Designing Fresnel microlenses for focusing astigmatic multi-Gaussian beams by using fractional order Fourier transforms
According to a scalar theory of diffraction, light propagation can be expressed by two-dimensional fractional order Fourier transforms. Since the fractional Fourier transform of a chirp function is a Dirac distribution, focusing a light beam is optically achieved by using a diffractive screen whose...
- Autores:
- Tipo de recurso:
- Fecha de publicación:
- 2011
- Institución:
- Universidad Tecnológica de Bolívar
- Repositorio:
- Repositorio Institucional UTB
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.utb.edu.co:20.500.12585/8764
- Acceso en línea:
- https://hdl.handle.net/20.500.12585/8764
- Palabra clave:
- Degrees of freedom (mechanics)
Diffraction
Fourier optics
Gaussian beams
Microlenses
Mines
Astigmatic Gaussian beam
Diffraction phenomenon
Dirac distribution
Fractional Fourier transforms
Fractional transforms
Fresnel microlense
Radii of curvature
Transmission function
Fourier transforms
- Rights
- openAccess
- License
- http://creativecommons.org/licenses/by-nc-nd/4.0/
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Designing Fresnel microlenses for focusing astigmatic multi-Gaussian beams by using fractional order Fourier transforms |
| title |
Designing Fresnel microlenses for focusing astigmatic multi-Gaussian beams by using fractional order Fourier transforms |
| spellingShingle |
Designing Fresnel microlenses for focusing astigmatic multi-Gaussian beams by using fractional order Fourier transforms Degrees of freedom (mechanics) Diffraction Fourier optics Gaussian beams Microlenses Mines Astigmatic Gaussian beam Diffraction phenomenon Dirac distribution Fractional Fourier transforms Fractional transforms Fresnel microlense Radii of curvature Transmission function Fourier transforms |
| title_short |
Designing Fresnel microlenses for focusing astigmatic multi-Gaussian beams by using fractional order Fourier transforms |
| title_full |
Designing Fresnel microlenses for focusing astigmatic multi-Gaussian beams by using fractional order Fourier transforms |
| title_fullStr |
Designing Fresnel microlenses for focusing astigmatic multi-Gaussian beams by using fractional order Fourier transforms |
| title_full_unstemmed |
Designing Fresnel microlenses for focusing astigmatic multi-Gaussian beams by using fractional order Fourier transforms |
| title_sort |
Designing Fresnel microlenses for focusing astigmatic multi-Gaussian beams by using fractional order Fourier transforms |
| dc.subject.keywords.none.fl_str_mv |
Degrees of freedom (mechanics) Diffraction Fourier optics Gaussian beams Microlenses Mines Astigmatic Gaussian beam Diffraction phenomenon Dirac distribution Fractional Fourier transforms Fractional transforms Fresnel microlense Radii of curvature Transmission function Fourier transforms |
| topic |
Degrees of freedom (mechanics) Diffraction Fourier optics Gaussian beams Microlenses Mines Astigmatic Gaussian beam Diffraction phenomenon Dirac distribution Fractional Fourier transforms Fractional transforms Fresnel microlense Radii of curvature Transmission function Fourier transforms |
| description |
According to a scalar theory of diffraction, light propagation can be expressed by two-dimensional fractional order Fourier transforms. Since the fractional Fourier transform of a chirp function is a Dirac distribution, focusing a light beam is optically achieved by using a diffractive screen whose transmission function is a two-dimensional chirp function. This property is applied to designing Fresnel microlenses, and the orders of the involved Fourier fractional transforms depend on diffraction distances as well as on emitter and receiver radii of curvature. If the emitter is astigmatic (with two principal radii of curvature), the diffraction phenomenon involves two one-dimensional fractional Fourier transforms whose orders are different. This degree of freedom allows us to design microlenses that can focus astigmatic Gaussian beams, as produced by a line-shaped laser diode source. |
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2011 |
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2011 |
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2019-11-06T19:05:20Z |
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2019-11-06T19:05:20Z |
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http://purl.org/coar/version/c_970fb48d4fbd8a85 |
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Conferencia |
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Journal of Physics: Conference Series; Vol. 274, Núm. 1 |
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1742-6588 |
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https://hdl.handle.net/20.500.12585/8764 |
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10.1088/1742-6596/274/1/012108 |
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Universidad Tecnológica de Bolívar |
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Repositorio UTB |
| identifier_str_mv |
Journal of Physics: Conference Series; Vol. 274, Núm. 1 1742-6588 10.1088/1742-6596/274/1/012108 Universidad Tecnológica de Bolívar Repositorio UTB |
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https://hdl.handle.net/20.500.12585/8764 |
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eng |
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eng |
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info:eu-repo/semantics/openAccess |
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Atribución-NoComercial 4.0 Internacional |
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application/pdf |
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Institute of Physics Publishing |
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Institute of Physics Publishing |
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2019-11-06T19:05:20Z2019-11-06T19:05:20Z2011Journal of Physics: Conference Series; Vol. 274, Núm. 11742-6588https://hdl.handle.net/20.500.12585/876410.1088/1742-6596/274/1/012108Universidad Tecnológica de BolívarRepositorio UTBAccording to a scalar theory of diffraction, light propagation can be expressed by two-dimensional fractional order Fourier transforms. Since the fractional Fourier transform of a chirp function is a Dirac distribution, focusing a light beam is optically achieved by using a diffractive screen whose transmission function is a two-dimensional chirp function. This property is applied to designing Fresnel microlenses, and the orders of the involved Fourier fractional transforms depend on diffraction distances as well as on emitter and receiver radii of curvature. If the emitter is astigmatic (with two principal radii of curvature), the diffraction phenomenon involves two one-dimensional fractional Fourier transforms whose orders are different. This degree of freedom allows us to design microlenses that can focus astigmatic Gaussian beams, as produced by a line-shaped laser diode source.Recurso electrónicoapplication/pdfengInstitute of Physics Publishinghttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessAtribución-NoComercial 4.0 Internacionalhttp://purl.org/coar/access_right/c_abf2https://www2.scopus.com/inward/record.uri?eid=2-s2.0-79953756121&doi=10.1088%2f1742-6596%2f274%2f1%2f012108&partnerID=40&md5=28f086ce707dfbdd91cc6f412e8684a6Scopus 57192275310Scopus 7202230088Scopus 6603213964Scopus 6701664259Designing Fresnel microlenses for focusing astigmatic multi-Gaussian beams by using fractional order Fourier transformsinfo:eu-repo/semantics/conferenceObjectinfo:eu-repo/semantics/publishedVersionConferenciahttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_c94fDegrees of freedom (mechanics)DiffractionFourier opticsGaussian beamsMicrolensesMinesAstigmatic Gaussian beamDiffraction phenomenonDirac distributionFractional Fourier transformsFractional transformsFresnel microlenseRadii of curvatureTransmission functionFourier transformsPatiño Vanegas, AlbertoDurand, P.E.Fogret, É.Pellat-Finet, P.Gao, X., Ohashi, H., Okamoto, H., Takasaka, M., Shinoda, K., Beam shaping technique for improving the beam quality of a high-power laser-diode stak (2006) Opt. Lett., 31, pp. 1654-1656Yamaguchi, S., Kobayashi, T., Saito, Y., Chiba, K., Collimation of emissions from a 1-cm aperture tightly arranged multistripe laser-diode bar with a multiprism array coupling (1997) Appl. Opt., 36, pp. 1875-1878Clarkson, W.A., Hanna, D.C., Two-mirror beam shaping technique for high-power diode bars (1996) Opt. Lett., 21, pp. 375-377Herzig, H.P., (1998) Micro-optics. Elements, Systems and Applications, , London: Taylor and FrancisZheng, G., Du, C., Zhou, C., Zheng, C., Micrograting-array beam-shaping technique for asymmetrical laser beams (2005) Appl. Opt., 44, pp. 3540-3544Leger, J.R., Goltsos, W.C., Geometrical transformation of linear diode-laser arrays for longitudinal pumping of solid-state lasers (1992) IEEE J. Quant. Electron., 28, p. 1088Pellat-Finet, P., Bonnet, G., Fractional order Fourier transform and Fourier optics (1994) Opt. Comm., 111, pp. 141-154Pellat-Finet, P., (2004) Lecciones de Óptica de Fourier, , Bucaramanga: Ediciones UISPellat-Finet, P., (2009) Optique de Fourier, Théorie Métaxiale et Fractionnaire, , Paris: SpringerNamias, V., The fractional order Fourier transform and its application to quantum mechanics (1980) J. Inst. Maths. Applics, 25, pp. 241-265McBride, A.C., Kerr, F.H., On Namias's fractional Fourier transform (1987) IMA J. Appl. Math., 39, pp. 159-175Bonnet, G., Introduction à l'optique métaxiale. Première partie: Diffraction métaxiale dans un espace homogène: trilogie structurale, dioptre sphérique (1978) Ann. Télécomm., 33, pp. 143-165Bonnet, G., Introduction à l'optique métaxiale. Deuxième partie: Systèmes dioptriques centrés (non diaphragmés et non aberrants) (1978) Ann. Télécomm., 33, pp. 225-243Pellat-Finet, P., Fogret, É., Complex order fractional Fourier transforms and their use in diffraction theory. Application to optical resonators (2006) Opt. Comm., 258, pp. 103-113Torres, R., Pellat-Finet, P., Torres, Y., Sampling theorem for fractional bandlimited signals: A self-contained proof. Application to digital holography (2006) IEEE Signal Process. Lett., 13, pp. 676-679Struik, D.J., (1988) Lectures on Classical Differential Geometry, , New York: DoverPellat-Finet, P., Diffraction entre un émetteur et un récepteur localement toriques. Application à l'étude des systèmes astigmates (1999) C. R. Ac. Sc. Paris, 327 (2 B), pp. 1269-1274http://purl.org/coar/resource_type/c_c94fORIGINALDOI10_10881742-65962741012108.pdfapplication/pdf2121574https://repositorio.utb.edu.co/bitstream/20.500.12585/8764/1/DOI10_10881742-65962741012108.pdfe054bfb05877ce7a4690d6353951bfcbMD51TEXTDOI10_10881742-65962741012108.pdf.txtDOI10_10881742-65962741012108.pdf.txtExtracted texttext/plain30251https://repositorio.utb.edu.co/bitstream/20.500.12585/8764/4/DOI10_10881742-65962741012108.pdf.txted0202082edb203a151ec4c7793a3691MD54THUMBNAILDOI10_10881742-65962741012108.pdf.jpgDOI10_10881742-65962741012108.pdf.jpgGenerated Thumbnailimage/jpeg34376https://repositorio.utb.edu.co/bitstream/20.500.12585/8764/5/DOI10_10881742-65962741012108.pdf.jpgd85c32da36f5453bab71ce5ef9a2fbdbMD5520.500.12585/8764oai:repositorio.utb.edu.co:20.500.12585/87642023-05-25 10:02:03.794Repositorio Institucional UTBrepositorioutb@utb.edu.co |