High Resolution through Graded-Index Microoptics

Abstract

By solving Helmholtz equations, relationships to describe propagating modes in an arbitrary graded-index planar waveguide are derived. We show that in the quadratic-and secant-index waveguides a minimal mode width is 0.4λ/n, where λ is the wavelength in free space and n is the refractive index on the fiber axis. By modeling in FullWAVE, we show that the high-resolution imaging can be achieved with half-pitch graded-index Mikaelian microlenses (ML) and Maxwell's "fisheye" lenses. It is shown that using a 2D ML, the point source can be imaged near the lens surface as a light spot with the full width at half maximum (FWHM) of 0.12λ. This value is close to the diffraction limit for silicon (n = 3.47) in 2D media FWHM = 0.44λ/n = 0.127λ. We also show that half-pitch ML is able to resolve at half-maximum two close point sources separated by a 0.3λ distance.

Sequences of exact analytical solutions for plane waves in graded media

“…The transfer matrix corresponding to the    ŝech -type profiles is easily computed by substituting in eq. ( A2)-(A3) the expressions for   waveguide [57]. The LC described in eq.…”

Near-field backflow of energy

“…Note, however, that while not making much of the effect, the authors just noticed that with a golden nanostrip applied on the surface, the normally incident light did not penetrate into InP. The energy backflow was also numerically shown to occur [10] when focusing light on the output end of a graded-index microlens. As a mechanism behind the energy backflow, the propagation of a surface wave along the microlens end, alternately leaving and entering the medium, was proposed.…”

“…The effect also occurs in the focus of linearly and circularly polarized nonparaxial vector beams [22], in various vector modal beams (e.g. Bessel [15,16] and non-paraxial Airy beams [24], X-waves [6]), as well as when the focus is on the medium interface [10] or close to nanostructured surfaces [9,13]. It is worth noting that for paraxial unbounded light fields, the longitudinal component of the Poynting vector is proportional to the intensity and changes no sign [8,26], meaning that for such fields the energy backflow cannot occur in free space.…”

Hyperbolic secant slit lens for subwavelength focusing of light

“…In this work, we combine the advantages of using a several-dozen nanometers wide slit for light confinement [4] and a gradient lens for the sharp focusing of light [10]. The finite-difference time-domain (FDTD) simulation has shown that a planar binary microlens in silicon with a 50 nm wide slit can generate a near-surface focal spot of size FWHM λ∕23 with a 44% energy efficiency.…”

“…Figure 1 depicts a scheme of a planar graded-index slit lens. We consider a hyperbolic secant (HS) lens whose refractive index depends on the transverse coordinate x as follows [10]: nx n 0 ch −1 πx∕2H, where n 0 is the refractive index on the axis and H is the lens length.…”