CN109033015B - Device for executing calculus operation on optical signal - Google Patents

Abstract

A device for executing calculus operation on optical signals is composed of a signal source 1, a calculus operator 2 and a signal receiver 3. The method is characterized in that: the optical signal sent by the signal source 1 can directly irradiate on the calculus arithmetic unit 2, the calculus arithmetic unit 2 realizes the regulation and control of the electric field intensity amplitude and phase by utilizing the special physical property (graded refractive index) and ingenious structure of the material, and further realizes the first derivative, the second derivative and the integral operation of the input signal profile in the optical signal propagation process, and the signal profile sent by the signal source 1 and the signal profile received by the signal receiver 3 form a mathematical calculus relation.

Description

A device for performing calculus operations on optical signals

technical field

The device utilizes the physical properties and special structure of the material to control the amplitude and phase of the input signal during the propagation of the optical signal, thereby realizing the calculus operation on the profile of the input optical signal, which belongs to the field of metamaterials.

Background technique

The current calculus operation is realized by the calculus circuit. The circuit whose output voltage is in a differential relationship with the input voltage is a differential circuit, usually composed of capacitors and resistors; the circuit whose output voltage is in an integral relationship with the input voltage is an integral circuit, usually composed of resistors and capacitors. Calculus operation circuits are widely used in computers, automatic control and electronic instruments. However, the circuit has disadvantages such as needing external energy, heating, and slow speed. In order to meet the needs of high-speed computing in the information age, a new computing mechanism is urgently needed.

Contents of the invention

The purpose of the present invention is to solve the deficiency of the above-mentioned calculus operation circuit, and to realize the calculus operation on the profile of the input optical signal by utilizing the properties of the graded-index material and through an ingenious structure. The device has the advantages of novel principle, simple structure, fast calculation, no external energy, no intermediate process and the like.

The present invention is achieved through the following technical solutions:

As shown in Figure 1, the device consists of a signal source 1, a calculus operator 2, and a signal receiver 3. It is characterized in that the optical signal sent by the signal source 1 can directly irradiate the calculus operator 2, and the calculus operator 2 realizes the first-order derivative, second-order derivative and integral operation of the input signal during the propagation of the optical signal. The device uses the physical properties (refractive index) and structure size of the material to control the amplitude and phase of the input optical signal, thereby realizing the calculus operation.

The beneficial effects of the invention are: the device has simple structure, fast signal processing speed, no external energy source, wide application range, and is widely used in photonic computer, photo and image storage, signal transmission and the like.

Description of drawings

FIG. 1 is a schematic structural diagram of a device for performing calculus operations on optical signals according to the present invention.

Detailed ways

As shown in Figure 1, the device consists of a signal source 1, a calculus operator 2, and a signal receiver 3. The optical signal sent by the signal source 1 can be directly irradiated on the calculus calculator 2. The material properties and structural dimensions of the calculus calculator 2 meet certain conditions, and only the material II in the calculus calculator 2 is adjusted without changing other parameters. The refractive index can realize the first-order derivative, second-order derivative and integral operation of the input signal, and the signal profile received by the signal receiver 3 and the signal profile sent by the signal source 1 form a mathematical calculus relationship.

Theoretical basis

If light travels in a medium along the positive direction of the x-axis, the refractive index of the medium in the y-direction is This kind of material is called graded index material, where η ₁ is the refractive index at y=0, η ₂ /η ₁ =[π/(2Lg)] ² , and Lg is the propagation distance in the medium. When a light wave propagates in a material with a graded-refractive index, the graded-refractive-index material will perform a Fourier transform on the electric field at the characteristic length Lg. Using this property, metamaterials with calculus functions can be designed. As shown in Figure 1, the calculus operator 2 is composed of three layers of materials (I, II and III), and if the wavelength of the incident optical signal is λ, and it propagates along the positive direction of the x-axis, the dimensions of the three materials in the x-direction are respectively For Lg=11.619λ, Δ=λ/3.012 and Lg, the dimension in the y direction is W=9.876λ. The coordinate origin is in the left middle. The refractive index of material I and material III satisfy η _I (y) = -η _III (y) = η (y), perform Fourier transform and inverse Fourier transform respectively, and the transformation performed by material II is a calculus operator 2's core transformation, which is named G(y). When the electric field intensity E(y) of the incident light signal is input to the left end of material I, the output from the right end of material I will be the Fourier transform of E(y), namely in Represents the Fourier transform, the Fourier variable ky and _y belong to the same area, so _ky is proportional to y. Because the transformation performed by Material II is G(y), the output function of Material II is At the same time, because material III performs inverse Fourier transform, the function of the final exit end should be If the derivative operation is implemented for the input electric field strength, then there is

Finding the Fourier transform on both sides of the above formula, we have

According to the differential properties of the Fourier transform The above formula can be transformed into

The transformation function G(y)=(ik _y ) ⁿ ∝(-iy) ⁿ of material II can be obtained from equations (2) and (3) (according to the debugging results, take k _y ∝-y). Since the size of the material along the y direction is W, and the coordinate origin is located at the center of W, the maximum value in the y direction is y ₀ =W/2, which is the normalized function G(y)∝(-iy/y ₀ ) ⁿ . In order to realize the calculus operation of the optical signal, the expression of the refractive index of the material II is also required, and some properties of electromagnetic waves can be used, as follows:

When a plane light wave propagates forward along the x-axis, the electric field intensity E(x) at x satisfies the following Helmholtz equation

in, λ is the wavelength of the incident wave, ε _r and μ _r are the relative permittivity and relative permeability of the medium, respectively. Because the relative permittivity and relative permeability satisfy the relationship ε _r μ _r = (η-iκ) ² with the refractive index, where η and κ represent the real and imaginary parts of the refractive index respectively, so k can also be expressed as k=(2π/λ)(η-iκ). Solving equation (4), we get

E(x)＝E ₀ e ^ikx (5)

Where E ₀ is the magnitude of the electric field intensity at x=0, and E(x) is the magnitude of the electric field strength at x. Because the electric field strength at the left end of material II is According to Equation (5), after the propagation of Δ distance in material II, the electric field intensity is because then there is

Right now

In order to make the output electric field proportional to the first derivative of the input electric field, take G(y)=(-iy/y ₀ ), according to equation (7), the refractive index of material II should satisfy

Similarly, if the second-order derivative operation is performed on the input function, G(y)=(-iy/y ₀ ) ² is taken, and the refractive index of material II should satisfy

Right now

Wherein, n=1 represents a first-order derivative operation, and n=2 represents a second-order derivative operation.

For the integral operation, formula (1) should be modified as

Finding the Fourier transform on both sides of the above formula, we have

According to the integral property of the Fourier transform From Equation (12), it can be obtained that the function G(y)=(ik _y )∝(-iy) ^-1 of the material II performing the integral operation, setting the normalization constant as d, and taking d=λ/4, then For the integral operation, G(y)=(-iy/d) ^-1 can be taken. In order to avoid the transmission coefficient of |y|<d area being greater than 1, set |y|=d as the turning point, and assume that |y|<d area The absolute value of the refractive index is constant, so the refractive index expression of material II that can be integrated is

Where sign(.) is a sign function.

The design scheme of the present invention has been disclosed above, but it is not intended to limit the present invention. All other calculus computing devices obtained by adopting equivalent ideas and methods are within the scope of protection of the present invention.

Claims (1)

1. The device for executing the calculus operation on the optical signal consists of a signal source (1), a calculus operator (2) and a signal receiver (3); the light signal emitted by the signal source (1) is directly irradiated on the calculus arithmetic unit (2), the calculus arithmetic unit (2) is formed by tightly connecting three layers of materials I, II and III, the dimensions of the three layers of materials in the x direction are lg= 11.619 λ, delta=λ/3.012 and lg= 11.619 λ respectively, the dimensions of the three layers of materials in the y direction are w= 9.876 λ respectively, and the structural parameters are based on the wavelength λ of the incident light signal; the material I and the material III are graded index materials, and the refractive index of the material II is different according to the different operation functions; the signal source (1), the calculus arithmetic unit (2) and the signal receiver (3) are directly connected by optical signals, and the whole device is in an air environment.

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