Planar Slab Waveguide Research Articles

Fabrication of inorganic GeO2:SiO2 channel waveguides by ultraviolet imprinting technique

The authors demonstrate the effective waveguiding channel formation inside an ∼3μm thick photosensitive GeO2(20%):SiO2(80%) planar slab waveguide film prepared using the sol-gel technique by the direct ultraviolet (UV) imprinting technique. This is possible because of the ability to induce large refractive index change (∼10−3) in the films by the UV radiation. Channel waveguides with various refractive index values have been fabricated. The measured modal profiles of the waveguides match well with the simulation results. The simplicity of the direct UV imprinting technique is also shown by the fabrication of a 1×2 multimode-interference 3dB light splitter in one single processing step.

Group velocity measurement using spectral interference in near-field scanning optical microscopy

Near-field scanning optical microscopy provides a tool for studying the behavior of optical fields inside waveguides. In this experiment the authors measure directly the variation of group velocity between different modes of a planar slab waveguide as the modes propagate along the guide. The measurement is made using the spectral interference between pulses propagating inside the waveguide with different group velocities, collected using a near-field scanning optical microscope at different points down the guide and spectrally resolved. The results are compared to models of group velocities in simple guides.

Scattering and radiation characteristics of step discontinuity in a double‐negative (DNG) slab waveguide operating in the evanescent surface mode

AbstractThe scattering and radiation characteristics of a step discontinuity in a double‐negative (DNG) slab waveguide operating in the evanescent surface mode are analyzed by a method which combines the rigorous mode‐matching method with multimode network theory. In the analysis, the radiation problem is transformed into a propagation problem so as to tremendously simplify the calculation procedure. The dispersion properties of the grounded planar DNG slab waveguide for ordinary and evanescent surface modes are examined, from which the left‐hand property of the operating mode is verified. The relative scattered power and radiation pattern of the step discontinuity are given for the first time, from which the backward radiation of the stepped DNG guide is clearly demonstrated. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 48: 1085–1088, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21607

Eigenmodes of index-modulated layers with lateral PMLs

Maxwell equations are solved in a layer comprising a finite number of homogeneous isotropic dielectric regions ended by anisotropic perfectly matched layers (PMLs). The boundary-value problem is solved and the dispersion relation inside the PML is derived. The general expression of the eigenvalues equation for an arbitrary number of regions in each layer is obtained, and both polarization modes are considered. The modal functions of a single layer ended by PMLs are found, and their orthogonality relation is derived. The present method is useful to simulate scattering problems from dielectric objects as well as propagation in planar slab waveguides. Its potential to deal with more complex problems such as the scattering from an object with arbitrary cross section in open space using the multilayer modal method is briefly discussed.

Physical realization of -symmetric potential scattering in a planar slab waveguide

A physical realization of scattering by ${\cal{PT}}$-symmetric potentials is provided: we show that the Maxwell equations for an electromagnetic wave travelling along a planar slab waveguide filled with gain and absorbing media in contiguous regions, can be approximated in a parameter range by a Schr\"odinger equation with a ${\cal{PT}}$-symmetric scattering potential.

Reflection and negative refraction of left-handed metamaterials at microwave frequencies

We experimentally investigated the microwave reflection of the negative permeability material composed of periodical arrays of the copper split-ring resonators (SRRs).The negative dielectric materials are composed of periodical arrays of copper wires and left-handed materials(LHMs) in a planar slab waveguide, and the microwave is incident to the surface in different directions.We also investigated the negative refraction through a prism fabricated from the LHMs.The experimental results show that for the negative permeability materials,there is a reflection peak at the resonance frequencies of the SRRs, and the reflectivity of the negative dielectric material is closed to 0dB.A single smaller reflection peak occurs in the reflected curve of the LHMs,the reflectivity of which increases with the incident direction,that is,the reflection increases.The reflection peak has a shift with respect to the transmission peak. It is demonstrated that negative refractive index of -0.796 occurs in the LHMs at the frequency o 800MHz.

Improved Analysis of the Coupling of Optical Waves into Multimode Waveguides Using Overlap Integrals

The optical multimode interconnection technology has become important due to increasing data rates in modern multi-processor systems. In this context, the coupling of optical waves into multimode waveguides has to be analyzed. Ray optical methods are preferred, but are not applicable for all geometries. As full-wave analysis using the mode matching technique is very extensive, we present a simple method based on overlap integrals, to calculate the coupling efficiency of impingingoptical waves. Our approach neglects reflected waves. The corresponding error is corrected by applying a transmission factor, which is that of a plane wave irradiating a dielectric half space. We verify our approach at a planar slab waveguide and a cylindrical fiber, as their mode spectra are well known. The mode matching technique is applied as reference method and the impinging wave is a Gaussian beam with varying angles of incidence and lateral displacements.

Plasma silicon oxide–silica xerogel based planar optical waveguides

In this study, silica xerogels are used as the cladding for high-refractive-index-contrast waveguide systems. Silicon oxide, due to its relatively low refractive index, is an extensively used cladding material. The lower-refractive-index silica xerogel films enable us, to report losses for planar-slab waveguide systems with silicon oxide as the core. A spin-on sol-gel process was used for the silica xerogel deposition. The silicon oxide core was deposited using plasma enhanced chemical vapor deposition (PECVD), with silane and nitrous oxide as the reactive gases. Slab waveguides systems with core thickness of 1 μm and refractive-index contrast (Δn) as high as 0.35 were fabricated. With regard to the PECVD process, a deposition temperature of 150 °C enabled a stable structure, however, unacceptably high optical losses of 7±1.01 dB/cm at a wavelength of 650 nm and 5.59±0.69 dB/cm at 830 nm were measured using a prism-coupler based setup. On increasing the deposition temperature of the silicon–oxide film to 225 °C, the losses decreased to 0.98±0.73 dB/cm at 650 nm and 0.69±0.46 dB/cm at 830 nm. The decrease in the losses resulting from increasing the deposition temperature provided the motivation to develop deposition conditions to reduce stress in the silicon–oxide films at higher deposition temperatures for improved stability on xerogel films. Reduction in the silicon–oxide film stress was achieved by varying the silane and nitrous oxide flow rates. The deposition stress in the film was reduced from ∼460 to ∼240 MPa, mainly by increasing the silane flow rate. The silicon oxide with the reduced stress was stable on xerogel film with porosities as high as 56%, even though a deposition temperature of 300 °C was used. However, the slab waveguide stack using the low-stress silicon oxide exhibited an optical loss of 1.81±0.18 dB/cm at 650 nm and 1.41±0.27 dB/cm at 830 nm. The higher loss, as compared to that obtained for the higher-stress film deposited at 225 °C, is attributed to scattering from the columnar structure of the lower-stress silicon–oxide film.

Fundamental wave phenomena on biased-ferrite planar slab waveguides in connection with singularity theory

In this paper, characteristic dispersion phenomena and interactions of the discrete surface- and leaky-wave modes supported by a grounded biased-ferrite slab waveguide are analyzed using singularity and critical-point theory. Surface- and space-wave leaky modes are studied for different orientations of the applied magnetic bias field. As the bias field is rotated away from a coordinate axis, the modes become hybrid, and mode coupling or modal degeneracies may occur. Mode coupling, in general, is governed by a Morse critical point (MCP), and the behavior of the MCP is found to be useful in explaining and predicting modal behavior on this complicated waveguiding structure. In addition, leaky-wave dispersion behavior and leaky-wave cutoff associated with a fold singular point is studied by varying the orientation of the applied magnetic bias field.

Pump-Probe Measurements Using Silicon Nanocrystal Waveguides

AbstractOptical pump-probe measurements were performed on planar slab waveguides containing silicon nanocrystals in an attempt to measure optical gain from photo-excited silicon nanocrystals. Two experiments were performed, one with a continuous-wave probe beam and a pulsed pump beam, giving a time resolution of approximately 25 ns, and the other with a pulsed pump and probe beam, giving a time resolution of approximately 10 ps. In both cases the intensity of the probe beam was found to be attenuated by the pump beam, with the attenuation increasing monotonically with increasing pump power. Time-resolved measurements using the first experimental arrangement showed that the probe signal recovered its initial intensity on a time scale of 45-70 μs, a value comparable to the exciton lifetime in Si nanocrystals. These data are shown to be consistent with an induced absorption process such as confined carrier absorption. No evidence for optical gain was observed.

Theory and simulation of a concave diffraction grating demultiplexer for coarse WDM systems

Reflective concave diffraction gratings in multimode planar waveguide geometries are considered as wavelength separation devices for coarse wavelength division multiplexing (WDM) systems. General expressions are derived relating the number of channels, the wavelength and channel wavelength separation, and the numerical aperture of the planar slabwaveguide. Scalar electromagnetic simulations performed for a particular grating design show that acceptable performance is theoretically achievable.

χ^(2) cascading by means of optical rectification in a planar slab waveguide

χ(2) cascading in a planar slab waveguide by means of optical rectification and the linear electro-optic effect is investigated theoretically. An optical wave generates a static polarization, which results in a static electric field. This field is calculated by a Green’s function method and is an exact solution for the geometry that is considered. The nonlinear phase shift of the optical wave caused by this static field through the electro-optic effect is considered. Results are shown for transversely and longitudinally produced static polarizations for a single-domain material and a material with periodically inverted domains.

Analysis of mode coupling on guided-wave structures using Morse critical points

New insight on mode coupling in waveguiding structures is obtained from the theory of Morse critical points (MCP's). It is shown that the traditional coupled-mode formalism has a clear analytical connection with functional properties of the characteristic determinant in the vicinity of the Morse critical point, which determines the minimum of coupling. The relationship between perturbed and independent modes in the mode-coupling region is obtained using the Taylor polynomial of order two about the Morse critical point, and it is found that the coupling factor is proportionally related to the value of a characteristic function at this point. The qualitative modal behaviour in the mode-interaction region is predicted by a simple normal form, which can be geometrically interpreted as a result of the intersection of a saddle surface and a plane corresponding to the minimum of the coupling factor. Numerical results for a variety of guided-wave structures, including printed-circuit transmission lines, planar-slab waveguides, and shielded microstrip-like lines demonstrate the efficiency of the proposed approach for the rapid identification of mode-coupling regions, and for reconstruction of dispersion behaviour in those regions via simple analytic (normal) forms.

Polarization coupling and transverse interaction of spatial optical solitons in a slab waveguide

The interaction of two initially parallel spatial optical solitons is analyzed numerically, with consideration of the nonlinear polarization coupling in a planar slab waveguide. The phase difference of the soliton pair associated with the TE and the TM fundamental modes is either 0 or π, and the orthogonal polarization is excited by a weak field of the same or an opposite transverse symmetry. Polarization coupling is shown to occur if the transverse spatial symmetries in both modes are different, although the linear birefringence is completely neglected. With this effect the nonlinear polarization instability in a weakly birefringent waveguide can be influenced by the choice of the initial transverse symmetries. The application of this interaction between even and odd fields for modulation or switching is discussed. The influence of the initial polarization errors of the strong field is shown to be reducible if the strong field and the modulating weak field have opposite transverse symmetries.

Two-dimensional analysis of optical waveguides with a nonuniform finite difference method

A nonuniform finite difference method is presented for an analysis of arbitrarily-shaped optical waveguides. By introducing preconditioning of discretised coefficient matrices by similarity transformations, it has become possible to improve the accuracy of the solution without paying any penalty in terms of computing time. From the comparison between the exact analytical method and the nonuniform finite difference method for an analysis of planar slab waveguides, it has been clarified that the mesh refinement near the material interfaces plays a dominant role in determining the accuracy of solutions. Furthermore, the nonuniform finite difference method is used to model buried-channel waveguides and is compared with the effective-index method. It has been indicated that differences between the non-uniform finite difference method and the effective-index method have become significant when the channel dimensions in both directions become less than the propagation wavelength.

Optically addressed variable-efficiency waveguide grating for switching arrays

An optically addressed waveguide grating switch is described and demonstrated. Its structure includes a planar slab waveguide with a surface relief grating and an active-material cladding layer. Photoinduced birefringence due to a polarized argon laser beam causes modulation of the refractive index of the cladding in the grating region and modulation of diffraction efficiency of the waveguide grating.

Planar microoptical multiplexer and demultiplexer for multimode optical transmission lines

A matching pair of 10-channel planar grating multiplexer/demultiplexer has been numerically analysed and fabricated. Basic construction elements are a planar slab waveguide with a cylindrical mirror facet, a standard plane blazed reflection grating and an array of input/output fibres. The arrangement has proved to work sufficiently well without special measures to reduce aberration such as inclining the input/output facet. The ray tracing method satisfactorily describes the characteristics of the devices. Measured insertion losses range from 2.2 to 7.8 dB, full 1-dB passband widths are 14 nm for the demultiplexer and 25 nm for the multiplexer.

Ion-exchanged Slab Waveguide Characterization

Methods for determining the refractive-index profile and mode spectrum of planar slab waveguides produced by ion-exchanged techniques are receiving increased attention. A general method of translating the experimentally determined ion-exchanged thin-film propagating mode spectrum into an analytical expression of the refractive-index profile is presented. It involves computer fitting by numerical integration of the exact WKB characteristic propagation mode equation to improve accuracy and preserve the distinction between TE and TM modes. The second-order polynomial refractive-index profile has been found to be well suited to planar thin films produced from soda-lime glass microscope slides in a silver-nitrate stirred dilute melt with sodium nitrate at 317°C - 1°C with fabrication times ranging from 0·5 to 36 min. The analysis was conducted with a view to ultimately fabricating self-imaging devices.

Light propagation in a planar dielectric slab waveguide with step discontinuities

The common matrix formalism for multi-layer systems is generalized to describe the optical field propagation along an arbitrary cascade of step discontinuities in a planar dielectric waveguide. The reflection and transmission properties of the step cascade are modelled by rigorous operator relations in a Hilbert-space calculus. In this way the complete propagation problem is reduced to two basic transformations. TE- and TM-polarized fields are treated simultaneously.

Light propagation in a planar dielectric slab waveguide with step discontinuities

Light propagation in a planar dielectric slab waveguide with step discontinuities