CN109033015B - Device for executing calculus operation on optical signal - Google Patents
Device for executing calculus operation on optical signal Download PDFInfo
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- CN109033015B CN109033015B CN201710445240.6A CN201710445240A CN109033015B CN 109033015 B CN109033015 B CN 109033015B CN 201710445240 A CN201710445240 A CN 201710445240A CN 109033015 B CN109033015 B CN 109033015B
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
- G06F17/13—Differential equations
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
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
Technical Field
The device utilizes the physical properties and special structures of materials to control the amplitude and the phase of an input signal in the optical signal propagation process, thereby realizing the calculus operation of the input optical signal profile, and belongs to the field of metamaterial.
Background
Current calculus operations are implemented by calculus circuits. The circuit with differential relation between the output voltage and the input voltage is a differential circuit, and is generally composed of a capacitor and a resistor; the circuit in which the output voltage is integrated with the input voltage is an integrating circuit, typically consisting of a resistor and a capacitor. Calculus arithmetic circuits are widely used in computers, automatic controls and electronic instruments. However, the circuit has the disadvantages of external energy source, heat generation, low speed and the like, and a new operation mechanism is urgently needed in order to meet the requirement of high-speed calculation in the information age.
Disclosure of Invention
The invention aims to solve the defects of the calculus operation circuit, and utilizes the property of graded index materials to realize calculus operation on the profile of an input optical signal through a smart structure. The device has the advantages of novel principle, simple structure, rapid operation, no external energy source, no intermediate process and the like.
The invention is realized by the following technical scheme:
as shown in fig. 1, the device is composed of a signal source 1, a calculus arithmetic unit 2 and a signal receiver 3. The method is characterized in that: the light signal emitted by the signal source 1 can directly irradiate the calculus arithmetic unit 2, and the calculus arithmetic unit 2 realizes the first derivative, the second derivative and the integral operation of the input signal in the light signal propagation process. The device utilizes the physical properties (refractive index) and the structural dimension of the material to control the amplitude and the phase of the input optical signal, thereby realizing the calculus operation.
The beneficial effects of the invention are as follows: the device has simple structure, high signal processing speed, no external energy source and wide application range, and has wide application in the aspects of photon computer, photo and image storage, signal transmission and the like.
Drawings
Fig. 1 is a schematic diagram of a device for performing calculus operation on an optical signal according to the present invention.
Detailed Description
As shown in fig. 1, the device is composed of a signal source 1, a calculus arithmetic unit 2 and a signal receiver 3. The light signal sent by the signal source 1 can directly irradiate the calculus arithmetic unit 2, the material property and the structure size of the calculus arithmetic unit 2 meet certain conditions, other parameters are not changed, the first derivative, the second derivative and the integral operation of the input signal can be realized by only adjusting the refractive index of the material II in the calculus arithmetic unit 2, and the signal profile received by the signal receiver 3 and the signal profile sent by the signal source 1 form a mathematical calculus relation.
Theoretical basis
If light is propagating in a medium in the positive x-axis direction, the refractive index of the medium is measured in the y-direction
Such materials are known as graded index materials, where η 1 Refractive index, η, at y=0 2 /η 1 ＝[π/(2Lg)] 2 Lg is the distance travelled in the medium. When a light wave propagates in a material with graded index, the graded index material will fourier transform the electric field over a characteristic length Lg, by which property a metamaterial with a calculus operation function can be designed. As shown in fig. 1, the calculus calculator 2 is composed of three layers of materials (I, II, and III), and assuming that the wavelength of an incident optical signal is λ and propagates in the positive x-axis direction, the dimensions of the three materials in the x-axis direction are lg= 11.619 λ, Δ=λ/3.012, and Lg, and the dimensions in the y-axis direction are w= 9.876 λ, respectively. The origin of coordinates is located in the middle of the left side. The refractive index of the material I and the material III meets eta I (y)＝-η III (y) =η (y), fourier transform and inverse fourier transform are respectively performed, and the transform performed by the material II is a core transform of the calculus operator 2, and is named G (y). When the magnitude E (y) of the electric field intensity of the incident optical signal is input to the left end of the material I, the right end of the material I outputs Fourier of E (y)Transformation, i.e.)>
Wherein->
Representing the Fourier transform, the Fourier variable k y Belongs to the same region as y, so k y Proportional to y. Since the transformation performed by material II is G (y), the output function of material II is +.>
At the same time, since material III performs the inverse Fourier transform, the function of the final exit end should be +.>
If the derivative operation is implemented on the input electric field intensity, there are
The above two sides are subjected to Fourier transform, and the method comprises
According to the differential properties of the Fourier transform
The above method can be used as
From equations (2) and (3), the transformation function G (y) = (ik) of material II can be determined y ) n ∝(-iy) n (taking k according to debug result) y C-y). Since the dimension of the material along the y direction is W, the origin of coordinates is located at the center of W, so the maximum value of the y direction is y 0 =w/2, i.e. normalized function G (y) ≡ (-iy/y) 0 ) n . In order to realize the calculus operation of the optical signal, the refraction of the material II is also requiredThe expression of the rate may take advantage of some properties of electromagnetic waves, in particular as follows:
when the planar lightwave propagates forward along the x-axis, the magnitude E (x) of the electric field strength at x satisfies the following Helmholtz equation
Wherein, the liquid crystal display device comprises a liquid crystal display device,
lambda is the wavelength of the incident wave epsilon r ，μ r The relative permittivity and relative permeability of the medium, respectively. Because the relative permittivity and relative permeability satisfy the relation epsilon between refractive index r μ r ＝(η-iκ) 2 Where η and κ represent the real and imaginary parts of the refractive index, respectively, so k may also be expressed as k= (2pi/λ) (η -iκ). Solving equation (4) to obtain
E(x)＝E 0 e ikx (5)
Wherein E is 0 For the magnitude of the electric field strength at x=0, E (x) is the magnitude of the electric field strength at x. Because the electric field intensity at the left end of the material II is
According to equation (5), the electric field strength after propagation over a distance delta in material II is
Because of->
Then there is
I.e.
In order to make the output electric field proportional to the first derivative of the input electric field, G (y) is taken＝(-iy/y 0 ) According to equation (7), the refractive index of material II should be such that
Similarly, if the second derivative operation is performed on the input function, then G (y) = (-iy/y) is taken 0 ) 2 The refractive index of material II should be such that
I.e.
Where n=1 represents a first derivative operation and n=2 represents a second derivative operation.
For the integration operation, (1) should be modified to
The above two sides are subjected to Fourier transform, and the method comprises
From the integral properties of fourier transforms
As can be derived from equation (12), the function G (y) = (ik) of the material II performing the integration operation y )∝(-iy) -1 Let d be the normalization constant and take d=λ/4, then for the integration operation we can take G (y) = (-iy/d) -1 In order to avoid that the transmission coefficient of the |y| < d region is larger than 1, |y|=d is set as the turning point, and the absolute value of the refractive index of the |y| < d region is assumed to be constant, so that the refractive index expression of the material II that can perform the integral operation is
Wherein sign () is a sign function.
The design scheme of the invention is disclosed above, but the invention is not limited to the above, and other calculus calculation devices obtained by adopting the same thought and method are all within the protection scope of the 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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