CN108646321B - A kind of two-dimensional material normal incidence Fresnel optical characterisation methods - Google Patents

A kind of two-dimensional material normal incidence Fresnel optical characterisation methods Download PDF

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CN108646321B
CN108646321B CN201810437661.9A CN201810437661A CN108646321B CN 108646321 B CN108646321 B CN 108646321B CN 201810437661 A CN201810437661 A CN 201810437661A CN 108646321 B CN108646321 B CN 108646321B
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王孝东
陈波
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Changchun Institute of Optics Fine Mechanics and Physics of CAS
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Abstract

Two-dimensional material normal incidence Fresnel optical characterisation methods provided by the invention, using traditional optical thin film basic theories-conductance matrix method, introduce optical admittance concept, derive without support and have substrate two-dimensional material under the conditions of normal incidence absorption, reflectivity, transmitance simple computation formula, derivation process is simple, is conducive to two-dimensional material in the application of photoelectric field.

Description

A kind of two-dimensional material normal incidence Fresnel optical characterisation methods
Technical field
The present invention relates to optical thin film and two-dimensional material field, in particular to a kind of two-dimensional material normal incidence Fresnel optics Characterizing method.
Background technique
2004, the two scientist An Deliegaimu (Andre Geim) and Constant of Univ Manchester UK The Ding Nuowo love (Konstantin Novoselov) that disappears successfully prepares single-layer graphene (thickness 0.335nm), opens New era of two-dimensional material research.Henceforth, the optics of graphene, electricity, magnetic property have all obtained extensive research.? In the OPTICAL PROPERTIES of graphene, it is used two kinds of models.One is thin-skin model, that is, thinks that graphene is a kind of thin Film, even if only one atomic layer of its thickness is so thin, this model is mainly used as the two-dimensional materials such as research graphene Optical constant；The other is INTERFACE MODEL, i.e., assign graphene as the infinitesimal interface of thickness or boundary, this model is extensive For absorption, reflectivity, the transmitance etc. for calculating the two-dimensional materials such as graphene.Most famous, the most peculiar optical property of graphene, It is it in the absorption of visible light wave range is a constant (A=π a=2.3%, a are fine-structure constant).This result is exactly base It derives in INTERFACE MODEL, and (is met very in the absorption approach value of 450-750nm wave band and experiment by experimental verification It is good, larger in 400-450nm deviation).
Then, people prepare the two-dimensional materials such as germanium alkene, silene, molybdenum disulfide, boron nitride again.Due to the thickness of two-dimensional material Only several angstroms of degree, it is generally the case that the two-dimensional material prepared is to be transferred in substrate.Stauber and Fang et al. exist On the basis of INTERFACE MODEL, it is differently deduced the calculating side that substrate two-dimensional material absorbs under the conditions of normal incidence Method: 4 π a/ (1+ns) 2, wherein ns is the refractive index of substrate.But two-dimensional material is substantially that thickness only has several angstroms thin Film, if calculating its optical property using INTERFACE MODEL, traditional optical thin film theory and commercial optical thin film software are just Lose effectiveness.
Summary of the invention
In order to solve the problems, such as it is above-mentioned one of exist, the embodiment of the invention provides a kind of two-dimensional material normal incidence Fresnel light Characterizing method is learned, using traditional optical thin film basic theories-conductance matrix method, introduces optical admittance concept, derivation process Simply, be conducive to two-dimensional material in the application of photoelectric field.
A kind of two-dimensional material normal incidence Fresnel optical characterisation methods provided by the invention, which comprises
Obtain position phase thickness δ, two-dimensional material optical admittance y, normalized electric field strength B and the magnetic field strength of two-dimensional material C；
Utilize pair between position phase thickness δ, two-dimensional material optical admittance y, normalized electric field strength B and magnetic field strength C It should be related to the absorption of determining two-dimensional material.
Optionally, position phase thickness δ, the two-dimensional material optical admittance y, normalized electric field strength for obtaining two-dimensional material B and magnetic field strength C, comprising:
Normalized electric field strength B and magnetic field strength C, second relationship are determined using the second relationship are as follows:
Figure BDA0001655082850000021
Position phase thickness δ, the third relationship are determined using third relationship are as follows:
The π Nd/ of δ=2 λ；
Optical admittance and index of refraction relationship, the 4th relationship are determined using the 4th relationship are as follows:
Y=H/E=NY；
Approximate processing is carried out to second relationship using institute rheme phase thickness δ and obtains the 5th relationship, the 5th relationship Are as follows:
Figure BDA0001655082850000022
It is described to utilize position phase thickness δ, two-dimensional material optical admittance y, substrate optical admittance ys, normalized electric field strength B Corresponding relationship between magnetic field strength C determines the absorption of two-dimensional material, comprising:
Utilize the electric field strength B, magnetic field strength C, institute rheme phase thickness δ, the Free Space Optics admittance y0And First relationship determines the 6th relationship that A is absorbed for characterizing two-dimensional material, first relationship are as follows:
Figure BDA0001655082850000023
6th relationship are as follows:
Wherein, Y is Free Space Optics admittance, y0For free air optical admittance, y is that the two-dimensional material optics is led It receives, ymFor substrate optical admittance, d is two-dimensional material thickness, and λ is wavelength, and H indicates magnetic field strength, if N0=1, N=n-ik, Ns= ns-iks, n expression two-dimensional material refractive index, k expression two-dimensional material extinction coefficient, nsIndicate substrate refractive index, ksIndicate that substrate disappears Backscatter extinction logarithmic ratio, EaFor incident field intensity, HaFor incident interface magnetic field strength, EbFor exit boundary interface electric field strength, HbTo be emitted magnetic field Intensity, B are normalized electric field strength, and C is normalized magnetic field strength, and i indicates imaginary part.
It optionally, is that absorption coefficient is reduced to the 6th relationship that A is absorbed for characterizing two-dimensional material using 4 π k/ λ 8th relationship, the 8th relationship are as follows:
A=α dn；
Wherein, α indicates absorption coefficient.
Optionally, the method also includes:
Two-dimensional material transmissivity, the 9th relationship are determined using the 9th relationship are as follows:
Figure BDA0001655082850000032
Wherein, ysIndicate substrate optical admittance.
Optionally, the method also includes:
The two-dimensional material reflectivity, the tenth relationship are determined using the tenth relationship are as follows:
Figure BDA0001655082850000033
Optionally, the method also includes:
9th relationship is simplified to obtain for characterizing the 11st relationship without support two-dimensional material transmitance, institute State the 11st relationship are as follows:
Figure BDA0001655082850000034
Optionally, the method also includes:
Tenth relationship is simplified to obtain for characterizing the 12nd relationship without support two-dimensional material reflectivity, institute State the 12nd relationship are as follows:
Figure BDA0001655082850000041
Optionally, the method also includes:
Work as N0=1, it is led using the electric field strength B, magnetic field strength C, institute rheme phase thickness δ, the two-dimensional material optics Receiving y and the first relationship determines for having the 13rd relationship of substrate two-dimensional material absorptivity, 13 relationship are as follows:
Figure BDA0001655082850000042
Optionally, the method also includes:
Work as N0=1, it is led using the electric field strength B, magnetic field strength C, institute rheme phase thickness δ, the two-dimensional material optics Receiving y and the 9th relationship determines for having the 14th relationship of substrate two-dimensional material transmitance T, the 14th relationship are as follows:
Figure BDA0001655082850000043
Wherein, T indicates transmitance, nsIndicate substrate refractive index.
Optionally, the method also includes:
Work as N0=1, it is led using the electric field strength B, magnetic field strength C, institute rheme phase thickness δ, the two-dimensional material optics Receiving y and the tenth relationship determines for having the 15th relationship of substrate two-dimensional material reflectivity R, the 15th relationship are as follows:
Figure BDA0001655082850000044
Two-dimensional material normal incidence Fresnel optical characterisation methods provided by the invention, are managed substantially using traditional optical thin film By-conductance matrix method, optical admittance concept is introduced, is derived without supporting and have substrate two-dimensional material to inhale under the conditions of normal incidence Receipts, reflectivity, transmitance simple computation formula, derivation process is simple, is conducive to two-dimensional material in the application of photoelectric field.
Detailed description of the invention
Fig. 1 is that the thin-skin model of the two-dimensional material normal incidence Fresnel optical characterisation methods provided in the embodiment of the present invention shows It is intended to；
Fig. 2 is in the two-dimensional material normal incidence Fresnel optical characterisation methods provided in the embodiment of the present invention to without support two Tie up the comparison schematic diagram of material transmitance calculation formula and experimental result.
Specific embodiment
In order to enable those skilled in the art to better understand the solution of the present invention, below in conjunction in the embodiment of the present invention Attached drawing, technical scheme in the embodiment of the invention is clearly and completely described, it is clear that described embodiment is only The embodiment of a part of the invention, instead of all the embodiments.Based on the embodiments of the present invention, ordinary skill people The model that the present invention protects all should belong in member's every other embodiment obtained without making creative work It encloses.
Description and claims of this specification and term " first ", " second ", " third ", " in above-mentioned attached drawing Four " etc. be to be used to distinguish similar objects, without being used to describe a particular order or precedence order.It should be understood that using in this way Data be interchangeable under appropriate circumstances, so that the embodiments described herein can be in addition to illustrating herein or describing Sequence other than appearance is implemented.In addition, term " includes " and " having " and their any deformation, it is intended that covering is non-exclusive Include, for example, the process, method, system, product or equipment for containing a series of steps or units are not necessarily limited to clearly arrange Those of out step or unit, but may include be not clearly listed or it is solid for these process, methods, product or equipment The other step or units having.
A kind of two-dimensional material normal incidence Fresnel optical characterisation methods provided by the invention, which comprises
S101, position phase thickness δ, two-dimensional material optical admittance y, normalized electric field strength B and the magnetic for obtaining two-dimensional material Field intensity C.
Specifically, normalized electric field strength B and magnetic field strength C, second relationship are determined using the second relationship are as follows:
Figure BDA0001655082850000051
Position phase thickness δ, the third relationship are determined using third relationship are as follows:
The π Nd/ of δ=2 λ；
Admittance and index of refraction relationship, the 4th relationship are determined using the 4th relationship are as follows:
Y=H/E=NY；
Approximate processing is carried out to second relationship using institute rheme phase thickness δ and obtains the 5th relationship, the 5th relationship Are as follows:
S102, using between position phase thickness δ, two-dimensional material optical admittance y, normalized electric field strength B and magnetic field strength C Corresponding relationship determine the absorptivity of two-dimensional material.
Utilize the electric field strength B, magnetic field strength C, institute rheme phase thickness δ, the two-dimensional material optical admittance y and One relationship determines the 6th relationship that A is absorbed for characterizing two-dimensional material, first relationship are as follows:
Figure BDA0001655082850000062
6th relationship are as follows:
Figure BDA0001655082850000063
Wherein, Y is Free Space Optics admittance, y0For free air optical admittance, y is that the two-dimensional material optics is led It receives, ymFor substrate optical admittance, d is two-dimensional material thickness, and λ is wavelength, and H indicates magnetic field strength, EbIndicate exit boundary interface electric-field strength Degree, if N0=1, N=n-ik, Ns=ns-iks, n expression two-dimensional material refractive index, k expression two-dimensional material extinction coefficient, nsIt indicates Substrate refractive index, ksIndicate substrate extinction coefficient, EaFor incident field intensity, HaFor incident magnetic intensity, EbTo go out radio field intensity Degree, HbTo be emitted magnetic field strength, B is normalized electric field strength, and C is normalized magnetic field strength, and i indicates imaginary part.
It optionally, is that absorption coefficient is reduced to the 6th relationship that A is absorbed for characterizing two-dimensional material using 4 π k/ λ 8th relationship, the 8th relationship are as follows:
A=α dn；
Wherein, α indicates absorption coefficient.
Optionally, the method also includes:
Two-dimensional material transmissivity T, the 9th relationship are determined using the 9th relationship are as follows:
Figure BDA0001655082850000071
Wherein, ysIndicate substrate optical admittance.
Optionally, the method also includes:
The two-dimensional material reflectivity R, the tenth relationship are determined using the tenth relationship are as follows:
Figure BDA0001655082850000072
Optionally, the method also includes:
9th relationship is simplified to obtain for characterizing the 11st relationship without support two-dimensional material transmitance T, 11st relationship are as follows:
Figure BDA0001655082850000073
Optionally, the method also includes:
Tenth relationship is simplified to obtain for characterizing without support the 12nd relationship of two-dimensional material reflectivity R, institute State the 12nd relationship are as follows:
Figure BDA0001655082850000074
Optionally, the method also includes:
Work as N0=1, it is led using the electric field strength B, magnetic field strength C, institute rheme phase thickness δ, the two-dimensional material optics Receiving y and the first relationship determines the 13rd relationship for there is substrate two-dimensional material to absorb A, 13 relationship are as follows:
Figure BDA0001655082850000075
Optionally, the method also includes:
Work as N0=1, it is led using the electric field strength B, magnetic field strength C, institute rheme phase thickness δ, the two-dimensional material optics Receiving y and the 9th relationship determines for having the 14th relationship of substrate two-dimensional material transmitance T rate, the 14th relationship are as follows:
Figure BDA0001655082850000076
Figure BDA0001655082850000087
Optionally, the method also includes:
Work as N0=1, it is led using the electric field strength B, magnetic field strength C, institute rheme phase thickness δ, the two-dimensional material optics Receiving y and the tenth relationship determines for having the 15th relationship of substrate two-dimensional material R, the 15th relationship are as follows:
Figure BDA0001655082850000081
For be divided into when two-dimensional material carries out optical characterisation without support two-dimensional material and having substrate two-dimensional material.
1. for carrying out optical characterisation without support two-dimensional material
Calculation formula without support two-dimensional material absorptivity, reflectivity, transmitance under the conditions of normal incidence.In these three public affairs In formula, refractive index, the product of absorption coefficient and thickness this three of no support two-dimensional material play crucial effect.
Figure BDA0001655082850000082
Figure BDA0001655082850000083
The π Nd/ λ of δ=2 (3)
Y=H/E=NY (4)
Figure BDA0001655082850000084
Figure BDA0001655082850000085
Figure BDA0001655082850000086
Attached drawing 1 gives the schematic diagram of two-dimensional material thin-skin model.In optical thin film theory, the absorptivity A of film can To be calculated by the first relationship (1)；B and C can be calculated by the second relationship (2)；δ is a phase thickness, is calculated by third relationship (3)；y It is admittance, is calculated by third formula formula (4).Wherein, y0, y and ysIt is the optics of free space, two-dimensional material and substrate respectively Admittance.D is two-dimensional material thickness, and λ is wavelength, and Y is the optical admittance of free space.In visible light wave range, the value of d/ λ is 10-3 Left and right, so, δ is minimum.Therefore approximate processing can be done to the second relationship (2), obtain the 5th relationship (5.) if we Set N0=Ns=1, the second relationship to the 5th relationship (2-5) is substituted into the first relationship (1), and remove the high-order term of d/ λ, it must It has arrived the absorptivity A that two-dimensional material simplifies and has calculated the 6th relationship (6).7th relationship (7) gives our calculation in absorption formula With INTERFACE MODEL in 450-750nm wave band numerically identical reason, wherein ε0It is permittivity of vacuum, σ is conductivity, and G is Conductance, c are the light velocity of light in a vacuum.Again since 4 π k/ λ are absorption coefficients, the 6th relationship (6) can further be write as 8th relationship (8).
A=α dn (8)
In optical thin film theory, the transmissivity and reflectivity of film can be by the 9th relationship (9) and the tenth relationships (10) It calculates.By the similar derivation process absorbed without support two-dimensional material, obtain without support two-dimensional material transmitance and reflectivity Simplified the 11st relationship (11) of calculating and the 12nd relationship (12).From the 6th relationship, the 8th relationship, the 11st relationship and 12 relationships (6,8,11,12) as can be seen that absorption coefficient, the refractive index of two-dimensional material and thickness this three product in no branch Crucial effect is played in the calculating of support two-dimensional material absorptivity, transmitance and reflectivity.
Figure BDA0001655082850000092
Figure BDA0001655082850000093
Figure BDA0001655082850000094
H indicates magnetic field strength, and Eb indicates exit boundary interface electric field strength, if N0=1, N=n-ik, Ns=ns-iks, n expression Two-dimensional material refractive index, k indicate two-dimensional material extinction coefficient, nsExpression substrate refractive index, km expression substrate extinction coefficient, Ea, Ha is incident field intensity and magnetic field strength, Eb、HbTo go out radio field intensity and magnetic field strength, B and C are normalized electric-field strength Degree and magnetic field strength, i indicate imaginary part.
Single layer and two layers are calculated without support stone by using the 11st relationship (11) is calculated without support two-dimensional material transmitance Transmitance of black alkene under the conditions of normal incidence, and with calculated result and the experimental result delivered on Science magazine and be based on The notional result of INTERFACE MODEL compares, as shown in Fig. 2, from attached drawing 2 as can be seen that using present invention method The calculated results meet more preferable with experimental data.
2. there is substrate two-dimensional material to carry out optical characterisation
There are substrate two-dimensional material absorptivity, the calculation formula of reflectivity and transmitance under the conditions of normal incidence, at these three In formula, the refractive index of two-dimensional material, the product of absorption coefficient and thickness this three play crucial effect.
Set N0=1, the second relationship to the 5th relationship (2-5) substitute into respectively the first relationship (1), the second relationship (9) and Tenth relationship (10), and remove the high-order term of d/ λ, obtain absorptivity, transmitance and reflectivity that substrate two-dimensional material simplifies Calculate the 13rd relationship (13), the 14th relationship (14) and the 15th relationship (15).
Figure BDA0001655082850000101
Figure BDA0001655082850000102
Figure BDA0001655082850000103
Two-dimensional material normal incidence Fresnel optical characterisation methods provided by the invention, are managed substantially using traditional optical thin film By-conductance matrix method, optical admittance concept is introduced, is derived without supporting and have substrate two-dimensional material to inhale under the conditions of normal incidence Receipts, reflectivity, transmitance simple computation formula, derivation process is simple, is conducive to two-dimensional material in the application of photoelectric field.
It is apparent to those skilled in the art that for convenience and simplicity of description, the system of foregoing description, The specific work process of device and unit, can refer to corresponding processes in the foregoing method embodiment, and details are not described herein.
In several embodiments provided herein, it should be understood that disclosed system, device and method can be with It realizes by another way.For example, the apparatus embodiments described above are merely exemplary, for example, the unit It divides, only a kind of logical function partition, there may be another division manner in actual implementation, such as multiple units or components It can be combined or can be integrated into another system, or some features can be ignored or not executed.Another point, it is shown or The mutual coupling, direct-coupling or communication connection discussed can be through some interfaces, the indirect coupling of device or unit It closes or communicates to connect, can be electrical property, mechanical or other forms.
The unit as illustrated by the separation member may or may not be physically separated, aobvious as unit The component shown may or may not be physical unit, it can and it is in one place, or may be distributed over multiple In network unit.It can select some or all of unit therein according to the actual needs to realize the mesh of this embodiment scheme 's.
It, can also be in addition, the functional units in various embodiments of the present invention may be integrated into one processing unit It is that each unit physically exists alone, can also be integrated in one unit with two or more units.Above-mentioned integrated list Member both can take the form of hardware realization, can also realize in the form of software functional units.
Those of ordinary skill in the art will appreciate that all or part of the steps in the various methods of above-described embodiment is can It is completed with instructing relevant hardware by program, which can be stored in a computer readable storage medium, storage Medium may include: read-only memory (ROM, Read Only Memory), random access memory (RAM, Random Access Memory), disk or CD etc..
Detailed Jie has been carried out to a kind of two-dimensional material normal incidence Fresnel optical characterisation methods provided by the present invention above It continues, for those of ordinary skill in the art, thought according to an embodiment of the present invention, in specific embodiments and applications There will be changes, in conclusion the contents of this specification are not to be construed as limiting the invention.

Claims (9)

1. a kind of two-dimensional material normal incidence Fresnel optical characterisation methods, which is characterized in that the described method includes:
Obtain position phase thickness δ, two-dimensional material optical admittance y, normalized electric field strength B and the magnetic field strength C of two-dimensional material；
Utilize institute rheme phase thickness δ, the two-dimensional material optical admittance y, the normalized electric field strength B and magnetic field strength C Between corresponding relationship determine the absorption of the two-dimensional material；
Wherein:
Position phase thickness δ, two-dimensional material optical admittance y, normalized electric field strength B and the magnetic field strength for obtaining two-dimensional material C, comprising:
Normalized electric field strength B and magnetic field strength C, second relationship are determined using the second relationship are as follows:
Figure FDA0002165050730000011
Position phase thickness δ, the third relationship are determined using third relationship are as follows:
The π Nd/ of δ=2 λ；
Two-dimensional material optical admittance y, the 4th relationship are determined using the 4th relationship are as follows:
Y=H/E=NY；
Approximate processing is carried out to second relationship using institute rheme phase thickness δ and obtains the 5th relationship, the 5th relationship are as follows:
Figure FDA0002165050730000012
Pair using between position phase thickness δ, two-dimensional material optical admittance y, normalized electric field strength B and magnetic field strength C It should be related to the absorption of determining two-dimensional material, comprising:
It is closed using the electric field strength B, magnetic field strength C, institute rheme phase thickness δ, the two-dimensional material optical admittance y and first System determines the 6th relationship that A is absorbed for characterizing two-dimensional material, first relationship are as follows:
Figure FDA0002165050730000021
6th relationship are as follows:
Wherein, Y is Free Space Optics admittance, y0For free air optical admittance, y is the two-dimensional material optical admittance, ymFor Substrate optical admittance, d are two-dimensional material thickness, and λ is wavelength, and H indicates magnetic field strength, and Eb indicates exit boundary interface electric field strength, if N0=1, N=n-ik, Ns=ns-iks, n expression two-dimensional material refractive index, k expression two-dimensional material extinction coefficient, nsIndicate substrate Refractive index, ksIndicate substrate extinction coefficient, EaFor incident field intensity, HaFor incident magnetic intensity, EbTo go out radio field intensity, Hb To be emitted magnetic field strength, B is normalized electric field strength, and C is normalized magnetic field strength, and i indicates imaginary part.
2. two-dimensional material normal incidence Fresnel optical characterisation methods according to claim 1, which is characterized in that utilize 4 π k/ λ is that absorption coefficient is reduced to the 8th relationship, the 8th relationship to the 6th relationship for absorbing A for characterizing two-dimensional material Are as follows:
A=adn；
Wherein, α indicates absorption coefficient.
3. two-dimensional material normal incidence Fresnel optical characterisation methods according to claim 1, which is characterized in that the method Further include:
Two-dimensional material transmissivity, the 9th relationship are determined using the 9th relationship are as follows:
Figure FDA0002165050730000023
Wherein, ysIndicate substrate optical admittance.
4. two-dimensional material normal incidence Fresnel optical characterisation methods according to claim 3, which is characterized in that the method Further include:
The two-dimensional material reflectivity, the tenth relationship are determined using the tenth relationship are as follows:
Figure FDA0002165050730000031
5. two-dimensional material normal incidence Fresnel optical characterisation methods according to claim 4, which is characterized in that the method Further include:
9th relationship is simplified to obtain for characterizing the 11st relationship without support two-dimensional material transmitance T, it is described 11st relationship are as follows:
Figure FDA0002165050730000032
6. two-dimensional material normal incidence Fresnel optical characterisation methods according to claim 4, which is characterized in that the method Further include:
Tenth relationship is simplified to obtain for characterizing the 12nd relationship without support two-dimensional material reflectivity R, it is described 12nd relationship are as follows:
Figure FDA0002165050730000033
7. two-dimensional material normal incidence Fresnel optical characterisation methods according to claim 1, which is characterized in that the method Further include:
Work as N0=1, using the electric field strength B, magnetic field strength C, institute rheme phase thickness δ, the two-dimensional material optical admittance y with And first relationship determine for have substrate two-dimensional material absorb A the 13rd relationship, 13 relationship are as follows:
Figure FDA0002165050730000034
8. two-dimensional material normal incidence Fresnel optical characterisation methods according to claim 3, which is characterized in that the method Further include:
Work as N0=1, using the electric field strength B, magnetic field strength C, institute rheme phase thickness δ, the two-dimensional material optical admittance y with And the 9th relationship determine for having the 14th relationship of substrate two-dimensional material transmitance T, the 14th relationship are as follows:
Figure FDA0002165050730000035
Wherein, T indicates transmitance, nsIndicate substrate refractive index.
9. two-dimensional material normal incidence Fresnel optical characterisation methods according to claim 4, which is characterized in that the method Further include:
Work as N0=1, using the electric field strength B, magnetic field strength C, institute rheme phase thickness δ, the two-dimensional material optical admittance y with And the tenth relationship determine for having the 15th relationship of substrate two-dimensional material reflectivity R, the 15th relationship are as follows:
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