RU2539850C2 - Planar cylindrical microlens - Google Patents

Abstract

FIELD: physics, optics.

SUBSTANCE: microlens can be used in planar imaging devices, integrated optical devices, for connecting optical waveguides, for inputting radiation into photonic crystal and planar waveguides etc. The planar cylindrical microlens has a rectangular entrance aperture and is in the form of a photonic crystal. A slit is made along the optical axis of the microlens. The length of the slit is less than or equal to the length of the microlens and reaches the focal plane of the microlens. The microlens can be easily made by nanolithography or photolithography.

EFFECT: enabling focusing of TM polarised light into a spot with a width less than the diffraction limit of the order of 0,03 times the light wavelength.

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Description

The invention relates to the focusing of coherent optical radiation to obtain a focal spot with a given width less than the diffraction limit in the 2D case (cylindrical planar lens). This microlens can be used in imaging planar devices, integrated optical devices, for connecting optical waveguides, for introducing radiation into photonic crystal and planar waveguides, etc.

. Various types of lenses are used for planar focusing of light. The simplest option is conventional spherical or aspherical lenses. Another embodiment of a focusing lens is described in Graded index photonic crystals / H. Kurt, DS Citrin / Optics Express, 2007. - V.15. - P.1240-1252 (analogue). In this work, we used a photonic crystal microlens for focusing light, an analog of a gradient lens. The photonic crystal was made by creating round holes in the material with a refractive index n = 3.47, the diameter of which was varied to obtain the average refractive index given by the formula

.

The disadvantage of this lens is the lack of sharp focusing of light. The authors obtained a focal spot width at half-intensity (FWHM) of about 0.5λ in a medium with a refractive index of n = 3.47. Using such a lens, it is impossible to obtain a focal spot with a width much smaller than the diffraction limit.

, где λ - длина волны в вакууме, n - показатель преломления среды, в которой происходит фокусировка света. To achieve sharp focus, high numerical aperture lenses should be used. If we assume that the focal spot is created only by propagating waves with a maximum slope to the optical axis equal to θ, then the focus width along the half-intensity should be equal to

where λ is the wavelength in vacuum, n is the refractive index of the medium in which the light is focused.

. Эту величину можно рассматривать как дифракционный предел в 2D случае.With a numerical aperture NA = nsinθ tending to n, the focus width in the 2D case cannot be better

. This value can be considered as the diffraction limit in the 2D case.

To obtain the sharpest focusing, one should focus light near the separation of two media, for example, the material of an optical element with a refractive index n> 1 and air with a refractive index of 1. Near the interface, surface light waves are excited, the constructive interference of which can lead to a decrease in the focal spot below the diffraction the limit. This is possible because surface waves have a projection of the wave vector k _x onto the transverse coordinate x greater than the wave number in the medium: k _x > k ₀ n, where k ₀ = 2π / λ is the wave number of light in vacuum.

The best focusing properties are gradient lenses. In particular, a microlens, the refractive index of which is described by a hyperbolic secant:

,

,

where L is the length of the lens, n ₀ is the maximum refractive index on the optical axis, x is the transverse coordinate (A. Mikaelyan, Application of the properties of a medium for focusing waves, Doklady Akademii Nauk SSSR. - 1951. - Issue 81. - S. 569-571).

Such lenses can be created by approximating the gradient refractive index by a diffraction subwavelength microstructure, for example, using photonic crystals.

Closest to this invention is the work described in Chien, N.T. Focusing of electromagnetic waves by periodic arrays of air holes with gradually varying radii / H.T. Chien and C.C. Chen // Opt. Exp. - 2006. - V.14. - P. 10759, taken as a prototype. However, the width of the focal spot in this lens is close to 0.5 of the wavelength of light.

In this invention, the task was to focus TM-polarized light into a spot with a width less than the diffraction limit, of the order of 0.03 wavelengths of light using a planar cylindrical microlens.

The problem is achieved due to the fact that in a planar cylindrical microlens having a rectangular input aperture made in the form of a photonic crystal, according to the invention, a gap is made along the optical axis of the microlens, while the length of the slit is less than or equal to the length of the microlens and reaches the focal plane of the microlens.

In the case of a gap, a TM-polarized wave can propagate in it as in a waveguide, and focusing the light with a gradient lens will concentrate the field energy inside the gap in the focal plane. The width of the focal spot formed at the boundary of the lens will be close to the width of the slit, which will create planar lenses with an arbitrarily small focus. The narrower the gap, the narrower the focus, but also the lower the light intensity and the amount of light energy in focus. The length of the slit N can be equal to the length of the lens, or be less than it. A microlens maintains its operability if the gap reaches the exit aperture of the lens, and its length is tenths of the wavelength of light in the material of which the microlens is made.

A microlens with a gradient refractive index with a subwave gap on the optical axis can be created in various ways. This can be either a microlens with a real gradient distribution of the refractive index (for example, created by a combination of sputtering of various materials), or with a piecewise constant distribution of the refractive index, for example, having the form of a binary diffraction grating or a photonic crystal (with square or round holes), medium the refractive index of which repeats the gradient analog. A lens can be made using silicon etching technology after applying a masking resist layer with a given microrelief (electronic lithography).

Figure 1 shows (in semitones) the distribution of the refractive index in a gradient hyperbolic secant lens.

Figure 2 shows the distribution of light intensity in relative units in the focal plane of the lens.

Figure 3 shows the distribution of the refractive index in a gradient lens with a slit.

Figure 4 shows the distribution of light intensity in the focal plane of a gradient lens with a slit.

Figure 5 shows the distribution of the refractive index in a photonic crystalline lens with a slit with staggered holes.

Figure 6 shows the distribution of light intensity in the focal plane of a photonic crystal lens with a checkerboard hole arrangement, without a gap.

Figure 7 shows the distribution of light intensity in the focal plane of a photonic crystal lens with staggered holes, with a slit.

Figure 8 shows the distribution of light intensity in the focal plane of a photonic-crystalline lens with a checkerboard pattern of holes, with a slit.

Figure 1 shows in grayscale the distribution of the refractive index in a gradient hyperbolic secant lens without a gap. It is seen that the refractive index is maximum in the center, reaching n ₀ = 3.47 (silicon, Si), and drops to the edges to n (R) = 1. The width of the microlens is 2R = 4.8 μm, the length L = 2 μm. The microlens is designed for a wavelength of light λ = 1.55 μm.

.Figure 2 shows the intensity distribution I of the TM polarized wave (the electric wave vector lies in the plane of the lens, and the magnetic vector is perpendicular to the plane of the lens) in relative units in the focal plane of the lens shown in Figure 1. The focal plane is located at the boundary of the lens at z = 2 μm. The light in the form of a plane wave in Figs. 1, 3, 5 propagates from the bottom up and falls normally at the input of the lens at Z = 0. In Fig.2, the width of the focal spot at the half-intensity is FWHM = 0.181 μm = 0.117λ. The diffraction limit of the width of the focal spot over the half-intensity for a given refractive index and wavelength is

.

Figure 3 shows the distribution of the refractive index in a gradient lens with a slit for focusing a TM polarized wave into a narrow focal spot of a given width W. The lens parameters are the same as in figure 1. The width of the slit W can be arbitrary and less than the diffraction limit, the slit passes along the optical axis through the entire lens.

Figure 4 shows the distribution of light intensity of a TM-polarized wave in the focal plane of a gradient lens with a slit, the refractive index of which is shown in Figure 3. The width of the slit is W = 50 nm, the width of the focal spot in terms of half-intensity is FWHM = 43 nm = 0.029λ at a distance of 10 nm behind the lens.

Figure 5 shows the distribution of the refractive index in a photonic crystal lens with a slit similar to a gradient lens for focusing a TM polarized wave into a narrow focal spot of a given width W. The width of the slit W can be arbitrary or less than the diffraction limit. The width of the lens is 2R = 4.6 μm, the length L = 2 μm, the maximum hole diameter is 0.25 μm, the minimum is 30 nm, the refractive index of the lens material is n = 3.47.

Figure 6 shows the distribution of light intensity of a TM-polarized wave in the focal plane of a photonic crystal lens, the refractive index of which is shown in Figure 5, but without a gap. The width of the focal spot in terms of the half-intensity is FWHM = 162 nm = 0.104λ at a distance of 10 nm behind the lens (Z = 2.01 μm). The diffraction efficiency of focusing light at the first intensity minima at the focus was 32%.

Figure 7 shows the light intensity distribution of a TM polarized wave in the focal plane of a photonic crystal lens, the refractive index of which is shown in Figure 5, with a slit along the optical axis of width W = 50 nm. The slit passes through the entire lens (H = 2 μm). The width of the focal spot at the half-intensity is FWHM = 59 nm = 0.038λ at a distance of 10 nm behind the lens. The maximum light intensity in the focal spot has increased, the width of the focus is comparable to the width of the slit. The focusing efficiency of the light at the first intensity minimums at the focus was 27%. By reducing the width of the slit W, narrower focal spots can be achieved, however, the amount of energy in them and the intensity will decrease.

Fig. 8 shows the light intensity distribution of a TM polarized wave in the focal plane of a photonic crystal lens, the refractive index of which is shown in Fig. 5, with a slit along the optical axis with a width of W = 50 nm, and the slit length is selected for the maximum light intensity in focus and is H = 0.24 μm. The width of the focal spot along the half-intensity is FWHM = 58 nm = 0.037λ at a distance of 10 nm behind the lens. The maximum light intensity in the focal spot is even greater than in the case of H = 2 μm (Fig.7). The focusing efficiency of the light at the first intensity minima at the focus also increased compared to the previous case and amounted to 45%.

It can be seen from the above example that a planar microlens with a slit forms a narrow focal spot with a given width (ceteris paribus) in contrast to simple gradient and similar lenses (prototype). It is also seen that, choosing the length of the slit H, it is possible to significantly increase the intensity (power) in the focus of the lens and even create a lens that has less focal spot width at the same time and the light focusing efficiency is higher than a similar lens without a slit.

The advantage of this lens also lies in the simplicity and convenience of manufacturing using nanolithography technologies (recording holes in a masking layer of an electronic resist like ERP-40 with an electron beam in an electron microscope with a lithographic attachment, followed by the manifestation of the resist and plasma-chemical etching of the substrate) or photolithography.

Claims (1)

A planar cylindrical microlens having a rectangular entrance aperture made in the form of a photonic crystal, characterized in that a gap is made along the optical axis of the microlens, while the length of the gap is less than or equal to the length of the microlens and reaches the focal plane of the microlens.

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