Leakage in LiNbO3 channel H-waveguides

Attenuation of leaky modes in LiNbO₃ channel H-waveguides is studied theoretically. It is shown that leakage significantly affects the parameters of waveguides made of X-and Y-cut crystals. An approximate expression for attenuation coefficients is obtained from the solution to the scalar eigenvalue problem.     

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.     

Optical fibre: Spatial transient and steady state

The concept of spatial transient is introduced to better appreciate the role of leaky modes on optical waveguides of circular cross section. Refracting leaky modes represent a relatively fast transient while tunnelling leaky modes represent a relatively slow transient. Bound modes provide the spatial steady-state solution. The greater the waveguide parameter V, the greater the duration of the transient. The relevance of leaky modes on fibres with loss and irregularities is discussed.     

Variational analysis of Er:Ti:LiNbO3 waveguide lasers based on Gaussian/two-half Gaussian mode field distribution

Starting with two dimensional, scalar wave equation, a variational equation was established for the fundamental TE and TM modes guided in Ti:LiNbO₃ waveguides on the basis of assuming a symmetric Gaussian mode field function in the width direction and two-half Gaussian trial functions in the depth direction. The controllable waveguide fabrication parameters, including channel width, diffusion temperature, initial Ti-strip thickness and diffusion time, dependent of fundamental mode size, effective pump area, coupling efficiency between pump and laser modes, and the coupling loss between a Ti:LiNbO₃ waveguide and a fiber were numerically calculated for Z-cut Er:Ti:LiNbO₃ channel waveguide lasers at three possible emission wavelengths 1532,1563 and 1576 nm and two possible pump wavelengths 1480 and 980 nm. The calculated results were compared with those of Gaussian/Hermite–Gaussian mode field distribution in detail.     

Leaky mode analysis of circular optical waveguides

A leaky mode is a bound mode below its cut-off frequency. It attenuates in the direction of propagation and approximates the portion of the radiation field within the optical waveguide that is significant far from the source. The characteristics, including attenuation coefficients, of leaky modes on the circular fibre are compared with those of the more familiar slab waveguide. Except for the HE_1m leaky modes, leaky modes attenuate much faster on the slab than on the circular fibre. The greater the /(azimuthal field variation) the smaller the attenuatioN. Thus, theI?1 leaky modes are important even at great distances from the source. An effective cut-off frequency is proposed. Above this frequency the mode is either weakly leaky or trapped. An expression for the number of weakly leaky and trapped modes is given. The power of leaky modes due to illuminating one end of the fibre is determined. The effect of material absorption is considered.     

Analysis of arbitrary index profile planar optical waveguides and multilayer nonlinear structures: a simple finite difference algorithm

we present here a simple numerical method to obtain the mode effective indices as well as field distributions of modes of any arbitrary profile planar optical waveguide. The method is based on the solutions of scalar and semivectorial Helmoltz’s equation by finite difference algorithm and devised with a field convergence technique. This approach is quite general and can be applied straightforwardly to calculate the guided as well as quasi- or leaky modes of any arbitrary planar structure without the need to solve any eigenvalue equation or any complex matrix formalism. Besides providing the ease of application, the algorithm is particularly useful for waveguides with any graded index profile or with irregular multilayered structure and multilayered waveguides with a localised arbitrary nonlinear film. The performance of our method is verified against typical problems with analytical solutions or having results known otherwise, and is shown to yield results with good accuracy.     

Circular Fourier analysis of modes in optical waveguides under critical and supercritical conditions

An extension of the circular Fourier analysis of the mode field is presented that makes it possible to obtain a successively correctable solution to the scalar waveguide problem posed for 3D optical waveguides. The critical frequencies of rectangular and elliptic waveguides, as well as the characteristics of leaky modes in microstructural optical fibers formed by elliptical air channels, are studied.     

Numerical algorithm for waveguide and leaky modes determination in multilayer optical waveguides

A new algorithm for waveguide and leaky modes spectrum calculation in multilayer planar waveguides is proposed. The method is of high computational efficiency due to the preliminary search for propagation constants approximation. Numerical efficiency of this algorithm is demonstrated for several waveguide structures. Waveguide and leaky modes propagation constants calculated for these structures using proposed method are in good agreement with previously published results.     

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.     

Design of Planar Optic Sensors for Hydrocarbon Detection

A realistic design of evanescent field optical sensors, constituted by three different kinds of planar waveguides covered by a sensing polymeric overlay, is performed. More precisely, the slab, the embedded strip and the ridge waveguides are considered. The sensor operation is simulated, in both the cases of lossy guided and leaky mode propagation, via a home made computer code. The optimal waveguide transverse section and length are identified, the advantages and drawbacks are shown. The ridge waveguide sensor exhibits appreciable characteristics: for a concentration C _w = 200 ppm of toluene in water, the absorbance pertaining to a device L = 2.6 cm long and for the guided quasi-TE₀₀ mode is A ≅ 5, while it is A ≅ 0.054 for a device long L ≅ 24.1 μm and the leaky quasi-TE₁₀ mode. The simulation results suggest that a selective excitation of the suitable propagation mode can enhance the sensor performance.     

Design and comparison of single-mode planar and ridge type electro-optic waveguide modulators

Electro-optic waveguide modulators utilizing phase retardation of two orthogonally polarized optical modes in LiNbO₃ and LiTaO₃ waveguides have been designed taking into consideration the optical field distribution in the waveguides and the electrical properties of the electrodes. The analysis has revealed that a driving-voltage to frequency-bandwidth ratio of 1 V/GHz is attainable at the wavelength of 1.05 m using presently available embedded and ridge waveguides. Improvement in waveguide fabrication techniques may reduce the ratio by at least a half. Thus, LiNbO₃ and LiTaO₃ waveguide modulators are considered to be promising candidates for practical application to single-mode optical-fibre transmission systems of higher than 1 Gbit/s.     

WKB analysis of guided and semileaky modes in graded-index anisotropic optical waveguides

WKB analysis of graded-index anisotropic optical waveguides is briefly presented. The angular dependencies of the propagation characteristics of both guided and semileaky modes are calculated numerically for the out-diffused and in-diffused LiNbO₃ waveguides with parabolic index profile. The results for the out-diffused waveguide are compared with those obtained from the rigorous theory and the applicability of the WKG method is discussed for semileaky mode loss calculations. The angular dependence of the propagation constants of a TiO₂-diffused LiNbO₃ waveguide is demonstrated experimentally, too.     

Mode classification and loss mechanism in air-core Bragg fibers

With an equivalent mode-solving model, the mode spectra in air-core Bragg fibers are systematically studied by using an improved full-vector finite-difference method. All supported modes are classified into four categories, namely, guided modes, cladding modes, leaky modes and PML modes, among which the leaky modes can be further subdivided into radiation-like and evanescence-like leaky modes. To ensure that the modes are solved accurately and efficiently with this model, the strategy for choosing model parameters is suggested. Benefiting from this convenient mode solver, the characteristics of cladding modes are observed in details, and potential applications are suggested. Moreover, the rapid loss of a hybrid mode at lower frequencies is explained by an evanescence-like leaky mode induced cutoff, which is different from that of TE₀₁ mode due to the failure of band gap confinement.     

Orthogonality Conditions for Leaky Modes

We consider various approaches for normalization of leaky modes of open waveguides. General properties of such modes and their relation to continuous-spectrum modes are studied. Applicability of perturbation theory for calculating the shift of mode propagation constants in the case of small variations in the waveguide structure is discussed. General relations are illustrated by an example of a waveguide in the form of a channel inside a dielectric. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 48, No. 5, pp. 388–401, May 2005.     

Tailoring of the spectral–directional characteristics of rare-earth fluorescence by metal–dielectric planar structures

It is demonstrated that the spectrum, direction and polarization of rare-earth fluorescence can be tailored by embedding the impurity ions into a planar metal–dielectric structure (MDS). The latter was designed by spin coating a rare-earth-doped oxide film (TiO₂:Sm³⁺) onto a gold-covered glass substrate. For spectral–directional investigations of Sm³⁺ fluorescence, the MDS was attached to a semi-cylindrical prism and excited by UV light from the flat side. An angular scan revealed a strongly polarized and directional emission of Sm³⁺ from the convex side of the prism. The tuning of TiO₂ film thickness in the MDS allows a control of the polarization and direction of the emission bands. A theoretical modeling of the reflectivity of the MDS suggests that the observed angular resonances in the fluorescence emission are caused by its effective coupling with surface plasmons on the gold–dielectric interface or coupling with leaky modes in sufficiently thick dielectric films working as a waveguides.     

Complete leaky mode coupling in dual-core photonic crystal fibre based on the coupled-mode theory

This paper theoretically investigates the dependence of leaky mode coupling between inner core fundamental mode and outer core defect mode on phase and loss matching in pure silica dual-core photonic crystal fibres with the multi-pole method. The complete mode coupling can take place when both the phase and loss matching conditions are satisfied at the avoided anti-crossing wavelength. It shows the influences of cladding structure parameters including the diameters of cladding air holes d₁, diameters of outer core holes d₂ and hole to hole pitch Λ on the characteristics of leaky modes coupling. The coupled-mode theory is used to analyse the mode transition characteristics and the complete coupling can be clearly indicated by comparing the real and imaginary parts of propagation constant of the leaky modes.     

New method for calculating the spectra and radiation losses of leaky waves in multilayer optical waveguides

The efficiency of a new method for calculating the spectrum and attenuation coefficient of leaky electromagnetic modes is demonstrated with multilayer planar optical waveguides the guiding properties of which are determined by antiresonant reflection from the multilayer cladding (antiresonant reflecting optical waveguides) rather than by total internal reflection from the core-cladding interface as in standard optical waveguides. The new method applies to calculation of both electromagnetic modes in dielectric waveguides and electron quantum states in multibarrier semiconductor heterostructures. The characteristics of multilayer waveguides calculated by the new method are compared with published data obtained from a complex dispersion relation by the transfer matrix method. As an example, the wavelength dependence of the radiation losses for the first TE mode of a planar optical waveguide containing 52 pairs of layers is calculated.     

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.     

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.     

Proton-implanted optical channel waveguides in Nd<Superscript><Emphasis Type="Bold">3+</Emphasis></Superscript>:MgO:LiNbO<Subscript><Emphasis Type="Bold">3</Emphasis></Subscript>: fabrication,guiding properties,and luminescence investigation

Optical channel waveguides in Nd³⁺:MgO:LiNbO₃ crystals are produced by using implantation of 500 keV protons at dose of 6×10¹⁶ ions/cm² with a stripe photoresist mask. With thermal annealing treatment at 400°C for 60 min, the propagation losses of the waveguides could be reduced down to ∼4 dB/cm at wavelength of 632.8 nm. The calculated modal profiles are in fairly good agreement with the experimental near-field intensity distributions of the waveguide modes. The microluminescence investigation indicates the emission intensity of Nd³⁺ ions is only slightly modified with respect to the bulk, exhibiting potentials for laser applications.