Full text of article: Russian language.

 PDF

Abstract:
In this paper we consider diffraction of a laser beam by a narrow axicon when the cone angle is much less than a limit (at which total internal reflection occurs). In this case, the correct description of the propagation of light through the axicon calls for the consideration of multiple internal reflections. The diffraction is considered using two models: through a  geometric optics approach and via solving the Helmholtz equation by a finite element method. Based on the geometrical model, analytical expressions are found for the angles defining the boundaries of the real and imaginary foci. Simulations conducted using the finite element method have confirmed the theoretical results.

Keywords:
conic axicon, total internal reflection, real and imaginary focus, finite element method.

Citation:
Ustinov AV, Degtyarev SA, Khonina SN. Diffraction by a conical axicon considering multiple internal reflections. Computer Optics 2015, 39(4): 500-7. DOI: 10.18287/0134-2452-2015-39-4-500-507.

References:

1. McLeod JH. The axicon: a new type of optical element. J Opt Soc Am 1954; 44: 592-7.
2. Jaroszewicz Z, Burvall A, Friberg AT. Axicon – the most important optical element. Optics & Photonics News 2005; 16: 34-39.
3. Durnin J, Miceli JJ Jr, Eberly JH. Diffraction-free beams. Physical Review Letters 1987; 58: 1499-1501.
4. McGloin D, Dholakia K. Bessel beams: diffraction in a new light. Contemporary Physics 2005; 46(1): 15-28.
5. Babadjanyan AJ, Margaryan NL, Nerkararyana KhV. Superfocusing of surface polaritons in the conical structure. J Appl Phys 2000; 87(8): 3785-8.
6. Novotny L, Hecht D. Principles of Nano-Optics. Cam-bridge: New York, 2006.
7. Goncharenko AV, Chang H-C, Wang J-K. Electric near-field enhancing properties of a finite-size metal conical nano-tip. Ultramicroscopy 2007; 107: 151-7.
8. Antosiewicz TJ, Wróbel P, Szoplik T. Nanofocusing of radially polarized light with dielectric-metal-dielectric probe.  Optics Express 2009; 17(11): 9191-6.
9. Choo H, Kim M-K, Staffaroni M, Seok TJ, Bokor J, Cabrini S, Schuck PJ, Wu MC, Yablonovitch E. Nano-focusing in a metal–insulator–metal gap plasmon waveguide with a three-dimensional linear taper. Nature Photonics 2012; 6: 838-44.
10. Berweger S, Atkin JM, Olmon RL, Raschke MB. Light on the tip of a needle: plasmonic nanofocusing for spectroscopy on the nanoscale. J Phys Chem Lett 2012; 3: 945-52.
11. Gramotnev DK, Vogel MW, Stockman MI. Optimized nonadiabatic nanofocusing of plasmons by tapered metal rods. J Appl Phys 2008; 104: 034311 (8pp).
12. Davoyan AR, Shadrivov IV, Kivshar YS, Gramotnev DK. Optimal tapers for compensating losses in plasmonic waveguides. Phys Status Solidi RRL 2010; 4(10): 277-9.
13. Degtyarev SA, Khonina SN, Alferov SV,Karpeev SV. Theoretical and experimental study of aperture size effects on the polarization sensitivity of near-field mi-croscopy fiber-optic probes. Proc of SPIE 2014; 9156: 915608 (13pp). DOI:10.1117/12.2054204.
14. Degtyarev SA, Khonina SN. Transmission of focused light signal through an apertured probe of a near-field scan-ning microscope. Pattern Recognition and Image Analysis 2015; 25(2): 306-13.
15. Gramotnev DK, Bozhevolnyi SI. Nanofocusing of elec-tromagnetic radiation. Nature Photonics 2014; 8: 14-23.
16. Degtyarev SA, Khonina SN, Ustinov AV, Kazanskiy NL. Lightning-rod effect near sharp dielectric structures. Proc of SPIE 2015; 9533: 95330A (6pp). DOI: 10.1117/12.2180353
17. Zhang Y, Wang L, Zheng C. Vector propagation of ra-dially polarized Gaussian beams diffracted by an axicon. J Opt Soc Am A 2005; 22(11): 2542-6.
18. Kotlyar VV, Stafeev SS. Modeling sharp focus radially-polarized laser mode with conical and binary microaxicons (in Russian). Computer Optics 2009; 33(1): 52-60.
19. Khonina SN, Degtyarev SA. A longitudinally polarized beam generated by a binary axicon. Journal of Russian Laser Research 2015; 36(2): 151-61.
20. Khonina SN, Alferov SV, Karpeev SV, Moiseev OYu. Study of polarization sensitivity OF near-field microscope using a binary phase plate. Computer Optics 2013; 37(3): 326-31.
21. Khonina SN, Karpeev SV, Alferov SV. Strengthening the longitudinal component of the sharply focused electric field by means of higher-order laser beams. Optics Letters 2013; 38(17): 3223-6.
22. Alferov SV, Khonina SN, Karpeev SV. Study of polarization properties of fiber-optics probes with use of a binary phase plate. J Opt Soc Am A 2014; 31(4): 802-7.
23. Khonina SN, Nesterenko DV, Morozov AA, Skidanov RV, Soifer V.A. Narrowing of a light spot at diffraction of linearly-polarized beam on binary asymmetric axicons. Optical Memory and Neural Networks (Information Optics) 2012; 21(1): 17-26.
24. Khonina SN, Karpeev SV, Alferov SV, Savelyev DA, Laukkanen J, Turunen J. Experimental demonstration of the generation of the longitudinal E-field component on the optical axis with high-numerical-aperture binary axicons illuminated by linearly and circularly polarized beams. Journal of Optics 2013; 15: 085704 (9pp).
25. Khonina SN, Savelyev DA. High-aperture binary axicons for the formation of the longitudinal electric field component on the optical axis for linear and circular polarizations of the illuminating beam. Journal of Experimental and Theoretical Physics 2013; 117(4): 623-30.
26. Ustinov AV, Khonina SN. Calculating the complex transmission function of refractive axicons. Optical Memory and Neural Networks (Information Optics) 2012; 21(3): 133-44.
27. Ustinov AV, Khonina SN. Analysis of laser beam diffraction by axicon with the numerical aperture above limiting. Computer Optics 2014; 38(2): 213-22.

---

© 2009, IPSI RAS
151, Molodogvardeiskaya str., Samara, 443001, Russia; E-mail:journal@computeroptics.ru; Tel: +7 (846) 242-41-24 (Executive secretary), +7 (846) 332-56-22 (Issuing editor), Fax: +7 (846) 332-56-20