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Encyclopedia of Laser Physics and Technology

© Dr. Rüdiger Paschotta

Last update: 2008-05-10

Definition: spatially inhomogeneous transparent structures for guiding light

A waveguide is a spatially inhomogeneous structure for guiding light, i.e., for restricting the spatial region in which light can propagate. This can be used e.g.

• for transmitting light over long distances (e.g. in telecom systems)
• for guiding light on integrated optical chips (→ silicon photonics)
• for maintaining high optical intensities over appreciable lengths (e.g. in waveguide lasers and frequency doublers)
• for stripping off higher-order transverse modes (→ mode cleaners)
• for interaction of the guided light with material in the evanescent field (e.g. in certain waveguide sensors)
• for splitting and combining beams

Usually, a waveguide contains a region of increased refractive index, compared with the surrounding medium (called cladding). However, guidance is also possible by the use of reflections e.g. at metallic interfaces.

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 for that is the channel waveguide shown on the right-hand side 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 (left part of Figure 1).

Waveguide Fabrication

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

• Planar waveguides can be fabricated on various crystal and glass materials with epitaxy or with polishing methods.
• Channel waveguides on semiconductor, crystal and glass materials can be made with lithographic methods in combination e.g. with epitaxy, ion exchange, or thermal indiffusion.
• Optical fibers can be fabricated by drawing from a preform, which is a large glass rod with a built-in refractive index profile. Fibers can again be drawn into waveguides of further reduced dimensions, resulting in nanofibers.
• Waveguides can be written into transparent media (e.g. glasses) with focused and pulsed laser beams, exploiting laser-induced breakdown and related phenomena.

The tradeoffs between different fabrication techniques can be complicated. They can involve aspects like cost, flexibility and reproducibility of manufacturing, achieved 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 value. Such distributions are associated with so-called waveguide modes. As an example, Figure 2 shows the modes of a multimode fiber. Each mode has a so-called propagation constant, the real part of which quantifies the phase delay per unit propagation distance.

Figure 1: Electric field contour lines 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 rather 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 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, i.e., which can propagate in the cladding. 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 modes (sometimes many thousands).

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.

Bibliography

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

Category: fibers and other waveguides