One-dimensional photonic crystal parameter measurement method based on transmission Goos-Hanchen shift

Abstract

A one-dimensional photonic crystal parameter measurement method based on transmission Goos-Haenchen shift is characterized by comprising the following steps: S1, measuring light spot position information of transmission TM polarized waves of a one-dimensional photonic crystal by using a transmission Goos-Haenchen shift measurement device; s2, according to the light spot position information, obtaining an incident wavelength-transmission Goos-Haenchen shift relation curve of the one-dimensional photonic crystal, and calculating to obtain transmission Goos-Haenchen shift under TM polarized waves; s3, establishing an evaluation function of parameters of the one-dimensional photonic crystal structure, substituting the transmission Goos-Haenchen shift, the substrate parameters and the film refractive index information into the evaluation function, carrying out inversion calculation, taking the cycle number of the one-dimensional photonic crystal and the thickness of each layer in the cycle as decision parameters, and judging the accuracy of a solution according to the size of the evaluation function. And obtaining a structural parameter vector a of the one-dimensional photonic crystal when the evaluation function is minimum. The method has the effect that the one-dimensional photonic crystal on any substrate surface can be quickly and nondestructively detected.

Description

Technical Field

[0001] The invention relates to the technical field of photonic crystal structure parameter measurement, and in particular to a one-dimensional photonic crystal parameter measurement method based on transmission Goos-Hanchen shift. Background Art

[0002] Photonic crystals are periodic optical structures. According to their structures, they can be divided into one-dimensional photonic crystals, two-dimensional photonic crystals, and three-dimensional photonic crystal structures. One-dimensional photonic crystals are composed of two or more dielectric constants with different refractive indices that change periodically in only one direction and are uniform in the other two directions. Because they have a photonic bandgap, light waves in the bandgap are reflected by the structure and cannot propagate in the photonic crystal. Therefore, they are widely used in optical communications, photovoltaic cells, sensors, energy, and many other fields.

[0003] Disadvantages of existing technologies: Currently, existing technologies usually use cross-sectional morphology and ellipsometry to realize one-dimensional photonic crystal parameter detection. Among them, the ellipsometry method has the problem of film thickness period, which will cause the thickness of the film to have multiple solutions. Based on the cross-sectional morphology method, a scanning electron microscope or a transmission electron microscope is usually used to characterize the cross section, and then the number of film system periods and the thickness of each unit layer are measured in combination with image processing methods. However, this method requires irreversible damage to the original sample, which makes the sample unable to be reused, resulting in a waste of resources. Summary of the invention

[0004] The present invention provides a one-dimensional photonic crystal parameter measurement method based on transmission Goos-Hanchen shift, which can realize rapid and non-destructive detection of one-dimensional photonic crystals on any substrate surface.

[0005] To achieve the above object, the present invention provides a one-dimensional photonic crystal parameter measurement method based on transmission Goos-Hanchen shift, the key of which is to include the following steps:

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

[0007] Step S2: Data processing to obtain an incident wavelength-transmission Goos-Hanchen shift relationship curve: According to the light spot position information, the incident wavelength-transmission Goos-Hanchen shift relationship curve of the one-dimensional photonic crystal is obtained, and the transmission Goos-Hanchen shift under TM polarization wave is calculated;

[0008] Step S3: establishing an evaluation function of the structural parameters of the one-dimensional photonic crystal, substituting the transmission Goos-Hanchen shift into the evaluation function, performing an inversion calculation, judging the accuracy of the solution according to the size of the evaluation function, and obtaining the structural parameter vector a of the one-dimensional photonic crystal when the evaluation function is minimum;

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

[0010] Through the above design, by collecting the TM polarization wave light spot position information under continuous incident wavelength, and by simultaneously inputting the incident wavelength-transmission Goos-Hanchen shift curve of the one-dimensional photonic crystal, the period number of the one-dimensional photonic crystal and the thickness of each layer in a single period can be solved, so as to realize a one-time rapid measurement and solution of the structural parameters of the one-dimensional photonic crystal, and has the advantages of high efficiency and high accuracy; at the same time, the method measures the light spot position information through a transmission Goos-Hanchen shift measuring device, and there is no need to use a scanning electron microscope or a transmission electron microscope to characterize the cross-section morphology, and will not cause damage to the one-dimensional photonic crystal, and can realize rapid and non-destructive detection of one-dimensional photonic crystals on any substrate surface.

[0011] Preferably, the structural parameters of the one-dimensional photonic crystal include the number of film periods N and the thickness d of each refractive index layer within the period. L d H .

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

[0013]

[0014]

[0015]

[0016]

[0017]

[0018] Among them, 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, B 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 transmission 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, nH 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 to the substrate, n0 is the refractive index of the substrate, and i is the imaginary part;

[0019] For TM polarized waves, the optical transfer coefficient q in a one-dimensional photonic crystal is f , transmission coefficient t TM , transmission phase φ TM and the transmission Goos-Hanchen shift Can be expressed as:

[0020]

[0021]

[0022] φ TM =arg(t TM ) (8)

[0023]

[0024] Among them, ε f represents the dielectric constant of the f layer, q0 represents the optical transmission coefficient of the substrate, and q m Represents the optical transfer constant of the dielectric layer.

[0025] Preferably, in step S3, the evaluation function determines the accuracy of the solution by comparing the difference between the transmission Goos-Hanchen shift obtained by inversion calculation and the transmission Goos-Hanchen shift measured experimentally. The smaller the difference between the transmission Goos-Hanchen shift obtained by inversion calculation and the transmission Goos-Hanchen shift measured experimentally, the higher the accuracy of the solution; the larger the difference, the lower the accuracy of the solution.

[0026] Preferably, in step S3, the evaluation function is expressed as follows:

[0027]

[0028] Where Q is the total number of incident wavelengths involved, (i,a) represents the transmitted Goos-Hanchen shift of TM polarization wave obtained by inversion calculation, (i) represents the transmitted Gous-Hanchen shift of the i-th reference point under TM polarization wave extracted from the experimentally measured transmitted Gous-Hanchen shift curve; a represents the structural parameter vector.

[0029] Preferably, in step S3, the refractive index of the high refractive index layer is greater than 2.0, and the refractive index of the low refractive index layer is in the range of [1.3, 1.5].

[0030] Compared with the prior art, the present invention has the following beneficial effects:

[0031] (1) By collecting the transmission Goos-Hanchen shift information of a one-dimensional photonic crystal at different incident wavelengths, the transmission Goos-Hanchen shift measuring device is used to measure the light spot position information. There is no need to use a scanning electron microscope or a transmission electron microscope to characterize the cross-section morphology, and no damage will be caused to the one-dimensional photonic crystal. Rapid and non-destructive detection of one-dimensional photonic crystals on any substrate surface can be achieved.

[0032] (2) The measurement is convenient and fast with a continuous incident wavelength and a fixed incident angle. The transmission Goos-Hanchen shift characterization mode is selected to solve the shortcomings of existing optical thin film structure detection methods and provide a new idea for the fast and high-precision solution of one-dimensional photonic crystal parameters.

[0033] (3) The present invention provides effective theoretical guidance and reference for non-destructive testing of the thickness of multi-layer films, and has the characteristics of good testing effect and strong applicability. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 It is the overall flow chart of the present invention;

[0035] Figure 2 A schematic diagram of a one-dimensional photonic crystal structure in an embodiment;

[0036] Figure 3 It is a comparison diagram of the incident wavelength-transmission Goos-Hanchen shift curve obtained in the embodiment and the curve obtained by calculation. DETAILED DESCRIPTION

[0037] The present invention is further described in detail below in conjunction with the accompanying drawings and specific examples. The following examples or drawings are used to illustrate the present invention, but are not used to limit the scope of the present invention.

[0038] like Figure 1 As shown: A one-dimensional photonic crystal parameter measurement method based on transmission Goos-Hanchen shift, comprising the following steps:

[0039] Step S1: measuring the light spot position information of the TM polarized wave transmitted by the one-dimensional photonic crystal: using a transmission Goos-Hanchen shift measuring device to measure the light spot position information of the TM polarized wave transmitted by the one-dimensional photonic crystal;

[0040] Step S2: Data processing to obtain an incident wavelength-transmission Goos-Hanchen shift relationship curve: According to the light spot position information, the incident wavelength-transmission Goos-Hanchen shift relationship curve of the one-dimensional photonic crystal is obtained, and the transmission Goos-Hanchen shift under TM polarization wave is calculated;

[0041] Step S3: establishing an evaluation function of the structural parameters of the one-dimensional photonic crystal, substituting the transmission Goos-Hanchen shift into the evaluation function, performing an inversion calculation, judging the accuracy of the solution according to the size of the evaluation function, and obtaining the structural parameter vector a of the one-dimensional photonic crystal when the evaluation function is minimum;

[0042] a=(d L , d H , N), where N represents the number of cycles, d L represents the thickness of the low refractive index layer within the period, d H Represents the thickness of the high refractive index layer within the period.

[0043] The structural parameters of the one-dimensional photonic crystal include the number of film periods N and the thickness d of each refractive index layer within the period. L d H .

[0044] In step S2, the calculation process of the transmission Goos-Hanchen shift is as follows:

[0045]

[0046]

[0047]

[0048]

[0049]

[0050] Among them, 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, B 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 transmission 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 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 to the substrate, n0 is the refractive index of the substrate, and i is the imaginary part;

[0051] For TM polarized waves, the optical transfer coefficient q in a one-dimensional photonic crystal is f , transmission coefficient t TM , transmission phase φTM and the transmission Goos-Hanchen shift Can be expressed as:

[0052]

[0053]

[0054] φ TM =arg(t TM ) (8)

[0055]

[0056] Among them, ε f represents the dielectric constant of the f layer, q0 represents the optical transmission coefficient of the substrate, and q m Represents the optical transfer constant of the dielectric layer.

[0057] In step S3, the evaluation function judges the accuracy of the solution by comparing the difference between the transmission Goos-Hanchen shift obtained by inversion calculation and the transmission Goos-Hanchen shift measured experimentally. The smaller the difference between the transmission Goos-Hanchen shift obtained by inversion calculation and the transmission Goos-Hanchen shift measured experimentally, the higher the accuracy of the solution; the larger the difference, the lower the accuracy of the solution.

[0058] In step S3, the evaluation function is expressed as follows:

[0059]

[0060] Where Q is the total number of incident wavelengths involved, (i,a) represents the transmitted Goos-Hanchen shift of TM polarization wave obtained by inversion calculation, (i) represents the transmitted Gous-Hanchen shift of the i-th reference point under TM polarization wave extracted from the experimentally measured transmitted Gous-Hanchen shift curve; a represents the structural parameter vector.

[0061] like Figure 2 As shown: The one-dimensional photonic crystal is made of high refractive index TiO2 film layers and low refractive index SiO2 film layers alternately stacked on a BK7 glass substrate. The medium in this embodiment is air. When the medium layer is other substances, the corresponding medium refractive index value can be used. The incident wavelength is [450,600]nm, d L The solution domain (0,400]nm, d H The solution domain of (0,200]nm, the solution domain of N (0,10]. Then, according to the incident wavelength-transmission Goos-Hanchen shift obtained in the experiment, it is substituted into the evaluation function, and the period number N of the one-dimensional photonic crystal is obtained to be 5 when the evaluation function is minimum. L 236.3nm,dH is 127.5nm. Figure 3 It can be seen that the transmission Goos-Hanchen shift curve obtained by fitting is almost consistent with the experimental curve, indicating that the one-dimensional photonic crystal structure parameters obtained by the present invention are reliable and effective.

[0062] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A one-dimensional photonic crystal parameter measurement method based on transmission Goos-Hanchen shift, characterized in that: The following steps are involved: Step S1: measuring the light spot position information of the TM polarized wave transmitted by the one-dimensional photonic crystal: using a transmission Goos-Hanchen shift measuring device to measure the light spot position information of the TM polarized wave transmitted by the one-dimensional photonic crystal; Step S2: Data processing to obtain an incident wavelength-transmission Goos-Hanchen shift relationship curve: According to the light spot position information, the incident wavelength-transmission Goos-Hanchen shift relationship curve of the one-dimensional photonic crystal is obtained, and the transmission Goos-Hanchen shift under TM polarization wave is calculated; Step S3: establishing an evaluation function of the structural parameters of the one-dimensional photonic crystal, substituting the transmission Goos-Hanchen shift into the evaluation function, performing an inversion calculation, judging the accuracy of the solution according to the size of the evaluation function, and obtaining the structural parameter vector a of the one-dimensional photonic crystal when the evaluation function is minimum; a=(d L , d H , N), where N represents the number of cycles, d L represents the thickness of the low refractive index layer within the period, d H Represents the thickness of the high refractive index layer within the period.

2. The one-dimensional photonic crystal parameter measurement method based on transmission Goos-Hanchen shift according to claim 1, characterized in that: The structural parameters of the one-dimensional photonic crystal include the number of film periods N and the thickness d of each refractive index layer within the period. L d H .

3. The one-dimensional photonic crystal parameter measurement method based on transmission Goos-Hanchen shift according to claim 1, characterized in that: In step S2, the calculation process of the transmission Goos-Hanchen shift is as follows: Among them, 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, B 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 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 to the substrate, n0 is the refractive index of the substrate, and i is the imaginary part; For TM polarized waves, the optical transfer coefficient q in a one-dimensional photonic crystal is f , transmission coefficient t TM , transmission phase φ TM and the transmission Goos-Hanchen shift Can be expressed as: Among them, ε f represents the dielectric constant of the f layer, q0 represents the optical transmission coefficient of the substrate, and q m Represents the optical transfer constant of the dielectric layer.

4. The one-dimensional photonic crystal parameter measurement method based on transmission Goos-Hanchen shift according to claim 3, characterized in that: In step S3, the evaluation function judges the accuracy of the solution by comparing the difference between the transmission Goos-Hanchen shift obtained by inversion calculation and the transmission Goos-Hanchen shift measured experimentally. The smaller the difference between the transmission Goos-Hanchen shift obtained by inversion calculation and the transmission Goos-Hanchen shift measured experimentally, the higher the accuracy of the solution; the larger the difference, the lower the accuracy of the solution.

5. The one-dimensional photonic crystal parameter measurement method based on transmission Goos-Hanchen shift according to claim 4, characterized in that: In step S3, the evaluation function is expressed as follows: Where Q is the total number of incident wavelengths involved, represents the transmitted Goos-Hanchen shift of TM polarization wave obtained by inversion calculation, represents the transmitted Gous-Hanchen shift of the i-th reference point under TM polarization wave extracted from the experimentally measured transmitted Gous-Hanchen shift curve; a represents the structural parameter vector.

6. The one-dimensional photonic crystal parameter measurement method based on transmission Goos-Hanchen shift according to claim 1, characterized in that: In step S3, the refractive index of the high refractive index layer is greater than 2.0, and the refractive index of the low refractive index layer is in the range of [1.3, 1.5].

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