560:(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. 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. 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
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564:. 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).
548:. 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.
559:
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
535:
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
526:
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.
552:
171:). 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
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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
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so-called Bloch modes. Such waveguides are referred to as segmented waveguides (with a 1D patterning along the direction of propagation) or as photonic crystal waveguides (with a 2D or 3D patterning).
555:
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.
212:). 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
1117:
838:
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".
424:
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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
179:. 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
441:
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.
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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.
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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,
471:, 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
578:
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
1268:
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,
495:
are frequently constructed as rectangular optical waveguides. Optical waveguides with rectangular geometry are produced by a variety of means, usually by a
1139:
Streltsov, AM; Borrelli, NF (1 January 2001). "Fabrication and analysis of a directional coupler written in glass by nanojoule femtosecond laser pulses".
198:
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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
905:
Kumar, A., K. Thyagarajan and A. K. Ghatak. (1983). "Analysis of rectangular-core dielectric waveguides—An accurate perturbation approach".
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Because guided modes are trapped in the slab, they cannot be excited by light incident on the top or bottom interfaces. Light can be
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The slab waveguide is essentially a one-dimensional waveguide. It traps light only normal to the dielectric interfaces. For guided
964:"Single-mode porous silicon waveguide interferometers with unity confinement factors for ultra-sensitive surface adlayer sensing"
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The field distribution in a rectangular waveguide cannot be solved analytically, however approximate solution methods, such as
270:
317:. Owing to their simplicity, slab waveguides are often used as toy models but also find application in on-chip devices like
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Optical waveguides can be classified according to their geometry (planar, strip, or fiber waveguides), mode structure (
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Marcatili, E. A. J. (1969). "Dielectric rectangular waveguide and directional coupler for integrated optics".
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Khrapko, Rostislav; Lai, Changyi; Casey, Julie; Wood, William A.; Borrelli, Nicholas F. (15 December 2014).
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1225:"Leaky Surface Plasmon Polariton Modes at an Interface Between Metal and Uniaxially Anisotropic Materials"
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can be solved by analytical or numerical methods for a full-field description of a dielectric waveguide.
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1118:"Optical Manufacturing: Femtosecond-laser direct-written waveguides produce quantum circuits in glass"
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1071:"Demonstration of highly efficient waveguiding in a photonic crystal slab at the 1.5-μm wavelength"
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A dielectric slab waveguide consists of three dielectric layers with different refractive indices.
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Talukdar, Tahmid H.; Allen, Gabriel D.; Kravchenko, Ivan; Ryckman, Judson D. (2019-08-05).
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is basically a strip of the layer confined between cladding layers. The simplest case is a
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175:. Each ray in air (black) can be mapped to a ray in the glass (blue), as shown in Figure
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The basic principles behind optical waveguides can be described using the concepts of
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Xiong, Jianghao; Hsiang, En-Lin; He, Ziqian; Zhan, Tao; Wu, Shin-Tson (2021-10-25).
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Using total internal reflection, we can trap and guide the light in a dielectric
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M. Hochberg; T. Baehr-Jones; C. Walker; J. Witzens; C. Gunn; A. Scherer (2005).
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AdvR nonlinear waveguides in rubidium-doped potassium titanyl phosphate
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made of plastic and glass, liquid light guides, and liquid waveguides.
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185:. They are incident on the glass-air interface at an angle above the
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of the middle layer is larger than that of the surrounding layers.
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1184:"Accumulated self-focusing of ultraviolet light in silica glass"
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material surrounded by another dielectric material with a lower
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S. Y. Lin; E. Chow; S. G. Johnson; J. D. Joannopoulos (2000).
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Ray optics only gives a rough picture of how waveguides work.
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The propagation of light through a multi-mode optical fiber.
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Optical waveguides find their most important application in
801:"Silicon Photonics", by Graham T. Reed, Andrew P. Knights
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Perhaps the simplest optical waveguide is the dielectric
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Ramo, Simon, John R. Whinnery, and
Theodore van Duzer,
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distribution (step or gradient index), and material (
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or as the transmission medium in local and long-haul
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Optical fiber is typically a circular cross-section
1029:"Segmented Waveguides in Thin Silicon-on-Insulator"
531:Segmented waveguide and photonic crystal waveguide
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216:in which light is guided along a high index glass
140:in which light is guided along a high index glass
624:materials are used for certain applications and
1263:https://doi.org/10.1016/j.optlastec.2022.108546
790:Fields and Waves in Communications Electronics
128:This mechanism can be used to trap light in a
792:, 2 ed., John Wiley and Sons, New York, 1984.
628:can be used for short-distance applications.
616:. Optical fibers are most commonly made from
57:Optical waveguides are used as components in
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947:: CS1 maint: multiple names: authors list (
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1036:Journal of the Optical Society of America B
197:in more-advanced formulations based on the
191:. These extra rays correspond to a higher
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112:Light refracts at a dielectric interface,
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27:Physical structure guiding light waves
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323:acousto-optic filters and modulators
271:adding citations to reliable sources
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136:This is the basic principle behind
825:10.1002/j.1538-7305.1969.tb01166.x
65:systems. They can also be used in
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738:Light: Science & Applications
426:which can be used to construct a
348:. The field in domains I and III
156:, as illustrated in the diagram.
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663:Equilibrium mode distribution
67:optical head-mounted displays
481:Mach–Zehnder interferometers
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508:Extended Marcatili's method
473:integrated optical circuits
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750:10.1038/s41377-021-00658-8
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42:. Common types of optical
658:Electromagnetic radiation
653:Digital planar holography
540:Laser-inscribed waveguide
448:Two-dimensional waveguide
439:end-fire or butte coupled
331:total internal reflection
239:Dielectric slab waveguide
182:total internal reflection
154:geometrical or ray optics
122:total internal reflection
104:Total internal reflection
870:10.1109/JLT.2012.2199464
50:waveguides, transparent
1188:Applied Physics Letters
1056:10.1364/JOSAB.22.001493
586:Optical fiber waveguide
220:in a lower index glass
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989:10.1364/OE.27.022485
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267:improve this article
1241:2013IPhoJ...500806L
1200:2014ApPhL.105x4110K
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648:Dielectric constant
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233:Maxwell's equations
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813:Bell Syst. Tech. J
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1296:Categories
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719:References
673:Leaky mode
610:dielectric
574:Light tube
568:Light pipe
452:See also:
346:plane wave
165:refraction
82:multi-mode
44:waveguides
1307:Photonics
998:1094-4087
907:Opt. Lett
758:2047-7538
708:Waveguide
546:photonics
408:→
405:β
396:ω
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363:β
206:waveguide
130:waveguide
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1103:18066198
1014:31510540
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878:23182579
776:34697292
632:See also
489:cavities
224:(Figure
222:cladding
208:(Figure
167:(Figure
146:cladding
46:include
1237:Bibcode
1196:Bibcode
1149:Bibcode
1083:Bibcode
1044:Bibcode
1006:1546510
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767:8546092
475:and in
333:if the
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1032:(PDF)
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622:glass
342:modes
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1128:(7).
1099:PMID
1010:PMID
1002:OSTI
994:ISSN
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