Determination of refractive index profiles of gradient optical waveguides by ellipsometry

Ag⁺-Na⁺ and K⁺-Na⁺ ion-exchanged optical waveguides in soda-lime glass are characterised by ellipsometry. Refractive index profiles of the waveguides are calculated from ellipsometric multiple angle of incidence data using the Newton-Kantorovitch type iterative procedure and compared with those reconstructed by inverse WKB method. It is demonstrated that such continuous profiles with relatively small index gradient (of the order of 0.1 and 0.01), extending to few micrometers in depth, can be determined by ellipsometric measurements. A good agreement is found between results obtained by ellipsometry and by the inverse WKB method at depths above 500–600 nm, while there is a difference in the subsurface region, where ellipsometry is more sensitive to the quality of the surface. The profiles obtained by the two methods are consistent if the surface thin layer is etched.     

Low-loss amorphous Si waveguides with gradient refractive index cladding structure

Amorphous Si waveguides with gradient refractive index cladding structure are proposed and fabricated using plasma-enhanced chemical vapor deposition method.Compared with 6 dB/cm for ridge waveguide without gradient cladding,the propagation loss of the gradient cladding waveguides is less than 1 dB/cm with both TE and TM polarizations.     

Determination of refractive index profiles in diffused optical waveguides

An improved method for the reconstruction of diffused waveguide index profiles from experimental mode spectra is proposed. The method uses a parabolic approximation between successive points. It is tested on the example of an exponential profile, and applied to the reconstruction of index profiles in Ag⁺ ion-exchanged waveguides from measured mode spectra. This method appears to work well also in the cases of very few mode wave-guides.     

An interferometric method for refractive index profiling of planar gradient index waveguides

In this paper, we present an interferometric method to determine the refractive index profile in graded-index planar waveguides. To begin, part of the soda-lime glass substrate surface was coated with aluminum and then was immersed in molten AgNO₃ to fabricate a planar waveguide on the uncoated part of the surface. After the ion exchange, the coating was removed. Then, the sample was polished obliquely along the boundary between the ion-exchanged and non-ion-exchanged regions, to form a wedge. Thereafter, it was placed inside a Mach–Zehnder interferometer. The fringe pattern was analyzed using the well-known Fourier method and the refractive index profile was determined. The sample preparation, data analysis and experimental results are presented.     

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.     

Simulation of refractive index profiles for titanium indiffused lithium niobate channel waveguides

A generally applicable method to simulate the two-dimensional profiles of Ti-concentration and refractive index of Ti:LiNbO₃, waveguides is presented. The influence of the fabricational parameters on the refractive index profiles has been studied in detail. The model parameters are extracted from the available experimental data. The computed values of surface refractive index change agree closely with the experimental results. The model is also extended for coupled waveguides.     

Improved inverse WKB procedure to reconstruct refractive index profiles of dielectric planar waveguides

A new method to reconstruct smooth refractive-index profiles from measured effective indices is presented. The profile form near the surface and its approach towards the bulk value are explicitely taken into account. Well behaved profiles such as Gaussian or exponential can be reconstructed within experimental accuracy from three modes only, and even two modes may provide useful information. The method is tested for numerical stability.     

Inverse method for the reconstruction of refractive index profile and power management in gradient index optical waveguides

Accurate semi-analytical technique is developed for reconstructing refractive index profiles of optical waveguide by near-field pattern. The approach is shown to be effective for the synthesis of single-mode waveguides. Optimising profiles of planar waveguides for managing power distribution of propagating waves is demonstrated.     

Optical delay lines using coupled slab waveguides and ring resonator with a negative refractive index core

Total delay time of a structure composed of a slab waveguide coupled with a ring resonator where negative refractive index material is replaced in the core of the structure is investigated in this work. In this paper, a two-port ring resonator (TPRR) which is made of a core with negative refractive index has been used to generate a time delay for a Gaussian-shaped pulse with 1 GHz bandwidth. It is shown that the creation of the ring how causes more n_g of a straight waveguide and results are compared with positive refractive index core TPRR. We have used metamaterial to make an n < 0 media and have used two cascaded metamaterial rings to increase the bandwidth.     

Measurements of refractive index profiles of proton－exchanged LiNbO_3 waveguidesusing TE－TM mode conversion

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Coupling coefficients of gratings with graded refractive index waveguides

In this paper, the effective coupling coefficient κeff and the self-coupling coefficient ζ1 are introduced to describe the characteristic of gratings in a resonant situation when the effects of radiation and other partial waves coupling are considered. The dependence of these two coupling coefficients on grating tooth shapes and depths and the dimensions of graded refractive index (GRIN) waveguides is numerically analysed. The results show that the gratings with linear GRIN waveguides have the largest |κeff|. The possibility of realizing a complex-coupled DFB laser, even a pure gain or loss coupled DFB laser, employing only a real refractive index coupled grating is also discussed. This revised version was published online in November 2006 with corrections to the Cover Date.     

Large photoinduced refractive index changes in pulsed-laser-deposited lead germanate glass waveguides with controllable refractive index sign change

Photosensitive lead germanate glass optical waveguides have been grown by pulsed laser deposition. The deposited waveguides are photosensitive over a broad ultraviolet spectral range (325-193 nm). Positive and/or negative refractive index changes have been observed, depending on the intensity of the ultraviolet radiation as well as on the deposition conditions. Absolute refractive index change values up to |(n|=1.06᎒^-2 have been measured.     

Numerical calculations of modes of optical waveguides with two-dimensional refractive index profiles by a field correction method

Abstact We describe a numerical method devised to calculate the lower-order modes of optical waveguides with two-dimensional transverse index profiles. This method is based on finite-difference approximation of the scalar wave equation and the minimization of the error in the field shape of a mode. The field correction method can be applied to waveguides with large index steps and generates the mode's scalar propagation constant and its field. To test the field correction method, it is applied to a three-layer optical fibre and the results are compared with exact solutions. The error in the calculations of the modal effective indices is found to be of the order of 10^-6. Example mode calculations are given for fused couplers and rib waveguides.     

多量子阱波导等效折射率的新公式

利用转移矩阵技术,建立了薄膜近似下的多量子阱波导芯子区域等效折射率的解析公式。该公式是偏振态和量子阱波导折射率分布的函数。     

A search-and-track algorithm for controlling the number of guided modes of planar optical waveguides with arbitrary refractive index profiles

A search-and-track algorithm is proposed for controlling the number of guided modes of planar optical waveguides with arbitrary refractive index profiles. The algorithm starts with an initial guess point in the parameter space that supports a specific number of guided modes. Then, it searches for, and tracks, the boundaries of this space or another space supporting different number of modes. It does so by monitoring the sign of a unified cutoff dispersion function. The algorithm is applied to both symmetric and asymmetric silicon-based parabolic-index waveguides. It shows that unlike asymmetric waveguides, the single-mode condition of symmetric waveguides is controlled by TM-, as opposed to TE-, polarization. This abnormal polarization control is strongest for high index contrast waveguides of sub-micrometer core sizes. The results are verified by full-vectorial beam propagation method.     

Omnidirectional photonic band gaps in one-dimensional gradient refractive index photonic crystals considering linear and quadratic profiles

By using the transfer matrix formalism, in this work it is presented the study of the optical properties of 1D photonic structures constructed with M periods of bilayers of dielectric material and slabs with gradient refractive index (GRIN) profile of two types: linear and quadratic. By varying the profile parameters, preserving the average value of the refractive index for the GRIN slab, the results show the formation of new photonic band gaps whose bandwidths depends on the slope and the curvature of the linear and quadratic profile respectively. Also, it can be observed the formation of omnidirectional photonic bandgaps for the TE and TM polarizations, one for the linear profile and three for the quadratic one, for which their bandwidths depend linearly on the slope and the curvature of the GRIN profiles. It is expected that the presented results could be useful in the construction of optical devices based in their optical response under oblique incidence.     

Fabrication of gradient refractive index ball lenses

The theoretical model of the Maxwell fish eye sphere lens has long been regarded as an absolute optical instrument without practical application since it was proposed. But the study on the theory of Maxwell fish eye micro-spherical lens shows that at certain condition it has fine image formation ability and coupling efficiency. Based on the Fick's diffusion equations, the distribution function of refractive index of gradient refractive index (GRIN) ball lenses is derived. Lithium-containing silicate glass is fabricated and GRIN ball lenses whose diameters are from 0.3 to 3.0 mm are made by ion exchange and the sagging method in sodium nitrate. Radial refractive index profiles of these GRIN ball lens are measured by interferometer. Results show that the distribution of the index of refraction is a parabolic curve and in concordance with the computational consequence and its Δn is 0.0002.     

Light-induced refractive index changes in LiNbO3:Ti waveguides

Holographic measurements of light-induced refractive index changes in LiNbO₃Ti waveguides are reported. The results demonstrate that Fe²⁺ centers are stabilized against oxidation in the region of large Ti concentration near the surface thus increasing the sensitivity to optical damage considerably. This undesired effect may be largely abolished by additional in-diffusion of protons.