TB photon picture. Received: 21 August 2000 / Revised version: 22 August 2000 / Published online: 9 November 2000     

Experimental observation and numerical simulation of guided modes in Nd:YLiF4 channel waveguides produced by carbon ion implantation

We report on, to our knowledge the first time, the channel waveguide formation in Nd:YLiF₄ laser crystal produced by 6 MeV carbon ion implantation. The guided modes are observed by using an end‐face arrangement. We construct the two‐dimensional (2D) refractive index profile of the channel waveguide cross section, which is based on the related planar waveguide index distribution as well as the rectangular shape of the waveguide cross sections. The modal intensity distribution is numerically calculated by using the beam propagation method according to the reconstructed index profile, which shows a reasonable agreement with the experimental result. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Influences of supercell termination and lateral row number on the determination of slow light properties of photonic crystal waveguides

We systematically analyze the effects of the use of an inaccurate supercell termination and an insufficient supercell size of plane-wave expansion method on the dispersion and the slow light properties of the photonic crystal waveguides. The inattentive use of supercells of photonic crystal waveguides appeared in the literature is found to be yielding errors in the dispersion and slow light characteristics of the fundamental guided mode of photonic crystal waveguides. In addition, extra modes appear in the photonic band gap of the photonic crystal waveguide due to inaccurate supercell termination. By examining the field distribution of the modes, the extra modes can be determined and removed from the band diagram. The dispersion, group index and bandwidth characteristics are observed to be less affecting from inaccurate supercell termination as the number of rows adjacent to the waveguide increases. Moreover, the dispersion and the group index-frequency curves of the fundamental guided mode of correctly terminated supercells are found to be converging as the lateral row number along the line-defect is increased.     

Nonlinear waves guided by a dielectric slab

An exact solution of Maxwell's equations is found for TM-polarized nonlinear guided waves which are guided by a linear dielectric slab embedded between two nonlinear uniaxial media. Additional waves in comparison with the linear case arise. Some of these waves have no counterpart in linear systems. Similarities and differences with respect to TE-polarized nonlinear guided waves are pointed out.     

Three-mode coupling in a passive dielectric waveguide with index modulation

The characteristics of a three-mode coupling in a passive dielectric waveguide are investigated for the case of even TE modes. The index is assumed to have a doubly periodic harmonic variation in the propagation direction. By a singular perturbation procedure using multiple space scales, the coupled-mode equations governing the Bragg interactions are systematically deduced. The three-mode coupling causes a stop band in frequency and the characteristics of the resulting evanescent mode are analyzed. For a periodic dielectric waveguide of finite length, the three coupled-mode equations are solved subject to suitable boundary conditions to obtain the reflection and the transmission coefficients. The frequency response of the reflection and the transmission coefficients are investigated and compared with the results of the pair of corresponding two-mode couplings. Representative numerical results are presented to illustrate the characteristics of the interaction of the three modes.     

Self-collimation and self-imaging effects in modulated waveguide arrays

Self-collimation and self-imaging are comparatively investigated for discretized light in engineered modulated arrays of optical waveguides. It is shown that self-imaging is a rather extraordinary effect related to a fortuitous band collapse and it is thus rather distinct from self-collimation.     

Low-loss, compact waveguiding with TE mode in metal/dielectric waveguides for planar lightwave circuit

We propose a low-loss metal/dielectric waveguide for compact planar lightwave circuit. The basic waveguide structure is a metal-defined high-index-contrast strip waveguide based on silicon/silica. As the guide is designed for TE single mode waveguiding, extremely low propagation loss (e.g. <0.04 dB/cm), very low bend loss (e.g. 0.0043 dB/90°-turn) and small waveguide pitch of zero-crosstalk are theoretically achievable, and can be further improved by compromising with component size and density. Examples of multi-bends and device integration are demonstrated with numerical simulations. The proposal is compatible with silicon technology and appealing for development of silicon-based planar lightwave circuit.     

Transverse mode competition in defect states of a waveguide with corrugated walls

We investigate the defect states arising in the Bragg and non-Bragg gaps by inserting a straight duct into a waveguide with periodically corrugated walls. In periodic waveguides, the Bragg gap is created by the interference of the same transverse modes whereas the different mode coupling leads to the non-Bragg one. Due to the involved high-order modes, there are two defect states observed in the non-Bragg gap while only one in the Bragg gap, indicating that transverse modes play a significant role in the creation of defect states. Furthermore, the frequency of each defect state highly relies on the defect geometries and their band widths can be optimized by the number of waveguide segments. The proposed transverse mode competition analysis reveals the mechanism of frequency shifting and provides an opportunity for guided wave control engineering, which would definitely benefit their applications in various functional devices, such as filters, sensors, and amplifiers.     

Design, realisation and analysis of an apodised, film-loaded acousto-optic tunable filter

The design and realisation of a SiO₂ film-loaded Ti:LiNbO₃ integrated acousto-optic tunable filter are presented. An optimised Hamming apodisation is achieved through introducing an angular offset between the acoustic and optical waveguides along with carefully placed acoustic absorbers. The realised device has a 20-mm acoustic interaction length and achieves a 3-dB linewidth of 1.8 nm with 19-dB sidelobe suppression. The realised device is highly efficient, requiring a RF drive power of only 10 mW to achieve complete polarisation conversion. The enhanced drive efficiency of the device is analysed using both acoustic and optical mode analysis. Based on this analysis, possible explanations for the improved behaviour are presented and directions that may lead to further enhancements are discussed. Received: 18 May 2001 / Revised version: 7 August 2001 / Published online: 23 October 2001     

Optical properties of MgxZn1−xO nanowire photonic crystals

We investigate the optical properties of two-dimensional periodic arrays of well-aligned Mg_xZn_1−xO nanowires, i.e., Mg_xZn_1−xO nanowire photonic crystals. The nanowire photonic crystal can exhibit a photonic band gap in the visible range. As the mole fraction of Mg, x, increases, the edge frequencies of the band gap increase and the band gap size decreases. The characteristics of relative band gap and vacant point defect mode are also studied with varying x. From the finite-difference time-domain simulations, we show that the light extraction from nanowires can be controlled by varying the distance between optically excited nanowires and a waveguide, and the mole fraction of Mg. Controlling the light extraction from nanostructures can be useful in the implementation of nanoscale light emitting devices.