CN1987548A - Film series stacking method based on MATLAB language - Google Patents

Abstract

Belonging to area for designing optical thin film series, the invention is especially related to method for accumulating film series based on MATLAB language. The method includes following steps: (1) setting up initial variable of film layer; (2) detecting attribute of film layer represented by first letter; (3) calculating combined admittance; (4) detecting next attribute of film layer circularly; (5) calculating combined admittance of multiple film layers; (6) calculating reflectivity of film layer; (7) drawing a curve diagram. Thickness of multiple film layers is times of 1/4 lambda. Output of the reflectivity image is based on deposition of two types of film material: TiO2 and SiO2. Film layers are in form H-L-H-L-H, where H is TiO2 in high refractive index, and L is SiO2 in low refractive index. Possessing complete functions, the invention is capable of generic function for stacking film series as well as capable of stacking film series with absorption coefficients.

Description

Film based on the MATLAB language is a stacking method

Technical field

The invention belongs to the system design of optical film field, relating in particular to a kind of film based on the MATLAB language is stacking method.

Background technology

Optical thin film has developed sets up the complete optical theory of a cover, and having developed the film that establishes one's own system is method for designing.Design has also been made various optical thin films: optical thin film products such as anti-reflection film, high-reflecting film, spectro-film, cutoff filter and various bandpass filters.Angus Macleod began to explain with interference matrix the application of calculating optical film and robot calculator along with 1969, and to the seventies in 20th century, by means of the method for designing of computer aided technique, the design and the calculating of film system have had very fast development.Along with the industrialization of film, the design software of some film systems also produces thereupon, as: MacLeod's film is a Specialty Design software.The MATLAB language is a kind of high performance scientific and the engineering calculation software of Mathworks company exploitation.It has been inherited and has calculated and visual and program design power.

Summary of the invention

The present invention is intended to overcome the deficiencies in the prior art part and a kind of perfect in shape and function is provided, and not only has the function that realizes general film system stack, but also the film based on the MATLAB language of stack that can realize having the film system of absorption coefficient is a stacking method.

The object of the present invention is achieved like this: the film based on the MATLAB language is a stacking method, can realize according to following steps:

1) initializaing variable of rete is set;

2) detect first letter and represent the rete attribute;

3) calculation combination admittance;

4) the next rete attribute of cycle detection;

5) calculate multiple film layer combination admittance;

6) calculate the rete reflectivity.

7) figure that runs a curve.

As a kind of preferred version, it is doubly inferior that the thickness of multiple film layer of the present invention can be 1/4 λ, and wherein λ is a wavelength.

As another kind of preferred version, the output of reflectivity image of the present invention is according to TiO ₂And SiO ₂The deposition of two kinds of coating materials, its rete are H-L-H-L-H; Wherein H is high index film material TiO ₂, L is low-refraction coating materials SiO ₂

This program worked out in the MATLAB language, program own powerful; The friendly interface of program is convenient to operation, only needs disposable input design parameter, and the reflectivity image just intuitively manifests; Not only have the function that realizes general film system stack, but also can realize having the stack of the film system of absorption coefficient; If set up the database of coating materials refractive index, realize the stack of irregular multilayer film, can make amendment to program easily, the simulation meeting of multilayer film is more perfect.These workers for Film Optics carry out the multilayer film design to be made very helpful.Because this language is indicative language, M file wherein can not generate executable file, therefore can only move under the MATLAB environment.

Description of drawings

The invention will be further described below in conjunction with the drawings and specific embodiments.

Fig. 1 is a program principle block diagram of the present invention;

Fig. 2 is a monofilm isoboles of the present invention;

Fig. 3 is a multilayer film isoboles of the present invention;

Fig. 4 is the reflectance curve figure of 300nm of the present invention to the 1200nm place.

Embodiment

The method of computing optical thin film is a lot, as eigenmatrix method, vector method, utilize the calculating of multilayer film of fourier series and synthetic.Here the method that is based on interference matrix is handled the accumulation of film system and the relevant issues of calculating.Though it is the computation process of interference matrix formula is loaded down with trivial details, very convenient with regard to what become by means of computer technology.A monofilm is regarded as the matrix of one 2 row 2 row, and calculate, be delivered to the relation of the other end from an end of film system at the electric field intensity at two medium face places and the component of magnetic field intensity.If the refractive index of single-layer dielectric film is n1, the geometric thickness of film is d1, and the refractive index of substrate glass is n2, the refractive index of incident medium is n0, and incident light wave is a plane wave, and incident angle is θ 0, at this moment electromagnetic field vector E and H can be decomposed into p polarization and s polarization, and Fig. 2 is the monofilm isoboles.

If E0, H0 are the tangential component of total intensity among the medium n0, for interface 1 application boundary condition, the using admittance formula, transmit relational expression mutually in conjunction with the position and obtain:

$\left[\begin{array}{c}k\&times;{\mathrm{<figure-callout\; id="0"\; label="E"\; filenames="A20061013440500121.png"\; state="\{\{state\}\}">E</figure-callout>}}_{0,\mathrm{<figure-callout\; id="0"\; label="t\; H"\; filenames="A20061013440500121.png"\; state="\{\{state\}\}">t</figure-callout>}}& \\ H_{}{}_{0,t}\end{array}\right]=\left[\begin{array}{cc}{e}^{j{\mathrm{\&delta;}}_1}& e^{-j{\mathrm{\&delta;}}_1}\\ {\mathrm{\&eta;}}_1{e}^{j{\mathrm{\&delta;}}_1}& -{\mathrm{\&eta;}}_1{e}^{-j{\mathrm{\&delta;}}_1}\end{array}\right]\left[\begin{array}{c}k\&times;E_{12,t}^{+}\\ k\&times;E_{12,t}^{-}\end{array}\right]$

For interface 2 application boundary conditions $E_{2,t}^{-}=0,$ $H_{2,t}^{-}=0,$ Can obtain equally:

$\left[\begin{array}{c}k\&times;{\mathrm{<figure-callout\; id="0"\; label="E"\; filenames="A20061013440500121.png"\; state="\{\{state\}\}">E</figure-callout>}}_{0,\mathrm{<figure-callout\; id="0"\; label="t\; H"\; filenames="A20061013440500121.png"\; state="\{\{state\}\}">t</figure-callout>}}& \\ H_{}{}_{0,t}\end{array}\right]=\left[\begin{array}{cc}\cos {\mathrm{\&delta;}}_1& j\sin {\mathrm{\&delta;}}_1/{\mathrm{\&eta;}}_1\\ j\sin {\mathrm{\&delta;}}_1{\mathrm{\&eta;}}_1& \cos {\mathrm{\&delta;}}_1\end{array}\right]\left[\begin{array}{c}k\&times;E_{2,t}^{+}\\ H_{2,t}^{+}\end{array}\right]$

The position phase ${\mathrm{\&delta;}}_1=\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}{n}_1{d}_1\cos {\mathrm{\&theta;}}_1$ In the formula: the incident angle when θ 1 is incident; N1 is the refractive index of rete; D1 is the actual (real) thickness of rete; M1 is the eigenmatrix of film system, $M1=\left[\begin{array}{cc}\cos {\mathrm{\&delta;}}_1& j\sin {\mathrm{\&delta;}}_1/{\mathrm{\&eta;}}_1\\ j\sin {\mathrm{\&delta;}}_1{\mathrm{\&eta;}}_1& \cos {\mathrm{\&delta;}}_1\end{array}\right]$ From this formula as can be seen, the tangential component of the electric field intensity of the whole field of light wave and magnetic field intensity has been delivered to the other end from an end of film system.

The stacking diagram of multilayer film as shown in Figure 3.Utilize the eigenmatrix of film system, calculate the stack of multilayer film:

$\left[\begin{array}{c}k\&times;{\mathrm{<figure-callout\; id="0"\; label="E"\; filenames="A20061013440500121.png"\; state="\{\{state\}\}">E</figure-callout>}}_{0,\mathrm{<figure-callout\; id="0"\; label="t\; H"\; filenames="A20061013440500121.png"\; state="\{\{state\}\}">t</figure-callout>}}& \\ H_{}{}_{0,t}\end{array}\right]=\left\{\underset{r=1}{\overset{k}{\mathrm{\&Pi;}}}\left[\begin{array}{cc}\cos {\mathrm{\&delta;}}_r& j\sin {\mathrm{\&delta;}}_r/{\mathrm{\&eta;}}_r\\ j\sin {\mathrm{\&delta;}}_r{\mathrm{\&eta;}}_r& \cos {\mathrm{\&delta;}}_r\end{array}\right]\right\}\left[\begin{array}{c}1\\ {\mathrm{\&eta;}}_{k+1}\end{array}\right](k\&times;E_{k+1,t}^{+})$

In the formula: K is the number of plies of film; R is that film is certain one deck, in addition:

$\left[\begin{array}{c}B\\ C\end{array}\right]=\left\{\underset{r=1}{\overset{k}{\mathrm{\&Pi;}}}\left[\begin{array}{cc}\cos {\mathrm{\&delta;}}_r& j\&CenterDot;\sin {\mathrm{\&delta;}}_r/{\mathrm{\&eta;}}_r\\ j\&CenterDot;\sin {\mathrm{\&delta;}}_r\&CenterDot;{\mathrm{\&eta;}}_r& \cos {\mathrm{\&delta;}}_r\end{array}\right]\right\}\left[\begin{array}{c}1\\ {\mathrm{\&eta;}}_{k+1}\end{array}\right]$

Y＝C/B

The amplitude reflectance of film system $r=\frac{{\mathrm{\&eta;}}_0-Y}{{\mathrm{\&eta;}}_0+Y}$

The reflectivity at respective wavelength place is $R=\left(\frac{{\mathrm{\&eta;}}_0-Y}{{\mathrm{\&eta;}}_0+Y}\right){\left(\frac{{\mathrm{\&eta;}}_0-Y}{{\mathrm{\&eta;}}_0+Y}\right)}^{*}$ So just obtain the reflectance value after multilayer film superposes, the formula of transmitance also can be tried to achieve by similar calculating.Can see by this calculation process, calculate multilayer film and when the reflectivity at some wavelength place, comprise relevant vector, plural number, matrix computations.

The film that the present invention is based on the MATLAB language is a stacking method, can realize according to following steps:

1) initializaing variable of rete is set;

2) detect first letter and represent the rete attribute;

3) calculation combination admittance;

4) the next rete attribute of cycle detection;

5) calculate multiple film layer combination admittance;

6) calculate the rete reflectivity.

7) figure that runs a curve.

The above-mentioned thickness of stating multiple film layer is that 1/4 λ is doubly inferior, and wherein λ is a wavelength, and the output of its reflectivity image is according to TiO ₂And SiO ₂The deposition of two kinds of coating materials, its rete are H-L-H-L-H; Wherein H is high index film material TiO ₂, L is the low-refraction coating materials.

MATLAB can handle prevailing value analysis, matrix operation, digital signal processing, modeling and application programs such as system's control and optimization, in the integration environment that union application program and figure use.Writing the M file in the MATLAB language is very easily.The M file is as the ASCII character file of command set, and therefore, M file grammer is simple, and man-machine interaction is strong.

In MATLAB, we use its mark function to realize the establishment of program.The MATLAB symbolic computation depends on existing database, can realize symbolic computation by the function that Maple.m directly calls the Maple system.Common optically-controlled signal deposition process generally can only be used for controlling the deposition process that optical thickness is the multilayer film of 1/4 λ, and therefore only introducing most widely used optical thickness here is 1/4 λ times time multilayer film and the program composition of exporting with the reflectivity image of two kinds of coating materials depositions.Only calculate and to carry out small change to computation process if realize the deposition simulation deposition process of any thicknesses of layers, just can realize.Set up the refractive index database of coating materials simultaneously, can design more accurately.Film system designs program schematic diagram as shown in Figure 1.

At first define independent variable, the wavelength X of position in mutually as independent variable, and reflectivity R as function, write out the expression formula of R=R (λ).Next is the computation process of rete stack.Utilize character and if-end to circulate and realize the banking process calculating of film system.The 3rd, the associative operation of pattern manipulation interface is programmed with GUI and is realized.Also need to determine following parameter simultaneously.Control wavelength X 1, the scope of definition independent variable, the refractive index η of the refractive index y1 medium of substrate, the refractive index value of two kinds of coating materials, below we realize the simulation process that film is with two kinds of height refractive index materials:

The loop program code is as follows:

% definition character variable is provided with the initial value of matrix;

result＝sym([1，0；0，1])；，’，...

’syms?tp，’，...

’syms?nmb，’，...

’for?k＝l∶n，’，...

The circulation of a certain control wave strong point input of % film system;

’if?abs(s(k))＝＝108|abs(s(k))＝＝76，’，...

’x＝u，’，...Charx＝Charcu

’q＝e，’，...Charq＝Charce

text1＝(pi*x)/(2*tp)

text2＝(pi*x)/(2*tp)

text3＝(pi*x)/(2*tp)

text4＝(pi*x)/(2*tp)

’result2＝sym([cos(text1)，j*sin(text2)/q；j*sin(text3)*q，cos(text4)])；，’，...

’end，’，...

’result＝symmul(result2，result)；，’，...

’end，’，...

The refractive index of % definition substrate is the matrix of one 2 row 1 row;

’result1＝sym([1；Y])；，’...

The % character variable is calculated reflectivity;

’result2＝symmul(result，result1)；，’，...

’vary＝sym(result2，2，1)/sym(result2，1，1)；，’，...

’last＝(abs((1-vary)/(1+vary)))^2；，’，...

’syms?Ssp，’，...

’syms?Lsp，’，...

% carries out the drawing that comprises character variable;

’ezplot(last，[Ssp，Lsp])；’])；

Now import a simple barrier system: center control wavelength is 600nm; Rete is H-L-H-L-H; H represents high index film material TiO ₂, L represents low-refraction coating materials SiO ₂, the refractive index of two kinds of coating materials is respectively 2.45 (λ=550nm), 1.46 (λ=550nm, T=260 ℃); Absorption coefficient is 0.01; The refractive index of substrate is 1.5, and the reflectance curve figure of wavelength from 300nm to 1200nm as shown in Figure 4.

As seen in Figure 4:

(1) bandwidth range of multilayer film.If when carrying out thin film deposition with these two kinds of coating materials under such condition, roughly about 250nm, in fact owing to the restriction of technological parameter, bandwidth is little more than this value for its bandwidth range.

(2) near the average reflectance of rete center control wavelength.Near this zone reflectivity is about 98% as can be seen.

Claims (3)

1, the film based on the MATLAB language is a stacking method, it is characterized in that, realizes according to following steps:

1) initializaing variable of rete is set;

2) detect first letter and represent the rete attribute;

3) calculation combination admittance;

4) the next rete attribute of cycle detection;

5) calculate multiple film layer combination admittance;

6) calculate the rete reflectivity.

7) figure that runs a curve.

2, the film based on the MATLAB language according to claim 1 is a stacking method, it is characterized in that: the thickness of described multiple film layer is that 1/4 λ is doubly inferior, and wherein λ is a wavelength.

3, the film based on the MATLAB language according to claim 1 and 2 is a stacking method, it is characterized in that: the output of described reflectivity image is according to TiO ₂And SiO ₂The deposition of two kinds of coating materials, its rete are H-L-H-L-H; Wherein H is high index film material TiO ₂, L is low-refraction coating materials SiO ₂

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