Gerd Mrozynski

Ray tracing technique and its verification for the analysis of highly multimode optical waveguides with rough surfaces

A novel hybrid ray tracing technique for the analysis of signal propagation in highly multimode optical waveguides with rough surfaces and its verification in part is presented. The technique combines geometrical optics with a light scattering model, based on wave optics by applying a Monte Carlo method. While the light scattering model takes mode coupling caused by surface irregularities into account, the ray tracing technique provides the analysis of light propagation in highly multimode waveguides with arbitrary shapes. The verification is obtained by calculating wave propagation within a slab waveguide with rough surfaces applying the well known coupled power theory, which provides the power of the guided modes versus the axial coordinate of the waveguide. Therefore, the ray tracing results are transformed into the discrete waveguide modes in order to compare the results.

Analytical determination of eddy currents in a hollow sphere excited by an arbitrary dipole

In this paper an analytical solution for the quasistationary eddy current distribution in a hollow sphere is presented using a divergence free vector potential derived from another spatial vector function by applying the curl operator. The field is excited by a dipole of arbitrary orientation and position. The dissipated power is also considered and hints are given for the analytical treatment of multishield problems excited by current loops.

Time domain simulation of optical multimode chip-to-chip interconnects

To increase the bandwidth of high-performance chip-to-chip interconnects optical on-board interconnects can be used. Since the design procedure of such optical interconnects has to be widely compatible with current computer aided board design processes, adequate simulation methods are required. In this paper an efficient and design process compatible method for simulating the transmission behavior of optical multimode chip-to-chip interconnects is presented. The approach is based on a time domain description where an optical multimode waveguide is represented by a multiport. The different transfer paths between the input- and output ports describe the transmission behavior of the entire waveguide. The transmission behavior of each individual path can be characterized by its step response, which can be computed by the aid of an extended ray tracing method. Due to some fundamental properties of these step responses, its piecewise approximation by simple exponential functions is possible. As a consequence the pulse responses of each transfer path can be determined analytically and they are also approximated by exponential functions. Finally this procedure enables the application of a semi-analytic recursive convolution method for the computation of the waveguide transmission behavior. The simulation procedure is illustrated and discussed by a set of examples.

Electro-optical circuit boards with four-channel butt-coupled optical transmitter and receiver modules

Chip-to-chip interconnects on printed circuit boards within high-speed electronic systems act increasingly as a limiting bottleneck for the achievable system performance, since local processing speed often exceeds the bandwidth capabilities of conventional electrical interconnects. In addition, rising signal frequencies or clock rates also result in increased susceptibility to electromagnetic interference. The well known limitations and problems of electrical interconnects can be overcome with optical interconnects, which have made their way from long haul telecommunication networks to parallel fiber optical modules for board-to-board interconnects within systems. Extending the advantages of optical signal transmission for very short reach interconnect applications, i.e. board or module level interconnects, therefore is a consequent logical step. This paper presents the integration of optical waveguides into conventional printed circuit boards to achieve hybrid electrical-optical boards with high- bandwidth optical interconnects. The realization of such electrical-optical boards is demonstrated with boards containing 4-channel transmitter and receiver modules, utilizing lead-frame based array GaAs-VCSEL and Si-PIN-diode components. The waveguides are manufactured by hot embossing and laminated into the boards within a standard printed circuit board production process. To couple light into and out of the optical waveguides a butt-coupling technique is applied.

Coupled Mode Analysis of Power Transport and Loss in Highly Multimodal Tapered Dielectric Waveguides for Coupling Applications

Power transport through the local guided modes and power loss by reflection and radiation in highly multimodal tapered dielectric waveguides is analyzed by a simplified coupled mode theory. Comparison with geometrical optics shows a very good agreement for long tapers. Application of tapered highly multimodal channel waveguides in PCBs is discussed.

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.

Models for the coupling of light into multimode waveguides

For the simulation of light transmission over optical interconnects an appropriate modeling of the coupling process is needed. Comprehensive methods like the mode matching method can offer accurate results as long as a very high number of modes on both sides of the coupling interface is available. In this paper, some simpler numerical methods are assessed and compared to the results of the mode matching method applied to a 2D coupling problem. It turns out that these methods can be used well under usual operating conditions for highly multimodal waveguides, but the errors increase with the deviation from the non-ideal coupling geometry.

Integration of wide-band service in time division multiplex systems

The authors present a TDM (time division multiplexing) channel access concept based on narrowband and wideband traffic requests which are queued in separated parallel queues. The system may be regarded as a part of a wideband integrated services digital network (ISDN). The channel access strategy follows the premise of allocating that type of customer first into service which fits best (fills out best) the nonoccupied channels. A Poisson arrival process and exponentially distributed service times for both are assumed for both traffic types, but they may have different bit rate requirements. The model involves four characteristic random variables; its joint probability is obtained by means of balance equations. Since it is difficult to determine the solution analytically, the authors develop the transition rate matrix and suggest a procedure for the numerical solution of the balance equations. Several numerical results are presented and discussed. >

Improved Time Domain Simulation of Optical Multimode Intrasystem Interconnects

To increase the bandwidth of high-performance intrasystem interconnections, optical multimode waveguides can be used. Since the design procedure of optical interconnections has to be widely compatible with conventional design processes, adequate simulation methods are required. This paper presents an improved time domain method for simulating the signal transmission along optical multimode interconnections. The improvements mainly result from the more efficient method for the piecewise approximation of the waveguides step responses by a few exponential functions. The adapted semi-analytical recursive convolution method decreases the computation times.

Influence of surface roughness on the bandwidth of optical multimode waveguides analyzed by modal noise theory

Modal noise is an undesired modulation of the guided light intensity in a multimode waveguide. Applying the frequency correlation function the frequency dependence of this noise as well as the bandwidth of a multimode waveguide can be estimated. In this paper the existing model of the frequency correlation function for a waveguide with smoothed dielectric interfaces is enhanced to analyze the influence of surface roughness on the achievable bandwidth. This surface roughness is caused by the manufacturing process of the waveguides.