Radiation Mode Method Research Articles

Measuring the radiation of sound sources with the radiation mode method: Towards realistic problems.

The measurement of the pressure field radiated by a sound source has many applications in the fields of noise control and loudspeaker system design. In this paper, the radiation mode method is used to measure the field radiated by a complex acoustic source whose surface impedance is arbitrary and does not correspond to the Neumann boundary condition used for the calculation of radiation modes. The most effective radiation modes are used as test functions to calculate a pressure expansion around the source under test, an expansion that matches the measured pressure at a limited number of points close to the source. This expansion is then used to calculate the radiated pressure at a greater distance at unmeasured locations. In a first step, numerical simulations are performed to evaluate the method's most influential parameters. Then, measurements are performed in a semi-anechoic room on two real sources of increasing complexity. Obtained results show that the radiation mode method allows an accurate evaluation of the pressure field radiated by the test object over a fairly wide frequency band (between 100 Hz and 2 kHz) even for complex sources.

Optical fibre facets: a vector analysis

A full vector, semi-analytical, yet accurate, analysis of coated optical fibre facets is presented, based upon the free space radiation mode method. This yields a simple final expression for the modal reflectivity. A highly efficient algorithm has been developed to implement this analysis. Example results for the reflectivity of the fundamental HE11 mode supported by typical single-mode fibres are given, which are compared to those obtained from an equivalent scalar investigation. Results show that correct modelling of the low reflectivities of coated facets requires a full vector analysis.

Novel hybrid method for efficient 3-D fiber-to-chip coupling analysis

An efficient hybrid method has been developed to analyze, for the first time, the three-dimensional problem of fiber-to-chip coupling. The method employs the numerical finite difference beam propagation method to model the fields in the planar chip guide and the semi-analytical free space radiation mode method to model the fields in the fiber guide. The two methods are linked via an iterative algorithm. The results for the transmission, backreflection, and radiation losses are presented for the case of direct butt-coupling and coupling via an antireflection coating. Finally, the effect of the vertical misalignment is analyzed and results are compared with the ones obtained experimentally.

Applicability of scalar theory for analysis of mode reflection from an optical dielectric waveguide end

Scalar and vector theories are compared for weakly guided modes reflected from a planar optical dielectric waveguide end or laser facet. By utilizing the free space radiation mode method the range of validity of the scalar theory over a wide range of reflectivities is given explicitly for the first time.

Efficient curvature analysis of buried waveguides

The highly efficient free space radiation mode method is extended, enabling for the first time its use in determining the lossy modes of curved buried semiconductor waveguides. Both the real and imaginary parts of the propagation constant along with the corresponding field profiles, are found with an accuracy comparable to that of more computationally intensive methods.

Fast and accurate reflectivity calculations for shaped core optical fibres

A novel scalar (i.e. paraxial) free space radiation mode method is presented for calculating the normal incidence facet reflectivity of the main guided mode of a step-index optical fibre with generally shaped smooth core. Numerical results are presented and discussed for several cases of the Nth order super-elliptical core shape, including the circular, elliptical, rectangular-type and slab limiting cases.

Novel half space radiation mode method for buried waveguide analysis

A new method is presented for the analysis of buried rectangular waveguides in the presence of a plane semiconductor–air interface. The method uses simple radiation modes for a half space to formulate closed form transcendental equations for the propagation constants in the scalar and polarized cases. Results are thereby obtained very efficiently and are shown to be highly accurate when compared to benchmark results obtained with the Finite Difference method.

Efficient and accurate models of buried spot-size convertors

The Free Space Radiation Mode method has been established as an accurate and extremely efficient technique for analysing buried optical waveguide structures. This work demonstrates its application to the simulation of spot-size convertors which are a crucially important component of many practical systems.

The free-space radiation mode method for the analysis of coated angled facets and comparison with a FDTD method

The free-space radiation mode method is extended to provide accurate semianalytical formulas for the reflectivity of a polarized optical waveguide mode incident on a coated laser facet at an arbitrary angle. Solutions may be obtained easily and with minimum computational effort. Results obtained are compared with those from a finite-difference-time-domain method. © 1997 John Wiley & Sons, Inc. Microwave Opt Technol Lett 15: 12–16, 1997.

Computationally efficient analysis of buried waveguides with applications to semiconductor lasers

The proven free space radiation mode method is extended for the first time to the important case of multilayered structures. Simple transcendental equations are obtained which can be solved in a matter of seconds, accurately yielding both propagation constants and field profiles. Further, the inclusion of lossy materials and active regions allows the approach to be used for the first time to model buried laser structures. A variety of practical examples are examined, and results are compared with those from complex finite element and finite difference calculations, demonstrating excellent agreement and a substantial reduction in computational effort.

Full vector analysis of two-dimensional angled and coated optical waveguide facets

We analyze the important problem of scattering from two-dimensional (2-D) optical waveguide facets, including the effects of both antireflection coatings and facet angle. The facet is allowed to be angled in both vertical and horizontal planes, necessitating a fully vectorial approach to model correctly the polarization coupling that occurs. To achieve this, the highly efficient Free Space Radiation Mode method has been extended to the general vector case, yielding novel expressions for both the reflectivity and the coupling coefficients which can be rapidly evaluated on a desktop PC for a wide variety of practical structures. Results are presented for both angled, coated and coated angled facets. Full field profiles, also available from the approach, are presented and provide useful design information and aids to understanding.

Antireflection-coated angled facet design

New and accurate semianalytical expressions, based on the free-space radiation mode method, are derived for the reflectivity of a polarised guided mode of a slab waveguide incident on a multicoated laser facet at an arbitrary angle. Solutions may be obtained simply and with minimum computational effort. Results presented confirm that the coated angled facet can reduce the guided-mode reflectivity to near zero for both polarisations. The far-field radiation pattern is also significantly modified by angling the waveguide to the facet.