Ukrainian Journal of Physical Optics 

Home page
 
 

Other articles 

in this issue
Torque-operated gradient-index axicon

Vasylkiv Yu., Smyk M., Skab I. and Vlokh R.

Download this article

Abstract. We describe a gradient-index axicon based on twisting of crystals. We demonstrate that the focal length of the axicon can be efficiently operated by the torsion moment. The working analytical relations describing the focal length of the axicon and its dependence on different geometrical parameters as well as the torsion moment has been derived.

Keywords: axicon, piezooptic effect, torsion stress, lithium niobate crystals

PACS: 42.79.Bh, 78.20.Hp
UDC: 535.316+535.55
Ukr. J. Phys. Opt. 15 9-16
doi: 10.3116/16091833/15/1/9/2014
Received: 18.09.2013

Анотація. В роботі описано аксікон граданного типу на основі кручення кристалів. Показано, що фокусна відстань аксікона може керуватись торсійним моментом. Отримані співвідношення, які описують залежність фокусної відстані аксікона від його геометричних параметрів та торсійного моменту. 

REFERENCES
  1. Durnin J, 1987. Exact solutions for nondiffracting beams. I. The scalar theory. J. Opt. Soc. Am. A 4: 651–654. doi:10.1364/JOSAA.4.000651
  2. Durnin J, Miceli J J Jr, and Eberly J H, 1987. Diffraction-free beams. Phys. Rev. Lett. 58: 1499–1501. doi:10.1103/PhysRevLett.58.1499 PMid:10034453 
  3. McLeod J H, 1954. The axicon: A new type of optical element. J. Opt. Soc. Am. 44: 592–592. doi:10.1364/JOSA.44.000592
  4. McLeod J H, 1960. Axicons and their uses. J. Opt. Soc. Am. 50: 166–169. doi:10.1364/JOSA.50.000166
  5. Manek I, Ovchinnikov Yu B, and Grimm R, 1998. Generation of a hollow laser beam for atom trapping using an axicon. Opt. Comm. 147: 67–70. doi:10.1016/S0030-4018(97)00645-7
  6. Zeng D, Latham W P, and Kar A, 2006. Characteristic analysis of a refractive axicon system for optical trepanning. Opt. Eng. 45: 094302–1. doi:10.1117/1.2353119
  7. Zeng D, Latham W P, and Kar A, 2006. Shaping of annular laser intensity profiles and their thermal effects for optical trepanning. Opt. Eng. 45: 14301–1. doi:10.1117/1.2150789
  8. Zhihua Ding, Hongwu Ren, Yonghua Zhao, J. Stuart Nelson, and Zhongping Chen, 2002. High-resolution optical coherence tomography over a large depth range with an axicon lens. Opt. Lett. 27: 243–245. doi:10.1364/OL.27.000243PMid:18007767 
  9. Dudley A, Lavery M, Padgett M, and Forbes A, 2013. Unraveling Bessel beams. Opt. & Photon. News, June, 22–29. doi:10.1364/OPN.24.6.000022
  10. Marchand E W, 1990. Axicon gradient lenses. Appl. Opt. 29: 4001–4002. doi:10.1364/AO.29.004001 PMid:20577335 
  11. Fischer D J, Harkrider C J, and Moore D T, 2000. Design and manufacture of a gradient-index axicon. Appl. Opt. 39: 2687–2694. doi:10.1364/AO.39.002687PMid:18345190 
  12. De Saint-Denis R, Cagniot E, Leprince P, Fromarger M, and Ait-Ameur K, 2008. Low cost adjustable axicon. Optoel. Adv. Mater. 2: 693–696.
  13. Tsai T, McLeod E, and Arnold C B, 2006. Generating Bessel beams with a tunable acoustic gradient index of refraction lens. Proc. SPIE 6326 Optical trapping and optical micromanipulations III 63261F.
  14. Sirotin Yu I and Shaskolskaya M P, Fundamentals of crystal physics. Moscow: Nauka (1979).
  15. Narasimhamurty T S, Photoelastic and electrooptic properties of crystals. New-York: Plenum Press (1981). doi:10.1007/978-1-4757-0025-1
  16. Vlokh R, Kostyrko M, and Skab I, 1998. Principle and application of crystallooptical effects induced by inhomogeneous deformation. Japan J. Appl. Phys. 37: 5418–5420. doi:10.1143/JJAP.37.5418
  17. Skab I, Smaga I, Savaryn V, Vasylkiv Yu, and Vlokh R, 2011. Torsion method for measuring piezooptic coefficients. Cryst. Res. Techn. 46: 23–36. doi:10.1002/crat.201000495
  18. Skab I, Vasylkiv Yu, Zapeka B, Savaryn V, and Vlokh R, 2011. Appearance of singularities of optical fields under torsion of crystals containing threefold symmetry axes. J. Opt. Soc. Am. A. 28: 1331–1340. doi:10.1364/JOSAA.28.001331PMid:21734730 
  19. Skab I, Vasylkiv Yu, Savaryn V, and Vlokh R, 2011. Optical anisotropy induced by torsion stresses in LiNbO3 crystals: appearance of an optical vortex. J. Opt. Soc. Am. A. 28: 633–640. doi:10.1364/JOSAA.28.000633 PMid:21478960 
  20. Vasylkiv Yu, Savaryn V, Smaga I, Skab I, and Vlokh R, 2011. On determination of sign of the piezo-optic coefficients using torsion method. Appl. Opt. 50: 2512–2518. doi:10.1364/AO.50.002512 PMid:21673752 
  21. Shaskolskaya M P, Acoustic crystals. Moscow: Nauka (1982).
  22. Fischer D J, Harkrider C J, and Moore D T, 2000. Design and manufacture of a gradient-index axicon. Appl. Opt. 39: 2687–2694. doi:10.1364/AO.39.002687PMid:18345190 
  23. Gonzalez R M, Linares J, and Gomez-Reino C, 1994. Gradient-index axicon lenses: a quasi-geometrical study. Appl. Opt. 33: 3420–3426. doi:10.1364/AO.33.003420PMid:20885722 
  24. Marchand E W, 1990. Axicon gradient lenses. Appl. Opt. 29: 4001–4002. doi:10.1364/AO.29.004001PMid:20577335 
  25. Berry M V, Jeffrey M R, and Mansuripur M, 2005. Orbital and spin angular momentum in conical diffraction. J. Opt. A: Pure Appl. Opt. 7: 685–690. doi:10.1088/1464-4258/7/11/011
  26. Vlokh R, Volyar A, Mys O, and Krupych O, 2003. Appearance of optical vortex at conical refraction. Examples of NaNO2 and YFeO3 crystals. Ukr. J. Phys. Opt. 4: 90–93. doi:10.3116/16091833/4/2/90/2003 
  27. Berry M V, 2004. Conical diffraction asymptotics: fine structure of Poggendorff rings and axial spike. J. Opt. A: Pure Appl. Opt. 6: 289–300. doi:10.1088/1464-4258/6/4/001
  28. Slussarenko S, Piccirillo B, Chigrinov V, Marrucci L, and Santamato E, 2013. Liquid-crystal spatial-mode converters for the orbital angular momentum of light. J. Opt. 15: 025406. doi:10.1088/2040-8978/15/2/025406
(c) Ukrainian Journal of Physical Optics
14224CD