Planar Gradient Hyperbolic Secant Lens for Subwavelength Focusing and Superresolution Imaging

Abstract

Integral relations to describe the propagation of a TE-wave from an external point source through the two-dimensional medium (plane interface) and the plane-parallel plate are proposed. We discuss three types of waves that contribute to the resulting light field, namely, the propagating waves and the first-and second-type surface waves. The comparison of near-field refractive lenses (SIL, NAIL) and a planar hyperbolic secant lens shows their numerical apertures to have close values, with the difference being as small as 5% for the Si-based optical elements. The FDTD-method simulation shows that by combining the gradient-index hyperbolic secant lens with a subwavelength diffraction grating or replacing it with its binary analog, the focal spot size can be made, respectively, 10% and 20% smaller than the diffraction-limited resolution in the 2D medium. We design a Si-based, planar binary microlens to generate a near-surface focal spot of full-width half-maximum size FWHM=0.102λ, where λ is the incident wavelength, which is practically devoid of side-lobes. It is shown that about 10 percent of the total incident beam energy goes to the far-field zone.

Propagation of hypergeometric laser beams in a medium with a parabolic refractive index

“…If in the LG mode of equation ( 22) the radius of the Gaussian beam does not meet the condition ω 2 = [1/(k 0 n 0 τ )] 1/2 , the LG beam is not a mode any longer. In the unbounded waveguide of equation ( 1) only Laguerre-Gaussian modes (22) can propagate, but if the waveguide is bounded by radius r 0 < ∞, then besides the modes (22) there would be other modes described by equation (19).…”

“…In [21], a graded-index HS lens was shown to form a focal spot of size FWHM = 0.40λ. A planar subwavelength graded-index binary HS lens to generate a focal spot of size FWHM = 159 nm = 0.102λ = 0.35λ/n (the refractive index is n = 3.47) was discussed in [22].…”

“…We show by numerical simulation that the well-known PI lens can find use for subwavelength focusing of laser light. In terms of its focusing performance the PI lens is on a par with unconventional lenses such as the Luneburg lens [16][17][18] and the hyperbolic secant lens [21,22]. The numerical simulation has shown that such a lens produces a focal spot of size FWHM = 0.42λ for a refractive index on the lens axis of n 0 = 1.5.…”

“…The elliptic focal spot's smaller size generated with the PI lens and calculated using the FDTD method (finite-difference time-domain) is FWHM = 0.45λ (FWHM of intensity). It is noteworthy that [16][17][18][19][20][21][22] conducted the analysis of planar graded-index lenses whose diffraction limit was defined by the sinc-function, resulting in an FWHM = 0.44λ, whereas in this work we study a 3D PI lens in which the diffraction limit is defined by the Airy disk size of (2J 1 (x)/x), producing a larger value of FWHM = 0.51λ.…”

Planar elliptical solid immersion lens based on a Cartesian oval

“…13 Numerous modifications and optimizations have been made on these designs. 14,15 In practice, it can be difficult to achieve the theoretical resolution for 3D SILs due to polishing imperfections or inaccurate truncation of the sphere.…”