JPH10186104A - Multi-layered anti-reflection film and optical element - Google Patents

Abstract

PROBLEM TO BE SOLVED: To secure a low reflection factor over a wide wavelength range by providing a reflection factor spectrum with wide-band low-reflection-factor characteristics which have two throughs of reflection factor and a reflection factor peak between them in a necessary wavelength band. SOLUTION: Two kinds of thin film consisting of a low-refractive-index material 1 and a high-refractive-index material 2 respectively are laminated alternately on an end surface of the substrate 3 of a semiconductor laser element, etc., to form a multi-layered structure of two layers, four layers, or N layers (N: even number). A mismatch condition of optical admittance is applied and layer thickness is determined to decide the structure of a multi-layered film with reflection factor spectrum characteristics which have two throughs with finite low values and a reflection factor peak between the depressions. The reflection factor can be suppressed low over the wide wavelength range including the two troughs on condition that the reflection factor at the reflection factor peak is suppressed below the permissible limit of an antireflection film.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a multilayer anti-reflection film capable of realizing low-reflectance characteristics over a wide band, and an optical device having the multilayer anti-reflection film.

[0002]

[Related Background Art] In a semiconductor laser amplifier,
It is necessary to suppress the Fabry-Perot mode oscillation by setting the end face reflectance to 10 ⁻³ or less. Further, in the wavelength-tunable external resonance mode-locked laser, it is necessary to keep the reflectance at the end face at an extremely low reflectance of 10 ⁻⁵ or less. Conventionally, as such an antireflection film having an extremely low reflectance, for example, a single-layer dielectric film having a thickness of λ ₀ / 4n _f (where λ ₀ is the center wavelength and n _f is the refractive index of the dielectric) is used. Used. Incidentally as the dielectric material forming the antireflection film of this kind, those having a _{[n f = (n s)} 1/2] becomes refractive index, or refractive index close to hand the refractive index n _s of the substrate Is used.

[0003]

In the case of a semiconductor laser, if a single-layer dielectric film is used to achieve an ultra-low reflectance of 10 ^-5 or less, for example, the refractive index n of the substrate may be reduced.
_{For s} [= 3.286], the refractive index n _f of the dielectric material is [=
1.813], a wavelength band of only about 9 nm can be secured at the most in theoretical calculation. Moreover, practically, there is almost no dielectric material having a refractive index satisfying the relationship of [ _nf = ( _ns ) ^1/2 ], and fluctuations in the refractive index occur when an actual reflecting film (dielectric film) is formed. Therefore, it is difficult to obtain a desired extremely low reflectance. In addition, the wavelength band is narrower than 9 nm obtained by the above theoretical calculation.

On the other hand, it has been proposed to form a multilayered dielectric film to form a broadband antireflection film. However, in this case, generally, a plurality of types of dielectric materials having the same number as the number N of layers are required. In addition, since there is no systematic design method when designing a multilayer structure film, it is necessary to set the target center wavelength λ ₀ , and then determine the refractive index of the material required for it and the layer thickness for each layer. . For this reason, a great deal of time and effort is required for the design. For example, even when the arithmetic processing is performed using a supercomputer, a calculation time of several hours to several days or more is required.

The reflectance spectrum in a target wavelength region of an antireflection film having a multilayer structure realized under the above-described design is as follows.
Normally, the target center wavelength λ ₀ is defined as a valley (bottom) (1
(Having two valleys), and the wavelength band of low reflectance is not so wide. That is, when an antireflection film made of a dielectric film is formed, generally, an optical admittance matching condition in which the optical admittance Y is [n ₀ ] (for example, in the case of air, n ₀ = 1) is used. , Its reflectivity
The film thickness (layer thickness) is designed to be [0]. Therefore, the reflectance spectrum has a narrow parabolic shape with the reflectance being [0] at the set center wavelength λ ₀ , and there is a problem that the wavelength band below the desired reflectance is narrow.

The present invention has been made in view of such circumstances, and has as its object to provide a multilayer antireflection film capable of securing a low reflectance over a wide wavelength range, and a multilayer antireflection film. Provided is an optical element having the same. Another object of the present invention is to provide a multilayer antireflection film capable of facilitating the structural design (determining the thickness of each layer) of the multilayer antireflection film and realizing a required low reflectance in a required wavelength range. To provide.

[0007]

In order to achieve the above-mentioned object, a multilayer antireflection film according to the present invention is a multilayer antireflection film formed by laminating a plurality of thin films made of materials having different refractive indexes. The reflectance spectrum is characterized by having broadband low reflectance characteristics having two valleys having low reflectance in a required wavelength band and a reflectance peak between them. For example, two types of thin films composed of a high-refractive-index material and a low-refractive-index material are alternately laminated, and the reflectance peak generated between two valleys formed in the low-reflectance wavelength region is set to be equal to or less than the target reflectance. By doing so, the required low reflectance is realized over a wide wavelength band.

[0008] In particular, the thickness of each layer is determined by an optimization algorithm based on a finite reflectance band evaluation given an optical admittance mismatch condition. Thus, the present invention is characterized in that the reflectance spectrum has two valleys of low reflectance and a reflectance peak equal to or lower than the target reflectance is provided between the valleys.

The reflectance is set to 10 ^-3 or less, 10 ^-4 or less, 10 ^-5 or less, 10 ^-6 or less, or the low reflectance wavelength band is set to 300 nm or more and 150 nm or less.
As described above, the feature is set to be 100 nm or more and 50 nm or more, respectively. Preferably, an antireflection film having a reflectance of 10 ^-3 or less and a wavelength band of 300 nm or more, and a reflectance of 1
0 ^-4 its wavelength band than 150nm or less of the anti-reflection film,
An antireflection film having a reflectance of 10 ⁻⁵ or less and a wavelength band of 100 nm or more, or an antireflection film having a reflectance of 10 ⁻⁶ or less and a wavelength band of 50 nm or more is characterized.

Further, as set forth in claim 11, a multilayer antireflection film having the above-mentioned reflectance characteristic is formed on an end face of an optical element such as a semiconductor laser amplifier.

[0011]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of the multilayer antireflection film and the optical device according to the present invention will be described below with reference to the drawings. The multilayer antireflection film according to the present invention, as shown in FIG. 1, alternately forms two types of thin films composed of a low-refractive-index material 1 and a high-refractive-index material 2 on an end face (laser end face) of a substrate 3 such as a semiconductor laser device. And has a multilayer structure of two layers, four layers, or N layers (N is an even number). The thickness of each of these thin film layers is, for example, as shown in FIGS.
The optical admittance mismatch condition is determined by a calculation process based on an optimization algorithm based on a finite reflectance band evaluation given a condition. As will be described later, calculation processing by the optimization algorithm is executed by a simple computer such as a personal computer. The thickness of each layer calculated here is λ / 4n which is generally used.
rather than the thickness of _f (1 optical quarter wavelength) is obtained as the thickness coefficient (parameter) w _r, which will be described later.

The characteristic matrix of an N-layer multilayer film is generally expressed as follows.

[0013]

(Equation 1)

However, the optical admittance Y is represented as [C / B], and the reflectance when [Y = 1] is [0].
In the above equation, n ₁ is the refractive index of the low refractive index material 1, n ₂ is the refractive index of the high refractive index material 2, n _s is the refractive index of the substrate 3, and δ _r is the center wavelength λ ₀ . when _{you, δ r = 2πn k d r} / λ 0, d r = w r H (orw r L)
(r = 1, 2,..., N) are given as H = λ ₀ / 4n ₂ and L = λ ₀ / 4n ₁ . Incidentally parameters are initialized in this calculation, N, is _{λ 0, n 1, n 2} , n s, also parameters to be obtained by the calculation is w _r (thickness coefficient).

The optimization algorithm for determining the thickness of each thin film layer according to the present invention is basically executed based on the above equation. First, as shown in FIG. 2, parameters N, λ ₀ , n ₁ ,
The process starts by initializing n ₂ and n _s [step S1]. Then, as a first stage of the calculation process, when realizing a multilayer structure composed of N layers, the film thickness δ of each layer up to N
_1, [delta] _2, ..., giving [delta] _N, respectively, the next optical admittance mismatch satisfying combination _{{δ 1, δ 2, ...} , δ N} to determine the thickness of each layer in the step S2, S3].

[0016]

(Equation 2)

Specifically, the upper and lower limits of the thickness of each layer are set to 2
H (2L) and 0.1H (0.1L), respectively, and the optical admittance Y (= C / B) and n ₀ shown in the above-described characteristic matrix for each combination of the thicknesses of the respective layers within that range. If the deviation is smaller than Δ, this is taken out as a solution. That is, the low refractive index material 1
Is limited to the range of 0.1L <d <2L, and the thickness d of the layer of the high refractive index material 2 is also limited to the range of 0.1H <d <2H. Then, within this limited thickness range, each thickness in all layers up to N is defined as a thickness coefficient w standardized with respect to the reference thickness H (L) of each layer, for example, in 0.001 steps, by a combination thereof. film structure _{{n s / w n Hw n} -1 L, ..., it examines all _{w 2 Hw 1 L / air)} , obtaining the thin-film structure of the optical admittance mismatch condition is satisfied combination.

Then, as a second step, as shown in FIG. 3, a set of coefficients w _r (r = 1, 2,..., N) obtained as described above has a specific wavelength band. For example, for a center wavelength λ ₀ = 1550 nm, 1
In the band of 350 nm to 1750 nm, a spectrum of the reflectance R with respect to the wavelength is obtained [Step S4]. For the calculation processing of the spectrum R (λ), for example, it is sufficient to calculate the reflectance R for each wavelength set pointwise in 1 nm steps in the above wavelength region.

Specifically, the above coefficient w _r (r = 1,..., N)
Structure n _s / w _N H multilayer film shown as a _{set, w N-1 L, ...} , w 2 H, for _{w 1 L / n 0 (air} ), the per wavelength step λ _step (= 1nm) From the minimum wavelength λ _start (= 1350 nm) of the wavelength band to the maximum wavelength λ
Calculate its reflectivity R over _end (= 1750 nm),
The reflectance spectrum R _k (λ) is obtained.

Thereafter, as a third step, the highest reflectance R _max given as a characteristic limit of the target antireflection film is set.
And the reflectance spectrum R _k (λ) calculated as described above are sequentially compared for each wavelength, and the number of points (wavelengths) of the reflectance R lower than the reflectance R _max is counted [Step S].
5, S6]. And evaluates the bandwidth of the low reflectivity from the number of points, determine a set of the largest coefficient w _r of the points. Finally, the central portion of the reflectance spectrum is shifted by the amount of the shift to match the central wavelength of the antireflection film [Step S7]. The solution w _r obtained in this manner is determined as follows reflectivity desired (low reflectance) widest of the thickness of each layer of the antireflection film to achieve a wavelength band calculation result w _r.

That is, in the present invention, as described above,
Since all possible solutions for the thickness of each layer in a plurality of thin film layers are obtained and the solutions are compared with each other to obtain an optimum solution, it is possible to obtain an optimized solution efficiently. . Therefore, it is different from the conventional method of examining the thickness of each layer one by one and converging the solution.Even if a simple personal computer is used, it takes about several hours to calculate the optimal solution efficiently, Can be determined.

In the present invention, when calculating the thickness of each layer in the multilayer film as described above, the optical admittance Y (= C / B) is replaced by the optical admittance matching condition of [n ₀ ]. It is characterized in that an optical admittance mismatch condition in which the admittance Y is shifted by a predetermined amount Δ is introduced. That is, under the optical admittance mismatch condition of | Y−n ₀ | <Δ, where the absolute value of [Y−n ₀ ] is smaller than the predetermined amount Δ, the layer thickness is determined by the above-described optimization algorithm. ing.

Incidentally, the layer thickness determination processing under the optical admittance matching condition is a processing for obtaining a layer thickness such that the point (wavelength) of the minimum reflectivity coincides with the center wavelength and its value is set to [0]. . Therefore, the spectrum in the target wavelength region has a narrow parabolic shape such that the reflectance at the center wavelength becomes [0]. On the other hand, when the above-described optical admittance mismatch condition is introduced, the point (wavelength) at which the minimum reflectance is shifted from the center wavelength,
Alternatively, the reflectance has a finite value that does not become [0]. Therefore, under the above-mentioned matching condition, only one solution that matches the center wavelength can be obtained. However, when the mismatching condition is introduced, the point (wavelength) is near the solution under the matching condition. A plurality of solutions shifted by Δ will be obtained.

Therefore, according to the present invention in which the layer thickness is determined by introducing the mismatch condition of the optical admittance, two valleys having a finite low reflectance are generated in a required wavelength band. And the peak of the reflectance between the valleys (mountain)
It is possible to determine the structure of the multilayer film having the reflectance spectrum characteristic having the following. In particular, if the reflectance R at the above-mentioned reflectance peak point is suppressed to the allowable limit as an antireflection film, that is, the target reflectance or less, the reflectance can be reduced over a wide wavelength band including the two valleys. It is possible to keep it low and widen its bandwidth.

Next, a description will be given of a four-layer antireflection film formed by calculating the layer thickness using actual material parameters. In this example, on a substrate 3 having a refractive index n _s of [3.286],
TiO ₂ (n ₂ = 2.378) and SiO ₂ (n ₁ = 1.445)
Are alternately laminated over four layers (N = 4), and the center wavelength λ
_An antireflection film having a structure optimized by setting ₀ to 1550 nm is formed. Specifically, first, in order to examine the entire range when the standardized layer thickness (film thickness) is changed from 0.1 to 2, δ _step = 0.01 (w _step = 0.0064) Δ = 5 were set and the layer thickness optimization calculation process was performed. In this case, the design for optimizing the multilayer film differs depending on the required reflectance R, and the required reflectance R is set to 10 ⁻³ ,
The value was set to 10 ^-4 , 10 ^-5 , or 10 ^-6 or less, and an optimized design under each condition was obtained. Table 1 shows the structure (layer thickness) of the antireflection film optimized under the above conditions.
And the maximum wavelength band.

[0026]

[Table 1]

In Table 1, regions (1) to (4) indicate the limit regions of the multilayer structure determined by optimization, which are indicated by the relationship of the thicknesses of the respective layers.
Indicates the case where the thickness of the first layer is the thinnest, the area (4) indicates the case where the first layer is the thickest, the area (2) indicates the case where the second layer is the thickest, and the area (3) indicates the case where the thickness of the second layer is the thickest. The cases where the layers are the thinnest are shown.

Next, in order to examine the condition of the above-mentioned region (1) in more detail, the following condition is satisfied: δ _step = 0.0018 (w _step = 0.001) Δ = 0,001, = 0.01, = 0.1 The optimization calculation process of the layer thickness was performed by setting. Table 2 shows the structure (layer thickness) of the antireflection film optimized under the above conditions and the maximum wavelength band.

[0029]

[Table 2]

Incidentally, the reflectance spectra obtained for each of the above-mentioned reflectance conditions (specifications) in the area (1) are as shown in FIGS. 4 to 7, respectively. As is clear from the reflectance spectra shown in these figures, the wavelength band for realizing a low reflectance increases as the deviation Δ of the mismatch condition increases. The reference maximum reflectance R
It can be seen that the lower the _max , the closer the spectrum shape becomes to a U-shape and the narrower the wavelength band.

However, as the wavelength band becomes maximum, the height of the peak at the center also increases, and the maximum reflectance R as a reference is set.
There is a problem that it is almost the same as _max . Therefore, in practice, the value of the reference maximum reflectance _Rmax may be set sufficiently lower than the target maximum reflectance. In this case, as illustrated in FIGS. 8A, 8B, and 8C, the wavelength band is slightly narrowed as the maximum reflectance is reduced. However, as described above, the shape of the reflectance spectrum approaches the U shape, From a practical point of view, a more stable reflectance spectrum can be obtained. For example, for a design of an anti-reflection film of 10 ⁻⁵ or less, the reference maximum reflectance R
_By setting the value of _max to 10 ⁻⁶ , it is possible to easily obtain a quasi-U-shaped reflectance spectrum as illustrated in FIG. 8C.

Thus, it is formed under condition setting as in the present invention, and has two valleys in its reflectance spectrum.
It can be seen that the multilayer antireflection film having the reflection characteristic having the reflectance peak suppressed to the maximum reflectance or less during that time can effectively widen the low reflectance region. still,
The present invention is not limited to the embodiments described above.
In the embodiment, TiO ₂ (n ₂ = 2.378) and SiO _2
Although the multilayer anti-reflection film is formed using two kinds of materials ₂ (n ₁ = 1.445), it is also possible to form the multilayer anti-reflection film using three or more kinds of materials. Even in this case, the thickness of each layer may be determined according to the optimization algorithm under the above-described optical admittance mismatch condition.

Further, when executing the above-mentioned optimization algorithm, the step amount δ for setting the layer thickness w _{r
The step} and the wavelength step λ _step for calculating the reflectance spectrum R (λ) may be set according to the required layer thickness accuracy, the arithmetic processing capability of the computer, and the like. Others
The present invention can be implemented with various modifications without departing from the scope of the invention.

[0034]

As described above, the multilayer anti-reflection film according to the present invention is a multi-layer anti-reflection film formed by laminating a plurality of thin films made of materials having different refractive indexes, and has a reflectance spectrum. And a broadband reflection characteristic having two valleys having a low reflectance in a required wavelength region and a reflectance peak therebetween.

More specifically, when two types of thin films of a high refractive index material and a low refractive index material are alternately formed, the thickness of each layer is optimized to obtain a reflectance spectrum in the low reflectance wavelength region. In this case, two valleys having low reflectance are formed, and the reflectance peak generated between the valleys is equal to or less than the target reflectance, thereby realizing low reflectance over a wide wavelength band. Therefore, according to the present invention, an antireflection film having a low reflectance necessary for preventing reflection in a wide wavelength band, such as an optical element such as a semiconductor laser amplifier, can be effectively obtained.

In particular, the thickness of each layer is determined by an optimization algorithm based on a finite reflectance band evaluation given an optical admittance mismatch condition, thereby realizing a broadband antireflection characteristic. Since a multi-layer film structure that can be obtained is obtained, the processing procedure required for the design itself is simple, and effects such as a simple and efficient multi-layer film structure can be obtained. According to the present invention, the reflectance is 10 ⁻³ or less, 10 ⁻⁴ or less, 10 ⁻⁵ or less,
^-6 multilayer antireflection film set respectively below, or a wavelength band 300nm or more, 150 nm or higher, 100 nm or more, it is possible to obtain a multilayer antireflection film 50nm or more and broadband, in particular reflectance is 10 ^-3 And its wavelength band is 3
An antireflection film having a reflectance of 10 nm or less, a reflectance of 10 ^-4 or less and a wavelength band of 150 nm or more, an antireflection film having a reflectance of 10 ^-5 or less and a wavelength band of 100 nm or more, or a reflectance of 10 nm or less. ^An antireflection film having a wavelength band of not more than ^-6 and a wavelength band of not less than 50 nm can be obtained.

Further, there can be obtained an effect that an optical element such as a semiconductor laser amplifier having a multilayer antireflection film having the above-mentioned reflectance characteristics (antireflection characteristics) formed on an end face thereof can be easily realized. .

[Brief description of the drawings]

FIG. 1 is a diagram schematically showing a structure of a multilayer antireflection film according to the present invention.

FIG. 2 is a diagram showing a process of determining the thickness of each layer in a procedure of an optimization algorithm used for determining a layer structure of a multilayer antireflection film according to the present invention.

FIG. 3 is a diagram showing a calculation of a reflectance and a process of evaluating the reflectance in a processing procedure of an optimization algorithm used for determining a layer structure of a multilayer antireflection film according to the present invention.

FIG. 4 is a view showing a reflectance spectrum in a layer structure optimized in [R <10 ⁻³ ] in a region (1).

FIG. 5 is a view showing a reflectance spectrum in a layer structure optimized in [R <10 ⁻⁴ ] in a region (1).

FIG. 6 is a diagram showing a reflectance spectrum in a layer structure optimized in a region (1) with [R <10 ⁻⁵ ].

FIG. 7 is a diagram showing a reflectance spectrum in a layer structure optimized in [R <10 ⁻⁶ ] in a region (1).

FIG. 8 is a diagram showing a change in a reflectance spectrum with respect to a mismatch condition Δ when the maximum reflectance is set to 10 ⁻⁵ or less in a region (1).

[Explanation of symbols]

 1 Low refractive index material 2 High refractive index material 3 Substrate

 ──────────────────────────────────────────────────続 き Continuing on the front page (72) Inventor Takeshi Kamiya 7-3-1 Hongo, Bunkyo-ku, Tokyo Within the Department of Electronic Engineering, Faculty of Engineering, The University of Tokyo (72) Inventor Li-Sone, 3-11-5, Gopongi, Meguro-ku, Tokyo No. Sun Heights 202 (72) Inventor Seiji Uchiyama 2-6-1 Marunouchi, Chiyoda-ku, Tokyo Furukawa Electric Co., Ltd.

Claims (11)

[Claims] An anti-reflection film having a multilayer structure in which a plurality of thin films made of materials having different refractive indices are stacked, and having two valleys having a low reflectance in a required wavelength band and a reflectance peak therebetween. A multilayer anti-reflection film characterized by having broadband low reflectance characteristics. 2. The broadband low-reflectance characteristic is defined by a thickness of each layer determined by an optimization algorithm based on an optical admittance mismatch condition and a finite reflectance band evaluation. 2. The multilayer antireflection film according to 1. 3. The multilayer antireflection film according to claim 1, wherein the reflectance is set to 10 ⁻³ or less. 4. A wavelength band having a low reflectance of 10 ⁻³ or less is 30.
3. The multilayer antireflection film according to claim 1, wherein the thickness is set to 0 nm or more. 5. The multilayer antireflection film according to claim 1, wherein the reflectance is set to 10 ⁻⁴ or less. 6. The wavelength band having a low reflectance of 10 ⁻⁴ or less is 15
3. The multilayer antireflection film according to claim 1, wherein the thickness is set to 0 nm or more. 7. The multilayer antireflection film according to claim 1, wherein the reflectance is set to 10 ⁻⁵ or less. 8. A wavelength band having a low reflectance of 10 ^-5 or less is 10
3. The multilayer antireflection film according to claim 1, wherein the thickness is set to 0 nm or more. 9. The multilayer antireflection film according to claim 1, wherein the reflectance is set to 10 ⁻⁶ or less. 10. A wavelength band having a low reflectance of 10 ⁻⁶ or less is 5
3. The multilayer antireflection film according to claim 1, wherein the thickness is set to 0 nm or more. 11. An optical device comprising the multilayer antireflection film according to claim 1 formed on an end face.