Waveguide (optics)

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An optical waveguide is a physical structure that guides electromagnetic waves in the optical spectrum. Common types of optical waveguides include optical fiber waveguides, transparent dielectric waveguides made of plastic and glass, liquid light guides, and liquid waveguides.

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Optical waveguides are used as components in integrated optical circuits or as the transmission medium in local and long-haul optical communication systems. They can also be used in optical head-mounted displays in augmented reality. [1]

Optical waveguides can be classified according to their geometry (planar, strip, or fiber waveguides), mode structure (single-mode, multi-mode), refractive index distribution (step or gradient index), and material (glass, polymer, semiconductor).

Total internal reflection

Light refracts at a dielectric interface, a., establishing a correspondence between rays in the two media, b. Some rays in the higher index medium are left out of the pairing (red) and are trapped by total internal reflection. c. This mechanism can be used to trap light in a waveguide. d. This is the basic principle behind fiber optics in which light is guided along a high index glass core in a lower index glass cladding. Ray optics and waveguides.svg
Light refracts at a dielectric interface, a., establishing a correspondence between rays in the two media, b. Some rays in the higher index medium are left out of the pairing (red) and are trapped by total internal reflection. c. This mechanism can be used to trap light in a waveguide. d. This is the basic principle behind fiber optics in which light is guided along a high index glass core in a lower index glass cladding.

The basic principles behind optical waveguides can be described using the concepts of geometrical or ray optics, as illustrated in the diagram.

Light passing into a medium with higher refractive index bends toward the normal by the process of refraction (Figure a.). Take, for example, light passing from air into glass. Similarly, light traveling in the opposite direction (from glass into air) takes the same path, bending away from the normal. This is a consequence of time-reversal symmetry. Each ray in air (black) can be mapped to a ray in the glass (blue), as shown in Figure b. There's a one-to-one correspondence. But because of refraction, some of the rays in the glass are left out (red). The remaining rays are trapped in the glass by a process called total internal reflection . They are incident on the glass-air interface at an angle above the critical angle . These extra rays correspond to a higher density of states in more-advanced formulations based on the Green's function.

Using total internal reflection, we can trap and guide the light in a dielectric waveguide (Figure c). The red rays bounce off both the top and bottom surface of the high index medium. They're guided even if the slab curves or bends, so long as it bends slowly. This is the basic principle behind fiber optics in which light is guided along a high index glass core in a lower index glass cladding (Figure d).

Ray optics only gives a rough picture of how waveguides work. Maxwell's equations can be solved by analytical or numerical methods for a full-field description of a dielectric waveguide.

Dielectric slab waveguide

A dielectric slab waveguide consists of three dielectric layers with different refractive indices. Slab waveguide 1.svg
A dielectric slab waveguide consists of three dielectric layers with different refractive indices.

Perhaps the simplest optical waveguide is the dielectric slab waveguide, [2] also called a planar waveguide. [3] Owing to their simplicity, slab waveguides are often used as toy models but also find application in on-chip devices like arrayed waveguide gratings and acousto-optic filters and modulators.

The slab waveguide consists of three layers of materials with different dielectric constants, extending infinitely in the directions parallel to their interfaces. Light is confined in the middle layer by total internal reflection if the refractive index of the middle layer is larger than that of the surrounding layers.

The slab waveguide is essentially a one-dimensional waveguide. It traps light only normal to the dielectric interfaces. For guided modes, the field in domain II in the diagram is propagating and can be treated as a plane wave. The field in domains I and III evanescently decay away from the slab. The plane wave in domain II bounces between the top and bottom interfaces at some angle typically specified by the , the wave vector in the plane of the slab. Guided modes constructively interfere on one complete roundtrip in the slab. At each frequency, one or more modes can be found giving a set of eigenvalues which can be used to construct a band diagram or dispersion relation.

Because guided modes are trapped in the slab, they cannot be excited by light incident on the top or bottom interfaces. Light can be end-fire or butte coupled by injecting it with a lens in the plane of the slab. Alternatively a coupling element may be used to couple light into the waveguide, such as a grating coupler or prism coupler.

There are 2 technologies: diffractive waveguides and reflective waveguides.

Two-dimensional waveguide

Strip waveguide

A strip waveguide is basically a strip of the layer confined between cladding layers. The simplest case is a rectangular waveguide, which is formed when the guiding layer of the slab waveguide is restricted in both transverse directions rather than just one. Rectangular waveguides are used in integrated optical circuits and in laser diodes. They are commonly used as the basis of such optical components as Mach–Zehnder interferometers and wavelength division multiplexers. The cavities of laser diodes are frequently constructed as rectangular optical waveguides. Optical waveguides with rectangular geometry are produced by a variety of means, usually by a planar process.[ citation needed ]

The field distribution in a rectangular waveguide cannot be solved analytically, however approximate solution methods, such as Marcatili's method, [4] Extended Marcatili's method [5] and Kumar's method, [6] are known.

Rib waveguide

A rib waveguide is a waveguide in which the guiding layer basically consists of the slab with a strip (or several strips) superimposed onto it. Rib waveguides also provide confinement of the wave in two dimensions and near-unity confinement is possible in multi-layer rib structures. [7]

Segmented waveguide and photonic crystal waveguide

Optical waveguides typically maintain a constant cross-section along their direction of propagation. This is for example the case for strip and of rib waveguides. However, waveguides can also have periodic changes in their cross-section while still allowing lossless transmission of light via so-called Bloch modes. Such waveguides are referred to as segmented waveguides (with a 1D patterning along the direction of propagation [8] ) or as photonic crystal waveguides (with a 2D or 3D patterning [9] ).

Laser-inscribed waveguide

Optical waveguides find their most important application in photonics. Configuring the waveguides in 3D space provides integration between electronic components on a chip and optical fibers. Such waveguides may be designed for a single mode propagation of infrared light at telecommunication wavelengths, and configured to deliver optical signal between input and output locations with very low loss.

Optical waveguides formed in pure silica glass as a result of an accumulated self-focusing effect with 193 nm laser irradiation. Pictured using transmission microscopy with collimated illumination. SF waveguides.jpg
Optical waveguides formed in pure silica glass as a result of an accumulated self-focusing effect with 193 nm laser irradiation. Pictured using transmission microscopy with collimated illumination.

One of the methods for constructing such waveguides utilizes photorefractive effect in transparent materials. An increase in the refractive index of a material may be induced by nonlinear absorption of pulsed laser light. In order to maximize the increase of the refractive index, a very short (typically femtosecond) laser pulses are used, and focused with a high NA microscope objective. By translating the focal spot through a bulk transparent material the waveguides can be directly written. [10] A variation of this method uses a low NA microscope objective and translates the focal spot along the beam axis. This improves the overlap between the focused laser beam and the photorefractive material, thus reducing power needed from the laser. [11] When transparent material is exposed to an unfocused laser beam of sufficient brightness to initiate photorefractive effect, the waveguides may start forming on their own as a result of an accumulated self-focusing. [12] The formation of such waveguides leads to a breakup of the laser beam. Continued exposure results in a buildup of the refractive index towards the centerline of each waveguide, and collapse of the mode field diameter of the propagating light. Such waveguides remain permanently in the glass and can be photographed off-line (see the picture on the right).

Light pipe

Light pipes are tubes or cylinders of solid material used to guide light a short distance. In electronics, plastic light pipes are used to guide light from LEDs on a circuit board to the user interface surface. In buildings, light pipes are used to transfer illumination from outside the building to where it is needed inside.[ citation needed ]

Optical fiber waveguide

The propagation of light through a multi-mode optical fiber. Optical-fibre.svg
The propagation of light through a multi-mode optical fiber.

Optical fiber is typically a circular cross-section dielectric waveguide consisting of a dielectric material surrounded by another dielectric material with a lower refractive index. Optical fibers are most commonly made from silica glass, however other glass materials are used for certain applications and plastic optical fiber can be used for short-distance applications.[ citation needed ]

See also

Related Research Articles

Refractive index contrast, in an optical waveguide, such as an optical fiber, is a measure of the relative difference in refractive index of the core and cladding. The refractive index contrast, Δ, is often given by , where n1 is the maximum refractive index in the core and n2 is the refractive index of the cladding. The criterion n2 < n1 must be satisfied in order to sustain a guided mode by total internal reflection. Alternative formulations include and . Normal optical fibers, constructed of different glasses, have very low refractive index contrast (Δ<<1) and hence are weakly-guiding. The weak guiding will cause a greater portion of the cross-sectional Electric field profile to reside within the cladding as compared to strongly-guided waveguides. Integrated optics can make use of higher core index to obtain Δ>1 allowing light to be efficiently guided around corners on the micro-scale, where popular high-Δ material platform is silicon-on-insulator. High-Δ allows sub-wavelength core dimensions and so greater control over the size of the evanescent tails. The most efficient low-loss optical fibers require low Δ to minimise losses to light scattered outwards.

<span class="mw-page-title-main">Photonic crystal</span> Periodic optical nanostructure that affects the motion of photons

A photonic crystal is an optical nanostructure in which the refractive index changes periodically. This affects the propagation of light in the same way that the structure of natural crystals gives rise to X-ray diffraction and that the atomic lattices of semiconductors affect their conductivity of electrons. Photonic crystals occur in nature in the form of structural coloration and animal reflectors, and, as artificially produced, promise to be useful in a range of applications.

<span class="mw-page-title-main">Gradient-index optics</span>

Gradient-index (GRIN) optics is the branch of optics covering optical effects produced by a gradient of the refractive index of a material. Such gradual variation can be used to produce lenses with flat surfaces, or lenses that do not have the aberrations typical of traditional spherical lenses. Gradient-index lenses may have a refraction gradient that is spherical, axial, or radial.

<span class="mw-page-title-main">Optical ring resonators</span>

An optical ring resonator is a set of waveguides in which at least one is a closed loop coupled to some sort of light input and output. The concepts behind optical ring resonators are the same as those behind whispering galleries except that they use light and obey the properties behind constructive interference and total internal reflection. When light of the resonant wavelength is passed through the loop from the input waveguide, the light builds up in intensity over multiple round-trips owing to constructive interference and is output to the output bus waveguide which serves as a detector waveguide. Because only a select few wavelengths will be at resonance within the loop, the optical ring resonator functions as a filter. Additionally, as implied earlier, two or more ring waveguides can be coupled to each other to form an add/drop optical filter.

<span class="mw-page-title-main">Photonic-crystal fiber</span> Class of optical fiber based on the properties of photonic crystals

Photonic-crystal fiber (PCF) is a class of optical fiber based on the properties of photonic crystals. It was first explored in 1996 at University of Bath, UK. Because of its ability to confine light in hollow cores or with confinement characteristics not possible in conventional optical fiber, PCF is now finding applications in fiber-optic communications, fiber lasers, nonlinear devices, high-power transmission, highly sensitive gas sensors, and other areas. More specific categories of PCF include photonic-bandgap fiber, holey fiber, hole-assisted fiber, and Bragg fiber. Photonic crystal fibers may be considered a subgroup of a more general class of microstructured optical fibers, where light is guided by structural modifications, and not only by refractive index differences. Hollow-core fibers are a related type of optical fiber which bears some resemblance to holey optical fiber.

In optics, an ARROW is a type of waveguide that uses the principle of thin-film interference to guide light with low loss. It is formed from an anti-resonant Fabry–Pérot reflector. The optical mode is leaky, but relatively low-loss propagation can be achieved by making the Fabry–Pérot reflector of sufficiently high quality or small size.

<span class="mw-page-title-main">Fiber Bragg grating</span> Type of distributed Bragg reflector constructed in a short segment of optical fiber

A fiber Bragg grating (FBG) is a type of distributed Bragg reflector constructed in a short segment of optical fiber that reflects particular wavelengths of light and transmits all others. This is achieved by creating a periodic variation in the refractive index of the fiber core, which generates a wavelength-specific dielectric mirror. Hence a fiber Bragg grating can be used as an inline optical filter to block certain wavelengths, can be used for sensing applications, or it can be used as wavelength-specific reflector.

<span class="mw-page-title-main">Distributed Bragg reflector</span> Structure used in waveguides

A distributed Bragg reflector (DBR) is a reflector used in waveguides, such as optical fibers. It is a structure formed from multiple layers of alternating materials with different refractive index, or by periodic variation of some characteristic of a dielectric waveguide, resulting in periodic variation in the effective refractive index in the guide. Each layer boundary causes a partial reflection and refraction of an optical wave. For waves whose vacuum wavelength is close to four times the optical thickness of the layers, the interaction between these beams generates constructive interference, and the layers act as a high-quality reflector. The range of wavelengths that are reflected is called the photonic stopband. Within this range of wavelengths, light is "forbidden" to propagate in the structure.

<span class="mw-page-title-main">Optical fiber</span> Light-conducting fiber

An optical fiber, or optical fibre, is a flexible glass or plastic fiber that can transmit light from one end to the other. Such fibers find wide usage in fiber-optic communications, where they permit transmission over longer distances and at higher bandwidths than electrical cables. Fibers are used instead of metal wires because signals travel along them with less loss and are immune to electromagnetic interference. Fibers are also used for illumination and imaging, and are often wrapped in bundles so they may be used to carry light into, or images out of confined spaces, as in the case of a fiberscope. Specially designed fibers are also used for a variety of other applications, such as fiber optic sensors and fiber lasers.

<span class="mw-page-title-main">Double-clad fiber</span>

Double-clad fiber (DCF) is a class of optical fiber with a structure consisting of three layers of optical material instead of the usual two. The inner-most layer is called the core. It is surrounded by the inner cladding, which is surrounded by the outer cladding. The three layers are made of materials with different refractive indices.

<span class="mw-page-title-main">Silicon photonics</span> Photonic systems which use silicon as an optical medium

Silicon photonics is the study and application of photonic systems which use silicon as an optical medium. The silicon is usually patterned with sub-micrometre precision, into microphotonic components. These operate in the infrared, most commonly at the 1.55 micrometre wavelength used by most fiber optic telecommunication systems. The silicon typically lies on top of a layer of silica in what is known as silicon on insulator (SOI).

<span class="mw-page-title-main">Slot-waveguide</span>

A slot-waveguide is an optical waveguide that guides strongly confined light in a subwavelength-scale low refractive index region by total internal reflection.

<span class="mw-page-title-main">Subwavelength-diameter optical fibre</span>

A subwavelength-diameter optical fibre is an optical fibre whose diameter is less than the wavelength of the light being propagated through it. An SDF usually consists of long thick parts at both ends, transition regions (tapers) where the fibre diameter gradually decreases down to the subwavelength value, and a subwavelength-diameter waist, which is the main acting part. Due to such a strong geometrical confinement, the guided electromagnetic field in an SDF is restricted to a single mode called fundamental.

Optofluidics is a research and technology area that combines the advantages of fluidics and optics. Applications of the technology include displays, biosensors, lab-on-chip devices, lenses, and molecular imaging tools and energy.

Microstructured optical fibers (MOF) are optical fiber waveguides where guiding is obtained through manipulation of waveguide structure rather than its index of refraction.

In physics, a high contrast grating is a single layer near-wavelength grating physical structure where the grating material has a large contrast in index of refraction with its surroundings. The term near-wavelength refers to the grating period, which has a value between one optical wavelength in the grating material and that in its surrounding materials.

<span class="mw-page-title-main">Hybrid plasmonic waveguide</span>

A hybrid plasmonic waveguide is an optical waveguide that achieves strong light confinement by coupling the light guided by a dielectric waveguide and a plasmonic waveguide. It is formed by separating a medium of high refractive index from a metal surface by a small gap.

<span class="mw-page-title-main">Plasmonics</span> Use of plasmons for data transmission in circuits

Plasmonics or nanoplasmonics refers to the generation, detection, and manipulation of signals at optical frequencies along metal-dielectric interfaces in the nanometer scale. Inspired by photonics, plasmonics follows the trend of miniaturizing optical devices, and finds applications in sensing, microscopy, optical communications, and bio-photonics.

Marcatili’s method is an approximate analytical method that describes how light propagates through rectangular dielectric optical waveguides. It was published by Enrique Marcatili in 1969.

<span class="mw-page-title-main">Ravindra Kumar Sinha (physicist)</span> Indian physicist and administrator

Prof. R K Sinha is the Vice Chancellor of Gautam Buddha University, Greater Noida, Gautam Budh Nagar Under UP Government. He was the director of the CSIR-Central Scientific Instruments Organisation (CSIR-CSIO) Sector-30C, Chandigarh-160 030, India. He has been a Professor - Applied Physics, Dean-Academic [UG] & Chief Coordinator: TIFAC-Center of Relevance and Excellence in Fiber Optics and Optical Communication, Mission REACH Program, Technology Vision-2020, Govt. of India Delhi Technological University Bawana Road, Delhi-110042, India.

References

  1. ↑ Xiong, Jianghao; Hsiang, En-Lin; He, Ziqian; Zhan, Tao; Wu, Shin-Tson (2021-10-25). "Augmented reality and virtual reality displays: emerging technologies and future perspectives". Light: Science & Applications. 10 (1). doi:10.1038/s41377-021-00658-8. ISSN   2047-7538. PMC   8546092 . PMID   34697292.
  2. ↑ Ramo, Simon, John R. Whinnery, and Theodore van Duzer, Fields and Waves in Communications Electronics, 2 ed., John Wiley and Sons, New York, 1984.
  3. ↑ "Silicon Photonics", by Graham T. Reed, Andrew P. Knights
  4. ↑ Marcatili, E. A. J. (1969). "Dielectric rectangular waveguide and directional coupler for integrated optics". Bell Syst. Tech. J. 48 (7): 2071–2102. doi:10.1002/j.1538-7305.1969.tb01166.x.
  5. ↑ Westerveld, W. J., Leinders, S. M., van Dongen, K. W. A., Urbach, H. P. and Yousefi, M (2012). "Extension of Marcatili's Analytical Approach for Rectangular Silicon Optical Waveguides". Journal of Lightwave Technology. 30 (14): 2388–2401. arXiv: 1504.02963 . Bibcode:2012JLwT...30.2388W. doi:10.1109/JLT.2012.2199464. S2CID   23182579.{{cite journal}}: CS1 maint: multiple names: authors list (link)
  6. ↑ Kumar, A., K. Thyagarajan and A. K. Ghatak. (1983). "Analysis of rectangular-core dielectric waveguides—An accurate perturbation approach". Opt. Lett. 8 (1): 63–65. Bibcode:1983OptL....8...63K. doi:10.1364/ol.8.000063. PMID   19714136.{{cite journal}}: CS1 maint: multiple names: authors list (link)
  7. ↑ Talukdar, Tahmid H.; Allen, Gabriel D.; Kravchenko, Ivan; Ryckman, Judson D. (2019-08-05). "Single-mode porous silicon waveguide interferometers with unity confinement factors for ultra-sensitive surface adlayer sensing". Optics Express. 27 (16): 22485–22498. Bibcode:2019OExpr..2722485T. doi: 10.1364/OE.27.022485 . ISSN   1094-4087. OSTI   1546510. PMID   31510540.
  8. ↑ M. Hochberg; T. Baehr-Jones; C. Walker; J. Witzens; C. Gunn; A. Scherer (2005). "Segmented Waveguides in Thin Silicon-on-Insulator" (PDF). Journal of the Optical Society of America B. 22 (7): 1493–1497. Bibcode:2005JOSAB..22.1493H. doi:10.1364/JOSAB.22.001493.
  9. ↑ S. Y. Lin; E. Chow; S. G. Johnson; J. D. Joannopoulos (2000). "Demonstration of highly efficient waveguiding in a photonic crystal slab at the 1.5-μm wavelength". Optics Letters. 25 (17): 1297–1299. Bibcode:2000OptL...25.1297L. doi:10.1364/ol.25.001297. PMID   18066198.
  10. ↑ Meany, Thomas (2014). "Optical Manufacturing: Femtosecond-laser direct-written waveguides produce quantum circuits in glass". Laser Focus World. 50 (7).
  11. ↑ Streltsov, AM; Borrelli, NF (1 January 2001). "Fabrication and analysis of a directional coupler written in glass by nanojoule femtosecond laser pulses". Optics Letters. 26 (1): 42–3. Bibcode:2001OptL...26...42S. doi:10.1364/OL.26.000042. PMID   18033501.
  12. ↑ Khrapko, Rostislav; Lai, Changyi; Casey, Julie; Wood, William A.; Borrelli, Nicholas F. (15 December 2014). "Accumulated self-focusing of ultraviolet light in silica glass". Applied Physics Letters. 105 (24): 244110. Bibcode:2014ApPhL.105x4110K. doi: 10.1063/1.4904098 .
  13. ↑ Liu, Hsuan-Hao; Chang, Hung-Chun (2013). "Leaky Surface Plasmon Polariton Modes at an Interface Between Metal and Uniaxially Anisotropic Materials". IEEE Photonics Journal. 5 (6): 4800806. Bibcode:2013IPhoJ...500806L. doi: 10.1109/JPHOT.2013.2288298 .

13. Yao Zhou, Jufan Zhang, Fengzhou Fang. Design of a dual-focal geometrical waveguide near-eye see-through display. Optics and Laser Technology, 2022, Volume 156, https://doi.org/10.1016/j.optlastec.2022.108546.

14. Yao Zhou, Jufan Zhang, Fengzhou Fang. Design of a large field-of-view two-dimensional geometrical waveguide. Results in Optics, Volume 5, 2021, 100147, https://doi.org/10.1016/j.rio.2021.100147.

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