Waveguides

Author: the photonics expert Dr. Rüdiger Paschotta (RP)

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 with other physical mechanisms, e.g. by the use of reflections at metallic interfaces, or with photonic crystal structures. Some waveguides also involve plasmonic effects at metals.

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, called planar waveguides.

Waveguide Fabrication

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

• Planar waveguides can be fabricated on various crystal and glass materials with epitaxy or with polishing methods. The waveguide may be made on the top of the device (as shown on the left side of Figure 1), but it can also be placed between other solid layers.
• Channel waveguides on semiconductor, crystal and glass materials can be made with lithographic methods in combination with, e.g., epitaxy, ion exchange, or thermal indiffusion. It is possible to make a buried waveguide by growing an additional layer on top of the waveguide. That may lead to lower propagation losses and a more symmetric mode profile.
• 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, in the extreme case resulting in nanofibers.
• Waveguides can be written into transparent media (e.g. glasses or crystals, and even in polymers) with focused and pulsed laser beams, exploiting laser-induced breakdown and related phenomena. In glasses, the affected volume often exhibits a somewhat increased refractive index, which can be directly used for guiding light. In crystals, the refractive index may be decreased; one then has to treat some region around the desired waveguide region.

A wide range of material platforms for the fabrication of channel waveguide has been developed, each one with adapted methods for fabrication steps. Some examples:

• Silica-based waveguides are widely used in telecommunications. Silica can be doped with various materials (e.g., Ge, P) to adjust its refractive index. These waveguides can be fabricated on silicon wafers (silicon-on-insulator, SOI) or as silica fibers.
• Silicon (Si) waveguides are central to silicon photonics, enabling high-density integration of optical components on a chip. They offer high refractive index contrast, allowing tight light confinement and small bending radii, which is crucial for making compact devices. However, silicon is opaque at wavelengths below 1.1 µm, limiting its use to near-infrared applications.
• III-V semiconductor materials like GaAs, InP and their alloys are used to fabricate waveguides that can also incorporate active elements like lasers and photodetectors. These materials cover a wide range of wavelengths from visible to mid-infrared and are essential for integrated optoelectronics.
• Polymer waveguides offer flexibility in processing and the potential for large-scale and low-cost fabrication. They can be easily doped with organic dyes or nonlinear optical molecules to enhance functionality. Polymers can be used for flexible and disposable devices, for example. See also the article on plastic optics.
• Lithium niobate (LiNbO₃) is known for its strong electro-optic and nonlinear optical properties, and is therefore suitable for optical modulators and other active devices. It allows for the integration of optical functions such as modulation, switching, and frequency conversion. Reverse-proton-exchanged (RPE) waveguides have been used for a long time. More recently, thin-film lithium niobate (TFLN) waveguides, implemented on LiNbO₃-on-insulator wafers, have been developed with high index contrast, thus tight modal confinement, and fairly low propagation losses.
• Chalcogenide glasses are based on sulfur, selenium, and tellurium, and have high nonlinear optical coefficients and a wide transparency range extending into the mid-infrared. They are suitable for nonlinear optical devices and for applications in infrared photonics.
• Hybrid waveguides combine different materials to leverage the advantages of each. For example, a silicon waveguide might be coated with a polymer layer to improve its nonlinear optical properties or to facilitate electro-optic modulation.

The trade-offs between different material platforms and fabrication techniques can be complicated. They can involve a wide range of 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, geometrical 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.

The modes of waveguides with radially symmetric refractive index profile and low index contrast (which is given for most all-glass fibers, for example) can be described as LP modes. 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.

Case Studies

Mode Structure of a Multimode Fiber

We explore various properties of guided modes of multimode fibers. We also test how the mode structure of such a fiber reacts to certain changes inthe index profile, e.g. to smoothening of the index step.

Case Studies

Telecom Fiber With Parabolic Index Profile

We investigate how intermodal dispersion of a multimode fiber can be minimized with a parabolic doping profile.

Waveguides with lower symmetry and/or a high refractive index contrast have substantially more complicated mode properties. Calculating the mode details then requires a more advanced type of mode solver, which cannot be based on a simple scalar approximation of the light field; longitudinal field components need to be considered.

Any initial field distribution, which may describe light injected 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 losses, 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 [15], 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 quite 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:

• Optical fibers allow the transmission of light over long distances, e.g. for optical fiber communications.
• On photonic integrated circuits, as used e.g. in silicon photonics, waveguides transport light between different optical components.
• In the future, silicon waveguides (→ silicon photonics) on digital processor chips and polymer waveguides in circuit boards may be used for fast optical data transmission between components of computers.
• Some waveguides are used for maintaining high optical intensities over appreciable lengths, e.g. in nonlinear devices such as frequency doublers, Raman lasers and supercontinuum sources. Active (amplifying) waveguides are used in waveguide lasers and amplifiers. Important examples are fiber lasers and fiber amplifiers.
• A waveguide can be used for stripping off higher-order transverse modes, thus acting as a mode cleaner for improving the beam quality.
• In some cases, an interaction of the guided light with material in the evanescent field is used, e.g. in certain waveguide sensors.
• Waveguides can also be employed for splitting and combining light beams, e.g. in integrated optical interferometers.

More to Learn

Suppliers

The RP Photonics Buyer's Guide contains 20 suppliers for waveguides. Among them:

Teem Photonics

Teem Photonics offers photonic integrated circuits based on its versatile and cost effective IoNext platform. Specifics include high quality waveguides with high or variable confinement for mode diameters from 3 to 20 μm, propagation losses below 0.1 dB/cm, low bending radius (<1 mm), efficient coupling to single-mode fibers (<0.2 dB loss), low polarization-dependent loss and a large optical bandwidth range (400–2100 nm).

Shalom EO

Periodically poled lithium niobate (PPLN) crystal is a type of nonlinear optical crystal with distinguished high conversion efficiencies and a wide transparent spectrum of 0.4–5 μm. The 5% MgO doping in LiNbO₃ improves the damage threshold of the PPLN to a significant extent and broadens its phase-matching bandwidth. MgO: PPLN crystals exhibit a unique quasi-phase-matching (QPM) phenomenon, which allows the utilization of a higher nonlinear coefficient than in the case of birefringent phase matching.

Shalom EO offers standard and off-the-shelf MgO:PPLN crystal and waveguides for SHG of 976 nm to 2100 nm and for various upconversion and downconversion applications including DFG, SFG, OPO, and OPA. Different dimensions, MgO concentrations and AR coatings are available.

Octave Photonics

Octave Photonics provides supercontinuum generation waveguides that are packaged into easy-to-use devices. These devices feature standard fiber connectors and enable femtosecond lasers to be broadened to octave-spanning supercontinuum with low pulse energies (<150 pJ). The devices can be customized depending on the desired output spectrum.

Covesion

Covesion’s MgO:PPLN waveguide solutions provide high efficiency for SHG and SFG wavelength conversion processes. Ideal for a wide range of pump sources, these solutions offer robust performance from femtosecond to continuous wave applications, ensuring reliable and versatile frequency conversion for both scientific research and industrial applications.

We offer a range of free space and fiber coupled solutions for one-off orders to large-volume manufacture with customizable options including:

• free space or fiber coupled solutions
• tailored AR coatings
• 2×1, 2×0, 1×1 or 1×0 fiber input/output configurations
• resistive or Peltier temperature control
• integrated or external temperature control
• custom wavelength coverage
• power monitoring, control and output filtering
• compatibility with both CW and pulsed lasers

HC Photonics

HC Photonics (HCP) provides high conversion efficiency PPLN waveguides (periodically poled lithium niobate waveguides) to enable full-spectrum applications (i.e. single photon or Solc filter modulator) available for up-conversion (SHG/SFG) and down-conversion (DFG/OPA/OPG) frequency mixing configurations.

Two types of the waveguide are available to fulfill different applications. One is a proton-exchanged waveguide (up to 50 mm long) and the other one is ridge waveguide for high power handling (i.e. >2 W at 780 nm output). Tailored waveguides are available based on specific demands.

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