Symmetric Planar Waveguide Research Articles

Discrete spectrum of waveguide modes of a linearly graded-index film introduced into a medium with a stepwise nonlinearity

Even and odd modes propagating along the symmetrical planar waveguide, which is a film embedded in a nonlinear medium, are described analytically. The dielectric function of the film is characterized by a linear spatial profile symmetrical about its center in transverse direction. The dielectric function of the nonlinear medium changes stepwise its value when the electric field amplitude exceeds the threshold value. Exact solutions of even and odd symmetry to the wave equation with such compound dielectric function are found. The solutions describe the waveguide modes existing with the discrete spectrum of the effective refractive index. Waveguide modes can be excited at certain discrete values of the angle of incidence of the exciting beam. Low-order modes are excited at large angles of incidence, and high-order modes are excited at small ones. The number of excited modes is limited and is determined by the parameters of the waveguide system, in particular, by the film thickness and the wavelength of the exciting radiation. Excitation of an even mode of certain order requires a wavelength longer than that of an odd mode of the same order. The intensity of the mode increases with an increasing film thickness, and it decreases with an increasing wavelength. The power flux and the radiation confinement factor are calculated analytically. The radiation confinement factor behaves in the same way as the intensity of the waveguide mode. It is shown that the minimum value of the radiation power required to excite the mode is reached at the critical value of the film thickness (or the critical wavelength), at which the radiation confinement factor is equal to a half.

Symmetrical Corner-Pumped Planar Waveguide Laser Amplifier

We present a novel structure of planar waveguide for Yb:YAG laser amplifiers as symmetrical corner-pumped planar waveguide, allowing large absorption length. We optimize the parameters of the waveguide using an amplification model. Performance including thermal effects of 10-kW symmetrical corner-pumped planar waveguide laser amplifier is simulated, demonstrating that pump absorption efficiency and uniformity are much better than end-pumped ones. Moreover, a good beam quality causing by less thermal distortion can be expected. The power is scaled from 200W to 7000W with the pump absorption efficiency of 98.2%, leading to an optical-to-optical efficiency of 68%.

Anti-resonance, inhibited coupling and mode transition in depressed core fibers.

The depressed core fiber (DCF), consisting of a low-index solid core, a high-index cladding and air surrounding, is in effect a bridge between the conventional step-index fiber and the tube-type hollow-core fiber from the point of view of the index profile. In this paper the dispersion diagram of a DCF is obtained by solving the full-vector eigenvalue equations and analyzed using the theory of anti-resonant and the inhibited coupling mechanisms. While light propagation in tube-type hollow-core fibers is commonly described by the symmetric planar waveguide model, here we propose an asymmetric planar waveguide for the DCFs in an anti-resonant reflecting optical waveguide (ARROW) model. It is found that the anti-resonant core modes in the DCFs have real effective indices, compared to the anti-resonant core modes with complex effective indices in the tube-type hollow-core fibers. The anti-resonant core modes in the DCFs exhibit similar qualitative and quantitative behavior as the core modes in the conventional step-index fibers. The full-vector analytical results for the simple-structure DCFs can contribute to a better understanding of the anti-resonant and inhibited coupling guidance mechanisms in other complex inversed index fibers.

Supperssion of higher order modes in gain-guided index-antiguided planar waveguide laser

In order to suppress the higher order modes and improve beam quality in high power waveguide laser, based on gainguided index-antiguided theory, a new symmetric layered waveguide structure is designed, and an interval layer is proposed to be sandwiched between waveguide layer and cladding layer in traditional symmetric GG-IAG waveguide structure. As a result, while reducing the leakage loss of fundamental mode, the threshold gain coefficient differences between fundamental mode and higher order modes will be further increased. When the gain in waveguide layer is between threshold gain coefficient of fundamental mode and that of higher order mode, the fundamental mode will have a greater advantage in mode competition than others, so higher order modes can be suppressed and the laser can obtain a single mode output. In the meantime, the guided-mode principle of this waveguide structure is explained with the theory of wave optics in this paper, the eigen equation of each mode is derived from the wave equation, and the field distributions of fundamental mode and higher order mode are also given. Additionally, in this paper we give the solution process of the threshold gain coefficient of each mode in this waveguide structure. The mode leakage losses of fundamental mode and higher order mode, after adding the interval layer, are numerically calculated, and the parameter optimization process of the interval layer is also given in this paper. In addition, the field distributions of fundamental mode and higher order mode are numerically simulated. The calculation results show that comparing with the traditional symmetric GG-IAG planar waveguide, after adding the interval layer, the loss of fundamental mode can be greatly reduced, while ensuring that the leakage loss of higher order mode reaches a maximum value by reasonably controlling the parameters of interval layer. In this way, we can suppress higher order modes and improve laser efficiency. This paper provides a new idea for improving the beam quality of high power waveguide laser with a large mode area.

Modes of a nonlinear planar waveguide with a dielectric layer immersed in a hyperbolic medium

The guided waves of a symmetric planar waveguide formed by an isotropic dielectric placed in a hyperbolic medium and having a cubic-nonlinear response are studied theoretically. The optical axis of the hyperbolic medium is directed along the normal to the interfaces between the media. If the permittivity of the waveguide core exceeds the main permittivity for an extraordinary wave in the hyperbolic medium, then each TM mode is characterised by two cut-off frequencies. Dispersion relations for these modes are found in the case of focusing and defocusing core media. The number of the modes possible at a given frequency depends on the radiation intensity. It is shown that zero values of the mode propagation constants are possible in the waveguide, which corresponds to the formation of a standing wave between the boundaries of the waveguide. In addition, in the case of a defocusing waveguide layer, such stopped modes can be obtained with increasing field intensity. The dependences of the propagation constant and the width of the transverse distribution of the mode field on the radiation intensity are found and analysed.

PROPAGATION AND CHARACTERIZATION OF NOVEL GRADED AND LINEARLY CHIRPED TYPE'S OF REFRACTIVE INDEX PROFILE SYMMETRIC PLANAR SLAB WAVEGUIDE BY NUMERICAL MEANS

We characterize the alpha power and chirped types of refractive index profile planar slab waveguide in terms of TE/TM mode study, waveguide dispersion study, mode profile properties, power confinement factor and universal b-V graph. Our own developed finite element method has been efficiently applied to analyze the symmetric planar slab waveguide having a complicated refractive index profile. There is a requirement for a high accuracy of numerical technique to analyze the arbitrary refractive index waveguide, as at some frequency the TE and TM modes are smeared on each other, and it is difficult to distinguish them while analyzing. This paper successfully demonstrates the different TE/TM modes supported by the waveguide with respect to alpha-power and linearly chirped types of refractive index profile. The main contribution of our work is to identify the TE/TM mode numerically for a complex refractive index planar slab waveguide and to characterize them in terms of their performance parameters. Then we apply the mode propagation concept to estimate the propagation phenomena in alpha-power and chirped types of refractive index profile waveguide. All the results presented in this paper are simulated in MATLAB only. Our study reveals that waveguide dispersion and number of allowed guided modes are small while for the case of triangular index profile followed by chirped profile and maximum for step index profile case. Hence triangular and chirped types of refractive index profile waveguide seem to be more efficient for long haul optical communication systems.

A determination of propagation constants of symmetric planar waveguide modes in a frequency domain

A determination of propagation constants of symmetric planar waveguide modes in a frequency domain

Mode-field half-width and divergence half-angle definitions for a planar waveguide

Mode-field half-width and divergence half-angle definitions for a planar waveguide with an arbitrary index profile are presented based on the near- and far-field distributions and their relations are given. Then, analytical formulae of these definitions are derived for the TE0 mode in a symmetrical step-index planar waveguide and numerical results prove that they are more suitable as the mode-field half-width and divergence half-angle of the Gaussian approximation for the near- and far-fields respectively.

Symmetric multilayer slab waveguide structure with a negative index material: TM case

The present paper deals with the theoretical modeling of symmetrical multilayer planar waveguide structure. One of the layers is considered as a negative refractive index material. We take the appropriate field distributions for p-polarization and impose the boundary conditions to derive the mode equation and other necessary formulae for the proposed structure. The effect of the negative-index layer on the modal refractive index, power flow, and penetration depth of the waveguide is studied. Also, we compare our computed results with those obtained for a similar conventional four-layer structure. It is observed that the presence of the negative-index material reduces the power flowing in the guiding layer and enhances the power flowing in the surroundings.

Comparative study of asymmetric versus symmetric planar slab dielectric optical waveguides

In this paper we have studied the asymmetric versus symmetric planar waveguide in terms of their usefulness in optical fiber communication systems. We have explored the thin waveguide versus thick waveguide first. Later on usefulness of asymmetric versus symmetric waveguide is carried out to target for WDM optical network application. All kinds of optical network components are fabricated on Si substrate with the point of view of their application. Here asymmetric planar structure may be more useful compared to symmetric waveguide in terms of their non-uniform power confinement properties. However, the symmetric waveguide structure may be more useful for their high power confinement properties. It is well known that the thin symmetric waveguide supports at least one mode. However the thick waveguide may support many even as well as odd modes. We study the power confinement properties for symmetric as well as asymmetric waveguide structure. We conclude that higher order modes show the nonlinear power variations. Mode field profile for various cases is discussed as well. Comparative study between asymmetric versus symmetric waveguide has a lot of significance in optical network area. It has been shown through analysis that in asymmetric waveguide, the power flows more through film region in the case of fundamental mode. Power confinement properties for asymmetric waveguide versus symmetric waveguide have been studied.

Synthesis of symmetric and asymmetric planar optical waveguides

A novel and accurate refractive index profile synthesis method for planar optical waveguides is presented and demonstrated using the transmitted near-electric-field-data. This method is based on the inverse transmission-line (TL) technique. From Maxwell's equations, a TL equivalent circuit (electric T-circuit) for the refractive index profile of a planar optical waveguide is derived. The authors demonstrate how to use this model to carry out the inverse problem and synthesise the exact refractive index profile numerically from near-field-data. The TL method can reconstruct arbitrary refractive index profiles for planar optical waveguides that support singlemode or multimodes. The cases of both symmetric and asymmetric arbitrary refractive index profile planar waveguides are discussed. The accuracy of the reconstructed waveguides is examined numerically.

EXPERIMENTAL OBSERVATION OF NONLINEAR BEAM SPLITTING IN DYE-DOPED LIQUID CRYSTAL WAVEGUIDES

Liquid crystals have effective nonlinear optical coefficients that are orders of magnitude larger than other materials exploited in integrated optics. The addition of some organic dyes in small amounts may further enhance the nonlinear optical response and even change its sign. We used a dye-nematic liquid crystal mixture exhibiting a negative optical nonlinearity. We observed the nonlinear spatial splitting of the guided modes in a symmetric planar waveguide whose core was the liquid crystal mixture. This non-linear effect has been observed with very low laser power input and the power threshold dependence on dye concentration and core thickness was investigated.

Single-mode mid-infrared silver halide planar waveguides

A single-mode silver halide symmetric step-index planar waveguide for 10.6 microm is described. We fabricate the waveguide from extruded multimode silver halide fiber by pressing the fiber between metal plates while heating. The device is therefore automatically pigtailed to a fiber, which could ease the difficulties of coupling light into it. We achieved single-mode confinement by suitably adjusting the refractive index of the core and the cladding and by reducing the core thickness to 30 microm. The output radiation from the planar waveguide was measured to confirm single-mode confinement. Silver halide single-mode waveguides for the mid-infrared can be used to enhance sensitivity in fiber-optic evanescent-wave infrared spectroscopy measurements or for the development of mid-infrared single-mode lasers and interferometers.

Single-mode operation in symmetric planar waveguides using isotropic chiral media

We present the dispersion relations for symmetric planar waveguides in general isotropic media. The planar waveguide structure that utilizes chiral media in the cladding regions is emphasized. Unlike other symmetric planar waveguide configurations in isotropic media, this structure possesses a nondegenerate lowest-order mode. Therefore symmetric planar waveguides using chiral cladding materials can support single-mode operation.

Electric field-induced mode splitting in a liquid crystal waveguide

The propagation of a cw TE polarized Ar + laser beam in a symmetric planar waveguide having a nematic liquid crystal core is studied both theoretically and experimentally as a function of an external voltage. It is shown that, due to the externally applied voltage, the change in the index profile leads to a separation of the guided mode into two separated beams. A strong reduction (up to 80 dB/cm) of the scattering losses in the guide was also observed. The devices are proposed as electrical guided mode beam-splitters for possible applications in the optical waveguide field.

Novel soliton states and bifurcation phenomena in nonlinear fiber couplers.

We find and analyze analytically and numerically two new families of coupled soliton states in nonlinear fiber couplers. The bifurcation diagram for the new types of soliton states is constructed. It is shown that the bifurcation diagram for the fiber coupler is similar to the bifurcation diagram for the stationary waves in a symmetric nonlinear planar waveguide. Physical reasons for this analogy are discussed.

Stability of the asymmetric nonlinear mode trapped in symmetric planar waveguides

The authors examine the reliability of the numerical approach for studying the asymmetric nonlinear mode trapped in a thin linear film sandwiched in an infinite self-focusing medium, and thus resolve a controversy in the literature on the stability of the mode trapped between the bifurcation point and the transition point on the dispersion curve reported. They demonstrate that as a result of the instability there exists a class of quasi-periodic solutions arising from the instability in the asymmetric mode on the unstable branch and weakly stable branch. In addition, the effect of loss on the propagation characteristics of the nonlinear mode is investigated. The evolution is shown to follow the dispersion curve adiabatically in the stable region provided the loss is small, whereas the initial excitation on the unstable branch leads to evolution away from oscillation around the dispersion curve.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Stability of TE 0 modes in self-defocusing core nonlinear planar waveguides

TE 0 modes in symmetric nonlinear planar waveguides with a self-defocusing core and self-focusing cladding and substrate are studied. A finite element method is used to calculate the modes and their power-dispersion curves. New stability results are presented.

Complex eigenvalues in stability analysis of nonlinear planar guided waves

The stability characteristics of the anti-symmetric TE 1 stationary wave in symmetric nonlinear planar waveguides (SNPW) is investigated both analytically and numerically. It is shown, for the first time, that eigenvalues of the corresponding linear stability analysis can be complex in a certain range of parameters. This fact makes the range of instability of the TE 1 wave broader than in studies where the eigenvalues are restricted to being only real or purely imaginary. Nevertheless, for high values of the propagation constant β, the TE 1 wave is stable, in contrast to the symmetric TE 0 wave which is unstable at high values of β.

Amplification of nonlinear waves in a symmetric planar waveguide.

The gain process of modes of a nonlinear symmetric planar waveguide is investigated. It is shown using numerical simulations that the gain process is adiabatic at low values of gain factor and that the wave envelope changes slowly, remaining close to the shape of the stable nonlinear mode. The representative point of the wave on the plane (energy integral, propagation constant) moves continuously along the stable branches of dispersion curves. When the representative point achieves the region of instability, the spatial solitons are split off from the guided mode. This process is repeated periodically due to the gain. We considered a number of typical cases of guided-wave propagation with symmetric as well as asymmetric initial conditions.