Showing papers on "Radiation mode published in 1979"

Propagation in glass optical waveguides

Abstract: The propagation theory of multimode and single-mode optical waveguide fibers is reviewed. The subjects reviewed include basic propagation theory, the influence of the glass medium on attenuation and pulse dispersion, and the effects of perturbations of the waveguide's geometry and index profile.

Mode conversion and optical filtering of obliquely incident waves in corrugated waveguide filters

Abstract: By employing a coupled-mode analysis, we reveal the presence of strong coupling between TE and TM modes in a periodically corrugated optical-waveguide when the wave propagates obliquely with respect to grating vector. The evidence of such mode coupling has been obtained by the polarized transmission and reflection experiment; then the measured strengths of coupling among various modes are successfully compared with calculated values. The effect of such coupling on the performance of a frequency demultiplexer is discussed with some preliminary experiments.

Measurement of refractive-index profile and transmission characteristics of a single-mode optical fiber from its exit-radiation pattern

Abstract: A new exit-radiation pattern method for measuring the refractive-index profile of a single-mode fiber is proposed and used experimentally. In this method the profile is computed from the far-field exit-radiation pattern of the HE11 mode at the end of the single-mode fiber. This method can be applied to a cabled fiber, and the propagation constant, field profile, and group delay of the HE11 mode, and the single-mode limit can be obtained as well as the index profile. The principle, computer simulations, experimental setup, and experimental results are first described. The profile obtained shows a good agreement with that obtained from the interference fringe pattern measured before drawing the fiber. Computations of the group delay of the HE11 mode and the single-mode limit from the measured exit-radiation pattern are discussed.

Cut-off wavelength measurements for single-mode optical fibers.

Abstract: A new technique has been proposed for direct measurement of the cut-off wavelength, at which the first higher-order mode disappears. It uses a change of a near-field pattern of a fiber, which is excited by a variable wavelength source. The cut-off wavelength can be measured with +/-5-nm accuracy. The most suitable fiber length for precise measurement is 10-20 mm. It is found, furthermore, that the first higher-order mode under the condition near cut-off rapidly attenuates because of waveguide imperfections, in which the loss due to core-cladding boundary distortions is the most dominant.

Interdependence of waveguide and material dispersion.

Abstract: Theoretical work on dispersion in single-mode fibers sometimes uses the assumption that waveguide dispersion Dw and material dispersion Dm are separate effects that contribute additively to the total amount of dispersion Dm+w. Using Gloge’s LP-mode approximation we compute the dispersion of the LP01 (HE11) mode by solving the eigenvalue equation taking dispersion of core and cladding materials into account. The dispersion of the LP01 mode is computed by numerical differentiation of the solution of the eigenvalue equation. The difference Dm+w − Dm is compared to waveguide dispersion Dw, which is computed by ignoring the dispersive properties of the core and cladding materials. We find large percentage deviations between Dm+w − Dm and Dw. The assumption of additivity of material and waveguide dispersion is thus not quite correct. However, because of the small contribution of waveguide dispersion to the total dispersion of the LP01 mode, even a large percentage error in the waveguide dispersion has little influence on the over-all dispersion of the LP01 mode.

Determination of modal power distribution in graded-index optical waveguides from near-field patterns and its application to differential mode attenuation measurement

Abstract: A technique is introduced that determines power distribution in fibers from the measured near-field pattern, assuming that: (1) the optical power distributes uniformly among degenerated modes with the same propagation constant, (2) enough modes are excited to ensure the validity of calculation by geometrical optics, and (3) the phase of each propagation mode has no correlation Experiments verifed that the fibers have the function of flattening power distribution among modes with the same propagation constant This fact shows that assumption (1) does not severely limit the applicability of the technique Wave optical calculation is done to determine the numbers of modes that must be excited to satisfy assumption (2) As an example of application of the technique, differential mode attenuation of graded-index fibers is determined from longitudinal variation of the measured near-field pattern

Analysis of approximations for the mode dispersion in monomode fibres

Abstract: A number of recent papers have discussed the mode dispersion in step-index, monomode fibres using formulae based on accurate approximations for the modal propagation constant. It is shown here that, since dispersion depends on the first and second derivatives of the propagation constant, the use of such formulae may often be invalid and that a different type of approximation may be more useful

Minimum dispersion in a single-mode step-index optical fiber

Abstract: The cancellation between material and waveguide dispersions for weakly guiding single-mode step-index fibers has been analyzed to predict the optimum wavelength λ0 for zero first-order dispersion and the residual second-order dispersion T. Greater accuracy in our numerical calculation of waveguide dispersion results in significant change in λ0 and T compared to the previous work by another investigator. The dependence of λ0 and T on the normalized frequency and relative index difference has also been improved and extended numerically. Physical origin of this dependence is discussed; it is considered to be due to different optical power distributions between core and cladding for different constituent wavelengths within the spectral width of the source.

Coupling of fibers to Ti-diffused LiNbO 3 waveguides by butt-joining

Abstract: The optical losses due to butt-joining a single-mode optical fiber to a 32-μm wide Ti-diffused LiNbO3 waveguide have been investigated. Measurements of the total insertion loss as a function of waveguide length show that the waveguide attenuation is 1.25 dB/cm and that coupling losses as low as 0.5 dB can be achieved. The coupling loss has been calculated by a numerical evaluation of the overlap integral of the fiber and waveguide mode profiles, and the results agree with the measured loss.

Determination of mode power distribution in a parabolic-index optical fibers: Theory and application

Abstract: A novel measurement method for determining mode power distribution in a multimode parabolic-index fiber is developed. Using this method, the mode power distributions are obtained in terms of the principal mode number by numerically processing the measured Fraunhofer diffraction patterns of the near-field patterns on an output fiber endface. As an example, differential mode attenuation of a multimode parabolic-index fiber is measured. It is confirmed experimentally that the method is practically applicable to the mode power distribution measurements in a parabolic-index fiber.

Oscillation characteristics in InGaAsP/InP DH lasers with self-aligned structure

Abstract: This paper presents new stripe geometry InGaAsP/InP DH lasers having mechanisms for suppressing current spreads and for controlling the transverse mode parallel to the junction plane. The theoretical study for optimum design of these lasers from which the analytic method of oscillation characteristics, including control of the transverse mode parallel to the junction plane attributable to refractive index and gain, was derived is discussed. The oscillation characteristics, especially the waveguide properties of the transverse mode are reported. Experimental results show excellent agreement with the theory and show that the transverse mode is totally confined by the built-in passive waveguide for a stripe width of 5 μm.

Guided‐radiation mode interaction in off‐axis propagation in anisotropic optical waveguides with application to direct‐intensity modulators

Abstract: A closed‐form solution of the coupled‐mode equations is derived for the guided–radiation mode interaction in optical waveguides by using a Lorentzian approximation to the coupling‐factor distribution. This solution does not neglect reconversion from radiation to guided modes as did the previous perturbation solution. It is thus more accurate for the case of higher‐order guided modes for which the power attenuation due to radiation conversion exhibits an oscillatory form and the ’’effective’’ perturbation assumption that the coupling factor is independent of the phase constant is not valid. Peaks in the mode conversion characteristics at certain eigenvalues of the relevant guided mode can be physically interpreted as the coupling to leaky waves. Illustrative examples and related discussions are given for the polarization‐rotated (TE→TM) guided‐to‐radiation mode conversion in off‐axis propagation in an anisotropic LiNbO3 waveguide. Also, an electro‐optic direct‐intensity modulator is described where the angle of propagation is used instead of a dc field to set a bias point for linear modulation.

Mode coupling in tapered optical waveguide structures and electro-optic switches (Invited Papaer)

Abstract: Mode coupling in optical parallel waveguide transitions is reviewed in terms of local normal modes. Analytic solutions for power transfer are provided for separating waveguides and tapered velocity couplers. General requirements for the low crosstalk operation of a crossed \Delta \beta electro-optic channel waveguide switch are derived.

Tapered waveguides for guided wave optics.

Abstract: Strip waveguides having half-paraboloid shaped tapers that permit efficient fiber to waveguide coupling have been fabricated by Ag ion exchange in soda-lime glass. A reduction in the input coupling loss has been accomplished by tailoring the diffusion to provide a gradual transition from a single-mode waveguide to a multimode waveguide having cross-sectional dimensions comparable to the core diameter of a single-mode fiber. Waveguides without tapers exhibit an attenuation of 1.0 dB/cm and an input coupling loss of 0.6 dB. The additional loss introduced by the tapered region is 0.5 dB. By way of contrast, an input coupling loss of 2.4 dB is obtained by coupling directly to a single-mode waveguide, indicating a net improvement of 1.3 dB for the tapered waveguides.

Scattering of surface waves at a slab waveguide discontinuity

Abstract: The analysis of a step discontinuity of single-mode slab waveguide excited in the dominant mode is presented for both TE- and TM-modes. The problem is formulated by using the mode-matching procedure parallel to that of Marcuse. The solutions for the reflection coefficient, transmitted power and radiated power are then obtained by the application of the residue-calculus technique, which leads to more general expressions than those so far obtained by others who used more complicated methods. Numerical results are given which are in good agreement with previous results for specific cases. For the general case, the results also agree very well with those obtained by the reciprocity theorem.

Ridge waveguides and electro-optical switches in LiNbO 3 fabricated by ion-bombardment-enhanced etching

Abstract: Narrow ridge waveguides with \sim 2-\mu m width have been fabricated in Ti-diffused LiNbO_3 by ion-bombardment-enhanced etching and the intensity modulation by switching the waveguide from guided mode to radiation mode through electro-optic effect has been demonstrated. The extinction coefficient of -19 dB was obtained at the applied voltage of \pm 10 V.

Method for making multiple mode waveguide having cylindrical perturbations

Abstract: A multiple mode optical waveguide includes a glass core and a glass cladding around the core. In order to promote coupling between guided modes of light propagation, the core has cylindrical perturbations spaced along its length. The perturbations include index of refraction variations in rings within the core.

Optical strip waveguide: an analysis.

Abstract: An analysis of the strip waveguide is presented with special emphasis on reflection and transmission of a wave obliquely incident on the side of a strip. Mode conversion and the contribution of radiation modes are taken into account in the formulation. The numerical results of the mode conversion and attenuation constant of the fundamental leaky mode are presented and compared with the results of other authors. The numerical accuracy of our analysis is also checked by two different procedures. It is found that the radiation modes have considerable effects on the waveguide characteristics.

Dispersion in graded single-mode fibres

Abstract: The normalised frequency for zero waveguide dispersion of the HE11 mode, called VOD, is highly dependent on profile shape. The more the profile departs from a step, the greater the increase of VOD above the effective single-moded region until, for example, VOD becomes infinite for profiles that fall off at a rate greater than or equal to the parabola.

Single-mode propagation in 2-mode region of optical fibre by using mode filter

Abstract: The effect of a mode filter using fibre bend has been clearly shown experimentally. The mode filter effectively removes the LP11-mode, and has a negligibly small effect on the attenuation of the LP01-mode. The single-mode propagation was attained at the V-value of 2.8 by using the filter.

Minimum dispersion at 1.55 μm for single-mode step-index fibres

Abstract: The single-mode step-index fibre parameters, relative index difference and core diameter, have been predicted to achieve first-order cancellation between material and waveguide dispersions at 1.55 μm. Our prediction by accurate solution of the characteristic equation results in fibre parameters different from those obtained by other investigators. The origin of this difference is examined.

Scattering characteristics of a beam mode in dielectric-slab optical waveguide

Abstract: The radiated power of scattered light caused by refractive-index inhomogeneities and waveguide wall irregularities in an asymmetric slab waveguide is investigated by using the stationary phase method on the basis of a first-order perturbation theory. The correlation between both imperfections of the refractive index and the waveguide wall is taken into consideration. It is found that the correlation between both imperfections hardly affects the radiated power caused by air radiation modes while it modifies the radiated power caused by substrate radiation modes.

Novel method for measuring cutoff wavelength of HE21-, TE01-and TM01-modes

Abstract: A new measurement method for the cutoff wavelength of HE21-, TE01-and TM01 modes using a polariser is described The experimental results show that higher measurement accuracy and sensitivity are obtained compared with the previous method

Dielectric bypass waveguide mode order converter

Abstract: The mode conversion characteristics of a bypass waveguide mode order converter, whose structure is a dielectric waveguide which divides into two branches that later unite with small dividing and uniting angles, are studied experimentally. The working principle of the mode order converter is based on adiabatic mode propagation in the branching waveguide. The features of the device are: 1) it can realize multimode order conversions at the same time, and 2) it does not require phase matching between coupled modes, which relieves the severe tolerance restriction placed on the conventional mode converter with uniform waveguide parameters.

Mode coupling between two connected multimode parabolic-index optical waveguides

Abstract: Both a displacement of axis and a change in the refractive index distribution function cause mode coupling to occur between two multimode parabolic-index optical waveguides. This coupling is investigated by the coherent states method and the method of the dynamical symmetry group. Expressions for the mode coupling coefficients are obtained and their relationship to the Franck-Condon factors is emphasized. Recurrence relations for the mode overlap integrals and sum rules for the mode coupling coefficients are presented. An analogue of the Franck-Condon principle for the mode coupling coefficients is formulated. A simple geometric method for finding the most intensively coupled modes is also proposed.

Effects of waveguide mode asymmetry on the laser diode-to-diffused waveguide coupling efficiency

Abstract: In the design and development of guided-wave optical cir­ cuits, it is important to be able to estimate the coupling effi­ ciency between the laser source and the optical waveguide. It was shown previously that the efficiency with which the out­ put of a double-heterostructure GaAlAs laser diode can be edge-coupled into a Ti indiffused LiNbO3 planar waveguide is well characterized by a simple coupling model. In that model, both the waveguide mode and the laser output mode were approximated by a Gaussian dependence upon the coordinate perpendicular to the plane of the waveguide. While this model is a simple one, it successfully predicts the dependence of the coupling efficiency upon both the longi­ tudinal (or axial) and transverse separation between the laser diode and the waveguide. The closed-form nature of the so­ lution for the coupling efficiency as a function of the various alignment parameters is an important feature of the model, since it is not necessary to resort to numerical techniques to obtain the desired results. While the Gaussian-Gaussian model is simple to use and leads to good agreement with experiment, it is nonetheless true that this model neglects the asymmetric character of the actual waveguide mode. Burns and Hocker have studied the effects of this asymmetry upon the edge-coupling efficiency by using numerical techniques to calculate the electric field appropriate for an assumed Gaussian variation of the re­ fractive index with depth in the waveguide. They concluded that approximating the waveguide mode by a symmetric Gaussian leads to an overestimation of the actual edge-cou­ pling efficiency by 4%. This Letter presents the results of a study of the effects of mode asymmetry upon the edge-cou­ pling efficiency using a waveguide mode profile which leads to a (nearly) closed-form solution for the coupling efficiency for several interesting cases. Among other things, it will be shown that for laser diode and waveguide parameters which are obtainable in practice, the asymmetry correction to the coupling efficiency calculated within the Gaussian-Gaussian model is negligible. Arguing that the depth variation of the refractive index in a planar diffused LiNbO3 or LiTaO3 waveguide does not de­ part substantially from a square-law behavior, and that the electric field almost vanishes at the air-waveguide interface, Arnaud has suggested that the electric field of the funda­ mental mode of a diffused waveguide should be well approx­ imated by the first asymmetric Hermite-Gauss function. If the air-waveguide interface is assumed to lie in the x = 0 plane with the refractive index decreasing with positive x, the as­ sumed electric field defining the waveguide mode has the form a comparison of ψ2(x) and the electric field obtained by Hocker for an assumed Gaussian refractive index profile and waveguide parameters b = 0.410 and V = 4.30. ψ2(x) was fit to Hocker's result by matching widths at the 1/e points, and the over-all agreement is quite good. As in the previous work, the electric field of the laser mode incident along the z direction upon the waveguide edge is given by

Modes in 2-D buried optical waveguide with asymmetric graded refractive index profile.

Abstract: A dielectric waveguide, whose guiding region is located beneath the substrate surface, will be a useful configuration to connect optical functional devices fabricated in the same substrate. A convenient refractive index profile, which is based on the Morse potential function and is similar to that which is observed in practically fabricated optical waveguides, is introduced in order to study the propagation characteristics of the 2-D buried optical waveguide.

Scanning technique for investigating optical fibre dispersion

Abstract: Differential mode delay measurements have been performed, both for step-index and for graded-index fibres, using a sinusoidally modulated optical source From a differential mode delay measurement, it is possible to get all the information on the fibre baseband response with or without the effect of skew rays, and in particular of leaky rays A theoretical model of mode coupling is developed and is used for computing the baseband response for fibres where mode coupling is not negligible