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Directional Couplers

This is a continuation from the previous tutorial - grating waveguide couplers. Directional couplers are multiple-waveguide couplers used for codirectional coupling. They can be used in many different applications, including power splitters, optical switches, wavelength filters, and polarization selectors. We consider in this tutorial two-channel directional couplers, which consist of two parallel waveguides, as shown schematically in figure 4 below.  Figure 4. Schematic diagram of (a) a two-channel directional coupler and (b) its index profile assuming two step-index waveguides on the same substrate. The coupler is symmetric if \(n_a=n_b=n_1\) and \(d_a=d_b=d\). For simplicity, we consider only the case where each...

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Grating Waveguide Couplers

This is a continuation from the previous tutorial - two-mode coupling. Grating waveguide couplers have many useful applications and are one of the most important kinds of waveguide couplers. They consist of periodic fine structures that form gratings in waveguides. The gratings in a waveguide can be either periodic index modulation or periodic structural corrugation. Periodic index modulation can be permanently written in a waveguide by periodically modulating the doping concentration in the waveguide medium, for example, or it can be created by an electro-optic, acousto-optic, or nonlinear optical effect. In the latter case, the grating can be time dependent...

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Two-Mode Coupling

This is a continuation from the previous tutorial - coupled-mode theory. In most applications, we are interested in the coupling between two modes. This includes coupling between two modes in the same waveguide, such as that in a periodic waveguide, or coupling between two parallel waveguides, such as that in a directional coupler. For coupling between two modes, the coupled-mode equations can be written in a simple form that can be solved analytically. In this tutorial, we consider the general formulation and general solutions for this important case of two-mode coupling. The characteristics of specific couplers are discussed in later...

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Coupled-Mode Theory

This is a continuation from the previous tutorial - coupled-wave theory. Coupled-mode theory deals with the coupling of spatial modes of different spatial distributions or different polarizations, or both. Although the theory described in this tutorial is formulated specifically in terms of the coupling of waveguide modes, it can be easily extended to other kind of spatial modes, such as Gaussian spatial modes. The mode fields in a lossless waveguide can be expressed in the forms of (1) and (2) [refer to the waveguide modes tutorial], which satisfy Maxwell's equations in (8) and (9) [refer to the optical waveguide field...

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Coupled-Wave Theory

This is a continuation from the previous tutorial - Dispersion in Fibers. The principles of many photonics devices are base do on the coupling between optical fields of different frequencies or different spatial modes. In general, the coupling mechanism can be described by a polarization ΔP on top of a background polarization representing the property of the medium in the absence of the coupling mechanism. In this tutorial, we present the general coupled-wave and coupled-mode formalisms, which provide the foundation for understanding the functions of many devices. The coupled-wave formalism deals with the coupling of optical waves of different frequencies, whereas...

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