CN109580552A - With the axial heteropical optical material spectrum property calculation method of refractive index - Google Patents

With the axial heteropical optical material spectrum property calculation method of refractive index Download PDF

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CN109580552A
CN109580552A CN201811525585.3A CN201811525585A CN109580552A CN 109580552 A CN109580552 A CN 109580552A CN 201811525585 A CN201811525585 A CN 201811525585A CN 109580552 A CN109580552 A CN 109580552A
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refractive index
optical material
equivalent
polarization
follows
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刘华松
刘丹丹
姜玉刚
季勤
季一勤
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Tianjin Jinhang Institute of Technical Physics
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/17—Systems in which incident light is modified in accordance with the properties of the material investigated
    • G01N21/55—Specular reflectivity
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/17—Systems in which incident light is modified in accordance with the properties of the material investigated
    • G01N21/59—Transmissivity
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/17—Systems in which incident light is modified in accordance with the properties of the material investigated
    • G01N21/55—Specular reflectivity
    • G01N2021/558—Measuring reflectivity and transmission

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Abstract

The invention discloses one kind to have the axial heteropical optical material spectrum property calculation method of refractive index, for calculating the spectral-transmission characteristics and reflection characteristic and absorption characteristic of parallel flat optical material.Due to the continuity of refractive index inhomogeneity, this method is to be sliced optical material in axially vertical direction, the light wave transmissions linear superposition relationship of multilayer wall, therefore can calculate the spectral characteristic under Refractive Index of Material heterogeneity by this method.This method has universality for the design of Optical System Design and optical thin film element.

Description

With the axial heteropical optical material spectrum property calculation method of refractive index
Technical field
The invention belongs to optical technical fields, more particularly to the spectral analysis technique of optical element and optical thin film, tool Body, which is related to one kind, has refractive index axially heteropical optical material spectrum property calculation method.
Background technique
Under normal conditions, for coated optical element, optical property is total to by the performance of optical substrate material and film With what is determined, and its performance is directly determined by the performance of optical substrate material without film optical element, is set in conventional optical system In meter, optical substrate material is considered as ideal homogeneous material, however, due to the heterogeneity of optical substrate material, especially Axial heterogeneity, not only influences the optical property of of optical element itself, while heterogeneous material is considered as desired homogeneous material Material will produce bigger effect Optical System Design precision.With the raising of Optical System Design precision, to optical element material The demand of heteropical distribution situation is also further strong, meanwhile, for coated optical element, grasp the non-homogeneous of optical material Property after the optical property of optical element can preferably be improved using the method for optimization film design, to further increase optical system System precision.
In conclusion how to solve material non-uniformity bring spectrum under the demand of high-precision optical element development The characterization problems of characteristic variations become one of the major issue in current high-precision optical element manufacturing field.
Summary of the invention
(1) goal of the invention
The purpose of the present invention is: optical material how is obtained with spectral characteristic in the case where longitudinal refractive index heterogeneity Calculating and problem analysis.
(2) technical solution
In order to solve the above technical problem, the present invention provides with the axial heteropical optical material spectrum of refractive index Energy calculation method comprising following steps:
S1: setting optical material surface is smooth；
S2: the heterogeneity equation of complex refractivity index is determined；
S3: the refractive index on two surfaces of optical material is calculated separately according to heterogeneity equation；
S4: being θ in incidence angle0, incident medium refractive index be N0In the case where, calculate incident medium and optical material Two surface equivalent refractive indexs；
S5: in incidence angle θ0In the case where, the reflectivity of calculating optical material first surface；
S6: in incidence angle θ0In the case where, the reflectivity of calculating optical material second surface；
S7: the optical material of parallel flat is subjected to planar slice, the refractive index complex refractivity index of Calculation Plane slice；
S8: the equivalent refractive index and equivalent extinction coefficient of Calculation Plane slice；
S9: the equivalent refractive index and extinction coefficient of substrate are calculated according to step S8；
S10: transmitance in longitudinal refractive index optical material heterogeneous is calculated；
S11: linear superposition theorem, the spectral characteristic of calculating optical material, including reflectivity and transmissivity are based on.
Wherein, in the step S2, heterogeneity equation is parabolic equation, as shown in formula (1):
N (λ, x)=Nmat(λ)+B1x+B2x2+B3x3+B4x5 (1)
N (λ, x) is the refractive index of arbitrary plane position x in material, Nmat(λ) is the zero defect refractive index of material, B1~B4 For the coefficient of refractive index gradient equation.
Wherein, in the step S3, the refractive index of optical material first surface is Na(λ)=na(λ)-i×ka(λ), second The refractive index on surface is Nb(λ)=nb(λ)-i×kb(λ)；The refractive index of first surface and the refractive index of second surface are multiple Number.
Wherein, in the step S4, two surface equivalent refractive indexs of incident medium and optical material calculate as follows:
The equivalent refractive index of incident medium are as follows:
The equivalent refractive index on first surface of optical material are as follows:
The equivalent refractive index on second surface of optical material are as follows:
Determine that refraction angle uses Fresnel law:
N0 cosθ0=Na sinθa=Nb sinθb (5)
Wherein, N0,s,pIndicate the equivalent refractive index of S- polarization, P- polarization, Na,s,pIndicate material first surface S- polarization, P- The equivalent refractive index of polarization, θaFor the refraction angle of first surface, Nb,s,pIt is equivalent to indicate that material second surface S- polarization, P- polarize Refractive index, θbFor the refraction angle of second surface.
Wherein, in the step S5, in incidence angle θ0In the case where, the reflectivity of calculating optical material first surface:
Na,sAnd Na,pRespectively indicate the S- polarization of first surface and the equivalent refractive index of P- polarization, N0,sAnd N0,pIt respectively indicates The S- polarization of incident medium and the equivalent refractive index of P- polarization.
Wherein, in the step S6, in incidence angle θ0In the case where, calculate the reflectivity of second surface:
Nb,sAnd Nb,pRespectively indicate the S- polarization of second surface and the equivalent refractive index of P- polarization.
Wherein, in the step S7, the refractive index complex refractivity index N of Calculation Plane slicej=nj-ikj, njAnd kjRespectively The refractive index and extinction coefficient of j layers of slice；Parallel flat material with a thickness of ds, the optical material of parallel flat is subjected to plane Slice, the section number of plies be N, every layer slice with a thickness of dsThe thickness of/N, planar slice are not more than λ0, λ0For operation wavelength or The central wavelength of operating spectrum band, the then complex refractivity index that jth layer is sliced are as follows:
Wherein, in the step S8, the equivalent refractive index of jth layer slice and the calculating process of equivalent extinction coefficient are as follows:
Light propagation angle in jth layer sliceMeet the Fresnel law of refraction:
Birefringence angle θ in jth layerjSine and cosine be expressed as follows:
sinθj=s'+js " cos θj=c'+jc " (9)
The equivalent refractive index of jth layer sliceWrite as following formula:
Jth layer is sliced equivalent extinction coefficient K and equivalent refractive indexMeet following relational expression:
Variable in formula (11) is the function of wavelength.
Wherein, in the step S9, equivalent refractive index and the delustring system of substrate are calculated by formula (8)~(11) Number, therefore any angle θ0Direction is incident, the interior transmitance u of jth layer slicejExpression formula is as follows:
In formula (12), dsFor the geometric thickness of substrate, λ is wavelength.Jth layer can be obtained by formula (8)~(12) The interior transmitance u of slicej。
Wherein, the calculation expression of transmitance U is such as in the step S10, in longitudinal refractive index optical material heterogeneous Under:
In step S11, it is based on linear superposition theorem, the spectrum of optical material is calculated from formula (5), (6) and (12) Characteristic difference is as follows:
Reflectivity R (λ) are as follows:
Transmissivity T (λ) are as follows:
(3) beneficial effect
There is refractive index axially heteropical optical material spectrum property calculation method provided by above-mentioned technical proposal, Certain thickness base material is subjected to planar slice layering, obtains whole interior transmission by calculating the interior transmitance of layering Rate, while using the reflective spectral property on two surfaces, the linear superposition theorem based on light wave obtains parallel flat optical material Spectral characteristic, this method has universality for transparent substrates or translucent base.
Detailed description of the invention
The optical constant of Fig. 1 zinc sulphide materials
The refractive index inhomogeneity of Fig. 2 zinc sulphide materials (with a thickness of 8mm)
The reflective spectral property of Fig. 3 zinc sulphide materials (with a thickness of 8mm, 0 degree of incidence angle)
The transmitted spectrum characteristic of Fig. 4 zinc sulphide materials (with a thickness of 8mm, 0 degree of incidence angle)
The reflective spectral property of Fig. 5 zinc sulphide materials (with a thickness of 8mm, 45 degree of incidence angles)
The transmitted spectrum characteristic of Fig. 6 zinc sulphide materials (with a thickness of 8mm, 45 degree of incidence angles)
Specific embodiment
To keep the purpose of the present invention, content and advantage clearer, with reference to the accompanying drawings and examples, to of the invention Specific embodiment is described in further detail.
The present invention have refractive index axially heteropical optical material spectrum property calculation method the following steps are included:
(1) setting optical material surface is smooth；
(2) determine the heterogeneity equation of complex refractivity index, the equation either be linearly also possible to parabola etc., below By taking parabolic equation as an example:
N (λ, x)=Nmat(λ)+B1x+B2x2+B3x3+B4x5 (1)
N (λ, x) is the refractive index of arbitrary plane position x in material, Nmat(λ) is the zero defect refractive index of material, B1~B4 For the coefficient of refractive index gradient equation.
(3) refractive index on two surfaces of optical material, the refractive index of first surface are calculated separately out according to above-mentioned equation For Na(λ)=na(λ)-i×ka(λ), the refractive index of second surface are Nb(λ)=nb(λ)-i×kb(λ)；The refraction of first surface Rate and the refractive index of second surface are plural number.
(4) in incidence angle θ0In the case where, the refractive index of incident medium is N0, then two of incident medium and optical material Surface equivalent refractive index calculation method is as follows:
The equivalent refractive index of incident medium are as follows:
The equivalent refractive index on first surface of optical material are as follows:
The equivalent refractive index on second surface of optical material are as follows:
Determine that refraction angle uses Fresnel law:
N0 cosθ0=Na sinθa=Nb sinθb (5)
Wherein, N0,s,pIndicate the equivalent refractive index of S- polarization, P- polarization, Na,s,pIndicate material first surface S- polarization, P- The equivalent refractive index of polarization, θaFor the refraction angle of first surface, Nb,s,pIt is equivalent to indicate that material second surface S- polarization, P- polarize Refractive index, θbFor the refraction angle of second surface.
(5) in incidence angle θ0In the case where, calculate the reflectivity of first surface:
Na,sAnd Na,pRespectively indicate the S- polarization of first surface and the equivalent refractive index of P- polarization, N0,sAnd N0,pIt respectively indicates The S- polarization of incident medium and the equivalent refractive index of P- polarization.
(6) in incidence angle θ0In the case where, calculate the reflectivity of second surface:
Nb,sAnd Nb,pRespectively indicate the S- polarization of second surface and the equivalent refractive index of P- polarization.
(7) the refractive index complex refractivity index N of Calculation Plane slicej=nj-ikj, njAnd kjThe respectively refractive index of jth layer slice And extinction coefficient.Parallel flat material with a thickness of ds, the optical material of parallel flat is subjected to planar slice, the section number of plies is N, every layer slice with a thickness of dsThe thickness of/N, planar slice are not more than λ0, λ0For operation wavelength or the middle cardiac wave of operating spectrum band It is long.The then complex refractivity index of jth layer slice are as follows:
(8) equivalent refractive index and equivalent extinction coefficient of jth layer slice are calculated.
Light wave is propagated in a manner of non uniform wave in absorbing medium, and equal-amplitude surface and equiphase surface separation are not overlapped, they distinguish There is respective normal direction, only when normal incidence, two normal directions are only coincidence.Therefore, using equal-amplitude surface and etc. phases The transmission of the normal direction characterization light wave in face, uses equivalent refractive index in absorbing medium(mould of equiphase surface normal), etc. Imitate extinction coefficient K (mould of equal-amplitude surface normal) and light true propagation angleCharacterize the transport behavior of light wave.
Light propagation angle in jth layer sliceMeet the Fresnel law of refraction:
Birefringence angle θ in jth layerjSine and cosine be expressed as follows:
sinθj=s'+js " cos θj=c'+jc " (9)
The equivalent refractive index of jth layer sliceIt can be write as following formula:
Jth layer is sliced equivalent extinction coefficient K and equivalent refractive indexMeet following relational expression:
Variable in formula (11) is the function of wavelength.
(9) equivalent refractive index and extinction coefficient of substrate, therefore random angle can be calculated by formula (8)~(11) Spend θ0Direction is incident, the interior transmitance u of jth layer slicejExpression formula is as follows:
In formula (12), dsFor the geometric thickness of substrate, λ is wavelength.Jth layer can be obtained by formula (8)~(12) The interior transmitance u of slicej。
(10) calculation expression of transmitance U is as follows in longitudinal refractive index optical material heterogeneous:
(11) it is based on linear superposition theorem, the spectral characteristic point of optical material is calculated from formula (5), (6) and (12) It is not as follows:
Reflectivity R (λ) are as follows:
Transmissivity T (λ) are as follows:
Embodiment
Example: Calculation of Spectral of the 8mm zinc sulphide materials at 7-14 μm
(1) optical constant of zinc sulphide materials is as shown in Fig. 1；
(2) 8mm zinc sulphide materials are layered, the number of plies is selected as 1000 layers；
(3) refractive index gradient of zinc sulphide materials is parabolic shape, and the equation coefficient of quartic polynomial is respectively as follows: B1 =-3.9550 × 10-6, B2=6.6235 × 10-4, B3=1.9249 × 10-7, B4=-37.0312 × 10-5；
(4) gradient equations of refractive index is as shown in Fig. 2 under 8 mum wavelengths；
(5) when incidence angle is 0 degree, the reflectance spectrum that zinc sulphide materials are calculated is as shown in Fig. 3, and average reflectance is 0.2021, the average reflectance of material in the ideal case is 0.2196, and the comparison with material without refractive index inhomogeneity is average Reflectivity decline 0.0175；
(6) when incidence angle is 0 degree, the transmitted spectrum that zinc sulphide materials are calculated is as shown in Fig. 4, and average transmittance is 0.6572, the average transmittance of material in the ideal case is 0.6404, and the comparison with material without refractive index inhomogeneity is average Transmissivity increases by 0.0168；
(7) when incidence angle is 45 degree, the reflectance spectrum that zinc sulphide materials are calculated is as shown in Fig. 5, average reflectance It is 0.2086, the average reflectance of material in the ideal case is 0.2245, and the comparison with material without refractive index inhomogeneity is put down Equal reflectivity decline 0.0159；
(8) when incidence angle is 45 degree, the transmitted spectrum that zinc sulphide materials are calculated is as shown in Fig. 6, average transmittance It is 0.6451, the average transmittance of material in the ideal case is 0.6299, and the comparison with material without refractive index inhomogeneity is put down Equal transmissivity increases by 0.0152.
The above is only a preferred embodiment of the present invention, it is noted that for the ordinary skill people of the art For member, without departing from the technical principles of the invention, several improvement and deformations can also be made, these improvement and deformations Also it should be regarded as protection scope of the present invention.

Claims (10)

1. one kind has the axial heteropical optical material spectrum property calculation method of refractive index, which is characterized in that including with Lower step:
S1: setting optical material surface is smooth；
S2: the heterogeneity equation of complex refractivity index is determined；
S3: the refractive index on two surfaces of optical material is calculated separately according to heterogeneity equation；
S4: being θ in incidence angle0, incident medium refractive index be N0In the case where, calculate two of incident medium and optical material Surface equivalent refractive index；
S5: in incidence angle θ0In the case where, the reflectivity of calculating optical material first surface；
S6: in incidence angle θ0In the case where, the reflectivity of calculating optical material second surface；
S7: the optical material of parallel flat is subjected to planar slice, the refractive index complex refractivity index of Calculation Plane slice；
S8: the equivalent refractive index and equivalent extinction coefficient of Calculation Plane slice；
S9: the equivalent refractive index and extinction coefficient of substrate are calculated according to step S8；
S10: transmitance in longitudinal refractive index optical material heterogeneous is calculated；
S11: linear superposition theorem, the spectral characteristic of calculating optical material, including reflectivity and transmissivity are based on.
2. there is refractive index axially heteropical optical material spectrum property calculation method as described in claim 1, it is special Sign is, in the step S2, heterogeneity equation is parabolic equation, as shown in formula (1):
N (λ, x)=Nmat(λ)+B1x+B2x2+B3x3+B4x5 (1)
N (λ, x) is the refractive index of arbitrary plane position x in material, Nmat(λ) is the zero defect refractive index of material, B1~B4For folding Penetrate the coefficient of rate gradient equations.
3. there is refractive index axially heteropical optical material spectrum property calculation method as claimed in claim 2, it is special Sign is, in the step S3, the refractive index of optical material first surface is Na(λ)=na(λ)-i×ka(λ), second surface Refractive index is Nb(λ)=nb(λ)-i×kb(λ)；The refractive index of first surface and the refractive index of second surface are plural number.
4. there is refractive index axially heteropical optical material spectrum property calculation method as claimed in claim 3, it is special Sign is, in the step S4, two surface equivalent refractive indexs of incident medium and optical material calculate as follows:
The equivalent refractive index of incident medium are as follows:
The equivalent refractive index on first surface of optical material are as follows:
The equivalent refractive index on second surface of optical material are as follows:
Determine that refraction angle uses Fresnel law:
N0cosθ0=Nasinθa=Nbsinθb (5)
Wherein, N0,s,pIndicate the equivalent refractive index of S- polarization, P- polarization, Na,s,pIndicate material first surface S- polarization, P- polarization Equivalent refractive index, θaFor the refraction angle of first surface, Nb,s,pIndicate the equivalent refraction of material second surface S- polarization, P- polarization Rate, θbFor the refraction angle of second surface.
5. there is refractive index axially heteropical optical material spectrum property calculation method as claimed in claim 4, it is special Sign is, in the step S5, in incidence angle θ0In the case where, the reflectivity of calculating optical material first surface:
Na,sAnd Na,pRespectively indicate the S- polarization of first surface and the equivalent refractive index of P- polarization, N0,sAnd N0,pRespectively indicate incidence The S- polarization of medium and the equivalent refractive index of P- polarization.
6. there is refractive index axially heteropical optical material spectrum property calculation method as claimed in claim 5, it is special Sign is, in the step S6, in incidence angle θ0In the case where, calculate the reflectivity of second surface:
Nb,sAnd Nb,pRespectively indicate the S- polarization of second surface and the equivalent refractive index of P- polarization.
7. there is refractive index axially heteropical optical material spectrum property calculation method as claimed in claim 6, it is special Sign is, in the step S7, the refractive index complex refractivity index N of Calculation Plane slicej=nj-ikj, njAnd kjRespectively jth layer is cut The refractive index and extinction coefficient of piece；Parallel flat material with a thickness of ds, the optical material of parallel flat is subjected to planar slice, The section number of plies be N, every layer slice with a thickness of dsThe thickness of/N, planar slice are not more than λ0, λ0For operation wavelength or work spectrum The central wavelength of section, the then complex refractivity index that jth layer is sliced are as follows:
8. there is refractive index axially heteropical optical material spectrum property calculation method as claimed in claim 7, it is special Sign is, in the step S8, the equivalent refractive index of jth layer slice and the calculating process of equivalent extinction coefficient are as follows:
Light propagation angle in jth layer sliceMeet the Fresnel law of refraction:
Birefringence angle θ in jth layerjSine and cosine be expressed as follows:
sinθj=s '+js " cos θj=c '+jc " (9)
The equivalent refractive index of jth layer sliceWrite as following formula:
Jth layer is sliced equivalent extinction coefficient K and equivalent refractive indexMeet following relational expression:
Variable in formula (11) is the function of wavelength.
9. there is refractive index axially heteropical optical material spectrum property calculation method as claimed in claim 8, it is special Sign is, in the step S9, the equivalent refractive index and extinction coefficient of substrate is calculated by formula (8)~(11), therefore Any angle θ0Direction is incident, the interior transmitance u of jth layer slicejExpression formula is as follows:
In formula (12), dsFor the geometric thickness of substrate, λ is wavelength.Jth layer slice can be obtained by formula (8)~(12) Interior transmitance uj。
10. there is refractive index axially heteropical optical material spectrum property calculation method as claimed in claim 9, it is special Sign is, in the step S10, the calculation expression of transmitance U is as follows in longitudinal refractive index optical material heterogeneous:
In step S11, it is based on linear superposition theorem, the spectral characteristic of optical material is calculated from formula (5), (6) and (12) It is as follows respectively:
Reflectivity R (λ) are as follows:
Transmissivity T (λ) are as follows:
CN201811525585.3A 2018-12-13 2018-12-13 With the axial heteropical optical material spectrum property calculation method of refractive index Pending CN109580552A (en)

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CN104792282A (en) * 2015-04-21 2015-07-22 中国科学院光电技术研究所 Method for determining surface roughness, optical constant and thickness of optical thin film simultaneously
CN106526840A (en) * 2016-12-06 2017-03-22 天津津航技术物理研究所 Calculating method of binary laminated optical-material directional-spectrum thermal radiation ratio
CN106680216A (en) * 2016-12-06 2017-05-17 天津津航技术物理研究所 Method for calculating reflectivity and transmissivity spectrums of binary laminated optical material
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Application publication date: 20190405