Intermode light diffusion in multimode optical waveguides with rough surfaces

A theoretical analysis of incoherent intermode light power diffusion in multimode dielectric waveguides with rough (corrugated) surfaces is presented. The correlation length a of the surface-profile variations is assumed to be sufficiently large (a less less than lambda/2pi) to permit light scattering into the outer space only from the modes close to the critical angles of propagation and yet sufficiently small (a less less than d, where d is the average width of the waveguide) to permit direct interaction between a given mode and a large number of neighboring ones. The cases of a one-dimensional (1D) slab waveguide and a two-dimensional cylindrical waveguide (optical fiber) are analyzed, and we find that in both cases the partial differential equations that govern the evolution of the angular light power profile propagating along the waveguide are 1D and of the diffusion type. However, whereas in the former case the effective conductivity coefficient proves to be linearly dependent on the transverse-mode wave number, in the latter one the linear dependence is for the effective diffusion coefficient. The theoretical predictions are in reasonable agreement with experimental results for the intermode power diffusion in multimode (700 x 700) optical fibers with etched surfaces. The characteristic length of dispersion of a narrow angular power profile evaluated from the correlation length and standard deviation of heights of the surface profile proved to be in good agreement with the experimentally observed changes in the output angular power profiles.     

Analysis of multimode effects in the free-propagation region of a silicon-on-insulator-based arrayed-waveguide grating demultiplexer

Multimode effects in the free-propagation regions (FPRs) of an arrayed-waveguide grating (AWG) demultiplexer based on silicon-on-insulator are considered. Some undesired multimode effects, such as the increase of the insertion loss and the cross talk, are studied by use of a method of three-dimensional guided-mode propagation analysis. It is found that the multimode effects for the edge channels are more serious than those for the central channel. For an AWG demultiplexer with a small channel number, the multimode effects can be minimized by choosing appropriate FPR parameters such as the length and the thickness of the FPR. The coupling coefficient between the FPR and an arrayed waveguide is sensitive to the thickness of the FPR.     

Electro-optic multimode interference device using organic materials

We present experimental results verifying the optical robustness of a 1 x 1 multimode interference (MMI) device that is directly butt coupled with optical fibers at 70 degrees C for 1050 h and discuss the gradual increase of polarization dependent loss. Based on this structure, an electro-optic (EO) MMI waveguide device that can control the output optical power by using an electrode structure located directly on top of the multimode is presented. As a proof of principle, we demonstrate the switching operation of the EO-MMI device using commercially available chromophore as the active EO material.     

Matrix method for two-dimensional waveguide mode solution

In this paper, we show that the transfer matrix theory of multilayer optics can be used to solve the modes of any two-dimensional (2D) waveguide for their effective indices and field distributions. A 2D waveguide, even composed of numerous layers, is essentially a multilayer stack and the transmission through the stack can be analysed using the transfer matrix theory. The result is a transfer matrix with four complex value elements, namely A, B, C and D. The effective index of a guided mode satisfies two conditions: (1) evanescent waves exist simultaneously in the first (cladding) layer and last (substrate) layer, and (2) the complex element D vanishes. For a given mode, the field distribution in the waveguide is the result of a ‘folded’ plane wave. In each layer, there is only propagation and absorption; at each boundary, only reflection and refraction occur, which can be calculated according to the Fresnel equations. As examples, we show that this method can be used to solve modes supported by the multilayer step-index dielectric waveguide, slot waveguide, gradient-index waveguide and various plasmonic waveguides. The results indicate the transfer matrix method is effective for 2D waveguide mode solution in general.     

Simulation of cross-talk reduction in multimode waveguide-based micro-optical switching systems by use of single-mode filters

We propose a method to reduce cross talk by using single-mode filters, namely, extracting the fundamental mode from a multimode optical network (EFMON). The EFMON effect is evaluated for a three-step switching system consisting of cascade electro-optic (EO) waveguide prism deflector (WPD) micro-optical switches (MOSs) and a multimode waveguide network. The WPD MOS is optimized for single-mode operation in lead lanthanum zirconate titanate thin films as EO slab waveguides with a driving voltage of 12 V, a length of 310 microm, and a channel distance of 20 microm. Beam propagation method simulation reveals that mode disturbance, higher-order modes, and cross talk are accumulated by switching steps. A single-mode filter for EFMON in the output region of the switching system reduces cross talk to below -20 dB at a propagation length of 2000 microm in the single-mode filter and below -30 dB at 20000 microm.     

Optimal design method of a low-loss broadband Y branch with a multimode waveguide section

An optimal design method for a low broadband silica-on-silicon Y branc is considered. A multimode waveguide section, which was used earlier to reduce the excess loss, is designed optimally when the light distribution at the end of the multimode waveguide section is matched to the profile of the symmetric supermode for the structure of the two branching waveguides. An optimization method that combines the genetic algorithm and a gradient-based search method is used to obtain the optimal geometrical parameters for the multimode waveguide section as well as the widths for the input and branching waveguides.     

Shannon capacity calculation on multimode fibres

As the ultimate transmission performance of installed multimode fibres is uncertain, there is a need to understand the practical maximum capacity limit that a multimode fibre can support. The authors therefore present a new model to determine the worst-case Shannon capacity limit for multimode fibres. Detailed calculations are reported for fibre-distributed-data-interface (FDDI)-grade and OM1 fibres for operation using serial transmission with a single wavelength near 1310 nm. The method is also applicable to FDDI-grade, OM1, OM2 and OM3 fibres at all wavelengths of operation. The Shannon capacity limit of a multimode fibre is calculated for 220 m link lengths, assuming a link power budget consistent with the IEEE 10GBASE-LRM Gigabit Ethernet standard. It is shown that the Shannon capacity for non-optimised and optimised transmission spectra are at least 42 and 52 Gb/s, respectively.     

Novel approach for design of low index contrast multimode interference devices

Self-imaging theory is widely accepted as a good method in designing multimode interference (MMI) couplers, but it is also true that self-imaging theory is not suitable for low-contrast structures. An improved self-imaging theory is proposed in this paper for the optimal design of low-contrast 1 × N MMI couplers. The average effective width of the MMI waveguide and the average effective propagation constant of the MMI waveguide are used in the improved self-imaging theory. An approach is given to find the average effective width. We use this approach in the optimal design of a 1?×?4 silica MMI coupler, and the results show that the improved self-imaging theory is more accurate than conventional self-imaging theory for low-contrast structures.     

Completely passive method of speckle reduction utilizing static multimode optical fibre and two-dimensional diffractive optical element

ABSTRACT

In this paper, we present experimental results on speckle noise suppression using a completely passive method. The passivity of the method is achieved owing to the absence of any mechanical, electronic, or other dynamic influences on the optical scheme elements. In the experiment, a multimode semiconductor 520?±?5-nm laser with a spectral bandwidth of 2?nm, static two-dimensional (2D) and 2?×?1D diffractive optical elements (DOEs), as well as multimode single-core optical fibre and multimode optical fibre bundle were used. The dependence of the speckle reduction efficiency as a function of the optical fibre type and optical fibre length was measured for different DOEs. A speckle contrast of 0.148 and speckle reduction coefficient of 2.38 were obtained for a 2.5-m-long multimode optical fibre bundle. The experimental results confirmed that it is possible to construct completely passive optical circuits with reduced speckle noises using static multimode optical fibres and diffraction optical elements.     

Taylor limit of equilibration and the multimode diffusion approximation

The multimode diffusion approximation for solute dispersion in transversely bounded shear flows owes its origin to the formal method of eigenmode expansion. It is put forth upon the premise that a quasi-steady condition termed the Taylor limit of equilibrium exists in the course of time when equilibrium estimates of the residual terms of the concentration distribution can be realistically made contingent to the evolution of their primary counterparts. By applying the Green's function for the diffusion equation, this paper provides a qualifying account for the establishment of the Taylor limit. A method of successive approximations is derived for the determination of the principal mode coefficient functions with the inclusion of bulk reaction and longitudinal diffusion. The resulting equations governing the evolution of these mode coefficient functions are truncated to conform to the multimode diffusion type and the special Taylor-limit results given by Smith are easily deduced. Examples are given to illustrate the attainment of a convergent solution.     

Anomalous side-shifted multimode spectra in proton-exchanged LiNbO3 waveguides

We report the presence of a curious and highly reproducible effect in multimode lithium niobate waveguides fabricated by proton exchange (PE) in molten benzoic acid at temperatures ranging from 160 degrees C to approximately 250 degrees C. The spectral lines in the mode spectra of these guides (measured using a prism coupler) are anomalously side-shifted out of the expected geometrical plane. Transforming these measurements back into the plane of the waveguide, we find that the direction of scattering (relative to the crystal axis) is extremely precise (<1% deviation about a mean), and that the effect can be explained by postulating the existence of precisely oriented, stress-induced gratinglike structures (with irregular periods in the 10-70-microm range) in the guides.     

Electro-optical logic application of multimode interference coupler by multivalued controlling

Electro-optical hybrid logic is a potential solution to implement both electrical and optical signal processing, which receives analog or digital, electrical or optical signals and produces logic signals in a desired manner. In light of the transfer matrix theory, we found that one can steer light into different output ports of a multimode interference coupler by controlling the phases in a multivalued manner on the image-extended arms. This implementation acts as an analog-to-digital convertor from electric domain to optical domain. Also, an electrical-to-optical 2-to-2(2) binary-coded decoder is described and examined by the 3D beam propagation method.     

Active control of terahertz multimode resonance transmission through subwavelength metal annular aperture arrays

Ultrafast optical properties of U-shaped annular aperture arrays (UAAAs) fabricated on a silicon substrate were investigated for varying photodoping levels of the silicon from the back to front interfaces of the sample. Experimental data demonstrate that the transmission modulation depth of the multimode resonance can be realized about 90% under optical power 60 mW, and the off switch of these resonance peaks transmission can be also simultaneously achieved within several picoseconds. Such plasmonic structure is able to be used for ultrafast optical modulators, active terahertz plasmonics, and ultrafast optical off switch.     

Modeling and experimental observation of an on-chip two-dimensional far-field interference pattern

In this paper, we model and experimentally observe the far-field radiation produced by interfering beams propagating in two-dimensional (2D) slab waveguides. Using a transmission-line analogy, we compare the 2D propagation with standard three-dimensional (3D) far-field representations and derive the 2D conditions for using standard far-field approximations. Then we test our theoretical results by experimentally observing the 2D far-field pattern produced by a 1×3 multimode interference (MMI) coupler on a silicon nanomembrane. The MMI outputs are connected to a slab silicon waveguide, and the far field is observed at the edge of the silicon slab. This represents the observation of 2D far-field pattern produced by an array of on-chip radiators.     

Three-dimensional power splitter based on self-imaging effect in multimode layer-by-layer photonic crystal waveguides

The self-imaging effect based on symmetrical interference in multimode layer-by-layer photonic crystal waveguides (PhCWs), is numerically studied with finite-difference time-domain simulations. With the properties of twofold images, a kind of three-dimensional (3D) PhCW-based power splitters with an ultracompact size using complete photonic bandgaps is proposed, calculated, and analyzed. The presented structure can be extended for the design of M×N power splitters for 3D photonic integrated circuits applications.     

Design of phased-array wavelength division multiplexers using multimode interference couplers

Novel designs for phased-array wavelength-division multiplexers based on self-imaging properties of multimode interference (MMI) couplers are presented. These devices, which operate on N equally spaced wavelength channels, consist of two MMI couplers connected by an array of N monomode waveguides. The MMI couplers function as power splitters/combiners, and the waveguide array is the dispersive element. The excellent characteristics of MMI couplers offer the possibility of designing small-size devices with low loss and with high uniformity among different channels. A general theoretical formulation for an N-channel multiplexer is presented, and a simple procedure for finding an optimum set of lengths for the array guides is given. We show that these multiplexers can function as N x N wavelength-selective interconnecting components. The simulated performance of three variations of a five-channel device, designed in a rib waveguide system, is given. It is demonstrated that sidelobes in the multiplexer spectral response can be suppressed by weighting the power samples in the array waveguides through appropriate design of a nonuniform MMI power splitter.     

Synthesis of Hadamard transformers by use of multimode interference optical waveguides

We propose a synthesis method of optical Hadamard transformer using multimode interference (MMI) couplers. By using the signal transfer matrix of 2 x 2, 4 x 4, and 8 x 8 MMI couplers, we show that sum and difference units of input signals can be synthesized. An interchange unit of two signals can also be synthesized. One synthesis method of Hadamard transformers is a combination of only 2 x 2 units, and the other is a combination of N x N(N > or = 4) units as well as 2 x 2 units. The design examples of operation units are shown, and the size and the output power of Hadamard transformers are estimated.     

Transformation of the multimode terahertz quantum cascade laser beam into a Gaussian, using a hollow dielectric waveguide

We demonstrate that a short hollow dielectric tube can act as a dielectric waveguide and transform the multimode, highly diverging terahertz quantum cascade laser beam into the lowest order dielectric waveguide hybrid mode, EH(11), which then couples efficiently to the free-space Gaussian mode, TEM(00). This simple approach should enable terahertz quantum cascade lasers to be employed in applications where a spatially coherent beam is required.     

Achieving stability in remote holography using flexible multimode image bundles

Commercial flexible image bundles (boroscopes, endoscopes, etc.) are made up of tens of thousands of coherently arrayed multimode optical fibers whose modal propagation characteristics are unavoidably affected by bending losses. Consequently, light wave fronts transmitted through such bundles are subject to significant changes whenever the bundle is flexed anywhere along its length. For this reason images transmitted through such multimode image bundles cannot normally be used to generate holograms unless the bundle is rigidly fixed at every point. This requirement represents a substantial limitation on the use of fiber optics to generate and record holograms of remote subjects. However, this study demonstrates an original technique using ultralow frequency in situ holograms that can be transmitted through a multimode image bundle and recorded remotely even while the bundle is being moved.     

Impulse dispersion in a multimode optical fiber from its far-field radiation pattern

A simple geometric-optical theory predicts impulse broadening in multimode fibers using the far-field power distribution of an incoherently excited waveguide with arbitrary refractive-index profile. The accuracy is comparable with that of scalar optical methods if they do not incorporate mode coupling and a differential mode attenuation model.