Formation and characteristics of graded-index optical waveguides buried in glass

Low-loss optical waveguides have been prepared through thermally induced ion exchange, where sodium ions in glass are replaced by silver ions from an unstirred silver nitrate melt. The index distributions of the inhomogeneous guides produced in the glass are deduced by analysing the measured mode spectra with the WKB-method. The increase in the refractive index caused by the presence of the silver is found to have a nearly Gaussian form with a peak of about 0.082. The index profile is correlated to the two parameters of the preparation process, the diffusion time and the operating temperature. In a typical case (9 hrs and 221°C) the index takes on its maximum value 2.6 μm below the surface of the glass and one obtains an 8-mode guide with five modes buried within the glass and three modes extending to the air-glass interface.A single-mode guide is formed in less than 5 min. The measurements yield an activation energy for the diffusion of Ag⁺ in glass of 8.4·10⁴J/mole and a diffusion coefficient at 221°C of 0.67·10⁻¹² cm²/s, in good agreement with the experimental results reported by other authors. The present observations suggest that a potential gradient is set up in the glass when silver diffuses into it so that the silver ions drift into the glass with a velocity of about 0.3μm/hr.     

Applications of multimode interference effects in gradient waveguides produced by ion-exchange in glass

The paper is concerned with applications of multimode interference structures (MMI) as the elements of integrated optic circuits. Investigations of MMI produced by ion-exchange in glass, obtained by visualization method of light propagation in gradient structures, using fluorescence of the substance covering the MMI section, are presented. Experimental results concern the self-imaging phenomena for symmetrical and paired interference for TE, TM and unpolarized light excitation. On the base of investigations and BPM simulations the applications of MMI are proposed.     

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.     

On the accuracy of WKB analysis of TE and TM modes in planar graded-index waveguides

The TE and TM mode spectra in inhomogeneous optical waveguides with various refractive index profiles have been calculated in the WKB approximation and compared with data obtained numerically from rigorous theory. The effective index errors better than 3 × 10^-4 and 1.5 × 10^-3 have been found for unburied profiles, respectively. The results obtained may help to take full advantage of the WKB analysis for practical purpose.     

On the scalar modal analysis of optical waveguides using approximate methods

We have discussed the approximate methods which are used for obtaining scalar guided modes of optical waveguides. The methods include the perturbation method, the variational method including the Rayleigh-Ritz method, and the Galerkin and the collocation method. The main purpose of this paper is to discuss the inter-relationships and equivalences of these methods, and to bring out the fact that these relationships have, in fact, not been recognized in the guided wave optics literature, although in the numerical electromagnetics and applied mathematics literature some of these relationships are well known. We have also pointed out specific examples where, due to this lack of recognition of relationships, there are repetitions in the literature. In particular, we have noted that the Rayleigh-Ritz method and the Galerkin method have been used using the same set of basis functions for the same kind of waveguides without recognizing the existing literature. We have also reported for the first time an explicit relationship between the Galerkin method and the collocation method. This relationship also points out in which cases one method is more accurate and/or numerically efficient than the other. Another interesting relationship explored is that between the perturbation method and the variational method.     

Kinetics of optical Kerr effect induced by picosecond laser pulses

By use of a double beam technique, we were able to observe, in the OKE dynamics of many non saturated organic compounds, a very fast decay response superimposed upon the much slower decline of the usual effect of molecular origin.     

A numerical investigation of the mode coupling among the local normal modes of sinusoidally modulated parabolic graded-index planar waveguides

We employ the propagating beam method (PBM) to study mode coupling in the framework of the local normal modes of planar, two-dimensional, graded-index optical waveguides. In particular, we examine the effects of periodic radial deformations along the axis of a parabolic, graded-index, waveguide and compare our results to those of perturbation theory. This comparison allows us to establish the accuracy of the PBM and to generate an improved version of a frequently cited PBM formalism based on the full scalar wave equation rather than the Fresnel approximation.     

On the classification of discrete modes in lossy planar waveguides: the modal analysis revisited

In integrated-optical components such as integrated optical detectors or semiconductor light amplifiers, multilayer dielectric waveguiding structures occur in which some layers may be strongly lossy or may have gain. In such structures, the classification of the guided modes may become impossible. This paper reviews the modal analysis in which modes are only considered in connection with their possible excitation with a current line-source. Starting from the lossless situation, the analysis is extended to the lossy case and the details of the classification problem are investigated numerically. It was found that the validity of a unique classification is always limited. For that reason it is investigated, whether the classification problem might be due to the fact that in the time-harmonic formulation, the physical requirement of causality has been lost. To test this hypothesis, wave propagation is investigated along lossy waveguides in the timeLaplace-transform domain and using Lerch's causality theorem. It surprisingly turns out that in the time-Laplace-transform domain, the discrete part of the longitudinal spectrum does not exist, so that the test of the hypothesis is not conclusive. The classification problem of guided modes in strongly lossy waveguides is still an open problem. This revised version was published online in November 2006 with corrections to the Cover Date.     

Review of numerical and approximate methods for the modal analysis of general optical dielectric waveguides

AbstactAbstact This paper reviews numerical and approximate methods for the modal analysis of general optical dielectric waveguides with emphasis on recent developments. Six groups of methods are reviewed, covering (1) the finite-element method, (2) the finite-difference method, (3) the integral-equation method, (4) methods based on series expansion, (5) approximate methods based on separation of variables, and (6) methods that do not fit into the above groups, ranging from the specialized ones for analysing restricted classes of waveguides to the most general ones for analysing inhomogeneous, arbitrarily-shaped, anisotropic waveguides. Some suggestions with regard to the selection of methods for particular applications are given.     

Experimental mode coupling analysis in optical waveguides for sensor and component optimization

A computer controlled mode coupling analyser is conceived and described in detail to characterize and to analyse mode coupling in all known kinds of cylindrical, multimode, step index, optical waveguides (CMSIOWs) by experimental measurement. These waveguides can be present in many ways like simple fibres, multimode fibre-optic sensors (MFOS) or other optical components like couplers or modulators. The computer processed results of measurements lead to transfer matrices and modulation transfer matrices. The transfer matrices describe the light distribution in the far field of these waveguides depending on the direction and power of the light that is injected into it. By visualizing the modulation transfer matrices in the form of mesh diagrams, the influence of external physical parameters, like a measured variable, on the mode coupling mechanisms inside CMSIOWs can be shown directly. The computer controlled mode coupling analyser will make the optimization of MFOS more efficient and, moreover, it will ease modelling of CMSIOWs and define their properties. The potential field of applications for the mode coupling analyser will be in engineering and optimization of intrinsic multimode fibre-optic sensors and their components.     

Breathing and beating dynamics of Gaussian beam in planar graded-index absorbing nonlinear waveguides

The spatial dynamics of laser beams in absorbing planar waveguides with a parabolic index profile in a saturable or cubic-quintic medium are calculated using the “collective variable approach” technique. In the absence of losses, we construct diagrams which define regions of self-focusing and self-diffractive beam propagation for both types of media. It is found that propagating pulses exhibit an oscillatory pattern, similar to breathing behavior in homogeneous media. If the incident pulse spatial profile and the center of the index profile are not aligned, the pulse oscillates around the index origin with a “beat” frequency that depends on the graded index. Both the breathing and the beat frequencies are also calculated for other graded-index profiles, such as those with additional higher-power terms, and are found to be extremely sensitive to the index profile. In media with linear and nonlinear absorption, we demonstrate the difference between the breathing behavior in graded-index and homogeneous waveguides.     

Thermally induced self-focusing and optical beam interactions in planar strontium barium niobate waveguides

We present an experimental study of thermally induced self-focusing effects and interactions of incoherent light beams in strontium barium niobate waveguides. Depending on the input power, a single parallel beam is strongly focused inside the sample up to diameters of several micrometers. For higher input power we observe the splitting of the beam in a sequence of several spots. We demonstrate that these thermally induced refractive-index patterns can be used to focus and deflect an incoherent guided probe beam in the waveguide with time constants below 1 ms.     

Precise design of integrated diffractive optical mode converter for fiber-to-waveguide coupling

Integrated diffractive optical mode converter, consisting of a diffractive optical element (DOE) and a slab waveguide, is used for fiber-to-waveguide coupling. The phase of the DOE is generally designed by optimization algorithm. In this paper, the precise design, a new method with one more restrictive way,is adopted to design the diffractive optical mode converter for fiber-to-waveguide coupling. Through this method, the intensity of any point on the output plane is fully filled with the required demand. Compared with what previously published, the coupling loss of the precise designed converter is lower.     

Realizing mode conversion and optical diode effect by coupling photonic crystal waveguides with cavity

We propose a novel two-dimensional photonic crystal structure consisting of two line defect waveguides and a cavity to realize mode conversion based on the coupling effect. The W1/cavity/W2 structure breaks the spatial symmetry and successfully converts the even(odd) mode to the odd(even) mode in the W2 waveguide during the forward(backward)transmission. When considering the incidence of only the even mode, the optical diode effect emerges and achieves approximate 35 d B unidirectionality at the resonant frequency. Moreover, owing to the narrow bandpass feature and the flexibility of the tuning cavity, utilization of the proposed structure as a wavelength filter is demonstrated in a device with a Y-branch splitter. Here, we provide a heuristic design for a mode converter, optical diode, and wavelength filter derived from the coupling effect between a cavity and adjacent waveguides, and expect that the proposed structure can be applied as a building block in future all-optical integrated circuits.     

Characterization and sensor properties of sol-gel SiO2:TiO2 film/ion-exchange glass optical waveguides

The paper presents the characterization and sensor properties of composite sol-gel SiO₂:TiO₂ film/ion-exchange glass optical waveguides. In the theoretical part of the paper the analysis involving the influence of the parameters of a uniform waveguide film on homogeneous sensitivity has been presented. It has been shown that the highest sensitivity can be obtained making use of the interference of TM₀-TM₁ modes. In the experimental part of the work the manufacturing technology of composite sol-gel SiO₂:TiO₂ film/ion-exchange glass optical waveguides has been described and the analysis results of the produced structures have been presented. The paper presents the influence of the thickness of the uniform waveguide film and the influence of the refractive index of the cover on effective refractive indexes. The produced waveguide structures are characterized by high homogeneous sensitivity.     

Deep subsurface optical waveguides produced by direct writing with femtosecond laser pulses in fused silica and phosphate glass

In the present work, we have analyzed the use of elliptical beam shaping along with low numerical aperture focusing optics in order to produce circular cross-section waveguides in different materials at large processing depths by direct femtosecond laser writing (100 fs, 800 nm, 1 kHz). A variable slit located before the focusing optics allows to generate a nearly elliptical beam shape and also to reduce the effective numerical aperture of the beam along the shat axis of the ellipse. The focusing optics allows to focus the beam deep inside the sample, which is translated at a constant speed transversely to the writing beam direction. The influence of several experimental parameters (energy per pulse, slit width, processing depth) on the properties of the produced waveguides has been analyzed. The influence of the intrinsic properties of the material (refractive index, composition) has been analyzed by comparing results obtained in fused silica and Er:Yb co-doped phosphate glass. The results obtained show that this approach leads to the successful production of deep subsurface (up to 7 mm) waveguides with circular cross-sections. Preliminary results using chirped pulses in the phosphate glass suggest that temporal pulse shaping can be used as an additional parameter to optimize the guided mode symmetry.     

Annealing effect on planar waveguides in LiNbO3 produced by oxygen ion implantation

We reported on planar waveguides in stoichiometric lithium niobate fabricated by 4.5 MeV oxygen ion implantation with a dose of 6 × 10¹⁴ ions/cm² at room temperature. After ion implantation, these samples were annealed at 240 °C, 260 °C, and 300 °C for 30 min. We investigated annealing effect on the guiding modes and near-field images in the waveguides by prism-coupling method and end-face coupling method respectively. We found that for the extraordinary refractive index a positive alternation occurred in the near-surface region while a negative alternation happened at the end of ion track. Moreover, we measured the transmission spectra for the pure sample and implanted samples before and after annealed at different temperatures, and we observed an absorption peak at ∼480 nm (2.6 eV) in all of these SLN samples.     

Construction of the refractive index profiles for few-mode planar optical waveguides

We present a nondestructive technique to predict the refractive index profiles of isotropic planar waveguides, on which a thin gold film is deposited to as the cladding. The negative dielectric constant of the metal results in significant differences of effective indices between TE and TM modes. The two polarized modes and a surface plasmon resonance (SPR) with abundant information of the surface index can be used to construct the refractive index profiles of single-mode and two-mode waveguides at a fixed wavelength.     

Locking in photosensitivity within optical fiber and planar waveguides by ultraviolet preexposure

Strong photosensitivity is locked in permanently after hydrogen outdiffusion of hydrogen-loaded waveguides presensitized with UV light by either pulsed 193-nm or cw 244-nm laser output.