Hybrid asymptotic method for analyzing caustics of optical elements in the axially symmetric case
S.I. Kharitonov, S.G. Volotovsky, S.N. Khonina

 

IPSI RAS – Branch of the FSRC “Crystallography and Photonics” RAS, Samara, Russia,
Samara National Research University, Samara, Russia

Full text of article: Russian language.

 PDF

Abstract:
In this work we propose a new approach to calculating the distribution of light fields in the framework of geometrical optics. A new integral operator for computing the intensity distribution in the geometrical optics approximation is suggested. Using the proposed method, we derive the intensity distributions of previously studied wavefronts. Singular points of these distributions are found and the intensity distributions near the caustics are calculated. The developed method is used to calculate the formation of caustics by harmonic diffractive optical elements in the axially symmetric case.

Keywords:
geometrical optics, caustic, fractional axicon, harmonic diffractive lens.

Citation:
Kharitonov SI, Volotovsky SG, Khonina SN. Hybrid asymptotic method for analyzing caustics of optical elements in the axially symmetric case. Computer Optics 2017; 41(2): 175-182. DOI: 10.18287/2412-6179-2017-41-2-175-182.

References:

  1. Bobrov ST, Greysukh GI, Turkevich YuG. Optics of diffractive elements and systems [In Russian]. Leningrad: “Mashinostroenie” Publisher; 1986.
  2. Greysukh GI, Ezhov EG, Stepanov SA. Comparative analysis of the chromatizm of diffractive and refractive lenses [in Russian]. Computer Optics 2005; 28: 60-65.
  3. Kazanskiy NL, Kharitonov SI, Karsakov AV, Khonina SN. Modeling action of a hyperspectrometer based on the Offner scheme within geometric optics. Computer Optics 2014; 38(2): 271-280.
  4. Kazanskii NL, Khonina SN, Skidanov RV, Morozov AA, Kharitonov SI, Volotovskiy SG. Formation of images using multi-level diffractive lens. Computer Optics 2014; 38(3): 425-434.
  5. Karpeev SV, Khonina SN, Kharitonov SI. Study of the diffraction grating on the convex surface as a dispersive element. Computer Optics 2015; 39(2): 211-217. DOI: 10.18287/0134-2452-2015-39-2-211-217.
  6. Soifer VA, ed. Computer Design of Diffractive Optics. Woodhead Publishing and Cambridge International Science Publishing; 2012. ISBN: 978-1845696351.
  7. Soifer VA, ed. Diffractive Nanophotonics. Boca Raton, USA: CRC Press; 2014. ISBN: 978-1466590694.
  8. Sweeney DW, Sommargen GE. Harmonic diffractive lenses. Applied Optics 1995; 34(14): 2469-2475. DOI: 10.1364/AO.34.002469.
  9. Rossi M, Kunz RE, Herzig HP. Refractive and diffractive properties of planar micro-optical elements. Applied Optics 1995; 34(26): 5996-6007. DOI: 10.1364/AO.34.005996.
  10. Kharitonov SI, Volotovsky SG, Khonina SN. Geometric-optical calculation of the focal spot of a harmonic diffractive lens. Computer Optics 2016; 40(3): 331-337. DOI: 10.18287/2412-6179-2016-40-3-331-337.
  11. Khonina SN, Volotovsky SG. Fracxicon – diffractive optical element with conical focal domain [In Russian]. Computer Optics 2009; 33(4): 401-411.
  12. Khonina SN, Ustinov AV, Volotovsky SG. Fractional axicon as a new type of diffractive optical element with conical focal region. Precision Instrument and Mechanology 2013; 2(4): 132-143.
  13. Panagiotopoulos P, Papazoglou DG, Couairon A, Tzortzakis S. Sharply autofocused ring-Airy beams transforming into non-linear intense light bullets. Nat Commun 2013; 4: 2622. DOI: 10.1038/ncomms3622.
  14. Jiang Y, Zhu X, Yu W, Shao H, Zheng W, Lu X. Propagation characteristics of the modified circular Airy beam. Optics Express 2015; 23(23): 29834-29841. DOI: 10.1364/OE.23.029834.
  15. Chremmos I, Efremidis NK, Christodoulides DN. Pre-engineered abruptly autofocusing beams. Optics Letters 2011; 36(10): 1890-1892. DOI: 10.1364/OL.36.001890.
  16. Kharitonov SI, Kazanskiy NL, Doskolovich LL, Strelkov YS. Modeling the reflection of the electromagnetic waves at a diffraction grating generated on a curved surface. Computer Optics 2016; 40(2): 194-202. DOI: 10.18287/2412-6179-2016-40-2-194-202.
© 2009, IPSI RAS
Institution of Russian Academy of Sciences, Image Processing Systems Institute of RAS, Russia, 443001, Samara, Molodogvardeyskaya Street 151; E-mail: journal@computeroptics.ru; Phones: +7 (846) 332-56-22, Fax: +7 (846) 332-56-20