Fourier lens, method for designing Fourier lens, and schlieren apparatus

Patent metadata

Field	Value
Publication number	US-10459127-B2
Application number	US-201715720221-A
Country	US
Kind code	B2
Filing date	Sep 29, 2017
Priority date	Aug 3, 2017
Publication date	Oct 29, 2019
Grant date	Oct 29, 2019

Abstract

Provided are a Fourier lens, a method for designing a Fourier lens, and a schlieren apparatus. The Fourier lens includes a substrate and a plurality of cuboid waveguides. The plurality of waveguides are arranged on the substrate in parallel and spaced from each other at a preset interval. The material of the substrate and the material of the waveguides are all transparent to the working waveband of the Fourier lens. The preset interval is smaller than a quotient obtained by dividing a center wavelength of the working waveband by the refractive index of the substrate. The waveguide has a plurality of widths, and the waveguides of different widths correspond to different phase delays. The individual waveguides are arranged on the substrate according to phase delays required at different positions. According to the embodiments, the range of the working angle of the Fourier lens can be increased.

First claim

The invention claimed is:

1. A method for designing a Fourier lens, wherein the Fourier lens comprises a substrate and a plurality of cuboid waveguides, wherein the plurality of waveguides are arranged on the substrate in parallel and spaced from each other at a preset interval; a material of the substrate and a material of the plurality of cuboid waveguides are all transparent to a working waveband of the Fourier lens, and the preset interval is smaller than a quotient obtained by dividing a center wavelength of the working waveband by a refractive index of the substrate, the plurality of cuboid waveguides have a plurality of widths, the plurality of cuboid waveguides of different widths correspond to different phase delays, and individual waveguides are arranged on the substrate according to phase delays required at different positions, the method comprising:
determining, according to a working waveband of the Fourier lens to be designed, a material of the substrate and a material of the waveguides;
performing, according to the working waveband, the material of the substrate and the material of the waveguides, an electromagnetic wave simulation to determine parameters of the waveguides, wherein the parameters of the waveguides comprise: a height of the waveguides, a plurality of widths of the waveguides, and a preset interval between adjacent waveguides;
determining, according to a designed focal length and the preset interval of the Fourier lens, positions where the plurality of waveguides are arranged on the substrate; and
manufacturing, with a micromachining technology, the Fourier lens according to the parameters and the positions where the waveguides are arranged,
wherein the performing further comprises:
selecting the height of the waveguides according to the working waveband, and selecting the preset interval between adjacent waveguides according to the material of the substrate and the working waveband;
performing, according to the material of the waveguides, the selected height of the waveguides and the preset interval, an electromagnetic wave simulation with a Finite Difference Time Domain method or a Finite Element Method, so as to obtain a set of simulation results representative of a correspondence between the widths of the waveguides and phase delays; and
selecting a plurality of simulation results from the set of simulation results, with the selected simulation results covering the phase delays greater than or equal to −π and smaller than π, and adding the widths of the waveguides, corresponding to the individual phase delays of the selected simulation results, into the parameters of the waveguides of the Fourier lens.

2. The method according to claim 1 , wherein the step of determining according to a designed focal length and the preset interval of the Fourier lens positions where the plurality of waveguides are arranged on the substrate comprises:
determining, according to the preset interval, a plurality of positions where the plurality of waveguides are to be arranged on the substrate;
determining phase arrangement of the Fourier lens, according to a distance between each of the positions where the plurality of waveguides are to be arranged and a centerline of the substrate, and according to the designed focal length, wherein the phase arrangement indicates a phase delay corresponding to each of the positions where the plurality of waveguides are to be arranged; and
determining, according to the phase arrangement, the positions where the plurality of waveguides are arranged on the substrate.

3. The method according to claim 2 , wherein the phase delay corresponding to one of the positions where the plurality of waveguides are to be arranged is calculated by the following formula:

φ
⁡

(
r
)

=

-

kr
2

2
⁢
f

,

where φ(r) represents the phase delay corresponding to r, r represents the distance, k represents a magnitude of a wave vector corresponding to a center wavelength of the working waveband, and f represents the designed focal length.

4. The method according to claim 1 , wherein the material of the substrate comprises glass, silicon dioxide or silicon nitride.

5. The method according to claim 1 , wherein the material of the waveguides comprises amorphous silicon, germanium, titanium dioxide or tellurium.

6. The method according to claim 1 , wherein the substrate is a glass substrate, and the waveguides are amorphous silicon waveguides;
the preset interval is 450nm; and the amorphous silicon waveguides have eight widths, with the eight widths being 390nm, 300nm, 250nm, 205nm, 160nm, 135nm, 120nm and 110nm, respectively.

7. The method according to claim 6 , wherein a height of each of the amorphous silicon waveguides is 1.05 μm, and a length of each of the amorphous silicon waveguides is greater than or equal to 10 μm.

Assignees

• Univ Nankai

Inventors

• Chen Shuqi
• Liu Wenwei
• Cheng Hua
• Tian Jianguo

Classifications

• G02B27/0012

  Optical design, e.g. procedures, algorithms, optimisation routines · CPC title

• G02B6/107

  Subwavelength-diameter waveguides, e.g. nanowires · CPC title

• G02B27/54 Primary

  Schlieren-optical systems · CPC title

• G02B3/08 Primary

  with discontinuous faces, e.g. Fresnel lens {(diffractive Fresnel lenses G02B5/1876)} · CPC title

• G02B27/0087

  Phased arrays · CPC title