CC BY
64
Computational nanotechnology
1-2014
ISSN 2313-223X
3.4. SUBWAVELENGTH FOCUSING OF LASER LIGHT BY MICROOPTICS DEVICES
Материалы статьи были доложены на 21 Международной конференции по лазерным технологиям (ALT'13)
Soifer Viktor A., Doctor of Science, academician of RAS. Image Processing Systems Institute of the Russian Academy of Sciences, Samara State Aerospace University, Samara
Kotlyar Viktor V., Doctor of Science in Physics and Mathematics, professor. Image Processing Systems Institute of the Russian Academy of Sciences, Samara State Aerospace University, Samara
Khonina Svetlana N., Doctor of Science in Physics and Mathematics, professor, Image Processing Systems Institute of the Russian Academy of Sciences, Samara State Aerospace University, Samara. E-mail: khonina@smr.ru
Abstract: We discuss particular realizations of optical elements and devices that enable one to break the diffraction limit. A planar binary photonic crystal lens, a zone plate and a binary spiral microaxicon are considered as examples of microoptics devices for subwavelength focusing of laser light.
Index terms: Microoptics, diffraction limit, subwavelength focusing, photonic crystal lens, zone plate, spiral microaxicon
The diffraction phenomenon, which was previously considered as a restrictive factor in optics, has currently become a fundamental basis for creating novel optical components and advanced information technologies. Since the 19-th century, the diffraction limit (DL), which can be defined as full-width half-maximum of the Airy disk size [1], was considered to be unbreakable in optics: Dmin=0.51X/NA, where X is incident wavelength, NA=nsin8 is the numerical aperture, n is the refractive index of medium, and 0 is one-half the maximal convergence angle at focus. Recent studies have shown that the DL can be broken. For instance, with use of an annular aperture or radially polarized light [2] it becomes possible to break the DL through enhancing the depth of focus and decreasing the energy efficiency. In this case, the focal spot size is equal to the Bessel beam's diameter of 0.36XNA. Using diffractive optical elements, the light energy can be redistributed to a side lobe, forming a bright ring around the focus. In this way, by decreasing the energy coming to the focal spot its size can be made smaller than the DL. This phenomenon is termed superoscillation [3]. By focusing light near the material boundary with use of gradient-index or diffractive optics, it becomes possible not only to attain the n-times higher resolution (based on solid-state immersion [4]) but also to break the DL due to constructive interference of the surface waves.
In this study, we discuss particular realizations of optical elements and devices that enable one to break the DL. By way of illustration, a planar binary photonic crystal lens that approximates the gradient-index hyperbolic secant lens [5] with n(x)=n0 ch1 (ax) , where n0 is the refractive index on the lens optical axis and a is the lens parameter that defines its focal length (Fig. 1a), can focus light near its surface into a focal spot of intensity FWHM = 0.31X (Fig. 1b). Such a microlens is suitable for matching two waveguides of different width (Fig. 1a) [6].
Fig. 1. (a) SEM image of a 3x5-^m planar photonic crystal lens fabricated in a Si film and (b) intensity profile cross-section in the focus obtained by FDTD method at the lens output for incident wavelength 1550 nm (relative units).
The next example is associated with focusing light by means of a zone plate (ZP). Figure 2 depicts the SEM image of a binary ZP realized in an electron resist for wavelength 532 nm. The ZP has NA=0.996. The focal spot size in Fig. 2b is FWHM = (0.42 ±0.02)X [7].
SUBWAVELENGTH FOCUSING OF LASER LIGHT BY MICROOPTICS DEVICES
Soifer V.A., Kotlyar V.V., Khonina S.N.
a)
b)
1
0,8
0,6 0,4 0,2 0
Fig. 2. (a) SEM image of a 14-^m binary microlens with focal length of 532 nm and (b) intensity distribution in the focal spot produced by the microlens illuminated by a linearly polarized Gaussian beam. The focal spot size measurement was conducted with a near-field scanning optical microscope (NSOM).
The example below deals with focusing laser vortex beams that are generated with a binary spiral microaxicon of period 560 nm and NA = 0.95 (Fig. 3a). The size of a focal spot in Fig. 3b is FWHM = 0.37A [8, 9]. This focal spot is also smaller in size than the DL.
0 2 4 6 8 10
Fig. 3. (a) SEM image of a 23-^m spiral microaxicon fabricated in resist for wavelength 532 nm and (b) measured by NSOM intensity distribution in the focal spot at distance 1 ^m. List of reference:
1. G.B. Airy. Transactions of the Cambridge Philosophical Society 5, 283-291 (1835).
2. R. Dorn, S. Quabis, G. Leuchs, "Sharper focus for a radially polarized light beam"
Phys. Rev. Lett., 91, 233901 (2003)
3. F.M. Huang, N. Zheludev, Y. Chen, F.J. Garcia de Abajo, "Focusing of light by a nanohole array" Appl. Phys. Lett. 90, 091119 (2007)
4. K. Karrai, X. Lorenz, L. Novotny, "Enchanced reflectivity contrast in confocal solid immersion lens microscopy" Appl. Phys. Lett. 77, 3459-3461 (2000)
5. A. L. Mikaelian, Dokl. Akad. Nauk USSR 81, 2406-2415 (1951) (in Russian).
6. M.I. Kotlyar, Y.R. Traindaphilov, A.A. Kovalev, V.A. Soifer, M.V. Kotlyar, L. O'Faolain, "Photonic crystal lens for coupling two waveguides" Appl. Opt., 48, 3722-3730 (2009)
7. V.V. Kotlyar, S.S. Stafeev, Y. Liu, L. O'Faolain, A.A. Kovalev, "Analysis of the shape of a subwavelength focal spot for the linearly polarized light" Appl. Opt. 52, 330-339 (2013)
8. S.N. Khonina, D.V. Nesterenko, A.A. Morozov, R.V. Skidanov, V.A. Soifer, Narrowing of a light spot at diffraction of linearly-polarized beam on binary asymmetric axicons, Optical Memory and Neural Networks (Information Optics), Allerton Press, 21(1), 17-26 (2012)
9 S.N. Khonina, S.V. Karpeev, S.V. Alferov, D.A. Savelyev, J. Laukkanen, J. Turunen, "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," J. Opt. 15, 085704 (9pp) (2013)
