Surface electromagnetic waves at the interface between a homogeneous medium and a system of coupled waveguides

An analysis is made of the experimental investigations of the surface waves existing at the interface between a homogeneous medium and a periodically stratified medium that represents a bounded system of coupled waveguides. It is shown that, in all cases of the observation of surface waves, the bounded system of coupled waveguides has its own spectrum of guided modes and a spectrum of leaky modes that become surface waves of the system. It is also demonstrated that a biosensor can successfully operate when two surface waves serve as leaky modes of a Bragg waveguide in which the periodic system of waveguides is used as a distributed Bragg mirror of this waveguide. A structure supporting surface waves is designed on the basis of ten pairs of Nb₂O₅-SiO₂ layers and implemented experimentally. The surface waves are detected with a K8 glass prism according to the Kretschmann scheme.     

Photon recycling in Fabry–Perot micro-cavities based on Si3N4 waveguides

We present a numerical analysis and preliminary experimental results on one-dimensional Fabry–Perot micro-cavities in Si₃N₄waveguides. The Fabry–Perot micro-cavities are formed by two distributed Bragg reflectors separated by a straight portion of a waveguide. The Bragg reflectors are composed of a few air slits produced within the Si₃N₄ waveguides. In order to increase the quality factor of the micro-cavities, we have minimized, with a multiparametric optimization tool, the insertion loss of the reflectors by varying the length of their first pairs (those facing the cavity). To explain the simulation results, the coupling of the fundamental waveguide mode with radiative modes in the Fabry–Perot micro-cavities is needed. This effect is described as a recycling of radiative modes in the waveguide. To support the modelling, preliminary experimental results of micro-cavities in Si₃N₄ waveguides realized with the focused ion beam technique are reported.     

Minimization of losses and calculation of the optical properties of Bragg fiber waveguides with a hollow core

A numerical method for solving the inverse problem of determining the geometry of the multilayer shell of a Bragg waveguide that has the lowest waveguide losses for a given mode has been developed with the use of the genetic algorithm. For the calculated designs of waveguides, the distribution of the coordinates of the boundaries of shell layers has been found to be aperiodic under the condition r ₁ ≤ λ due to the axial symmetry of the problem. Waveguide losses for the TE ₀₁, TM ₀₁, and HE ₁₁ modes satisfy the conditions \(\alpha _{TM_{01} } > \alpha _{HE_{11} } > \alpha _{TE_{01} } \). It follows from the dependence of n _eff obtained for these modes on the core radius and number of shell layers that any change in the structure of the waveguide leads to the violation of the optimal propagation regime for these modes. A Bragg fiber waveguide with a hollow core that is designed for the TE ₀₁ mode and directs light in the single-mode regime is presented. The main fraction of losses in this waveguide is attributed to material absorption.     

Analytical solution of the scalar wave equation for slightly deformed optical Bragg waveguide

Using a simple analytical method, we study the electromagnetic-wave propagation in an optical Bragg waveguide which is slightly deformed at one side. We show the results of computations in the form of dispersion curves and provide a comparison with standard circular Bragg waveguides and step-index circular waveguides. We show that the correspondence between the cutoff V values for the standard step-index fiber and the new Bragg waveguide, which is slightly flattened on one side, is quite close for the lowest mode under the weak guidance condition.     

Bragg waveguide grating as a 1D photonic band gap structure: COST 268 modelling task

Modal reflection, transmission and loss of deeply etched Bragg waveguide gratings were modelled by six European laboratories using independently developed two-dimensional (2D) numerical codes based on four different methods, with very good mutual agreement. It was found that (rather weak) material dispersion of the SiO₂/Si₃N₄ system does not significantly affect the results. The existence of lossless Floquet–Bloch modes in deeply etched gratings was confirmed. Based on reliable numerical results, the physical origin of out-of-plane losses of 1D or 2D photonic band gap structures in slab waveguides is briefly discussed.     

Bragg waveguide grating as a 1d photonic band gap structure: COST 268 modelling task

Modal reflection, transmission and loss of deeply etched Bragg waveguide gratings were modelled by six European laboratories using independently developed two-dimensional (2D) numerical codes based on four different methods, with very good mutual agreement. It was found that (rather weak) material dispersion of the SiO₂/Si₃N₄ system does not significantly affect the results. The existence of lossless Floquet-Bloch modes in deeply etched gratings was confirmed. Based on reliable numerical results, the physical origin of out-of-plane losses of 1D or 2D photonic band gap structures in slab waveguides is briefly discussed.     

Frequency dependence of acoustooptic interaction efficiency in anisotropic graded-index waveguide

An analysis of the dependence of the Bragg acoustooptical interaction efficiency of TE modes in a graded-index optical waveguide on the acoustic surface wave (ASW) frequency has been made. It is shown that two waveguides having different optical parameters but the same number of modes are described practically by the same frequency dependence. This conclusion is confirmed by the calculation for two four-mode waveguides on the Y-cut lithium niobate. The frequency dependence for various processes in the range 50÷550 MHz has been experimentally measured.     

Field transformation in a multimode optical waveguide with random irregularities of the film surface

A self-consistent mathematical model for the transformation of the average intensity of the mode spectrum I(z) of a waveguide field in a multimode planar optical waveguide with a step profile and rough surface is developed. This model is based on the matrix model for multiple scattering of modes in an optical waveguide. The elements of the intermode scattering matrix are found, which describe the process of mutual transfer of the energy of modes along a waveguide and their transformation into radiation modes. The transformation of the I(z) modes in waveguides with large-and small-scale inhomogeneities is investigated. It is shown that the largest qualitative differences in the noted dependences manifest themselves only in the initial portions of the optical waveguide. The length z of these portions is much smaller than the characteristic scale length L _k at which the fundamental energy of the kth mode excited in the optical waveguide is renewed. The effect of self-filtration of the mode spectrum I(z) is described, as a result of which a stable (normalized), independent of distance z, distribution I* is formed. It is established that irregularities of the optical waveguide boundaries exert a depolarizing effect on a guided light beam. The specific features of the normalization of the radiative dissipation of a group of modes I_i(z) in an optical waveguide are investigated. It is ascertained that, in the case of small-scale irregularities, the attenuation coefficient is described by a nonlinear monotonic dependence α(z), which asymptotically converges to the value α*, characteristic of the normalized field I*. When the optical-waveguide film has large irregularities, the dependence α(z) is characterized by a pronounced maximum due to the formation of alternative channels of radiative dissipation of the energy of waveguide modes.     

Fundamental losses in planar Bragg waveguides

This paper considers a planar Bragg waveguide. The guided modes and their dissipation due to the fundamental absorption are described. In the interacting-wave approximation, an analytical relation between the characteristics of the modes and parameters of the Bragg-waveguide geometry was established. Absorption losses in hollow Bragg waveguides were shown to be significantly lower than in a regular waveguide fabricated from the same material. Quantitative estimates of the fundamental and radiation losses in Bragg waveguides are given for materials used at wavelengths of 1.55, 10.6, and 0.245 μm.     

On the propagation characteristics of metal clad waveguides with a quantum well

The electromagnetic modes of planar metal clad dielectric waveguides containing an n-doped quantum well (QW) are studied theoretically. Special attention is paid on the coupling between metal surface plasmons and intersubband plasmons and the manifestation of this coupling in the propagation characteristics of metal/QW/dielectric and multimode metal/QW/dielectric/metal waveguide structures. The results obtained indicate that the modification of the propagation characteristic induced by the above-mentioned coupling is substantial only in the case of metal/QW/dielectric waveguide structures.     

Wave propagation in a waveguide with continuous right-angled corners: Numerical simulations and experiment measurements

This paper studied the acoustic wave propagation in a waveguide with continuous right-angled corners, with emphasis on the effect brought by the distance between the corners. The numerical analyses showed that at middle to high frequencies, the transmission loss (TL) of a multi-cornered waveguide was 2–5 dB higher than that of single-cornered and varied with frequency. To explain the performance at peaks and dips in the TL curve, analyses on eigenmodes and sound intensity distribution were conducted. The performance of multi-cornered waveguides was experimentally investigated, which fit well with the numerical results. The present study indicates that, for a waveguide with continuous corners, its acoustic performance is not simply a “summation” of two individual single-cornered ones. Both the standing wave modes and the evanescent modes between the corners lead to its complicated frequency performance.     

FWM in silicon nanocrystal-based sandwiched slot waveguides

The observation of four-wave mixing in a 6 mm long sandwiched slot waveguide filled with Si-nc/SiO₂ is reported for optical powers usually employed in telecommunication systems. A −47 dB conversion efficiency is measured in fabricated waveguides for input signal powers around 12 dBm on chip and a waveguide length of 6 mm. Furthermore, the calculated non-linear coefficient is found to be n₂ = 2.67 × 10⁻¹⁷ m²/W. It is also expected that, by using longer waveguides, it would be possible to achieve wavelength conversion.     

Bragg reflection waveguide: Anti-mirror reflection and light slowdown

The effect of the light group velocity reduction in dielectric Bragg reflection waveguide structures (SiO₂/TiO₂) in the vicinity of the cutoff frequency is studied experimentally. The effect of anti-mirror reflection specific to Bragg reflection waveguides is described and employed to detect slow light. Experiments were performed using Ti:sapphire laser pulses ∼100 fs in length. The group index n _g ∼ 30 with a fractional pulse delay (normalized to the pulse width) of ∼10 is demonstrated. The problems and prospects of the implementation of slow-light devices based on Bragg reflection waveguide structures are discussed.     

Asymmetric planar luminescent waveguide based on amorphous silicon carbide with polarized radiation in leaky modes

Plasma-enhanced chemical vapor deposition is used to fabricate asymmetric planar luminescent waveguides (APWs) based on amorphous silicon-carbide films with submicron thickness on quartz substrates. Narrow peaks of linearly (P and S) polarized radiation related to the emission in the APW leaky modes are detected in the APW emission spectra from the end surface of a substrate under excitation of photoluminescence. The dependence of the spectral positions of peaks on the angle at which the radiation is emitted from the end surface and the film thickness is analyzed. At grazing angles of emission, the radiation wavelength is almost independent of the angle. It is demonstrated that the difference between the wavelengths of the P- and S-polarized peaks in the PL spectra decreases with an increase in the waveguide thickness. The waveguide works as an optical microcavity for leaky modes. The amplitude of the S-polarized peak is higher than the amplitude of the P-polarized peak due to the fact that the Q factor for the S-polarized leaky modes is greater than the Q factor for the P-polarized leaky mode. The luminescent APWs can be used to generate optical beams with radial and azimuthal polarizations.     

Property study of Si + -ion-implanted Nd:YVO 4 waveguides

Planar waveguides were formed in Nd:YVO₄ crystals by 3.0-MeV Si⁺-ion implantation at doses of 1×10¹³–1.5×10¹⁵ ions/cm² at room temperature. The effective refractive indices of the waveguide propagation modes were measured by using a prism-coupling method. It was found that the number of the propagation modes is dependent on the doses for the waveguides in Nd:YVO₄. The atom displacement in the near-surface region (about 2 μm beneath the surface) of the Nd:YVO₄ crystal induced by the implantation was simulated by using the TRIM 98 (transport and range of ions in matter) code. The possible reasons for the waveguide formation are discussed in a primary way. Received: 17 July 2002 / Revised version: 20 September 2002 / Published online: 11 December 2002 RID="*" ID="*"Corresponding author. Fax: +86-531-8565167, E-mail: drfchen@sdu.edu.cn     

Enhanced refractive index well-confined planar and channel waveguides in KTiOPO<Subscript>4</Subscript> produced by MeV C<Superscript>3+</Superscript> ion implantation with low dose

We report on the fabrication and characterization of planar and channel waveguides in KTiOPO₄ crystals by 6.0 MeV C³⁺ ion implantation with the dose of 1×10¹⁴ ions/cm². The dark mode spectroscopy of the planar waveguide was measured using a prism coupling arrangement. An increase of the both n _x and n _y refractive indices induced by the annealing after implantation is believed to be responsible for waveguide formation. The bright near-field intensity distribution of the transverse-electric and transverse-magnetic modes in the annealed channel waveguide was collected and studied by end-coupling method.     

High-Frequency Backward Waves in Longitudinally Magnetized Gyrotropic Waveguides

Backward waves in waveguides completely filled with magnetoactive plasma (gaseous or semiconductor plasma) have been investigated numerically. It is shown that two types of backward waves exist in such waveguides: cyclotron backward waves and waveguide HE-modes. While the cyclotron modes are backward waves at arbitrary system parameters (plasma density, magnetic field and waveguide radius), the waveguide backward waves appear only at certain values of there parameters. In addition the cyclotron backward waves can propagate at arbitrary wave-number k_z and at arbitrary phase velocity. The backward waveguide modes exist only at limited values of k_z and of phase velocities.     

Direct laser-writing of dielectric-loaded surface plasmon–polariton waveguides for the visible and near infrared

We demonstrate flexible and low-cost fabrication of dielectric-loaded surface plasmon–polariton waveguides. The waveguide structures are fabricated by two-photon polymerization of commercially available, spin-coatable epoxy-based UV-lithographic resist on a metal covered glass slide. The excitation and guiding properties of the plasmonic waveguides are investigated in the far-field at a wavelength of 632.8 nm by imaging the leakage radiation from the waveguide modes. The optimum bending radius for right angle bends is measured to 6 μm providing a transmission of up to 70%. The functionality of more complex Y-splitters is demonstrated.     

The phonon spectra of trigonal selenium at 77 and 298°K

Phonon dispersion curves in the principal symmetry directions of trigonal selenium single crystals have been measured by neutron inelastic scattering, using a three-axis spectrometer. The acoustic modes and the three lowest-lying optical modes (q = 0 energy transfers of 13·5 and 18·5 meV) have been measured at 77°K. The acoustic modes have also been measured at 298°K. There are small frequency shifts between the two temperatures, but the general agreement between the acoustic mode frequencies measured at the two temperatures is excellent. The data have been fit by a force constant model which assumes completely general harmonic forces between the first two neighbors in the same covalently bonded chain and axially symmetric forces derived from a potential of the form V = ? Ar^?m + Br^?n between all other atoms out to an interatomic distance of 6·5 . Fits were carried out with (m; n) = (3; 5) and (6; 12). For the former, the best values of A and B correspond to a Van der Waals equilibrium distance of 3·9and a minimum energy at this distance of 1·5 × 10^?13 ergs (about 2 kcal/mol). There are, however, significant discrepancies between the calculated and observed dispersion curves which indicate that a more sophisticated force model is needed.     

Liquid-core/liquid-cladding integrated silicon ARROW waveguides

The fabrication and characterization of a liquid-core/liquid-cladding integrated antiresonant reflecting optical waveguide (L²-ARROW) is presented. In this waveguide, the light is confined vertically by the ARROW mechanism, whereas the lateral confinement is obtained by using liquid-core/liquid-cladding (L² waveguides) with different refractive indexes. This approach permits to realize L² waveguides with very low refractive index core (n ≈ 1.333) and represents a new solution to solve the difficulty to reduce the optical losses in 2D-ARROWs due to the TM polarization in lateral direction. The device has been fabricated with standard silicon technology. The results show that the optical properties can be tuned by changing the type and the flow velocity of the core and the cladding liquids.