Peculiarities of the Gaussian beam transformation in the optical scheme with an axicon and a biaxial crystal

The transformation of a conical-type light beam by a biaxial crystal during propagation along one of its optical axes is herein investigated. The beam is formed by an axicon from the circularly polarized Gaussian input field. Depending on the position of the axicon either a Bessel beam or a combination of Bessel and conical beams falls on the crystal. The conversion coefficient from a zero-order Bessel beam to a first-order beam with phase dislocation is calculated. We show that if the angle of the beam cone and its diameter are large enough, then it is transformed into a field that is a first-order BesselGaussian beam with high accuracy. At the same time the conversion coefficient is close to 1. The case of a small cone angle of an incident Bessel beam is also investigated. In this case the efficiency of transformation significantly depends on the type of the spatial spectrum. At a small cone angle, the shape of the spatial spectrum is determined by the diameter of the incident Gaussian beam. Namely, as the diameter decreases, the beam spectrum changes from annular to close to Gaussian, passing through an intermediate form in the form of a superposition of these two profiles. The influence of the spatial spectrum is the conversion coefficient decreasing with a decrease of the of the ring component contribution to the spectrum. In this case, the conversion coefficient is always higher than for a scheme without an axicon when a Gaussian beam falls on the crystal. Consequently, the introduction of even a small conicity into the beam makes it possible to increase the field transformation coefficient. It can be implemented, for example, using a scheme with two axicons having close angles of a ray deflection. The results obtained are also of practical interest, in particular, for the development of conical-type laser emitters with a small cone angle for long-range reconnaissance and optical communication in free space.

1. Berry M. V., Jeffrey M. R., Lunney J. G. Conical diffraction: observations and theory. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2006, vol. 462, no. 2070, pp. 1629–1642. https://doi.org/10.1098/rspa.2006.1680

2. Peet V. Biaxial crystal as a versatile mode converter. Journal of Optics, 2010, vol. 12, no. 9, pp. 095706. https://doi.org/10.1088/2040-8978/12/9/095706

3. Peet V. Improving directivity of laser beams by employing the effect of conical refraction in biaxial. Optics Express, 2010, vol. 18, no. 19, pp. 19566–19573. https://doi.org/10.1364/oe.18.019566

4. Phelan C. F., O’Dwyer D. P., Rakovich Y. P., Donegan J. F., Lunney J. G. Conical diffraction and Bessel beam formation with a high optical quality biaxial crystal. Optics Express, 2009, vol. 17, no. 15, pp. 12891–12899. https://doi.org/10.1364/ oe.17.012891

5. Turpin A., Loiko Y. V., Kalkandjiev T. K., Mompart J. Conical refraction: Fundamentals and applications. Laser & Photonics Reviews, 2016, vol. 10, no. 5, pp. 750–771. https://doi.org/10.1002/lpor.201600112

6. Peet V. Experimental study of internal conical refraction in a biaxial crystal with Laguerre – Gauss light beams. Journal of Optics, 2014, vol. 16, no. 7, p. 075702 (8 pp). https://doi.org/10.1088/2040-8978/16/7/075702

7. Abdolvand A., Wilcox K. G., Kalkandjiev T. K., Rafailov E. U. Conical refraction Nd:KGd(WO4)2 laser. Optics Express, 2010, vol. 18, no. 3, pp. 2753–2759. https://doi.org/10.1364/oe.18.002753

8. Phelan C. F., O’Dwyer D. P., Pakovich Y. P., Donegan J. F., Lunney J. G. Conical diffraction and Bessel beam formation with a high optical quality biaxial crystal. Optics Express, 2009, vol. 17, no. 15, pp. 12891–12899. https://doi.org/10.1364/oe.17.012891

9. Phelan C. F., Donegan J. F., Lunney J. G. Generation of a radially polarized light beam using internal conical diffraction. Optics Express, 2011, vol. 19, no. 22, pp. 21793–21802. https://doi.org/10.1364/oe.19.021793

10. Peet V. Conical refraction and formation of multiring focal image with Laguerre-Gauss light beams. Optics Letters, 2011, vol. 36, no. 15, pp. 2913–2915. https://doi.org/10.1364/ol.36.002913

11. Belskii A., Khapalyuk A. Internal conical refraction of bounded light beams in biaxial crystals. Optics and Spectroscopy, 1978, vol. 44, pp. 436–439.

12. Belsky A. M., Stepanov M. A. Internal conical refraction of coherent light beams. Optics Communications, 1999, vol. 167, no. 1–6, pp. 1–5. https://doi.org/10.1016/s0030-4018(99)00251-5

13. Berry M. V. Conical diffraction asymptotics: Fine structure of Poggendorff rings and axial spike. Journal of Optics A: Pure and Applied Optics, 2004, vol. 6, no. 4, pp. 289–300. https://doi.org/10.1088/1464-4258/6/4/001

14. Kazak N. S., Khilo N. A., Ryzhevich A. A. Generation of Bessel light beams under the conditions of internal conical refraction. Quantum Electronics, 1999, vol. 29, no. 11, pp. 1020–1024. https://doi.org/10.1070/qe1999v029n11abeh001627

15. King T. A., Hogervorst W., Kazak N. S., Khilo N. A., Ryzhevich A. A. Formation of higher-order Bessel light beams in biaxial crystal. Optics Communications, 2001, vol. 187, no. 4–6, pp. 407–414. https://doi.org/10.1016/s0030-4018(00)01124-x

16. Stepanov M. A. Transformation of Bessel beams under internal conical refraction. Optics Communications, 2002, vol. 212, no. 1–3, pp. 11–16. https://doi.org/10.1016/s0030-4018(02)01993-4

17. Khilo N. A. Conical diffraction and transformation of Bessel beams in biaxial crystals. Optics Communications, 2013, vol. 286, pp. 1–5. https://doi.org/10.1016/j.optcom.2012.07.030

18. Filippov V. V., Kuleshov N. V., Bodnar I. T. Negative thermo-optical coefficient and athermal directions in monoclinic KGd(WO4)2 and KY(WO4)2 laser host crystals in the visible region. Applied Physics B, 2007, vol. 87, no. 4, pp. 611–614. https://doi.org/10.1007/s00340-007-2666-y

19. Khilo N. A., Ropot P. I., Petrov P. K., Belyi V. N. The formation of Bessel light beams at large distances from annular fields. Vestsі Natsyianal’nai akademіі navuk Belarusі. Seryia fіzіka-matematychnykh navuk = Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics series, 2022, vol. 58, no 1, pp. 90–100 (in Russian). https://doi.org/10.29235/1561-2430-2022-58-1-90-100