A nano-supergrating and optical quantum computing device

Abstract

The present invention provides a nano super grating and optical quantum computing device, comprising: a substrate, a plurality of nano units and a filling unit; the substrate is made of a light-transmitting material; a plurality of nano units are arranged on the upper surface of the substrate, and the nano units are arranged at intervals between each other; the width of the nano unit is much smaller than the length of the substrate; the number of nano units is greater than the highest order of the prolate ellipsoid wave function PSWFs; the filling units are respectively arranged between the nano units and at both ends of the substrate; the height of the filling unit arranged between the nano units is the same as the height of the nano unit; the lower surface of the filling unit arranged at both ends of the substrate is flush with the lower surface of the substrate, and the upper surface is flush with the upper surface of the nano unit; the filling unit is made of a material with a large imaginary part of the complex refractive index and completely absorbs the working wavelength. The nano super grating breaks through the existing theoretical limit, and its total area can be less than one wavelength, but it can still achieve infinite precision and efficiency at the nanoscale.

Description

Technical Field

[0001] The present invention relates to the technical field of nano gratings, and in particular to a nano super grating and an optical quantum computing device. Background Art

[0002] Traditional optical devices (such as general lenses) can use the thickness variation of natural materials to change the wavefront of light to achieve functions such as convergence, refraction, reflection and diffraction, but they have disadvantages such as large size, single function and inability to achieve complex optical functions. In contrast, optical metasurfaces composed of a special arrangement of multiple "superatoms" with controllable refractive index allow us to accurately "cut" the wavefront at the nanoscale to achieve a variety of advanced optical functions such as ultra-thin superlenses. Optical metasurfaces can be used in photonic quantum chips to achieve light quantity calculations.

[0003] However, all current optical metasurfaces still face a problem, that is, their area cannot be smaller than a wavelength, that is, they can only reach the order of a few microns at most. Traditional theory holds that a wavelength is considered to be the theoretical limit of the minimum area (width) of any diffraction-type optical device. When the area of ​​the metasurface is reduced to a few wavelengths (sub-wavelength order), due to the effect of diffraction, light will scatter in all directions after passing through the back surface of the device; at this time, no matter how the fine structure of the metasurface is edited, its diffraction result outside the near field will tend to a divergent bright spot due to the attenuation of the evanescent wave, so effective optical information processing cannot be achieved. Summary of the invention

[0004] In view of this, the present invention provides a nano-supergrating and an optical quantum computing device to solve the problem that when the size of an optical supersurface is smaller than the wavelength, divergent bright spots are formed due to severe diffraction, making it impossible to perform effective optical information processing.

[0005] A nano super grating, comprising: a substrate, a plurality of nano units and a filling unit; the substrate is made of a light-transmitting material; a plurality of nano units are arranged on the upper surface of the substrate, and the nano units are arranged at intervals between each other; the width of the nano unit is much smaller than the length of the substrate; the number of the nano units is greater than the highest order of the prolate spheroidal wave function PSWFs;

[0006] The filling units are respectively arranged between the nano units and at both ends of the substrate; the height of the filling units arranged between the nano units is the same as the height of the nano units; the lower surfaces of the filling units arranged at both ends of the substrate are flush with the lower surface of the substrate, and the upper surfaces are flush with the upper surfaces of the nano units; the filling units are made of a material with a large imaginary part of the complex refractive index and complete absorption of the working wavelength.

[0007] Optionally, the complex refractive indexes of the plurality of nano-units are different.

[0008] Optionally, a plurality of the nano units are arranged at equal intervals on the upper surface of the substrate.

[0009] Optionally, the length of the substrate is less than one wavelength.

[0010] Optionally, the complex refractive index of the plurality of nano-units is determined by a material function formed on the surface of the nano-unit when monochromatic coherent incident light is irradiated onto the substrate and passes through the nano-unit.

[0011] Optionally, the expression of the physical function is:

[0012]

[0013] Among them, t(x o ) represents the plane coordinate x on the surface of the nanounit o The physical function at n (c,x o ) represents the prolate spheroidal wave function PSWFs, c = ΩD / 2 is the spatial bandwidth product of the prolate spheroidal wave function PSWFs, Ω is the spatial unilateral bandwidth of the prolate spheroidal wave function PSWFs, k is the wave number of the monochromatic coherent incident light, b n represents the material function coefficient, and D represents the length of the substrate.

[0014] Optionally, the wavelength of the monochromatic coherent incident light is λ=2π / k, wherein k is the wave number of the monochromatic coherent incident light.

[0015] Optionally, the material function coefficient is calculated by the following formula:

[0016]

[0017]

[0018] Wherein, T(ω) represents the target light field function formed by the monochromatic coherent incident light on the substrate and in the propagation band interval after passing through the nano-unit, and the value is an arbitrary function; represents the prolate spheroidal wave function PSWFs after Fourier transformation.

[0019] The nano supergrating in the embodiment of the present application includes: a substrate, a plurality of nano units and a filling unit; the substrate is made of a light-transmitting material; a plurality of nano units are arranged on the upper surface of the substrate, and the nano units are arranged at intervals between each other; the width of the nano unit is much smaller than the length of the substrate; the number of nano units is greater than the highest order of the prolate spheroidal wave function PSWFs; the filling units are respectively arranged between the nano units and at both ends of the substrate; the height of the filling units arranged between the nano units is the same as the height of the nano units; the lower surface of the filling units arranged at both ends of the substrate is flush with the lower surface of the substrate, and the upper surface is flush with the upper surface of the nano unit; the filling units are made of a material with a large imaginary part of the complex refractive index and complete absorption of the working wavelength.

[0020] The nano-supergrating in the embodiment of the present application breaks through the existing theoretical limits. Its total area can be smaller than one wavelength, but it can still achieve infinite precision (theoretical resolution is 100%) and high efficiency (energy utilization efficiency is 100%) at the nanoscale.

[0021] Based on the above-mentioned nano supergrating, an embodiment of the present application also provides an optical quantum computing device.

[0022] An optical quantum computing device comprises one or more of the above-mentioned nano-super gratings.

[0023] The optical quantum computing device in the embodiment of the present application uses a nano-supergrating, which can achieve infinite precision and efficiency at the nanoscale. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0025] Figure 1 A schematic diagram of a nano supergrating structure provided by an embodiment of the present invention;

[0026] Figure 2 A schematic diagram of the function and geometric relationship of a nano-supergrating provided in an embodiment of the present invention;

[0027] Figure 3 A schematic diagram of a grating function and propagation result of a nano-supergrating provided in an embodiment of the present invention;

[0028] Figure 4 A schematic diagram of the Hadamard gate structure provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0029] The technical solutions in the embodiments of the present invention are described clearly and completely below. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0030] In order to illustrate the present invention in more detail, a nano super grating provided by the present invention is specifically described below with reference to the accompanying drawings.

[0031] Please refer to Figure 1 A nano super grating comprises: a substrate 10, a plurality of nano units 20 and a filling unit 30; the substrate 10 is made of a light-transmitting material; a plurality of nano units 20 are arranged on the upper surface of the substrate, and the nano units 20 are arranged at intervals between each other; the width of the nano unit 20 is much smaller than the length of the substrate; the number of the nano units 20 is greater than the highest order of the prolate ellipsoid wave function PSWFs; the filling units 30 are respectively arranged between the nano units 20 and at both ends of the substrate 10; the height of the filling units 30 arranged between the nano units 20 is the same as the height of the nano units 20; the lower surface of the filling units 30 arranged at both ends of the substrate 10 is flush with the lower surface of the substrate 10, and the upper surface is flush with the upper surface of the nano units 20; the filling units 30 are made of a material with a large imaginary part of the complex refractive index and complete absorption of the working wavelength.

[0032] In one embodiment, the complex refractive indices of the plurality of nano-elements are different.

[0033] In one embodiment, a plurality of nano-units are arranged at equal intervals on the upper surface of the substrate.

[0034] In one embodiment, the length of the substrate is less than one wavelength.

[0035] In one embodiment, the complex refractive index of the plurality of nano-units is determined according to a material function formed on the surface of the nano-units when monochromatic coherent incident light irradiates the substrate and passes through the nano-units.

[0036] In one embodiment, the expression of the physical function is:

[0037]

[0038] Among them, t(x o ) represents the plane coordinate x on the surface of the nanounit o The physical function at n (c,x o ) represents the prolate spheroidal wave function PSWFs, c = ΩD / 2 is the spatial bandwidth product of the prolate spheroidal wave function PSWFs, Ω is the spatial unilateral bandwidth of the prolate spheroidal wave function PSWFs, k is the wave number of the monochromatic coherent incident light, bn represents the material function coefficient, and D represents the length of the substrate.

[0039] In one embodiment, the wavelength of the monochromatic coherent incident light is λ=2π / k, where k is the wave number of the monochromatic coherent incident light.

[0040] In one embodiment, the material function coefficient is calculated by the following formula:

[0041]

[0042]

[0043] Wherein, T(ω) represents the target light field function formed by the monochromatic coherent incident light on the substrate and in the propagation band interval after passing through the nano-unit, and its value is an arbitrary function; represents the prolate spheroidal wave function PSWFs after Fourier transformation.

[0044] Specifically, N nanounits with different complex refractive indices are arranged at equal intervals on a transparent substrate, where N must be greater than the highest order of the PSWFs used, and the geometric scale of the nanounit is significantly smaller than the device aperture D, so that its geometric shape does not significantly affect the diffraction effect; a high absorption layer (i.e., a filling unit) with a very high absorption rate at the working wavelength is filled between the nanounits and around the device. The high absorption layer refers to a material with a large imaginary part of the complex refractive index, which almost completely absorbs the light of the working wavelength. The refractive index distribution function n(x o ), so that the light passes through the device and forms an equivalent discretized function of the target function on its rear surface N (x o ), when the number of nanounits N used increases, the actual physical function is closer to the theoretical value t(x o ).

[0045] Furthermore, the core principle of the nano-supergrating is: suppose a monochromatic coherent plane light source with a wavelength of λ = 2π / k is irradiated on an aperture of D (i.e., the length of the substrate), and the lateral distribution function of the refractive index is n(x o ).like Figure 2 As shown, after the light source passes through the optical structure or device (i.e., nano-super grating), a transverse electric field t(x o ), where the transverse electric field is parallel to the rear surface of the device and perpendicular to the optical axis. The transverse electric field is usually called the physical function, x o is the plane coordinate of the rear surface of the device.

[0046] It is generally believed that when the device thickness h is much smaller than the wavelength λ, t(x o )≈exp(ikhn(x o)), where i is an imaginary unit. In this embodiment, Figure 1 and Figure 2 The two-dimensional image shown is used as an example for explanation, and the three-dimensional image is similar. Figure 2 , at any point behind the device r0=(x i , z) can be strictly expressed according to the vector Rayleigh-Sommerfeld diffraction formula as follows:

[0047]

[0048] where G(r)≡e ikr / r is the Green's function; The horizontal coordinate from this point to the back surface of the device is x o A point of distance; and are the unit vectors perpendicular to and parallel to the optical axis, respectively. o = Taylor expansion around 0:

[0049] |r|=|r0|-sin(θ0)x o +o(x o ) (2)

[0050] where o(x o ) is a high-order expansion quantity. When the propagation distance meets the far-field condition

[0051] |r0| / λ>>(D / 2λ) 2 (3)

[0052] When the denominator of the Green function in equation (1) is retained to the 0th order |r|≈|r0|, the distance term in the phase term is retained to the first order |r|≈|r0|-sin(θ0)x o , then formula (1) can be effectively expressed as

[0053] E(r0)≈F(ω)G (4)

[0054] in is the physical function t(x o )’s Fourier transform (i.e. its spectrum). is a o Transitive function t(x o ) is an independent function. Note that for sub-wavelength devices with apertures smaller than the wavelength, the propagation distance |r0| can quickly satisfy equation (2) within a wavelength range.

[0055] Then, we use a special set of superoscillator functions of orthogonal complete functions, namely Prolate Spheroidal Wave Functions (PSWFs) ψ n(c,x) for the physical function t(x o ) to expand:

[0056]

[0057] Where c = ΩD / 2 is the spatial bandwidth product of PSWFs, and Ω is its spatial unilateral bandwidth. Select the spatial bandwidth product c = kD / 2, where k is the wave number of the incident light. According to the special Fourier transform properties of PSWFs:

[0058]

[0059] in

[0060] Then formula (4) can be rewritten as

[0061] in

[0062] Due to ψ n (c,ωD / 2k) is orthogonally complete in the propagation interval [-k,k], so it can be found on the surface Construct an arbitrary function on θ′∈[-π / 2,π / 2](12):

[0063]

[0064] Where T(ω) represents the target light field function on the surface r′.

[0065] Since the resolution of light field manipulation is infinite in theory, that is, infinitely accurate, and the high-energy sidelobes of the prolate ellipsoidal wave function outside the interval [-k, k] all fall into the evanescent band and do not carry energy, the theoretical energy conversion efficiency of the nano-supergrating is 100%. This result meets the design requirements for the nano-supergrating.

[0066] The nano-supergrating in the embodiment of the present application breaks through the existing theoretical limits. Its total area can be smaller than one wavelength, but it can still achieve infinite precision (theoretical resolution is 100%) and high efficiency (energy utilization efficiency is 100%) at the nanoscale.

[0067] Effect embodiment:

[0068] In order to verify the effectiveness of the nano-super grating of this application, two intuitive examples are selected to illustrate the design and actual optical effect of the nano-super grating. Where λ = 520nm, substrate D = 0.5λ = 260nm, and at any point after the device Take the construction of a super-diffraction-limited spot as an example. The image function to be constructed is T(ω)=δ(rr′). According to formulas (7)-(13), the superposition coefficient of the object function is:

[0069]

[0070] Where ω′=ksin(θ′).

[0071] Since discrete nanostructures are used to replace continuous structures in the specific design, a discrete prolate spheroidal wave function sequence (DPSS) ψ is used in this embodiment. n N (c,x) replaces the continuous prolate ellipsoid wave function ψ n (c,x), where N>n+1 is the number of points in the sequence. Consider the working wavelength λ=520nm, and the total length of the nano-supergrating D=0.5λ=260nm. Consider using 26 discrete nanostructures to construct a nano-supergrating, with each nanopoint spaced 10nm apart; consider using the first 13 discrete long ellipsoid wave function sequences to construct the corresponding nano-supergrating at two target points r1′=(1λ,0) and r2′=(1λ,arcsin(0.97)), and the diffraction results and the corresponding physical functions are as follows: Figure 3 (a)-(b) and (c)-(d). Figure 3 It can be seen from (a) and (c) that the super-oscillation bright spot appears at the corresponding positions r1′=(1λ,0) and r2′=(1λ,arcsin(0.97)), and the spot width has exceeded the traditional diffraction limit. In addition, due to the disappearance of the high-energy super-oscillation sidelobes, the energy convergence efficiency of the super-oscillation bright spot is theoretically unitary. Figures (a) and (c) are the propagation results and grating morphology of the nano-supergrating designed to generate a sub-wavelength hotspot at point r′=(1λ,0rad); Figure (a) shows the diffraction result at the dotted line ||E(r′)|| 2 (i.e., the dotted line graph), the transverse electric field component ||E x (r′)|| 2 (i.e., the solid line graph) and the longitudinal electric field component ||E z (r′)|| 2 (i.e., the dotted line graph); (c) The columnar shape is the amplitude of the fine structure of the nano-super grating function, and the needle line is its phase, and the spacing between each fine structure is 10nm. (b) and (d) are the propagation results and grating morphology of the nano-super grating designed to produce a sub-wavelength hotspot at point r′=(1λ,arcsin(0.97)); (b) is the diffraction result at the dotted line ||E(r′)|| 2 (i.e., the dotted line graph), the transverse electric field component ||E x (r′)|| 2 (i.e., the dotted line graph) and the longitudinal electric field component ||E z (r′)|| 2 (i.e. solid line graph).

[0072] Based on the above-mentioned nano supergrating, an embodiment of the present application also provides an optical quantum computing device.

[0073] An optical quantum computing device comprises one or more of the above-mentioned nano-super gratings.

[0074] The optical quantum computing device in the embodiment of the present application uses a nano-supergrating, which can achieve infinite precision and efficiency at the nanoscale.

[0075] Application examples:

[0076] The combination of nano-supergratings can realize quantum information processing at the nanoscale (subwavelength scale). Figure 4 An example of using nano-supergratings to form a "Hadamard Gate" is given. The Hadamard Gate is a very important and basic quantum logic gate in quantum computing. Its function is to convert any input state: By changing formula (15), it becomes Among them, |+>=|1>+|0>(17), |->=|1>-10>(18).

[0077] If we express it in matrix

[0078] Please refer to Figure 4 The optical path shown in the figure is that two nano-super gratings are placed vertically, and their diffraction results are as follows: Figure 4 As shown on the right side of the figure. Consider that the photon propagates to the right in the |1> state and propagates upward in the |0> state; consider that a photon can only be input as a |1> state after passing through several front optical paths and pass through the No. 1 nano-supergrating (No. 1 gate) or as a |0> state after passing through the No. 2 nano-supergrating (No. 2 gate). After passing through the two nano-supergratings, it can be projected in both directions. Consider that the complex amplitude of its wave function is the relative normalized complex amplitude of the light in the two directions after passing through the nano-supergrating, as shown in Figure 4 As shown in the illustration on the right, the Hadamard gate effect can be realized at the nanoscale.

[0079] For other quantum logic gates, due to the unitary conversion properties of the nano-supergrating, we can achieve them by defining the complex amplitude distribution of light at different positions or directions after it passes through it. Then, through different combinations of nano-supergratings, the effect of nano-photonic quantum gate can be realized at the subwavelength scale.

[0080] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A nano supergrating, characterized in that: include: A substrate, a plurality of nano-units and a filling unit; the substrate is made of a light-transmitting material; a plurality of nano-units are arranged on the upper surface of the substrate, and the nano-units are arranged at intervals between each other; the width of the nano-unit is much smaller than the length of the substrate; the number of the nano-units is greater than the highest order of the prolate ellipsoidal wave function PSWFs; The filling units are respectively arranged between the nano units and at both ends of the substrate; the height of the filling units arranged between the nano units is the same as the height of the nano units; the lower surfaces of the filling units arranged at both ends of the substrate are flush with the lower surface of the substrate, and the upper surfaces are flush with the upper surfaces of the nano units; the filling units are made of a material with a large imaginary part of the complex refractive index and completely absorbs the working wavelength; The complex refractive index of the plurality of nano-units is determined according to a material function formed on the surface of the nano-unit when monochromatic coherent incident light is irradiated onto the substrate and passes through the nano-unit; The expression of the physical function is: ； in, Represents the plane coordinates of the nanounit surface The physical function at represents the prolate spheroidal wave function PSWFs, is the spatial bandwidth product of the prolate spheroidal wave functions PSWFs, is the spatial unilateral bandwidth of the prolate spheroidal wave function PSWFs, k is the wave number of the monochromatic coherent incident light, represents the material function coefficient, and D represents the length of the substrate.

2. The nano supergrating according to claim 1, characterized in that: The complex refractive indexes of the plurality of nano-units are different.

3. The nano supergrating according to claim 1, characterized in that: A plurality of the nanometer units are arranged at equal intervals on the upper surface of the substrate.

4. The nano supergrating according to claim 1, characterized in that: The length of the substrate is less than one wavelength.

5. The nano supergrating according to claim 1, characterized in that: The wavelength of the monochromatic coherent incident light is λ=2 , where k is the wave number of the monochromatic coherent incident light.

6. The nano supergrating according to claim 1, characterized in that: The material function coefficient is calculated by the following formula: ； ； in, represents a target light field function formed by the monochromatic coherent incident light on the substrate and in the propagation band interval after passing through the nano-unit, and the value is an arbitrary function; represents the prolate spheroidal wave function PSWFs after Fourier transformation.

7. An optical quantum computing device, characterized in that: Comprising one or more nano supergratings as described in any one of claims 1-6.

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