CN108646321A - 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 PDFInfo
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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 is simple, is conducive to application of the two-dimensional material in photoelectric field.
Description
Technical field
The present invention relates to optical thin film and two-dimensional material field, more particularly to a kind of two-dimensional material normal incidence Fresnel optics
Characterizing method.
Background technology
2004, the two scientist An Deliegaimu (Andre Geim) and Constant of Univ Manchester UK
The Ding Nuowo loves (Konstantin Novoselov) that disappear successfully prepare single-layer graphene (thickness 0.335nm), open
New era of two-dimensional material research.Henceforth, the optics of graphene, electricity, magnetic property are obtained for 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 atomic layer is so thin there are one its thickness, 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,
Be it in the absorption of visible light wave range it 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 absorption approach value and the experiment of 450-750nm wave bands by experimental verification
It is good, larger in 400-450nm deviations).
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, which is substantially 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.
Invention content
In order to solve the problems, such as it is above-mentioned one of exist, an embodiment of the present 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
Simply, be conducive to application of the two-dimensional material in photoelectric field.
A kind of two-dimensional material normal incidence Fresnel optical characterisation methods provided by the invention, the method includes：
Obtain position phase thickness δ, two-dimensional material optical admittance y, normalized electric field strength B and the magnetic field intensity 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 intensity C
It should be related to the absorption of determining two-dimensional material.
Optionally, the position phase thickness δ, two-dimensional material optical admittance y, normalized electric field strength for obtaining two-dimensional material
B and magnetic field intensity C, including：
Determine that normalized electric field strength B and magnetic field intensity C, second relationship are using the second relationship：
Determine that position phase thickness δ, the third relationship are using third relationship：
The π Nd/ of δ=2 λ；
Determine that optical admittance and index of refraction relationship, the 4th relationship are using the 4th relationship：
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
For：
It is described to utilize position phase thickness δ, two-dimensional material optical admittance y, substrate optical admittance ys, normalized electric field strength B
Correspondence between magnetic field intensity C determines the absorption of two-dimensional material, including：
Utilize the electric field strength B, magnetic field intensity C, institute rheme phase thickness δ, the Free Space Optics admittance y0And
First relationship determines that the 6th relationship that A is absorbed for characterizing two-dimensional material, first relationship are：
6th relationship is：
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 intensity, if N0=1, N=n-ik, Ns=
ns-iks, n expression two-dimensional material refractive index, k expression two-dimensional material extinction coefficients, nsIndicate substrate refractive index, ksIndicate that substrate disappears
Backscatter extinction logarithmic ratio, EaFor incident field intensity, HaFor incident interface magnetic field intensity, EbFor outgoing interface electric field strength, HbTo be emitted magnetic field
Intensity, B are normalized electric field strength, and C is normalized magnetic field intensity, and i indicates imaginary part.
Optionally, it 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：
A=α dn；
Wherein, α indicates absorption coefficient.
Optionally, the method further includes：
Determine that two-dimensional material transmissivity, the 9th relationship are using the 9th relationship：
Wherein, ysIndicate substrate optical admittance.
Optionally, the method further includes：
Determine that the two-dimensional material reflectivity, the tenth relationship are using the tenth relationship：
Optionally, the method further includes：
9th relationship is simplified to obtain for characterizing the 11st relationship without support two-dimensional material transmitance, institute
Stating the 11st relationship is：
Optionally, the method further includes：
Tenth relationship is simplified to obtain for characterizing the 12nd relationship without support two-dimensional material reflectivity, institute
Stating the 12nd relationship is：
Optionally, the method further includes：
Work as N0=1, it is led using the electric field strength B, magnetic field intensity C, institute rheme phase thickness δ, the two-dimensional material optics
Receiving y and the first relationship determines that the 13rd relationship for there is substrate two-dimensional material absorptivity, 13 relationship are：
Optionally, the method further includes：
Work as N0=1, it is led using the electric field strength B, magnetic field intensity C, institute rheme phase thickness δ, the two-dimensional material optics
Receiving y and the 9th relationship determines that the 14th relationship for there is substrate two-dimensional material transmitance T, the 14th relationship are：
Wherein, T indicates transmitance, nsIndicate substrate refractive index.
Optionally, the method further includes：
Work as N0=1, it is led using the electric field strength B, magnetic field intensity C, institute rheme phase thickness δ, the two-dimensional material optics
Receiving y and the tenth relationship determines that the 15th relationship for there is substrate two-dimensional material reflectivity R, the 15th relationship are：
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 be inhaled under the conditions of normal incidence
The simple computation formula of receipts, reflectivity, transmitance, derivation is simple, is conducive to application of the two-dimensional material in photoelectric field.
Description of the drawings
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 implementation mode
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 every other embodiment that member is obtained without making creative work should all belong to the model that the present invention protects
It encloses.
Term " first ", " second ", " third " in description and claims of this specification and above-mentioned attached drawing, "
Four " etc. be for distinguishing similar object, without being used to describe specific sequence or precedence.It should be appreciated that using in this way
Data can be interchanged in the appropriate case, so that the embodiments described herein can be in addition to illustrating or describing herein
Sequence other than appearance is implemented.In addition, term " comprising " and " having " and their any deformation, it is intended that covering is non-exclusive
Include to be not necessarily limited to clearly arrange for example, containing the process of series of steps or unit, method, system, product or equipment
Those of go out step or unit, but may include not listing clearly or solid for these processes, method, product or equipment
The other steps or unit having.
A kind of two-dimensional material normal incidence Fresnel optical characterisation methods provided by the invention, the method includes：
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, determine that normalized electric field strength B and magnetic field intensity C, second relationship are using the second relationship：
Determine that position phase thickness δ, the third relationship are using third relationship：
The π Nd/ of δ=2 λ；
Determine that admittance and index of refraction relationship, the 4th relationship are using the 4th relationship：
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
For：
S102, using between position phase thickness δ, two-dimensional material optical admittance y, normalized electric field strength B and magnetic field intensity C
Correspondence determine the absorptivity of two-dimensional material.
Utilize the electric field strength B, magnetic field intensity C, institute rheme phase thickness δ, the two-dimensional material optical admittance y and
One relationship determines that the 6th relationship that A is absorbed for characterizing two-dimensional material, first relationship are：
6th relationship is：
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 intensity, EbIndicate outgoing 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 coefficients, 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 intensity, B is normalized electric field strength, and C is normalized magnetic field intensity, and i indicates imaginary part.
Optionally, it 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：
A=α dn；
Wherein, α indicates absorption coefficient.
Optionally, the method further includes：
Determine that two-dimensional material transmissivity T, the 9th relationship are using the 9th relationship：
Wherein, ysIndicate substrate optical admittance.
Optionally, the method further includes：
Determine that the two-dimensional material reflectivity R, the tenth relationship are using the tenth relationship：
Optionally, the method further includes：
9th relationship is simplified to obtain for characterizing the 11st relationship without support two-dimensional material transmitance T,
11st relationship is：
Optionally, the method further includes：
Tenth relationship is simplified to obtain for characterizing without support the 12nd relationships of two-dimensional material reflectivity R, institute
Stating the 12nd relationship is：
Optionally, the method further includes：
Work as N0=1, it is led using the electric field strength B, magnetic field intensity C, institute rheme phase thickness δ, the two-dimensional material optics
Receiving y and the first relationship determines that the 13rd relationship for there is substrate two-dimensional material to absorb A, 13 relationship are：
Optionally, the method further includes：
Work as N0=1, it is led using the electric field strength B, magnetic field intensity C, institute rheme phase thickness δ, the two-dimensional material optics
Receiving y and the 9th relationship determines that the 14th relationship for there is substrate two-dimensional material transmitance T rates, the 14th relationship are：
Optionally, the method further includes：
Work as N0=1, it is led using the electric field strength B, magnetic field intensity C, institute rheme phase thickness δ, the two-dimensional material optics
Receiving y and the tenth relationship determines that the 15th relationship for there is substrate two-dimensional material R, the 15th relationship are：
For be divided into without support two-dimensional material when two-dimensional material carries out optical characterisation 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.
The π Nd/ λ of δ=2 (3)
Y=H/E=NY (4)
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
The absorptivity A for having arrived two-dimensional material simplification calculates the 6th relationship (6).7th relationship (7) gives our calculation in absorption formula
With INTERFACE MODEL in 450-750nm wave bands 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 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.
H indicates magnetic field intensity, and Eb indicates outgoing interface electric field strength, if N0=1, N=n-ik, Ns=ns-iks, n expressions
Two-dimensional material refractive index, k indicate two-dimensional material extinction coefficient, nsExpression substrate refractive index, km expression substrate extinction coefficients, Ea,
Ha is incident field intensity and magnetic field intensity, Eb、HbTo go out radio field intensity and magnetic field intensity, B and C are normalized electric-field strength
Degree and magnetic field intensity, 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 is used in combination result of calculation and the experimental result delivered on Science magazines and is 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, 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 the reflectivity of substrate two-dimensional material simplification
Calculate the 13rd relationship (13), the 14th relationship (14) and the 15th relationship (15).
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 be inhaled under the conditions of normal incidence
The simple computation formula of receipts, reflectivity, transmitance, derivation is simple, is conducive to application of the two-dimensional material in 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 division of logic function, formula that in actual implementation, there may be another division manner, such as multiple units or component
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 the indirect coupling by some interfaces, device or unit
It closes or communicates to connect, can be electrical, machinery or other forms.
The unit illustrated as separating component may or may not be physically separated, aobvious as unit
The component shown may or may not be physical unit, you can be located at a place, or may be distributed over multiple
In network element.Some or all of unit therein can be selected according to the actual needs to realize the mesh of this embodiment scheme
's.
In addition, each functional unit in each embodiment of the present invention can be integrated in a processing unit, it can also
It is that each unit physically exists alone, it can also be during two or more units be integrated in one unit.Above-mentioned integrated list
The form that hardware had both may be used in member is realized, can also be realized in the form of SFU software functional unit.
One of ordinary skill in the art will appreciate that all or part of step 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, the thought of embodiment according to the present invention, in specific embodiments and applications
There will be changes, in conclusion the content of the present specification should not be construed as limiting the invention.
Claims (10)
1. a kind of two-dimensional material normal incidence Fresnel optical characterisation methods, which is characterized in that the method includes：
Obtain position phase thickness δ, two-dimensional material optical admittance y, normalized electric field strength B and the magnetic field intensity 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 intensity C
Between correspondence determine the absorption of the two-dimensional material.
2. two-dimensional material normal incidence Fresnel optical characterisation methods according to claim 1, which is characterized in that the acquisition
Position phase thickness δ, two-dimensional material optical admittance y, normalized electric field strength B and the magnetic field intensity C of two-dimensional material, including：
Determine that normalized electric field strength B and magnetic field intensity C, second relationship are using the second relationship：
Determine that position phase thickness δ, the third relationship are using third relationship：
The π Nd/ of δ=2 λ；
Determine that two-dimensional material optical admittance y, the 4th relationship are using the 4th relationship：
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 is：
Pair using between position phase thickness δ, two-dimensional material optical admittance y, normalized electric field strength B and magnetic field intensity C
It should be related to the absorption of determining two-dimensional material, including：
It is closed using the electric field strength B, magnetic field intensity C, institute rheme phase thickness δ, the two-dimensional material optical admittance y and first
System determines that the 6th relationship that A is absorbed for characterizing two-dimensional material, first relationship are：
6th relationship is：
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 that magnetic field intensity, Eb indicate outgoing 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 coefficients, 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 intensity, B is normalized electric field strength, and C is normalized magnetic field intensity, and i indicates imaginary part.
3. two-dimensional material normal incidence Fresnel optical characterisation methods according to claim 2, 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
For：
A=α dn；
Wherein, α indicates absorption coefficient.
4. two-dimensional material normal incidence Fresnel optical characterisation methods according to claim 2, which is characterized in that the method
Further include：
Determine that two-dimensional material transmissivity, the 9th relationship are using the 9th relationship：
Wherein, ysIndicate substrate optical admittance.
5. two-dimensional material normal incidence Fresnel optical characterisation methods according to claim 4, which is characterized in that the method
Further include：
Determine that the two-dimensional material reflectivity, the tenth relationship are using the tenth relationship：
6. two-dimensional material normal incidence Fresnel optical characterisation methods according to claim 5, 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 is：
7. two-dimensional material normal incidence Fresnel optical characterisation methods according to claim 5, 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 is：
8. two-dimensional material normal incidence Fresnel optical characterisation methods according to claim 2, which is characterized in that the method
Further include：
Work as N0=1, using the electric field strength B, magnetic field intensity C, institute rheme phase thickness δ, the two-dimensional material optical admittance y with
And first relationship determine the 13rd relationship for there is substrate two-dimensional material to absorb A, 13 relationship is：
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 intensity C, institute rheme phase thickness δ, the two-dimensional material optical admittance y with
And the 9th relationship determine that the 14th relationship for there is substrate two-dimensional material transmitance T, the 14th relationship are：
Wherein, T indicates transmitance, nsIndicate substrate refractive index.
10. two-dimensional material normal incidence Fresnel optical characterisation methods according to claim 5, which is characterized in that the side
Method further includes：
Work as N0=1, using the electric field strength B, magnetic field intensity C, institute rheme phase thickness δ, the two-dimensional material optical admittance y with
And the tenth relationship determine that the 15th relationship for there is substrate two-dimensional material reflectivity R, the 15th relationship are：
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| CN110567882A (en) * | 2019-08-16 | 2019-12-13 | 华中科技大学 | Method for determining complex optical conductivity of two-dimensional material |
| CN112462154A (en) * | 2020-11-10 | 2021-03-09 | 武汉大学 | Device and method for measuring electric field intensity on surface of hardware fitting of electrical equipment |
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