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Waveguides

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Definition: spatially inhomogeneous transparent structures for guiding light

German: Wellenleiter

Category: fiber optics and waveguides

How to cite the article; suggest additional literature

An optical waveguide is a spatially inhomogeneous structure for guiding light, i.e. for restricting the spatial region in which light can propagate. Usually, a waveguide contains a region of increased refractive index, compared with the surrounding medium (called cladding). However, guidance is also possible, e.g., by the use of reflections, e.g. at metallic interfaces. Some waveguides also involve plasmonic effects at metals.

channel waveguide

Figure 1: Two different kinds of waveguides. Planar waveguides guide light only in the vertical direction, whereas channel waveguides guide in two dimensions.

Most waveguides exhibit two-dimensional guidance, thus restricting the extension of guided light in two dimensions and permitting propagation essentially only in one dimension. An example is the channel waveguide shown in Figure 1. The most important type of two-dimensional waveguide is the optical fiber. There are also one-dimensional waveguides, often called planar waveguides.

Waveguide Fabrication

There are many different techniques for fabricating dielectric waveguides. Some examples are:

The trade-offs between different fabrication techniques can be complicated. They can involve aspects such as cost, flexibility and reproducibility of manufacturing, propagation losses, possible side effects on the material (e.g. via heating or indiffused materials), optimum mode size and symmetry for coupling to other waveguides, etc.

Waveguide Modes

For waveguides with large extensions, ray optics are often used for describing the propagation of injected light. Such a description, however, becomes invalid when interference effects occur, and this is particularly the case for very small waveguide dimensions. In that case, a wave description of the light is required – normally on the basis of Maxwell's equations, often simplified with approximating assumptions.

It is common to consider the field distribution for a given optical frequency and polarization in a plane perpendicular to the propagation direction. Of special interest are those distributions which do not change during propagation, apart from a common phase change. Such field distributions are associated with so-called waveguide modes. As an example, Figure 2 shows the guided modes of a multimode fiber. Each mode has a so-called propagation constant, the imaginary part of which quantifies the phase delay per unit propagation distance. A fiber also has a large number of unguided modes (cladding modes), which are not restricted to the vicinity of the fiber core.

modes of a fiber

Figure 2: Electric field amplitude profiles for all the guided modes of an optical fiber. The two colors indicate different signs of electric field values. The lowest-order mode (l = 1, m = 0, called LP01 mode) has an intensity profile which is similar to that of a Gaussian beam. In general, light launched into a multimode fiber will excite a superposition of different modes, which can have a complicated shape.

Any initial field distribution, which may be generated at the beginning of the waveguide, can be decomposed into a linear combination of the field distributions of the guided waveguide modes, plus some function which can not be expressed as such a combination. The latter part corresponds to light which can not be guided. Depending on the type of waveguide, the not guided light may propagate in the cladding or may be reflected. The propagation of the guided part is easily calculated, using a linear combination of the waveguide modes with local expansion coefficients calculated from the propagation constants of the modes.

A waveguide with a small transverse spatial extension and/or a small refractive index difference (small numerical aperture) may be able to guide only a single transverse mode (for a given optical frequency and polarization) and no higher-order modes; it is then called a single-mode waveguide (→ single-mode fibers). The field distribution after a certain propagation distance then always resembles the constant mode field distribution, independent of the initial field distribution, provided that the unguided modes have been lost (e.g. in the cladding). Multimode waveguides are those supporting several or even many guided modes (sometimes many thousands).

Some types of waveguides (e.g. the channel waveguide on the right side of Figure 1) exhibit modes with strongly asymmetric intensity profiles. It also happens that guided modes exist only for one polarization direction, or that the modes for different polarization directions have very different properties.

Various properties such as the propagation loss, the bend sensitivity (for fibers), the propagation constant and the chromatic dispersion (see below) can substantially depend on the type of guided mode.

Waveguide Dispersion

Confinement of light in a waveguide leads to wave vectors which are tilted against the propagation direction. This affects the phase delay per unit length and thus the chromatic dispersion properties (→ waveguide dispersion). For example, the dispersion of a photonic crystal fiber with small mode area can be anomalous in the visible spectral region, although the silica material would have normal dispersion.

Plasmonic Waveguides for Nano Optics

For various applications, for example in the context of photonic integrated circuits, it is of great interest to strongly localize light in waveguides to dimensions far below the optical wavelength. Here, dielectric waveguides exhibit serious limitations. For example, although nanofibers can have diameters far below the wavelength, the electric field distributions of light guided in nanometer-scale fibers extend far beyond dielectric structure. Therefore, new waveguide technologies based on other physical guiding mechanisms are investigated. A promising field is that of nanoplasmonics [11], where nanometer-scale metallic structures embedded in dielectric materials are used. In that way, it is possible to obtain much more localized field distributions than possible with dielectric structures alone. However, the propagation losses are typically very high. Additional challenges are to efficiently couple light into such structures and to realize various passive and active photonic components such as strong bends, couplers, filters, amplifiers and detectors.

Applications

The applications of waveguides are manifold. Some examples are:

Bibliography

[1]R. A. Soref and J. P. Lorenzo, “Single-crystal silicon: a new material for 1.3 and 1.6 μm integrated-optical components”, Electron. Lett. 21 (21), 953 (1985)
[2]R. V. Ramaswamy and R. Srivastava, “Ion-exchanged glass waveguides: a review”, J. Lightwave Technol. 6 (6), 984 (1988)
[3]B. Schüppert et al., “Optical channel waveguides in silicon diffused from GeSi allow”, Electron. Lett. 25 (22), 1500 (1989)
[4]N. Takato et al., “Silica-based single-mode waveguides on silicon and their application to guided-wave optical interferometers”, J. Lightwave Technol. 6, 1003 (1988)
[5]K. M. Davis et al., “Writing waveguides in glass with a femtosecond laser”, Opt. Lett. 21 (21), 1729 (1996)
[6]M.-K. Chin et al., “High-index-contrast waveguides and devices”, Appl. Opt. 44 (15), 3077 (2005)
[7]H. Hu et al., “Lithium niobate ridge waveguides fabricated by wet etching”, IEEE Photon. Technol. Lett. 19 (6), 417 (2007)
[8]J. I. Mackenzie, “Dielectric solid-state planar waveguide lasers: a review”, IEEE J. Sel. Top. Quantum Electron. 13 (3), 26 (2007)
[9]M. E. Solmaz et al., “Compact bends for achieving higher integration densities for LiNbO3 waveguides”, IEEE Photon. Technol. Lett. 21 (9), 557 (2009)
[10]J. Hu and C. R. Menyuk, “Understanding leaky modes: slab waveguide revisited”, Adv. Opt. Photon. 1, 58 (2009)
[11]D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit”, Nature Photon. 4, 83 (2010)
[12]D. Geskus et al., “Giant optical gain in a rare-earth-ion-doped microstructure”, Adv. Mater. 24 (10), OP19 (2012)
[13]A. W. Snyder and J. D. Love, Optical Waveguide Theory, Chapman and Hall, London (1983)
[14]Website on "Optical waveguides: numerical modeling"

(Suggest additional literature!)

See also: fibers, nanofibers, numerical aperture, modes, mode coupling, higher-order modes, effective mode area, mode size converters, integrated optics, waveguide lasers, frequency doubling, waveguide dispersion, silicon photonics

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