Method for Measuring Parameters of One-Dimensional Photonic Crystal Based on Transmitted Goos-Hänchen Shift

Abstract

A method for measuring parameters of a one-dimensional photonic crystal based on the transmitted Goos-Hänchen shift, characterized by comprising the following steps: Step S1: Measuring the spot position information of the transmitted TM polarized wave of the one-dimensional photonic crystal by using a transmitted Goos-Hänchen shift measuring device; Step S2: Obtaining the relationship curve between the incident wavelength and the transmitted Goos-Hänchen shift of the one-dimensional photonic crystal according to the spot position information, and calculating the transmitted Goos-Hänchen shift under the TM polarization wave; Step S3: Establishing an evaluation function for the structural parameters of the one-dimensional photonic crystal, substituting the transmitted Goos-Hänchen shift, the substrate parameters, and the film refractive index information into the evaluation function, and performing inverse calculation, taking the number of periods of the one-dimensional photonic crystal and the thickness of each layer within the period as decision parameters, and judging the accuracy of the solution according to the magnitude of the evaluation function, so as to obtain the structural parameter vector a of the one-dimensional photonic crystal when the evaluation function is the smallest. Effect: It can achieve rapid and non-destructive detection of one-dimensional photonic crystals on any substrate surface.

Description

Technical Field

[0001] The present invention relates to the technical field of measuring structural parameters of photonic crystals, and particularly to a method for measuring parameters of a one-dimensional photonic crystal based on the transmitted Goos-Hänchen shift. Background Art

[0002] A photonic crystal is an optical structure with periodicity. According to the structure of the photonic crystal, it can be divided into one-dimensional photonic crystal, two-dimensional photonic crystal, and three-dimensional photonic crystal structures. Among them, a one-dimensional photonic crystal is composed of two or more dielectrics with different refractive indices, and the permittivity changes periodically only in one direction and is uniform in the other two directions. Due to its photonic bandgap, the light waves in the bandgap are reflected by the structure and cannot propagate in the photonic crystal. Therefore, it is widely used in many fields such as optical communication, photovoltaic cells, sensors, and energy.

[0003] Disadvantages of the prior art: Currently, the prior art usually adopts the cross-sectional morphology method and the ellipsometry method to detect the parameters of one-dimensional photonic crystals. Among them, the ellipsometry method has the problem of film thickness period, which will cause the phenomenon of multiple solutions for the film thickness. And based on the cross-sectional morphology method, a scanning electron microscope or a transmission electron microscope is usually used to characterize the morphology of the cross-section, and combined with an image processing method, the number of film system periods and the thickness of each unit layer are measured. However, this method will cause irreversible damage to the original sample, resulting in the sample being unable to be reused, causing waste of resources. Summary of the Invention

[0004] A method for measuring parameters of a one-dimensional photonic crystal based on the transmitted Goos-Hänchen shift provided by the present invention can achieve rapid and non-destructive detection of one-dimensional photonic crystals on any substrate surface.

[0005] To achieve the above object, a method for measuring parameters of a one-dimensional photonic crystal based on the transmitted Goos-Hänchen shift provided by the present invention is characterized in that it includes the following steps:

[0006] Step S1: Measuring the spot position information of the transmitted TM polarized wave of the one-dimensional photonic crystal: Measuring the spot position information of the transmitted TM polarized wave of the one-dimensional photonic crystal by using a transmitted Goos-Hänchen shift measuring device;

[0007] Step S2: Processing data to obtain the incident wavelength - transmitted Goos-Hänchen shift relationship curve: According to the spot position information, obtaining the incident wavelength - transmitted Goos-Hänchen shift relationship curve of the one-dimensional photonic crystal, and calculating the transmitted Goos-Hänchen shift under the TM polarized wave;

[0008] Step S3: Establishing an evaluation function for the structural parameters of the one-dimensional photonic crystal, substituting the transmitted Goos-Hänchen shift into the evaluation function, performing inversion calculation, judging the accuracy of the solution according to the magnitude of the evaluation function, and obtaining the structural parameter vector a of the one-dimensional photonic crystal when the evaluation function is the smallest;

[0009] a = (d L , d H , N), where N represents the number of periods, and d L represents the thickness of the low-refractive-index layer within a period, and d H represents the thickness of the high-refractive-index layer within a period.

[0010] Through the above design, by collecting the position information of TM-polarized light spots at continuous incident wavelengths and by simultaneously inputting the incident wavelength-transmission Goos-Hänchen shift curve of the one-dimensional photonic crystal, the number of periods of the one-dimensional photonic crystal and the thickness of each layer within a single period can be solved and calculated, achieving a one-time rapid measurement and solution of the structural parameters of the one-dimensional photonic crystal, with the advantages of high efficiency and high precision; at the same time, this method measures the position information of the light spots through a transmission Goos-Hänchen shift measurement device, without the need to use a scanning electron microscope or a transmission electron microscope to characterize the cross-sectional morphology, will not cause damage to the one-dimensional photonic crystal, and can achieve rapid and non-destructive detection of the one-dimensional photonic crystal on any substrate surface.

[0011] Preferably: The structural parameters of the one-dimensional photonic crystal include the number of film system periods N and the thickness d L , d H .

[0012] Preferably: In step S2, the calculation process of the transmission Goos-Hänchen shift is as follows:

[0013]

[0014] where S is the characteristic matrix of the one-dimensional photonic crystal, S H is the characteristic matrix of the high-refractive-index layer in the one-dimensional photonic crystal, S L is the characteristic matrix of the low-refractive-index layer in the one-dimensional photonic crystal, λ represents the incident light wavelength, β H is the phase factor of the high-refractive-index layer, β L is the phase factor of the low-refractive-index layer, N is the number of periods, q H is the optical transfer coefficient of the high-refractive-index layer, q L is the optical transfer coefficient of the low-refractive-index layer, d H is the thickness of the high-refractive-index layer, d L is the thickness of the low-refractive-index layer, n H is the refractive index of the high-refractive-index layer, n L is the refractive index of the low-refractive-index layer, θ0 is the angle of incidence on the substrate, n0 is the refractive index of the substrate, and i is the imaginary part;

[0015] For TM-polarized waves, the optical transfer coefficient q f , the transmission coefficient t TM, the transmission phase φ TM and the transmission Goos-Hänchen shift can be respectively expressed as:

[0016]

[0017] φ TM = arg(t TM ) (8)

[0018]

[0019] where ε f represents the dielectric constant of the f layer, q0 represents the optical transfer coefficient of the substrate, and q m represents the optical transfer constant of the dielectric layer.

[0020] Preferably: in the step S3, the evaluation function determines the accuracy of the solution by comparing the difference between the transmission Goos-Hänchen shift obtained by the inversion calculation and the transmission Goos-Hänchen shift measured experimentally. The smaller the difference between the transmission Goos-Hänchen shift obtained by the inversion calculation and the transmission Goos-Hänchen shift measured experimentally, the higher the accuracy of the solution; the larger the difference, the lower the accuracy of the solution.

[0021] Preferably: in the step S3, the expression of the evaluation function is as follows:

[0022]

[0023] where Q is the total number of incident wavelengths involved, represents the transmission Goos-Hänchen shift under the TM polarized wave obtained by the inversion calculation, represents the transmission Goos-Hänchen shift of the i-th reference point under the TM polarized wave extracted from the experimentally measured transmission Goos-Hänchen shift curve; a represents the structural parameter vector.

[0024] Preferably: in the step S3, the refractive index of the high refractive index layer is greater than 2.0, and the refractive index range of the low refractive index layer is [1.3, 1.5].[[]END]]

[0025] Compared with the prior art, the beneficial effects of the present invention are:

[0026] (1) By collecting the transmission Goos-Hänchen shift information of the one-dimensional photonic crystal at different incident wavelengths, this process measures the spot position information through the transmission Goos-Hänchen shift measurement device, without the need to use a scanning electron microscope or a transmission electron microscope to perform morphological characterization on the cross-section, and will not cause damage to the one-dimensional photonic crystal, and can realize the rapid and non-destructive detection of the one-dimensional photonic crystal on any substrate surface.

[0027] (2) Measure by using a fixed incident angle with a continuous incident wavelength, which is convenient and fast. Select the transmission Goos-Hänchen shift characterization mode, solve the deficiencies of existing optical thin film structure detection methods, and provide a new idea for realizing the rapid and high-precision calculation of one-dimensional photonic crystal parameters;

[0028] (3) The present invention provides effective theoretical guidance and reference for non-destructively detecting the thickness of multi-layer thin films, and has the characteristics of good detection effect and strong applicability. Description of the Drawings

[0029] Figure 1 is the overall flowchart of the present invention;

[0030] Figure 2 is the schematic diagram of the one-dimensional photonic crystal structure in the embodiment;

[0031] Figure 3 is the comparison diagram of the incident wavelength - transmission Goos-Hänchen shift curve obtained in the embodiment and the curve obtained by calculation. Detailed Embodiments

[0032] The present invention will be further described in detail below with reference to the drawings and specific examples. The following examples or drawings are used to illustrate the present invention, but not to limit the scope of the present invention.

[0033] As Figure 1 shown: A method for measuring one-dimensional photonic crystal parameters based on transmission Goos-Hänchen shift includes the following steps:

[0034] Step S1: Measure the spot position information of the transmitted TM polarized wave of the one-dimensional photonic crystal: Use the transmission Goos-Hänchen shift measurement device to measure the spot position information of the transmitted TM polarized wave of the one-dimensional photonic crystal;

[0035] Step S2: Process the data to obtain the incident wavelength - transmission Goos-Hänchen shift relationship curve: According to the spot position information, obtain the incident wavelength - transmission Goos-Hänchen shift relationship curve of the one-dimensional photonic crystal, and calculate the transmission Goos-Hänchen shift under TM polarization;

[0036] Step S3: Establish an evaluation function for the structural parameters of the one-dimensional photonic crystal, substitute the transmission Goos-Hänchen shift into the evaluation function, perform inversion calculation, judge the accuracy of the solution according to the magnitude of the evaluation function, and obtain the structural parameter vector a of the one-dimensional photonic crystal when the evaluation function is minimized;

[0037] a = (d L , d H , N), where N represents the number of periods, d L represents the thickness of the low-refractive-index layer within a period, and d H represents the thickness of the high-refractive-index layer within a period.

[0038] The structural parameters of the one-dimensional photonic crystal include the number of film system periods N and the thickness d of each refractive index layer within the period L , d H .

[0039] In step S2, the calculation process of the transmitted Goos-Hänchen shift is as follows:

[0040]

[0041] where S is the characteristic matrix of the one-dimensional photonic crystal, S H is the characteristic matrix of the high refractive index layer in the one-dimensional photonic crystal, S L is the characteristic matrix of the low refractive index layer in the one-dimensional photonic crystal, λ represents the wavelength of the incident light, β H is the phase factor of the high refractive index layer, β L is the phase factor of the low refractive index layer, N is the number of periods, q H is the optical transfer coefficient of the high refractive index layer, q L is the optical transfer coefficient of the low refractive index layer, d H is the thickness of the high refractive index layer, d L is the thickness of the low refractive index layer, n H is the refractive index of the high refractive index layer, n L is the refractive index of the low refractive index layer, θ0 is the angle of incidence on the substrate, n0 is the refractive index of the substrate, and i is the imaginary part;

[0042] For TM polarized waves, the optical transfer coefficient q f , the transmission coefficient t TM , the transmission phase φ TM and the transmitted Goos-Hänchen shift can be respectively expressed as:

[0043]

[0044] φ TM = arg(t TM )(8)

[0045]

[0046] where ε f represents the dielectric constant of the f layer, q0 represents the optical transfer coefficient of the substrate, and q m represents the optical transfer constant of the dielectric layer.

[0047] In the step S3, the evaluation function determines the accuracy of the solution by comparing the difference between the transmitted Goos-Hänchen shift obtained through inversion calculation and the transmitted Goos-Hänchen shift measured experimentally. The smaller the difference between the transmitted Goos-Hänchen shift obtained through inversion calculation and the transmitted Goos-Hänchen shift measured experimentally, the higher the accuracy of the solution; the larger the difference, the lower the accuracy of the solution.

[0048] In the step S3, the expression of the evaluation function is as follows:

[0049]

[0050] where Q is the total number of incident wavelengths involved, represents the transmitted Goos-Hänchen shift under TM polarization obtained through inversion calculation, represents the transmitted Goos-Hänchen shift of the i-th reference point under TM polarization extracted from the experimentally measured transmitted Goos-Hänchen shift curve; a represents the structural parameter vector.

[0051] As Figure 2 shown: The one-dimensional photonic crystal is made by alternately stacking high-refractive-index TiO2 film layers and low-refractive-index SiO2 film layers on a BK7 glass substrate. In this embodiment, the medium is selected as air. When the medium layer is other substances, the corresponding medium refractive index values can be used. The incident wavelength is selected as [450, 600] nm, the solution domain of d L is (0, 400] nm, the solution domain of d H is (0, 200] nm, and the solution domain of N is (0, 10]. Then, according to the incident wavelength-transmitted Goos-Hänchen shift obtained in the experiment, substituting it into the evaluation function, the number of periods N of the one-dimensional photonic crystal is obtained as 5 when the evaluation function is at its minimum value, d L is 236.3 nm, d H is 127.5 nm. It can be seen from Figure 3 that the fitted transmitted Goos-Hänchen shift curve is almost the same as the curve obtained experimentally, indicating that the structural parameters of the one-dimensional photonic crystal obtained by the present invention are reliable and effective.

[0052] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention can have various modifications and changes. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for measuring the parameters of a one-dimensional photonic crystal based on the transmitted Goos-Hänchen shift, characterized in that It includes the following steps: Step S1: Measuring the spot position information of the transmitted TM polarized wave of the one-dimensional photonic crystal: Using the transmitted Goos-Hänchen shift measurement device to measure the spot position information of the transmitted TM polarized wave of the one-dimensional photonic crystal; Step S2: Processing the data to obtain the incident wavelength - transmitted Goos-Hänchen shift relationship curve: According to the spot position information, obtain the incident wavelength - transmitted Goos-Hänchen shift relationship curve of the one-dimensional photonic crystal, and calculate the transmitted Goos-Hänchen shift under the TM polarized wave; Step S3: Establish an evaluation function for the structural parameters of the one-dimensional photonic crystal, substitute the transmitted Goos-Hänchen shift into the evaluation function, perform inversion calculation, judge the accuracy of the solution according to the size of the evaluation function, and obtain the structural parameter vector a of the one-dimensional photonic crystal when the evaluation function is the smallest; a = (d L , d H , N), where N represents the number of periods, and d L represents the thickness of the low-refractive-index layer within a period, and d H represents the thickness of the high-refractive-index layer within a period; The expression of the evaluation function is as follows: where Q is the total number of incident wavelengths involved, (i,a) represents the transmitted Goos-Hänchen shift under TM polarization obtained by inversion calculation, (i) represents the transmitted Goos-Hänchen shift of the i-th reference point under TM polarization extracted from the experimentally measured transmitted Goos-Hänchen shift curve; a represents the structural parameter vector.

2. The one-dimensional photonic crystal parameter measurement method based on the transmitted Goos-Hänchen shift according to claim 1, wherein: The structural parameters of the one-dimensional photonic crystal include the number of film system periods N and the thicknesses d of each refractive index layer within the period L , d H .

3. The one-dimensional photonic crystal parameter measurement method based on the transmitted Goos-Hänchen shift according to claim 1, characterized in that: In step S2, the calculation process of the transmitted Goos-Hänchen shift is as follows: Among them, S is the characteristic matrix of the one-dimensional photonic crystal, S 11 , S 12 , S 21 , S 22 represent four elements in the matrix S, S H is the characteristic matrix of the high refractive index layer in the one-dimensional photonic crystal, S L is the characteristic matrix of the low refractive index layer in the one-dimensional photonic crystal, λ represents the wavelength of the incident light, β H is the phase factor of the high refractive index layer, β L is the phase factor of the low refractive index layer, N is the number of periods, q H is the optical transfer coefficient of the high refractive index layer, q L is the optical transfer coefficient of the low refractive index layer, d H is the thickness of the high refractive index layer, d L is the thickness of the low refractive index layer; n H is the refractive index of the high refractive index layer, n L is the refractive index of the low refractive index layer, θ0 is the angle incident on the substrate, n0 is the refractive index of the substrate, and i is the imaginary part; For TM-polarized waves, the optical transmission coefficient q f , the transmission coefficient t TM , the transmission phase φ TM and the transmission Goos-Hänchen shift are respectively expressed as: φ TM = arg(t TM ) (8) Among them, ε f represents the dielectric constant of the f layer, q0 represents the optical transfer coefficient of the substrate, and q m represents the optical transfer constant of the dielectric layer, H represents the high refractive index layer, L represents the low refractive index layer, and m represents the dielectric layer.

4. The method for measuring one-dimensional photonic crystal parameters based on the transmitted Goos-Hänchen shift according to claim 3, wherein: In step S3, the evaluation function judges the accuracy of the solution by comparing the difference between the transmitted Goos-Hänchen shift obtained by inversion calculation and the experimentally measured transmitted Goos-Hänchen shift. The smaller the difference between the transmitted Goos-Hänchen shift obtained by inversion calculation and the experimentally measured transmitted Goos-Hänchen shift, the higher the accuracy of the solution; the larger the difference, the lower the accuracy of the solution.

5. The method for measuring one-dimensional photonic crystal parameters based on the transmitted Goos-Hänchen shift according to claim 1, wherein: In step S3, the refractive index of the high refractive index layer is greater than 2.0, and the refractive index range of the low refractive index layer is [1.3, 1.5].

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