JP3338869B2 - Method for optimizing refractive index distribution of dispersion compensating mirror, dispersion compensating mirror manufactured based on the method, and its application device - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a dispersion compensating mirror which contributes to shortening the pulse and increasing the reliability of ultrahigh-speed lasers in the femtosecond and picosecond regions, and in particular, optimizes the refractive index distribution along the optical path length. And a dispersion compensating mirror manufactured based on the method, and an application device thereof.

[0002]

2. Description of the Related Art For example, a double prism has been used for dispersion compensation of a femtosecond solid-state laser. This is to make an optical path difference by using the wavelength dependence of the refraction angle by the prism, but 1) technology is required for optical axis alignment, and it is easy to accompany time-dependent changes due to positional deviation and angle deviation, 2) desired In order to obtain the dispersion characteristics of (1), a certain long distance is required. 3) The dispersion compensation characteristics basically remain linear (linear). 4) The dispersion characteristics of the materials constituting the prism are added. 5) There are many shortcomings, such as a lack of prism materials with sufficient transmission characteristics in the 1.5 micron band.

[0003] Therefore, there has been an attempt to make the laser system compact and stable by replacing such a prism with a dispersion compensating mirror. As is well known, the refractive index of a material generally increases as the wavelength becomes shorter, so that the speed of light changes depending on the wavelength (positive chromatic dispersion). As in the case of Fourier expansion of the function, when the light in the band is in phase, it becomes narrow. For example, in a pulse of 30 femtoseconds, the phase of light in a band of 30 nm needs to match. On the contrary, if the chromatic dispersion caused by the gain medium or the like can be compensated for by the optical element having the opposite dispersion characteristic in the resonator of the solid-state laser (negative dispersion compensation), the nonlinearity of the laser crystal (coherent patent car mode) Due to rocking, etc., oscillation is more stable in a pulse than in a continuous wave, and a mode-locked laser can be realized.

However, as a mirror designed to delay or advance only a specific wavelength, there is a mirror called “Gires-Tournois mirror”, which resonates at a wavelength to be delayed. Has an etalon structure to wake up. On the other hand, a dielectric mirror having a 1 / 4λ period has a dispersion characteristic at a position deviated from the center wavelength. However, if the wavelength deviates greatly from the center wavelength, the reflectance is reduced, and dispersion of 100 fs ² or more cannot be obtained, and the light has a predetermined wavelength dependency. Further, there is a two-stack dielectric mirror or the like in which two 1 / 4λ-period dielectric mirrors having different center wavelengths are stacked. In this case, a dispersion of about 500 fs ² can be generated. Actually, in order to reduce the third-order dispersion, there is an example in which an optical pulse of about 50 fs is generated by setting the chromatic dispersion value to about 200 fs ² (Yamashita, IEEE J. QEQE-23).
—2005, 1987). There is also an example in which the wavelength dispersion of the phase of a reflected wave is controlled by changing the reflection wavelength near the surface and the reflection wavelength at the back by chirping the lamination period of the dielectric (R. Szipocs Optics Letter19 (3. 201, 1994).

[0005] However, none of the above methods is satisfactory.
rag) A method to suppress the resonance effect by oscillating the period like a sine wave (Gabriel Tempea and Frenc Krausz, 'Dispersion
Control Over 150THz withChirped Dielectric Mirror
s'IEEE J. of Selected Topics in Quantum Elec.Vol.
4. No2. 1998, p193) and a method to weakly set the coupling on the surface side of the chirp mirror (Nicolai matsucheek, Franz
X Kartner, and Urshula Keller, “Theoryof Double−
Chirped Mirrors ”, IEEE J. of Slectcte Topics in Qu
antum Elec. vol.4.no.2 1998, p.197).

[0006]

However, since these new methods also predict the resulting dispersion characteristics after determining the structure, it is difficult to correct the higher-order dispersion characteristics of the material. Or utilize only some of the predictable effects (e.g., resonance at a particular wavelength, or the dependence of the wavelength on the penetration length due to chirp), thereby optimizing the physically possible refractive index distribution. There is no problem. In fact, in such a method, since the amount of dispersion correction at the coating film thickness that can be formed is small, it was necessary to repeat multiple reflections several times in the laser cavity.

The present invention has been made under such circumstances. Instead of relying on empirical and experimental methods, a more rational and highly reproducible method is used to obtain the largest possible variance correction amount and accurate An object of the present invention is to provide a dispersion compensating mirror capable of obtaining a chromatic dispersion compensation profile, in other words, a dispersion compensating mirror having an optimum refractive index distribution along an optical path length according to a wavelength range of light to be incident. In view of the results obtained by the present invention, the present invention can provide not only a dielectric multilayer structure as a mirror but also a mirror structure applicable to an optical fiber grating and a semiconductor waveguide structure. Also disclosed are techniques or structures that can meet the demands for adding dispersion and compensating in.

[0008]

According to the present invention, as a method of optimizing a refractive index distribution of a dispersion compensating mirror having a refractive index distribution along an optical path length in order to achieve the above-mentioned object, a method according to incident light is used. Assuming a mirror having a desired reflectance in the required wavelength range as an auxiliary system; calculating the pole position and intensity of the impedance of the auxiliary system; and exhibiting the desired chromatic dispersion in the required wavelength range described above. Is set to an optimization system in which the positions and intensities of the poles are moved; a refractive index distribution for realizing the impedance function of the optimization system is obtained by an inverse spectrum method, and this is set as an optimized refractive index distribution. And a method for optimizing the refractive index distribution of the dispersion compensating mirror.

The present inventor has already given a lecture title “Ti ₂ O ₅ / SiO ₂ dispersion compensating mirror manufactured by ion beam sputtering” at the 1998 Spring Society of Applied Physics (29-aX-1). Although it has been proposed to optimize the refractive index distribution, this stage still includes an empirical method, and after calculating the position and intensity of the pole of the "impedance" of the auxiliary system as in the present invention described above. Assuming an optimization system in which the “pole position and intensity are moved” so as to exhibit a desired chromatic dispersion in a required wavelength range, the refractive index distribution for realizing the “impedance function” of the optimization system is inverted. It has not been possible to specifically disclose a unique method of obtaining the spectrum by the spectrum method. The present invention has been presented as a general and reproducible method as a result of research after this lecture.

The refractive index distribution optimized according to the present invention as described above can be realized by a periodic structure of a plurality of medium layers having different refractive indexes. Here, typically, the plurality of medium layers can be composed of first and second dielectric thin films having different refractive indices. However, the first and second dielectric layers having different refractive indices are different from each other. The semiconductor thin film may be constituted by an air layer or a dielectric medium layer sandwiched between the semiconductor thin film and an adjacent semiconductor thin film and having a different refractive index from the semiconductor thin film. The air layer is also a dielectric layer, but in fact it can be formed as a groove formed by etching a certain medium layer such as a semiconductor thin film, and if it is filled with any suitable dielectric medium, it becomes a dielectric medium layer .

[0011]

FIG. 1 shows an example of a refractive index distribution of a dispersion compensating mirror having an optimized refractive index distribution obtained by the method of the present invention. A method for obtaining such a refractive index distribution can be described with reference to FIG. In the present invention, as shown in FIG. 2, an auxiliary system having a desired reflectance in a necessary wavelength range according to incident light is first assumed. This is a mirror having a uniform layer on the surface and a periodic structure of a quarter-wave (1 / 4λ) dielectric multilayer film having a desired reflectance. In the auxiliary system of FIG. 2, a dielectric multilayer film is formed at a period of 1 / 4λ on a homogeneous dielectric surface of 4.5 microns. There are two types of dielectrics. For example, the dielectric having a relatively low refractive index is silicon dioxide (SiO ₂ ), and the dielectric having a relatively high refractive index is tantalum pentoxide (Ta ₂ O ₅ ). The absolute value of the reflectivity of such a system does not change as long as the impedance of the system (electric field / magnetic field in the case of a plane wave) is a pure imaginary number. Is adjusted, an optimization system having desired reflectance and dispersion characteristics can be set. Therefore, next, a refractive index distribution for realizing the impedance function of the system thus optimized is obtained by the inverse spectrum method, and finally, a periodic structure for realizing the obtained refractive index distribution is specifically produced. Note that the inverse spectrum method itself has already been disclosed by the present inventor (Ref. 1: “Dispersive
mirror in AlGaAs designed by inverse spectral the
ory ”, Steven RA Dods and Mutsuo Ogura 20th Octobe
r 1997 vol.36, No.30 Applied optics page 7741).

More specifically, the present invention has one feature in focusing on the impedance of the line. The impedance Z _1f of the auxiliary system shown in FIG. The following analogy can be applied, and Z _1f = −jZo cotβ (1) Zo is the characteristic impedance.

Here, if β = ω / c = (2πf) / c; α = 2lf / c (1 = line length, c = light speed), it can be expanded into a series as shown in the following equation (2).

(Equation 1)

On the other hand, the reflectance is as follows: Γv = (Z _1f -Zo) / (Z _1f + Zo) = (jb-a) / (jb + a) (3) When there is no loss, the impedance (Z _1f =
Since jb) is an imaginary number, the reflectance remains 1 in the stop band at any impedance.
The delay is a value obtained by differentiating the phase angle of the reflectance with the angular velocity, and τ = −darg (Γ) / dω (4) Therefore, the dispersion compensation optimizes the impedance function to obtain a desired delay. Getting characteristics is the first step.

The impedance function of the reference system shown in FIG. 2 is expressed by the following equation (5), and has a pole according to the uniform thickness of the medium portion.

(Equation 2)

For example, when the thickness of the uniform medium is 2.5 μm,
Each stopband order (first and third order in the table) has two poles as shown in Table 1 below.

[Table 1]

In this method, as illustrated in Table 1, specific values are assumed for an optimization system in which a desired impedance function is obtained by moving the position and intensity of the poles of the auxiliary system. That is,

(Equation 3) Of the first and third poles (1 / ρm) and the position are moved as shown in Table 1.

Thus, as shown in FIG. 3, in this case, a group velocity delay characteristic optimized for 4 mm Ti-doped sapphire can be obtained. Therefore, when the actual refractive index distribution is obtained by the inverse spectrum method for this impedance function, the distribution becomes as shown in FIG. 1. Therefore, a mirror may be manufactured to realize this. Although the refractive index distribution in FIG. 1 is a continuous distribution, it can be equivalently realized as a discrete refractive index distribution.

In the actual film forming process, the continuous refractive index distribution shown in FIG. 1 may be realized as it is,
An equivalent discrete refractive index distribution may be realized. For example, according to the latter, it is easy to use a two-layer film structure such as silicon dioxide and tantalum pentoxide, so each of these layers is further decomposed into ultrathin films in the range of 2 to 10 nm, and their film thickness and the like are determined. By adjusting and stacking,
It is possible to construct a dispersion compensating mirror having the refractive index distribution to be realized shown in FIG. In addition, the method itself of taking a correspondence with an equivalent continuous refractive index distribution by digitally changing the refractive index distribution by decomposing into two layers in this manner is known,
It is called the Harpin method.

FIG. 5 to be described later shows the expected value expected for the dispersion compensation film having the continuous refractive index distribution manufactured as described above, and the expected value of the actually manufactured dielectric film of the approximate binary refractive index type. Although the dispersion characteristics are shown, they are almost the same.

Empirical, based on a conventional actual refractive index structure,
In the case of experimental optimization, changing the distribution of the refractive index also changes the real component of the reflectance. In addition, since the refractive index distribution has a very high degree of freedom, only adjustment based on estimation is possible.However, such an empirical method involves adjusting the equivalent reflecting surface back and forth by wavelength, for example, by chirping. Is possible, but at the same time, resonance occurs at a specific wavelength, and undesirable parasitic dispersion characteristics appear.
Such is not the case according to the invention.

FIG. 4 shows the electric field strength in the dielectric at several wavelengths of the manufactured dielectric multilayer dispersion compensation mirror. This dispersion compensating mirror is designed to reflect the short wavelength component that tends to be delayed in the gain medium of the solid-state laser first, and to delay the long wavelength component that is likely to advance in the gain medium. The electric field intensity of (820 nm) is localized on the right-hand surface of the mirror in the figure, and penetrates a little inside the mirror at the intermediate wavelength (860 nm). Even longer wavelengths of 880
In the nm component, an electric field peak exists inside the mirror,
It can be seen that the above-described resonator type delay is realized. That is, it is possible to construct a dispersion compensating mirror having a group velocity delay characteristic that is 1 / q (q is an integer of 1 or more) which is the inverse characteristic of the solid-state laser crystal used.

In summary, the method of the present invention requires that the chirp structure and the resonance delay structure of the dispersion compensating mirror, which have conventionally relied only on experience and trial and error, can be realized with good reproducibility without occurrence of spurious or the like. It is excellent in that the compensation characteristics can be approximated including the curved part, and that the degree of freedom of the approximation is high, and that the accuracy can be freely increased according to the number of poles, that is, the film thickness of the dielectric. ,
In fact, the retardation characteristics obtained by the present invention show
(7.278 μm), the result was about three to five times greater than the compensation amount of a general chirped mirror obtained at (7.278 μm).

However, in the above-described mirror design, the refractive index distribution obtained by the inverse spectrum method may exceed the physically achievable range. When such a limit is reached in the optimization of the lower-order pole, the optimization of the lower-order pole may be stopped at that point, and the optimization of the higher-order pole may be performed. In some cases, the refractive index range required by the inverse spectrum method may be relaxed due to the movement of the higher-order poles. Returning to optimization was effective. Also, regarding the auxiliary system, it was effective to assume a structure in which an anti-reflection coating was applied in advance and start from there.

The dispersion compensating mirror having the characteristics shown in FIG. 5 was actually manufactured by an ion beam sputtering method. The film formation conditions were as follows: high frequency power of ion source 200W, ion source argon 7scc
m, ion current 90 mA, ion accelerating voltage 850 V, neutralizer 100 mA, and deposition rate of about 0.5 Å / sec. The mirror is made up of 474 layers with an average thickness of 15.3 nm and has a thickness of 7.3 μm. 74 for areas with a reflectance of 98% or more
0 nm to 820 nm, the area where dispersion compensation is obtained is 760 nm
From about to 830 nm, about 60 nm is secured as a band that can be inserted into the laser resonator and compensate for dispersion.

By increasing the film thickness, it is possible to increase the number of poles, perform higher-order dispersion compensation using a larger number of optimum parameters, and broaden the reflectance. FIG. 6 shows an example in which the oscillation band is extended by increasing the film thickness to about 9 μm. Furthermore, it is possible to freely design a 1.3 μm band forsterite laser or a 1.5 μm band chrome yag laser. For example 1.
In a 3 μm band long wavelength laser, as shown in FIG.
With a total of 567 dielectrics and a dielectric thickness of 11.7 μm, dispersion compensation suitable for the dispersion characteristics of the laser crystal becomes possible.

FIG. 8 shows a configuration example of a mode-locked laser 10 as an applied device using the dispersion compensating mirror of the present invention. In the device shown, 4 mm is used as a solid-state laser crystal.
A long Ti-doped sapphire crystal 12
The output 13 is output via the output coupler 14. Except for the dispersion compensating mirrors 11a and 11b, the principle structure, the element arrangement, the element elements used, and the like may be already known.

The arrangement of the resonators is also a known arrangement of a Z-fold type. However, instead of the conventionally known Brewster-type prism pair (prism interval 29 cm), two dispersion compensating mirrors manufactured according to the present invention are used. 11a and 11b are used. As a result, the threshold value of the laser mode-locked oscillation constructed was only 2.7 W compared to 4 W in the case of using the prism pair. Output coupler R = 95%, output both 2
It was about 00 mW, and no problem was found due to the use of the present invention.

9 and 10 show an autocorrelation waveform and an oscillation pulse spectrum of the mode-locked laser 10, respectively. Assuming a Sech2 pulse waveform, the pulse width is 35 fs and the spectrum width is 19 nm, which satisfies the condition (transform limit) that gives a substantially minimum pulse width for a given spectrum width. In the case of oscillation by a prism, the pulse width was 34 fs, which is almost the same, but the spectrum width is as wide as 34 nm, which is not the transform limit. This is because, according to the prism, high-order dispersion compensation is not optimized only by linear dispersion compensation. Further, since the loss is smaller than that of the prism, the oscillation threshold value is kept low. In the 1.3 or 1.5 μm band, the loss due to the prism pair is particularly problematic, and the dispersion compensating mirror according to the present invention is advantageous.

The dispersion compensating mirror exemplified here has a band of
Although it is a relatively narrow mirror of about 30 nm, the dispersion compensation value is large, so that a small number of mirrors can realize a compact and stable laser. In order to further increase the dispersion compensation band, means such as 1) changing to a silicon dioxide / titanium oxide system having a large difference in the refractive index of the dielectric, 2) starting from a pre-chirped system as an auxiliary system, and the like can also be adopted. . In any case, for a given refractive index difference and maximum film thickness, the technique of the present invention can provide maximum optimization. In the recent design example of the chirped multilayer film, the resonance effect is suppressed by oscillating the Bragg period like a sine wave. However, in the present invention, effective dispersion compensation is provided by simultaneously utilizing the resonance effect. In fact, it is also a feature of this method that further optimization is possible starting from the mirror design already published.

To further illustrate a structural application example of the dispersion compensating mirror according to the present invention, it is widely practiced to manufacture a distributed reflector by periodically changing the refractive index of an optical fiber by, for example, ultraviolet exposure. By optimizing this period with the inverse spectrum method according to the present invention, dispersion compensation can be performed. The line width of the exposure is limited to a minimum of about 0.2 μm by the resolution of the exposure apparatus, but it is possible to increase the arrangement and the width of the exposure. Further, since the arrangement is discretized to about 10 nm depending on the accuracy of the DA converter of the exposure apparatus, it is possible to incorporate the effects of these discretizations into the calculation simulation in advance. FIG. 11 is a schematic diagram of an optical fiber grating 20 which is a specific example of a dispersion compensation mirror formed according to the method of the present invention. The periodic structure in which the length (film thickness) of each of the first medium region having the first refractive index indicated by solid filling and the second medium region having the second refractive index indicated by white is optimized according to the present invention. ing. In the case of the optical fiber grating 20, the band of the reflectance is narrow because the difference in the refractive index is small. However, by starting from a grating that has been chirped in advance, the necessary band can be secured.

On the other hand, when a semiconductor multilayer film is used, as described in Reference 1, the band of the mirror is narrow because the distribution of the refractive index is small, but the dielectric constant of the material is high. Because of the lattice matching, a long optical path length can be obtained, and it is possible to secure a dispersion compensation amount of about 1000 fs ² by one reflection. Further, it is possible to form a laser capable of self-excited oscillation by providing an excess absorption layer inside the semiconductor multilayer film.

In the ultrahigh-speed semiconductor laser, the wavelength dispersion in the semiconductor active layer and the waveguide constituting the resonance system mirror portion is corrected by the present invention, so that the ultrashort pulse of the Q switch and the mode-locked laser can be realized. Become.
FIG. 12 shows an example in which the mode-locking type solid-state semiconductor laser 30 is provided at both ends with dispersion compensating mirrors that can be manufactured according to the present invention, that is, modulation gratings 31 for dispersion compensation. Other structural parts may be the same as those of the known structure, and the case shown in the drawing is a mere example. In FIG. 3A, the BB cross section of the laser gain region 32 in which the saturable absorption region 33 is provided, which is an existing component, is also shown in FIG. 3B. And is not limiting. The construction substrate is a p-GaAs substrate 46, and the constituent layer members are p-Al _0.4 GaAs cladding 41 and p-Ga
It has an As guide 42, an i-Al _0.2 GaAs barrier 43, an InGaAs wire 44 which is a substantially active region, and an n-Al _0.4 GaAs cladding 45. In general, in the case of a semiconductor laser, it is important that an optical pulse of about 1 ps is stable and satisfies a transform limit condition, and does not unnecessarily occupy a wavelength band. The structure shown is suitable to meet such requirements, and a semiconductor grating of about 100 cm ^-1 has an equivalent refractive index difference of about 1/10 compared to a semiconductor multilayer film, and the dispersion compensation band is reduced to about 1 nm. As a result, the light penetration length is expanded, and 10,000 fs ² can be used as the compensation amount.

The modulation grating portion 31 can be formed by etching. The resist is perforated and selectively etched from that portion. In this case, the optimized refractive index distribution obtained according to the present invention is determined by the divided semiconductor thin layer (first medium layer) and the air layer (second medium layer) as a dielectric layer in the etching groove. Will be realized above. In order to make the depth of the grating constant, it is preferable that the size of the opening is constant and only the interval between the openings is adjusted. In the electron beam exposure method, the exposure position is 1.2
Because the coordinates are limited to positive multiples such as 5, 2.5, and 5 nm, the spacing is discrete even at the aperture. Can be overcome.

[0035]

According to the present invention, the chirp structure and the resonance delay structure of the dispersion compensating mirror, which have conventionally relied only on experience and trial and error, can be realized with good reproducibility without generating spurious components, and the necessary compensation characteristics can be obtained. It can be approximated including the curve.
In addition, the degree of approximation is high, and the accuracy can be freely increased according to the number of poles, that is, the thickness of the dielectric. Accordingly, the dispersion compensating mirror having the optimized refractive index distribution has a wide application to various fields and has a great effect.

[Brief description of the drawings]

FIG. 1 is a diagram showing a relationship between an optical path length and a refractive index in an example of a refractive index distribution to be obtained by the present invention and to be realized in a dispersion compensation mirror.

FIG. 2 is a diagram showing a relationship between an optical path length and a refractive index of an example of a refractive index distribution of an auxiliary system used in the present invention.

FIG. 3 shows a 4 mm Ti obtained in one embodiment of the present invention.
FIG. 5 is a group velocity delay characteristic diagram optimized for doped sapphire.

FIG. 4 is a diagram of the electric field strength in a dielectric at various wavelengths of a dielectric multilayer film type dispersion compensating mirror obtained in one embodiment of the present invention.

FIG. 5 is a graph showing expected values expected of a dispersion compensation film having a continuous refractive index distribution manufactured according to an embodiment of the present invention and dispersion characteristics of an actually manufactured dielectric film of a binary refractive index approximation type. It is a characteristic diagram.

FIG. 6 is a characteristic diagram of dispersion characteristics similar to FIG. 5 in an example in which the oscillation band is extended by increasing the film thickness.

FIG. 7 is a characteristic diagram of a dispersion characteristic similar to FIG. 5 in another example in which the oscillation band is extended by increasing the film thickness.

FIG. 8 is a schematic configuration diagram of a mode-locked laser using the dispersion compensation mirror of the present invention.

9 is an autocorrelation waveform diagram of the mode-locked laser shown in FIG.

FIG. 10 is an oscillation pulse spectrum of the mode-locked laser shown in FIG.

FIG. 11 is a schematic configuration diagram of an optical fiber grating formed according to the present invention.

FIG. 12 is a schematic configuration diagram of a mode-locked solid-state semiconductor laser having a modulation grating for dispersion compensation manufactured according to the present invention.

[Explanation of symbols]

 10 Mode-locked laser 11a, b Dispersion compensating mirror 12 Sapphire crystal 20 Dispersion-compensating optical fiber grating 30 Dispersion-compensating mode-locked laser 31 Modulating grating 32 Laser gain region Supersaturated absorption region

Continuing from the front page (72) Inventor Shigo Zhang 1-4-1 Umezono, Tsukuba-shi, Ibaraki Pref. In-house Research Institute of Electronics and Technology (56) References JP-A-10-48567 (JP, A) Patent 2754214 (JP) , B2) (58) Fields investigated (Int. Cl. ⁷ , DB name) G02B 5/26 G02B 5/28 H04B 10/02 H04B 10/18 G02B 6/00

Claims (6)

(57) [Claims] 1. A method of optimizing a refractive index distribution of a dispersion compensating mirror having a refractive index distribution along an optical path length; a mirror having a desired reflectance in a required wavelength range according to incident light. After calculating the position and intensity of the pole of the impedance of the auxiliary system; and optimizing the system by shifting the position and intensity of the pole so as to exhibit a desired chromatic dispersion in the required wavelength range. Setting a refractive index distribution for realizing the impedance function of the optimization system by an inverse spectrum method and setting the obtained refractive index distribution as an optimized refractive index distribution; Optimization method. 2. The method of claim 1, wherein the poles are in a higher order Bragg reflection wavelength band. 3. The method according to claim 1, wherein a periodic structure of a plurality of medium layers having different refractive indexes is used to realize the optimized refractive index distribution. Optimization method of refractive index distribution of mirror. 4. The method according to claim 3, wherein the plurality of medium layers include first and second dielectric thin films having different refractive indices from each other. Distribution optimization method. 5. The method according to claim 3, wherein the plurality of medium layers include first and second semiconductor thin films having different refractive indexes from each other. Optimization method. 6. The method according to claim 3, wherein the plurality of medium layers are sandwiched between a semiconductor thin film and the adjacent semiconductor thin films, and an air layer having a different refractive index from the semiconductor thin film. A method of optimizing a refractive index distribution of a dispersion compensating mirror, comprising a dielectric medium layer.