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This paper deals with the self-imaging effect in multimode waveguides. Analogies and differences to the free-space case are shown. The fields in multimode waveguides are studied. Particularly, the behavior of the fields is examined, when a periodic perturbation is introduced. (DOI: 10.2971/jeos.2009.09031)
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... recognize e.g. a monotonic change (with t) of the lower modes, whereas e.g. the phase of the 11 th is relatively constant. Since the lower order modes are the main responsible ones for the behavior of the device, we took a closer look at them in Figure 11. As mentioned before, we are not interested in the absolute val- ues of the phases (because an arbitrary value can be added), but merely in the change. ...
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Citations
... The input varies from the paraxial to nonparaxial regime. The Talbot effect, often studied in the paraxial limit, has been verified experimentally in classical, quantum, and plasmonic setups, for hybrid or all-optical integrated circuits and the relevance to classical and quantum information processing [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Self-imaging can reduce the cascading inefficiency while designing or improving existing designs of optical devices and circuit elements [6,[21][22][23][24][25]. Miniaturization of optical circuit designs using metamaterial structures including plasmonic logic gates, with the possibility of integrating subwavelength light sources, has revived interest in using the self-imaging phenomenon [11,[26][27][28]. ...
We demonstrate the precise variation of self-imaging distance with width of a Gaussian input, centrally fed into a symmetric dielectric slab waveguide of width ∼20λ0. The width of the Gaussian is varied from the paraxial to completely nonparaxial domain. Unlike the paraxial case, the self-imaging distance is found to depend on the beam width and change with the number of excited modes in the waveguide. These features should be useful in designing devices that exploit self-imaging for improved efficiency, especially in nanophotonic circuits.
... When the propagation parameters k m z are real, i.e. in the limit of negligible absorption, self-imaging must occur at specific forward propagation distances that are an integer multiple of a characteristic value. For symmetric illumination the characteristic distance is [33,34]: ...
Waveguides for short-wavelength x-rays have been successfully employed for microbeam and nanobeam production and microscopy experiments. The coherence of hard x-ray sources is generally poor, and therefore the spatial coherence filtering characteristics of waveguides have been attractive for high-resolution microscopy experiments. To quantify the spatial coherence filtering properties of a waveguide, we here report a theoretical study of the propagation of a partially coherent beam in a waveguide in the paraxial approximation. By propagating the cross-spectral density function associated with the partially coherent field, we quantify in detail the evolution of the spatial coherence as the beam proceeds along the waveguide. The propagation is efficiently accomplished using the communication-modes formalism. The generality of the approach makes it suitable to study more complex phenomena such as the second-order Talbot self-imaging effect and coherence revivals in waveguides. Numerical results are shown for waveguides illuminated by partially coherent hard x-rays.
... Filtering effects may be achieved by specific output waveguides that are positioned in the self-imaging plane with e.g. smaller layer width or specific structuring (Helfert et al. 2009). ...
In this article, we examine spectral transmission characteristics based on the self-imaging effect in plasmonic multimode
waveguides. For the analysis, we calculate the correlation between an input field and the field in the self-imaging plane.
We perform full vectorial computations using the Method of Lines as numerical method. The resulting transmission profile is
discussed with regards to the attenuation, the even and odd mode sets and for several structural parameters of the plasmonic
waveguide. The introduced transmission characteristic may offer the opportunity for the implementation of filtering operations
in plasmonic waveguides.
KeywordsPlasmonic waveguides–Self-imaging effect–Transmission characteristic
... 1). However, as shown in [16], one can describe the virtual periodicity approximately by p x ≈ 2w. The theory of self-imaging in multimode waveguides was described in detail in [10]. ...
... The analysis of plasmonic devices by different numerical methods including the MoL was presented in192021. Since we perform full 3-D calculations here, we also This waveguide was studied in [16] ; the Talbot distance was determined as z T ¼ 3600 μm. mention [22,23], because these papers showed how the numerical effort can be kept moderate when analyzing such 3-D structures. ...
We present studies on the propagation of plasmon waves in metallic multimode waveguides surrounded by a dielectric medium. The permittivity of the metal was determined by a Drude model. The propagation was simulated by the method of lines. The propagating field exhibited the well-known self-imaging phenomenon known as the Talbot effect. The metallic waveguides are lossy. The influence of various parameters on the losses was examined. By a suitable choice of parameters, propagation distances of several Talbot periods are possible. Our investigation also includes simulations for the propagation of eigenmodes of the waveguides and results for the calculation of the effective index.
... In this paper, we have discussed the spatial properties of stationary, monochromatic wave fields. Numerical studies of light propagation in periodically modulated multimode waveguides have simultaneously been carried out [21] . The extension of these results to the nonstationary case, including short pulses in particular, is another interesting case to consider. ...
The propagation of stationary wave fields that exhibit simultaneously lateral and longitudinal periodicity is investigated. As a model, we use a Fabry-Perot resonator with periodically structured mirrors under monochromatic plane wave illumination. The resonator leads to a longitudinal periodicity, the grating mirrors to a lateral periodicity. The angular spectrum of the transmitted wave field is given as the product of two terms, one related to the lateral, the other to the longitudinal properties. Its modal structure can vary significantly depending on the ratio of the lateral and longitudinal periods and the reflectivity of the resonator's mirrors. For example, it is possible to generate bandgap behavior despite the fact that the periods may be significantly larger than the wavelength. The results of this investigation apply to the design of phase-coupled array resonators and multiplexers.
Color conversion by (tapered) nanowire arrays fabricated in GaInP with bandgap emission in the red spectral region are investigated with blue and green source light LEDs in perspective. GaInP nano- and microstructures, fabricated using top-down pattern transfer methods, are derived from epitaxial Ga0.51In0.49P/GaAs stacks with pre-determined layer thicknesses. Substrate-free GaInP micro- and nanostructures obtained by selectively etching the GaAs sacrificial layers are then embedded in a transparent film to generate stand-alone color converting films for spectrophotometry and photoluminescence experiments. Finite-difference time-domain simulations and spectrophotometry measurements are used to design and validate the GaInP structures embedded in (stand-alone) transparent films for maximum light absorption and color conversion from blue (450 nm) and green (532 nm) to red (~ 660 nm) light, respectively. It is shown that (embedded) 1 μm-high GaInP nanowire arrays can be designed to absorb ~ 100% of 450 nm and 532 nm wavelength incident light. Room-temperature photoluminescence measurements with 405 nm and 532 nm laser excitation are used for proof-of-principle demonstration of color conversion from the embedded GaInP structures. The (tapered) GaInP nanowire arrays, despite very low fill factors (~ 24%), can out-perform the micro-arrays and bulk-like slabs due to a better in- and out-coupling of source and emitted light, respectively.
We discuss the self-imaging effect that occurs in a multimode planar x-ray waveguide (WG) with a nanometer vacuum gap, where an additional longitudinal periodicity has been imposed by a periodical structure (a micron scale step-like grating) on the reflecting sidewalls. Taking into account the general Montgomery conditions and the particular case of Talbot effect, we show that this additional longitudinal periodicity, if suitably designed, can filter out the asymmetric and the high order resonance modes, providing a coherent beam at the exit, even if the WG is illuminated by an incoherent source.
