NOTCH FILTER

A notch filter 1 has a free filter region, and one or more stopbands which are located between lower and upper limits of the free filter region. The notch filter 1 includes a base material 2; and an optical multilayer film formed directly or indirectly on a base material surface M which is a surface of the base material 2. The optical multilayer film 4 is formed on the basis of a basic filter repeat structure in which a basic filter structure in which low refractive index layers L and high refractive index layers H are alternately arranged is repeated a plurality of times. A film thickness of each layer in the optical multilayer film 4 corresponds to a modulation film thickness number sequence obtained by addition of modulation to a basic film thickness number sequence.

FIELD OF THE INVENTION

The present invention relates to a notch filter that suppresses transmission of light in a relatively narrow wavelength range (stopband) and transmits light in other wavelength ranges within a free filter region which is a predetermined wavelength range.

BACKGROUND OF THE INVENTION

As a notch filter (also called minus filter or band-stop filter), a filter described in JP 4575052 B is known.

In this notch filter, for example, as described as (d) in a paragraph [0019] of JP 4575052 B, an alternately repeated structure of high refractive index layers and low refractive index layers which includes (0.65H 0.35L)10is found with a designed reference wavelength, i.e., design wavelength λ=500 nm, a reflection band centered at the design wavelength λ is realized, and transmission in the reflection band due to reflection is blocked. Here, “0.65H” indicates a high refractive index layer having an optical film thickness that is 0.65 times the design wavelength λ, and “0.35L” indicates a low refractive index layer having an optical film thickness that is 0.35 times the design wavelength λ. In addition, “10” at the right shoulder of the round brackets indicates that the structure in the brackets is repeated 10 times. The first 0.65H is closest to a base material.

Recently, there has been a need for a notch filter having a wider free filter region such as 400 nm or more and 1200 nm or less, or 400 nm or more and 1800 nm or less.

For example, in the medical or biotechnological fields or the like, there is an attempt to nondestructively analyze the characteristics, etc., of an object to be observed by applying a laser onto the object to be observed, capturing secondarily generated weak signal light by an imaging device, and analyzing the signal light (spectral analysis). For better analysis, a notch filter having a stopband at the wavelength of the laser is placed in an optical path to the imaging device to suppress reach of relatively strong lasers, which interfere with analysis, to the imaging device and to transmit light in a wide wavelength range necessary for analysis. In addition, for better analysis, it is expected that an imaging device having a wider range of sensitivity wavelengths will be adopted. For example, the sensitivity wavelength of an imaging device using a silicon photodiode is about 400 nm or more and 1200 nm or less. In addition, the sensitivity wavelength of an imaging device using both a silicon photodiode and an indium gallium arsenide (InGaAs) photodiode is about 400 nm or more and 1800 nm or less.

However, in the above notch filter of JP 4575052 B, a stopband is formed on the wavelength side shorter than the design wavelength λ by the monotonous repeated structure of the high refractive index layers and the low refractive index layers. Therefore, the notch filter cannot have only a stopband centered at the wavelength of a laser having a wavelength (1064, 1550 nm, etc.) on the relatively long wavelength side, in a wider free filter region. For example, if a stopband centered at 1550 nm is provided in the notch filter (design wavelength λ=1550 nm), a stopband centered at 1550×1/2.5=620 nm and a stopband centered at 1550×1/3.5≈442.9 nm occur together in a region of 400 nm or more and 1800 nm or less. Stopbands other than such a stopband centered at the design wavelength λ block light in that wavelength band from reaching the imaging device, resulting in a decrease in the quality of analysis.

Meanwhile, when two types of materials having a small refractive index difference are used, appearance of a stopband up to ⅓ of the design wavelength is suppressed by setting an optical film thickness ratio as H:L=1:1 (a=b), even with conventional {(b/2)L aH (b/2)L}° design. Here, “H” indicates a high refractive index layer having an optical film thickness that is ¼ (0.25) times the design wavelength λ, “aH” indicates a high refractive index layer having an optical film thickness of a×0.25×λ, “L” indicates a low refractive index layer having an optical film thickness that is 0.25 times the design wavelength λ, and “(b/2)L” indicates a low refractive index layer having an optical film thickness of (b/2)×0.25×λ. In addition, “c” at the right shoulder of the curly brackets indicates that the structure in the brackets is repeated c times. The first (b/2)L on the leftmost side is closest to the base material. Hereinafter, unless otherwise noted, a film structure is shown in the same manner as above.

However, if the optical film thickness ratio is shifted (a >b or a<b) in order to improve the quality of analysis by forming a stopband having a narrower wavelength width (size between the upper and lower wavelength limits) and allowing signal light having wavelengths adjacent to the wavelength of the laser to be imaged as much as possible, a stopband is formed at ½ of the design wavelength as in the above-described notch filter of JP 4575052 B, so that a notch filter having a free filter region that is wide on the wavelength side shorter than the design wavelength λ cannot be obtained.

One main object of the present disclosure is to provide a notch filter having a wider free filter region.

Another main object of the present disclosure is to provide a notch filter having a stopband having a narrower wavelength width.

SUMMARY OF THE INVENTION

The present specification discloses a notch filter. The notch filter has a free filter region which is a wavelength range in which light is transmitted, and one or more stopbands which are located between lower and upper limits of the free filter region and in which transmission of light in a predetermined wavelength range is suppressed. In addition, the notch filter incudes: a base material; and an optical multilayer film formed directly or indirectly on a base material surface which is a surface of the base material. The optical multilayer film is formed on the basis of a basic filter repeat structure in which a basic filter structure in which low refractive index layers made of a low refractive index material and high refractive index layers made of a high refractive index material are alternately arranged is repeated a plurality of times. A film thickness of each layer in the optical multilayer film corresponds to a modulation film thickness number sequence obtained by addition of modulation to a basic film thickness number sequence in which the film thickness of each layer in the basic filter repeat structure is arranged in order from the base material side. The modulation has a period different from a basic period which is a period of the basic filter structure.

One main effect of the present disclosure is that a notch filter having a wider free filter region is provided.

Another main effect of the present disclosure is that a notch filter having a stopband having a narrower wavelength width is provided.

DETAILED DESCRIPTION OF THE INVENTION

Hereinafter, examples of an embodiment according to the present invention will be described with appropriate reference to the drawings. The embodiment of the present invention is not limited to these examples.

As shown inFIG.1, a notch filter1according to the present invention has a base material2and an optical multilayer film4.

The base material2has a base material surface M on which the optical multilayer film4is directly formed. At the optical multilayer film4laminated on the base material surface M, the notch filter1transmits light in a wavelength range corresponding to a free filter region, and suppresses transmission of light in a wavelength range corresponding to a stopband, among the light that passed through a medium (e.g., air).

The stopband is located between the upper and lower limits of the free filter region. The size between the upper and lower limits (wavelength width) of the stopband is smaller than the wavelength width of the free filter region.

The average transmittance of the free filter region (excluding the stopband) is preferably 85% or more and more preferably 90% or more. The free filter region may be grasped in terms of spectral transmittance (e.g., as a wavelength range where a transmittance is 85% or more), or may be grasped in terms of design (specifications, predetermined range) (e.g., as a wavelength range of 400 nm or more and 1200 nm or less or 400 nm or more and 1800 nm or less).

The optical multilayer film4may be formed on the base material surface M, which is the surface of the base material2, through another film such as an adhesion film of the optical multilayer film4, that is, indirectly on the base material surface M. Also, another type of film such as a protective film may be placed on the outer side (medium side, anti-base material side) of the optical multilayer film4. The other film and the other type of film may be a single-layer film, or may be a multilayer film. At least one of the other film and the other type of film may be included in the configuration of the optical multilayer film4.

The base material2has translucency at least for light in the free filter region.

The material of the base material2is not particularly limited and is, for example, non-metallic glass, crystal, ceramics, or resin.

The shape of the base material2is not particularly limited, and the base material2is, for example, a parallel plate.

The optical multilayer film4is an inorganic multilayer film for which two or more dielectric materials are used, and is a dielectric multilayer film.

The optical multilayer film4is formed on a part or the entirety of at least one surface of the base material2.

The optical multilayer film4includes a plurality of low refractive index layers L and a plurality of high refractive index layers H. In the optical multilayer film4, the low refractive index layers L and the high refractive index layers H are preferably arranged alternately.

The design of the optical multilayer film4is changed by changing design elements such as selection of the numbers and materials of the high refractive index layers H and the low refractive index layers L and increase or decrease of the thickness in each layer (physical or optical film thickness for the layer).

In designing the optical multilayer film4, the film thickness of each high refractive index layer H is grasped on the basis of an optical film thickness, so that each high refractive index layer H may be formed from any high refractive index material as long as the optical film thickness is satisfied. Similarly, the film thickness of each low refractive index layer L is grasped on the basis of an optical film thickness, so that each low refractive index layer L may be formed from any low refractive index material as long as the optical film thickness is satisfied. In order to make manufacturing easier, it is preferable that at least one of the high refractive index material and the low refractive index material for the optical multilayer film4is one type.

Each high refractive index layer H is formed from, for example, a high refractive index material such as zirconium oxide (ZrO2), titanium oxide (TiO2), tantalum oxide (Ta2O5), niobium oxide (Nb2O5), hafnium oxide (HfO2), lanthanum oxide (La2O3), silicon (Si), or praseodymium oxide (Pr2O3), or a mixture of two or more of these.

Each low refractive index layer L is formed from, for example, a low refractive index material such as silicon oxide (SiO2), aluminum oxide (Al2O3), calcium fluoride (CaF2), magnesium fluoride (MgF2), a combination of aluminum oxide and praseodymium oxide (Al2O3—Pr2O3), a combination of aluminum oxide and lanthanum oxide (Al2O3—La2O3), or a combination of aluminum oxide and tantalum oxide (Al2O3—Ta2O5), or a mixture of two or more of these.

The magnitudes of the refractive indexes of each high refractive index layer H and each low refractive index layer L are relative, and the optical multilayer film4can be formed from at least two materials having refractive indexes different from each other.

The low refractive index layers L and the high refractive index layers H of the optical multilayer film4are formed, for example, by physical vapor deposition, and more specifically by vacuum deposition, ion-assisted vapor deposition, ion plating, sputtering, or the like.

The optical multilayer film4may be formed on a plurality of surfaces in the base material2. That is, the base material2may have a plurality of base material surfaces M on which the optical multilayer film4is formed. For example, the optical multilayer film4may be formed on both the front and back surfaces of the base material2which is a parallel plate.

The structure of the optical multilayer film4is based on a basic filter repeat structure in which a basic filter structure is repeated a plurality of times.

Hereinafter, a film structure is shown as appropriate in the form of (aL bH)c, unless otherwise noted, as described above. The design wavelength, is, for example, 500 nm.

For example, a first basic filter structure is 1.17L 0.32H 0.32L 2.31H 0.32L 0.32H 1.17L, anda first basic filter repeat structure is (1.17L 0.32H 0.32L 2.31H 0.32L 0.32H 1.17L)q,
where q is the number of repeats.

In the first basic filter repeat structure, a low refractive index layer L (hereinafter referred to as first layer), closest to the medium, in an initial first basic filter structure B1closest to the base material2and a low refractive index layer L, closest to the base material2, in an adjacent second first basic filter structure B2are one low refractive index layer L (1.17L+1.17L=2.34L; seventh layer). Similarly, at the boundary of an odd-numbered first basic filter structure and an even-numbered first basic filter structure, the low refractive index layers L are connected into one. Thus, in the first basic filter repeat structure, a basic period p which is a period in which the same film thickness appears on the basis of the basic filter structure is 6. Also, in the first basic filter repeat structure, the total number of layers is q×p+1. Here, +1 is based on the fact that the low refractive index layers L at both ends are not shared. For example, in the case of q=50, the number of film layers is 50×6+1=301.

FIG.2shows a spectral transmittance exhibited by the first basic filter repeat structure in the case of q=50.

In the first basic filter repeat structure, a stopband in which a transmittance is around 0 is formed in a wavelength range of about 1330 nm or more and 1660 nm or less, and a free filter region is formed in a state where a large ripple (around 370, 500 nm) exists in a wavelength range of about 305 nm or more and less than 1330 nm.

This first basic filter repeat structure has a free filter region of approximately 400 nm or more and 1200 nm or less.

In the second basic filter repeat structure as well, as in the first basic filter repeat structure, the linkage of predetermined low refractive index layers L occurs. In the second basic filter repeat structure, a basic period p in which the same film thickness appears is 14. In addition, in the second basic filter repeat structure, in the case of r=40, the number of film layers is 40×14+1=561.

FIG.3shows a spectral transmittance exhibited by the second basic filter repeat structure in the case of r=40.

In the second basic filter repeat structure, a stopband in which a transmittance is around 0 is formed in a wavelength range of about 1800 nm or more and 2230 nm or less, and a free filter region is formed in a state where a large ripple (around 320, 400, 500, 680, 1000 nm) exists in a wavelength range of about 300 nm or more and less than 1800 nm.

This second basic filter repeat structure has a free filter region of approximately 400 nm or more and 1800 nm or less.

In the third basic filter repeat structure as well, as in the first basic filter repeat structure, the linkage of predetermined low refractive index layers L occurs. In the third basic filter repeat structure, a basic period p in which the same film thickness appears is 10. In addition, in the third basic filter repeat structure, in the case of s=40, the number of film layers is 40×10+1=401.

FIG.4shows a spectral transmittance exhibited by the third basic filter repeat structure in the case of s=40.

In the third basic filter repeat structure, a stopband in which a transmittance is around 0 is formed in a wavelength range of about 1800 nm or more and 2230 nm or less, and a free filter region is formed in a state where a large ripple (around 320, 400, 680, 1000 nm) exists in a wavelength range of about 300 nm or more and less than 1800 nm.

This third basic filter repeat structure has a free filter region of approximately 400 nm or more and 1800 nm or less.

The structure of the optical multilayer film4fundamentally has an optical film thickness obtained by modulating each optical film thickness in the basic filter repeat structure. That is, to each term belonging to one number sequence in which the optical film thickness of each layer in the basic filter repeat structure is arranged in order from the first layer (optical film thickness number sequence in the basic filter repeat structure; basic optical film thickness number sequence), a corresponding modulation component is added, thereby obtaining one number sequence in which the optical film thickness of each layer in the optical multilayer film4is arranged from the first layer (optical film thickness number sequence in the optical multilayer film4; modulation optical film thickness number sequence). Even when each optical film thickness is converted to another film thickness such as a physical film thickness, the basic film thickness number sequence, modulation, and each film thickness of the optical multilayer film4(modulation film thickness number sequence) are obtained similarly.

First, the case of forming one stopband will be described.

When the nth term (film thickness of the nth layer) of the film thickness number sequence in the basic filter repeat structure is denoted by Dn(n=1, 2, . . . , L0, where L0is the total number of terms (total number of layers) (L0is a natural number)), and the amplitude, period, and phase of the modulation are denoted by a1, Λ1, and φ1, respectively, the nth term (film thickness of the nth layer) dnof the film thickness number sequence of the basic optical multilayer film4is expressed by the following Expression (1).

In the optical multilayer film4having such a film thickness structure, the center wavelength, the wavelength width, etc., of the stopband are adjusted from those in the basic filter repeat structure.

As a tendency, the wavelength width of the stopband is adjusted by adjusting the amplitude a1of the modulation (the larger the amplitude a1, the wider the wavelength width), the center wavelength of the stopband is adjusted by adjusting the period Λ1of the modulation (the larger the period Λ1, the longer the center wavelength), and the ripple of the transmittance distribution is adjusted by adjusting the phase (1of the modulation.

Next, the case of forming a plurality of stopbands will be described.

In this case, one modulation period corresponds to the formation of one stopband, and thus modulations with modulation periods different from each other are added the number of times equal to the number of stopbands.

That is, when the amplitude, period, and phase of the modulation for the kth stopband are denoted by ak, Λk, and φk, respectively (k=1, 2, . . . , u, where u is the number of stopbands to be formed (u is a natural number)), the nth term dnof the film thickness number sequence of the basic optical multilayer film4is expressed by the following Expression (2). In order to form each stopband more clearly, each period Λkof the modulation is preferably larger than the basic period p, and is preferably different from a natural number multiple of the basic period p.

The above Expression (1) is equivalent to the case where k=1 in the aforementioned Expression (2). The aforementioned Expression (2) contains the above Expression (1).

FIG.5is a graph showing the relationship between the modulation period Λ1and the center wavelength of the stopband.

FromFIG.5, it is found that in the basic optical multilayer film4based on any of the basic filter repeat structures, the center wavelength of the stopband monotonically increases with increase of the modulation period Λ1. The center wavelength of the stopband is a function of the modulation period Λ1, and this function can be obtained, for example, by repeating simulation with the modulation period Λ1being variously changed, and calculating fitting curves as appropriate (see three fitting curves (polynomials) inFIG.5).

FIG.6is a graph showing an example of the relationship between the modulation amplitude a1and the wavelength width of the stopband.

FromFIG.6, it is found that when the modulation amplitude a1added to the basic optical multilayer film4based on the first basic filter repeat structure (number of repeats q=50) increases from 0.1 to 0.2, the wavelength width of the stopband around 1064 nm increases. Here, the period Λ1of the modulation is 15.6.

For the film thickness number sequence of such a basic optical multilayer film4, adjustment for achieving some or all of various objects, such as mitigating the ripple of the transmittance distribution in the free filter region, can be further performed, to form an adjusted optical multilayer film4. Such adjustment may be performed by a designer on the basis of know-how, etc., may be performed automatically by a computer equipped with a design program, or may be performed by a combination of both. The design program may have a processing section related to Al (artificial intelligence).

Even in the adjusted optical multilayer film4, periodicities related to the basic period p and the modulation period Λ1remain in the film thickness number sequence.

These periodicities can be found by Fourier analysis of the film thickness number sequence. Since this is analysis of periodicity, the film thickness may be an optical film thickness, a physical film thickness, or another film thickness.

Thus, the structure of the optical multilayer film4can be found by Fourier analysis of the film thickness number sequence.

For example, from a broader point of view, if discrete Fourier transform is performed for the film thickness number sequence of a certain optical multilayer film, and each maximum value (peak) corresponding to the basic period p and the modulation period Λ1exists in a spectrum thereof, the optical multilayer film has periodicities related to the basic period p and the modulation period Λ1, so that it is found that the optical multilayer film is the basic or adjusted optical multilayer film4.

More specifically, when the number of the discrete Fourier transform is denoted by m (m=1, 2, . . . , L0/2), an intensity Pmof the discrete Fourier transform spectrum is given by the following Expressions (3) to (5). The division by P1in Expression (3) is performed for normalization. The reason why the upper limit of the number m is set to L0/2 is that half of the analysis is sufficient to grasp the overall periodicity. This is based on known sampling theorem. If L0/2 is not a natural number (L0is an odd number), the fraction is rounded off to a natural number.

Then, a period Λ′mof a trigonometric function corresponding to the Fourier coefficient at the number m is given by the following Expression (6).

Therefore, when there is one stopband, if, in a discrete Fourier transform spectrum, a peak exists at least either at a number m′ where Λ′m=p or in the vicinity thereof, and a peak exists at least either at a number m″ where Λ′m=Λ1or in the vicinity thereof, it can be said that the optical multilayer film is the above-described basic or adjusted optical multilayer film4. Here, the range of the number m′ where Λ′m=p or the vicinity thereof is defined, for example, as follows. That is, the range includes the spectral number m′, spectral numbers m′−1 and m′+1, which are one before and one after the spectral number m′, and numbers m′−2 and m′+2, which are adjacent thereto. Also, the range of the number m″ where Λ′m=Λ1or the vicinity thereof is defined, for example, as follows. That is, the range includes the spectral number m″ and spectral numbers m″−1 and m″+1, which are one before and one after the spectral number m″. Since there can be a basic or adjusted optical multilayer film4that exhibits a mixed nature of a plurality of types of basic periods p, it may be confirmed that at the plurality of basic periods p (e.g., p=6, 14, 10), corresponding peaks exist, respectively. Similarly, since there can be a basic or adjusted optical multilayer film4that exhibits a mixed nature of a plurality of types of modulation periods determined in accordance with the basic period p and the center wavelength of the stopband, it may be confirmed that at spectral numbers corresponding to the plurality of modulation periods, corresponding peaks exist, respectively. In the case of modulation periods, the range of spectral numbers may be from the smallest number to the largest number among spectral numbers corresponding to the plurality of modulation periods.

When there are a plurality of stopbands, the applicability of the basic or adjusted optical multilayer film4can be confirmed in the same manner as when there is one stopband, except that the number of times the existence of a peak is confirmed at the above number m″ where Λ′m″=Λ1, the number m″−1, and the number m″+1 is increased from one time (k=1) to the number of times (k=1, 2, . . . , u) equal to the number of stopbands.

For reference,FIGS.7to9show the respective discrete Fourier transform spectra and the periods corresponding to the numbers m in the first to third basic filter repeat structures for the respective numbers of repeats described above.

In each discrete Fourier transform spectrum (FIG.7) for the first basic filter repeat structure (number of repeats q=50), for a peak with the smallest number m among three existing peaks, m=50, and from the above Expression (6), Λ′50=(301−1)/50=6.0. Accordingly, it is found that the first basic filter repeat structure has a periodicity of period Λ′50=6.0. In fact, as described above, the basic period p=6 for the first basic filter repeat structure.

In each discrete Fourier transform spectrum (FIG.8) for the second basic filter repeat structure (number of repeats r=40), for a peak with the smallest number m among seven existing peaks, m=40, and from the above Expression (6), Λ′40=(561−1)/40=14.0. Accordingly, it is found that the second basic filter repeat structure has a periodicity of period Λ′40=14. In fact, as described above, the basic period p=14 for the second basic filter repeat structure.

In each discrete Fourier transform spectrum (FIG.9) for the third basic filter repeat structure (number of repeats s=40), for a peak with the smallest number m among five existing peaks, m=40, and from the above Expression (6), Λ′40=(401−1)/40=10.0. Accordingly, it is found that the third basic filter repeat structure has a periodicity of period Λ′40=10. In fact, as described above, the basic period p=10 for the third basic filter repeat structure.

FIG.10is a flowchart showing an example of a method for designing the optical multilayer film4.

In designing the optical multilayer film4, the designer first obtains a basic filter structure (step S1), and obtains a basic filter repeat structure (step S2).

Next, the designer modulates a film thickness number sequence of the basic filter repeat structure by the above Expression (2) (step S3).

By up to step S3, a basic optical multilayer film4(film thickness number sequence therefor) is obtained.

Subsequently, the designer adjusts the film thicknesses of one or more layers in the basic optical multilayer film4(values of one or more terms in the film thickness number sequence) if necessary (step S4).

If step S4is performed, an adjusted optical multilayer film4(film thickness number sequence therefor) is obtained.

Next, examples conforming to the above embodiment of the present invention and comparative examples falling outside the scope of the present invention are shown.

However, the examples do not limit the scope of the present invention.

Also, depending on how the present invention is viewed, an example may become a substantial comparative example, or a comparative example may become a substantial example that is within the scope of the present invention.

As Example 1, a notch filter having a basic optical multilayer film4on one surface (base material surface M) of a base material2(substrate) which is a parallel plate was formed by simulation.

The substrate is made of quartz glass, the refractive index thereof is 1.453, and the thickness thereof is 1 millimeter. Various values for the substrate can be changed in various ways.

The optical multilayer film4of Example 1 is designed considering a state where the wavelength range of a stopband includes 1064 nm (preferably, the center wavelength of the stopband is 1064 nm) and a free filter region is formed as a wavelength range including a wavelength range of 400 nm or more and 1200 nm or less.

The optical multilayer film4of Example 1 is designed by adding the modulation of the above Expression (1) to the first basic filter repeat structure (number of repeats q=50, L0=301). Here, the amplitude a1=0.1, the period Λ1=15.7, and the phase φ1=0.

FIG.11is a graph showing a spectral transmittance exhibited by Example 1.

According toFIG.11, in Example 1, a stopband having a center wavelength of 1064 nm is formed, and a free filter region is formed as a wavelength range including a wavelength range of 400 nm or more and 1200 nm or less. Moreover, the wavelength width of the stopband is about 20 nm (about 1050 nm or more and 1070 nm or less), which is sufficiently narrow.

FIG.12is a graph showing a discrete Fourier transform spectrum of a film thickness number sequence of Example 1 and a period corresponding to a number m.

InFIG.12, there is one more peak in the discrete Fourier transform spectrum at the number m=19 than before modulation (first basic filter repeat structure in the case of the number of repeats q=50;FIG.7). For this peak, from the above Expression (6), Λ′19=(301−1)/19=15.8, which corresponds to the period Λ1=15.7.

Also, inFIG.12, as before modulation, there is a peak at m=50 (Λ′50=6.0) corresponding to the basic period p=6.

Thus, in Example 1, in the discrete Fourier transform spectrum, there are peaks corresponding to the basic period p and the period Λ1, respectively.

Example 2 has an adjusted optical multilayer film4designed by adjusting the values of appropriate terms in the film thickness number sequence of the basic optical multilayer film4of Example 1 for the purpose of reducing the ripple of the transmittance distribution in the free filter region.

The film structure in the optical multilayer film4of Example 2 is shown below in physical film thickness format.

FIG.13is a graph showing a spectral transmittance exhibited by Example 2.

According toFIG.13, Example 2 has the same free filter region and stopband as Example 1, but the ripple of the transmittance distribution in the free filter region is reduced.

FIG.14is a graph showing a discrete Fourier transform spectrum of a film thickness number sequence of Example 2 and a period corresponding to a number m.

InFIG.14, even in Example 2 (after adjusting the values of the appropriate terms in the film thickness number sequence), as in Example 1 (FIG.12), there is a peak at m=19 (Λ′19=15.8) corresponding to the period Λ1of the modulation, and there is a peak at m=50 (Λ′50=6.0) corresponding to the basic period p.

As Example 3, one similar to Example 1 was formed, except that a basic optical multilayer film4was designed on the basis of the second basic filter repeat structure instead of the first basic filter repeat structure.

The optical multilayer film4of Example 3 is designed considering a state where the wavelength range of a stopband includes 1550 nm (preferably, the center wavelength of the stopband is 1550 nm) and a free filter region is formed as a wavelength range including a wavelength range of 400 nm or more and 1800 nm or less.

The optical multilayer film4of Example 3 is designed by adding the modulation of the above Expression (1) to the second basic filter repeat structure (number of repeats r=40, L0=561). Here, the amplitude a1=0.1, the period Λ1=50, and the phase φ1=0.

FIG.15is a graph showing a spectral transmittance exhibited by Example 3.

According toFIG.15, in Example 3, a stopband having a center wavelength of 1550 nm is formed, and a free filter region is formed as a wavelength range including a wavelength range of 400 nm or more and 1800 nm or less. Moreover, the wavelength width of the stopband is about 60 nm (about 1520 nm or more and 1580 nm or less), which is sufficiently narrow.

FIG.16is a graph showing a discrete Fourier transform spectrum of a film thickness number sequence of Example 3 and a period corresponding to a number m.

InFIG.16, there is one more peak in the discrete Fourier transform spectrum at the number m=11 than before modulation (second basic filter repeat structure in the case of the number of repeats s=40;FIG.8). For this peak, from the above Expression (6), Λ′11=(561−1)/11=50.9, which corresponds to the period Λ1=50.

Also, inFIG.16, as before modulation, there is a peak at m=40 (Λ′40=14.0) corresponding to the basic period p=14.

Thus, in Example 3, in the discrete Fourier transform spectrum, there are peaks corresponding to the basic period p and the period Λ1, respectively.

Example 4 has an adjusted optical multilayer film4designed by adjusting the values of appropriate terms in the film thickness number sequence of the basic optical multilayer film4of Example 3 for the purpose of reducing the ripple of the transmittance distribution in the free filter region.

FIG.17is a graph showing a spectral transmittance exhibited by Example 4.

According toFIG.17, Example 4 has the same free filter region and stopband as Example 3, but the ripple of the transmittance distribution in the free filter region is reduced.

FIG.18is a graph showing a discrete Fourier transform spectrum of a film thickness number sequence of Example 4 and a period corresponding to a number m.

InFIG.18, even in Example 4 (after adjusting the values of the appropriate terms in the film thickness number sequence), as in Example 3 (FIG.16), there is a peak at m=11 (Λ′11=50.9) corresponding to the period Λ1of the modulation, and there is a peak at m=40 (Λ′40=14.0) corresponding to the basic period p. In addition, as a result of adjusting the film thickness number sequence, the value at m=10 (Λ′10=56.0) has the same spectral intensity as the peak at m=11 (Λ′11=50.9).

As Example 5, one similar to Example 3 was formed, except that the phase φ1was changed from 0 to π/2 in the modulation of the above Expression (1).

FIG.19is a graph showing a spectral transmittance exhibited by Example 5.

According toFIG.19, the spectral transmittance of Example 5 is similar to that of Example 3.

FIG.20is a graph showing a discrete Fourier transform spectrum of a film thickness number sequence of Example 5 and a period corresponding to a number m. According toFIG.20, the discrete Fourier transform spectrum of Example 5 is similar to that of Example 3.

That is, in Example 5 as well, there are peaks in the discrete Fourier transform spectrum corresponding to the basic period p and the period Λ1, respectively (Λ′40=14.0=p, Λ′11=50.9≈Λ1).

As Example 6, one similar to Example 3 was formed, except that the amplitude a1was changed from 0.1 to 0.3 and the period Λ1was changed from 50 to 15.7 in the modulation of the above Expression (1).

FIG.21is a graph showing a spectral transmittance exhibited by Example 6.

According toFIG.21, in Example 6, a stopband having a center wavelength of 1064 nm is formed, and a free filter region is formed as a wavelength range including a wavelength range of 400 nm or more and 1800 nm or less. Moreover, the wavelength width of the stopband is about 40 nm (about 1040 nm or more and 1080 nm or less), which is sufficiently narrow.

FIG.22is a graph showing a discrete Fourier transform spectrum of a film thickness number sequence of Example 6 and a period corresponding to a number m.

InFIG.22, there are peaks in the discrete Fourier transform spectrum at the numbers m=36 and 40. Of these peaks, for the peak at m=36, from the above Expression (6), Λ′36=(561−1)/36=15.6, which corresponds to the period Λ1=15.7.

Also, for the peak at m=40, from the above Expression (6), Λ′40=(561−1)/40=14.0, which corresponds to the basic period p=14.

Thus, in Example 6, in the discrete Fourier transform spectrum, there are peaks corresponding to the basic period p and the period Λ1, respectively.

Example 7 has an adjusted optical multilayer film4designed by adjusting the values of appropriate terms in the film thickness number sequence of the basic optical multilayer film4of Example 6 for the purpose of reducing the ripple of the transmittance distribution in the free filter region.

FIG.23is a graph showing a spectral transmittance exhibited by Example 7.

According toFIG.23, Example 7 has the same free filter region and stopband as Example 6, but the ripple of the transmittance distribution in the free filter region is reduced.

FIG.24is a graph showing a discrete Fourier transform spectrum of a film thickness number sequence of Example 7 and a period corresponding to a number m.

InFIG.24, even in Example 7 (after adjusting the values of the appropriate terms in the film thickness number sequence), as in Example 6 (FIG.22), there is a peak at m=36 (Λ′36=15.6) corresponding to the period Λ1of the modulation, and there is a peak at m=40 (Λ′40=14.0) corresponding to the basic period p.

As Example 8, one similar to Example 3 (second basic filter repeat structure (basic period p=14, number of repeats r=40), L0=561) was formed, except that the modulation of the above Expression (2) (number of stopbands u=2) was used instead of the above Expression (1). Here, the amplitude a1=0.3, a2=0.1, the period Λ1=15.7, Λ2=50, the phase1=0, and φ2=0.

FIG.25is a graph showing a spectral transmittance exhibited by Example 8.

According toFIG.25, in Example 8, a first stopband having a center wavelength of 1064 nm and a second stopband having a center wavelength of 1550 nm are formed, and a free filter region is formed as a wavelength range including a wavelength range of 400 nm or more and 1800 nm or less. Moreover, the wavelength widths of these stopbands are about 20 nm (about 1050 nm or more and 1070 nm or less) for the first stopband and about 60 nm (about 1520 nm or more and 1580 nm or less) for the second stopband, which are both sufficiently narrow.

FIG.26is a graph showing a discrete Fourier transform spectrum of a film thickness number sequence of Example 8 and a period corresponding to a number m. InFIG.26, there are peaks in the discrete Fourier transform spectrum at the numbers m=11, 36, and 40. Of these peaks, for the peak at m=11, from the above Expression (6), Λ′11=(561−1)/11=50.9, which corresponds to the period Λ2=50. Furthermore, for the peak at m=36, from the above Expression (6), Λ′36=(561−1)/36=15.6, which corresponds to the period Λ1=15.7.

Also, for the peak at m=40, from the above Expression (6), Λ′40=(561−1)/40=14.0, which corresponds to the basic period p=14.

Thus, in Example 8, in the discrete Fourier transform spectrum, there are peaks corresponding to the basic period p and the periods Λ1and Λ2, respectively.

Example 9 has an adjusted optical multilayer film4designed by adjusting the values of appropriate terms in the film thickness number sequence of the basic optical multilayer film4of Example 8 for the purpose of reducing the ripple of the transmittance distribution in the free filter region.

FIG.27is a graph showing a spectral transmittance exhibited by Example 9.

According toFIG.27, Example 9 has the same free filter region as in Example 8 and two stopbands in that region, but the ripple of the transmittance distribution in the free filter region is reduced.

FIG.28is a graph showing a discrete Fourier transform spectrum of a film thickness number sequence of Example 9 and a period corresponding to a number m. InFIG.28, even in Example 9 (after adjusting the values of the appropriate terms in the film thickness number sequence), as in Example 8 (FIG.26), there are peaks at m=12(Λ′12=46.7) and m=36 (Λ′36=15.6) corresponding to periods Λ2and Λ1of the modulation, and there is a peak at m=40 (Λ′40=14.0) corresponding to the basic period p. As a result of adjusting the film thickness number sequence, the peak at m=11 (Λ′11=50.9) in Example 8 is replaced by the peak at m=12 in Example 9. In Example 9, the spectral intensity at the peak at m=11 is slightly lower than the spectral intensity at the peak at m=12.

As Example 10, one similar to Example 1 was formed, except that a basic optical multilayer film4was designed on the basis of the third basic filter repeat structure instead of the first basic filter repeat structure.

The optical multilayer film4of Example 10 is designed considering a state where the wavelength range of a stopband includes 1550 nm (preferably, the center wavelength of the stopband is 1550 nm) and a free filter region is formed as a wavelength range including a wavelength range of 400 nm or more and 1800 nm or less.

The optical multilayer film4of Example 10 is designed by adding the modulation of the above Expression (1) to the third basic filter repeat structure (number of repeats s=40, L0=401). Here, the amplitude a1=0.1, the period Λ1=36, and the phase φ1=0.

FIG.29is a graph showing a spectral transmittance exhibited by Example 10.

According toFIG.29, in Example 10, a stopband having a center wavelength of 1550 nm is formed, and a free filter region is formed as a wavelength range including a wavelength range of 400 nm or more and 1800 nm or less. Moreover, the wavelength width of the stopband is about 60 nm (about 1520 nm or more and 1580 nm or less), which is sufficiently narrow.

FIG.30is a graph showing a discrete Fourier transform spectrum of a film thickness number sequence of Example 10 and a period corresponding to a number m. InFIG.30, there is one more peak in the discrete Fourier transform spectrum at the number m=11 than before modulation (third basic filter repeat structure in the case of the number of repeats r=40;FIG.9). For this peak, from the above Expression (6), Λ′11=(401−1)/11=36.3, which corresponds to the period Λ1=36.

Also, inFIG.30, as before modulation, there is a peak at m=40 (Λ′40=10.0) corresponding to the basic period p=10.

Thus, in Example 10, in the discrete Fourier transform spectrum, there are peaks corresponding to the basic period p and the period Λ1, respectively.

Example 11 has an adjusted optical multilayer film4designed by adjusting the values of appropriate terms in the film thickness number sequence of the basic optical multilayer film4of Example 10 for the purpose of reducing the ripple of the transmittance distribution in the free filter region.

FIG.31is a graph showing a spectral transmittance exhibited by Example 11.

According toFIG.31, Example 11 has the same free filter region and stopband as Example 10, but the ripple of the transmittance distribution in the free filter region is reduced.

FIG.32is a graph showing a discrete Fourier transform spectrum of a film thickness number sequence of Example 11 and a period corresponding to a number m.

InFIG.32, even in Example 11 (after adjusting the values of the appropriate terms in the film thickness number sequence), as in Example 10 (FIG.30), there is a peak at m=11 (Λ′11=36.3) corresponding to the period Λ1of the modulation, and there is a peak at m=40 (Λ′40=10.0) corresponding to the basic period p.

As Comparative Example 1, a notch filter similar to Example 1 was formed, except for the film structure of the optical multilayer film4.

The optical multilayer film4of Comparative Example 1 is designed considering a state where the center wavelength of a stopband is 500 nm and a free filter region is formed as a wavelength range including a wavelength range of 400 nm or more and 1800 nm or less.

The film structure of the optical multilayer film4of Comparative Example 1 is (0.90L 0.20H 0.90L)30.

FIG.33is a graph showing a spectral transmittance exhibited by Comparative Example 1.

According toFIG.33, in Comparative Example 1, the center wavelength of the stopband is 500 nm, and a free filter region is formed as a wavelength range including a wavelength range of 400 nm or more and 1800 nm or less.

FIG.34is a graph showing a discrete Fourier transform spectrum of a film thickness number sequence of Comparative Example 1 and a period corresponding to a number m.

According toFIG.34, there is no peak in the discrete Fourier transform spectrum of the film thickness number sequence of Comparative Example 1, and the maximum value appears at m=30 (Λ′30=(61−1)/30=2.0), indicating a doubled period.

As Comparative Example 2, a notch filter similar to Comparative Example 1 was formed, except for the film structure of the optical multilayer film4.

The optical multilayer film4of Comparative Example 2 is designed considering a state where the center wavelengths of two stopbands are 532 and 1064 nm, and a free filter region is formed as a wavelength range including a wavelength range of 400 nm or more and 1800 nm or less.

The film structure of the optical multilayer film4of Comparative Example 2 is (0.95L 0.10H 0.95L)70.

FIG.35is a graph showing a spectral transmittance exhibited by Comparative Example 2.

According toFIG.35, in Comparative Example 2, the center wavelengths of the respective stopbands are 532 and 1064 nm, respectively, and a free filter region is formed as a wavelength range including a wavelength range of 400 nm or more and 1800 nm or less.

FIG.36is a graph showing a discrete Fourier transform spectrum of a film thickness number sequence of Comparative Example 2 and a period corresponding to a number m.

According toFIG.36, there is no peak in the discrete Fourier transform spectrum of the film thickness number sequence of Comparative Example 2, and the maximum value appears at m=70 (Λ′70=(141−1)/70=2.0), indicating a doubled period.

As Example 12, one similar to Example 3 was formed, except that the refractive index nHof the high refractive index material was changed from 2.18 to 2.4.

The film structure in the optical multilayer film4of Example 12 is shown below in physical film thickness format.

FIG.37is a graph showing a spectral transmittance exhibited by Example 12.

According toFIG.37, the spectral transmittance of Example 12 is similar to that of Example 3.

FIG.38is a graph showing a discrete Fourier transform spectrum of a film thickness number sequence of Example 12 and a period corresponding to a number m.

According toFIG.38, the discrete Fourier transform spectrum of Example 12 is similar to that of Example 3.

That is, in Example 12 as well, there are peaks in the discrete Fourier transform spectrum corresponding to the basic period p and the period Λ1, respectively (Λ′40=14.0=p, Λ′11=50.9≈Λ1).

From the viewpoint of easier design with modulation of the film thickness number sequence, the refractive index nHof the high refractive index material is preferably 2.0 or more and 3.0 or less. For example, the refractive index of Ta2O5(for light having a wavelength of 500 nm; the same applies below) is 2.18, and the refractive indexes of TiO2and Nb2O5are 2.4, and the refractive indexes of HfO2, ZrO2, and LaxTiyOz are 2.0.

Similarly, the refractive index nLof the low refractive index material is preferably 1.4 or more and 1.5 or less. For example, the refractive index of SiO2is 1.475.

Example 13 has an adjusted optical multilayer film4designed by adjusting the values of appropriate terms in the film thickness number sequence of the basic optical multilayer film4of Example 12 for the purpose of reducing the ripple of the transmittance distribution in the free filter region.

The film structure in the optical multilayer film4of Example 13 is shown below in physical film thickness format.

FIG.39is a graph showing a spectral transmittance exhibited by Example 13.

According toFIG.39, Example 13 has the same free filter region and stopband as Example 12, but the ripple of the transmittance distribution in the free filter region is reduced.

FIG.40is a graph showing a discrete Fourier transform spectrum of a film thickness number sequence of Example 13 and a period corresponding to a number m.

InFIG.40, even in Example 13 (after adjusting the values of the appropriate terms in the film thickness number sequence), as in Example 12 (FIG.38), there is a peak at m=11 (Λ′11=50.9) corresponding to the period Λ1of the modulation, and there is a peak at m=40 (Λ′40=14.0) corresponding to the basic period p.

As Example 14, one similar to Example 3 was formed, except that the total number of layers L0was changed from 561 to 551.

That is, the layer structure of Example 14 is a layer structure obtained by removing the ten layers on the medium side from the layer structure of Example 3.

FIG.41is a graph showing a spectral transmittance exhibited by Example 14.

According toFIG.41, the spectral transmittance of Example 14 is similar to that of Example 3 in the general framework including stopband, free filter region, etc., although a comparatively large number of ripples appear.

In Example 14, the average transmittance in the free filter region (400 nm or more and 1800 nm or less) is less than 85%, unlike other examples, due to the omission of some film structures (decrease in periodicity of film structure) from the film structure of Example 3.

FIG.42is a graph showing a discrete Fourier transform spectrum of a film thickness number sequence of Example 14 and a period corresponding to a number m.

According toFIG.42, the discrete Fourier transform spectrum of Example 14 is slightly different from that of Example 3 on the basis of the decrease in periodicity of the film structure, but there are peaks in the discrete Fourier transform spectrum corresponding to the basic period p and the period Λ1, respectively (Λ′39=14.1≈p, Λ′11=50.9≈Λ1).

Even when a part of the film structure is not a basic filter structure as in the film structure of Example 14, if the other parts of the film structure are repeats of the basic filter, the film structure can be said to have a basic filter repeat structure. In this case, due to the repeated parts of the basic filter, a peak is located at the number m corresponding to the basic period in the discrete Fourier transform spectrum of the film thickness number sequence.

Example 15 has an adjusted optical multilayer film4designed by adjusting the values of appropriate terms in the film thickness number sequence of the optical multilayer film4of Example 14 for the purpose of reducing the ripple of the transmittance distribution in the free filter region.

FIG.43is a graph showing a spectral transmittance exhibited by Example 15.

According toFIG.43, Example 15 has the same free filter region and stopband as Example 14, but the ripple of the transmittance distribution in the free filter region is reduced.

In addition, the average transmittance of the free filter region (400 nm or more and 1800 nm or less) is 85% or more.

FIG.44is a graph showing a discrete Fourier transform spectrum of a film thickness number sequence of Example 15 and a period corresponding to a number m.

InFIG.44, even in Example 15 (after adjusting the values of the appropriate terms in the film thickness number sequence), as in Example 14 (FIG.42), there is a peak at m=10 (Λ′11=55) corresponding to the period Λ1of the modulation, and there is a peak at m=39 (Λ′40=14.1) corresponding to the basic period p.

If the layer structure of the basic optical multilayer film4is changed to a greater extent by increasing the portion that does not have the basic filter structure in the basic filter repeat structure and performing the modulation of the above Expression (2), or adjusting the film thickness of an arbitrary layer in the film structure to a greater extent after modulation, the periodicity of the film thickness number sequence is broken to a greater extent. Then, the film structure thus changed becomes closer to the film structure related to the film thickness number sequence not subjected to modulation. Thus, the film structure thus changed deviates from the ideal shape of spectral transmittance required more for notch filters, for example, the number of ripples in the free filter region increases, or the ripple becomes larger (the minimum value of the transmittance becomes smaller).

In Examples 16 and 17 below, such changes are deliberately made without considering reducing the ripple in the free filter region as much as possible, etc.

As Example 16, one similar to Example 3 was formed, except that the total number of layers L0was changed from 561 to 433 (the number of repeats r was changed from 40 to 31), and film thickness adjustment was performed to a greater extent. In order to set the center wavelength of a stopband to 1550 nm in the second basic filter repeat structure (basic period p=14), the period of the modulation is Λ1=50.

The film structure in the optical multilayer film4of Example 16 is shown below in physical film thickness format.

FIG.45is a graph showing a spectral transmittance exhibited by Example 16.

According toFIG.45, the spectral transmittance of Example 16 is similar to that of Example 3 in the general framework including stopband, free filter region, etc.

FIG.46is a graph showing a discrete Fourier transform spectrum of a film thickness number sequence of Example 16 and a period corresponding to a number m.

According toFIG.46, the discrete Fourier transform spectrum of Example 16 is slightly different from that of Example 3, but there are peaks in the discrete Fourier transform spectrum corresponding to the basic period p and the period Λ1, respectively (Λ′29=(433−1)/29=14.9≈p, Λ′8=(433−1)/8=54.0≈Λ1).

Even when adjustment is performed to a relatively great extent from the basic filter repeat structure as in the film structure of Example 16, if peaks corresponding to the basic period p and the period Λ1, respectively, appear in the discrete Fourier transform spectrum, the periodicities of the basic period p and the period Λ1of the modulation are maintained, so that the characteristics required for notch filters are sufficiently obtained.

As Example 17, one similar to Example 3 was formed, except that the total number of layers L0was changed from 561 to 343 (the number of repeats r was changed from 40 to 24), and film thickness adjustment was performed to a greater extent. In Example 17, six more layers are added on the medium side to the second basic filter repeat structure for the number of repeats r=24. In other words, in Example 17, eight layers on the medium side are removed from the second basic filter repeat structure for the number of repeats r=25. In order to set the center wavelength of a stopband to 1550 nm in the second basic filter repeat structure (basic period p=14), the period of the modulation is Λ1=50.

The film structure in the optical multilayer film4of Example 17 is shown below in physical film thickness format.

FIG.47is a graph showing a spectral transmittance exhibited by Example 17.

According toFIG.47, the spectral transmittance of Example 17 is similar to that of Example 3 in the general framework including stopband, free filter region, etc., although a relatively large number of ripples appear and are relatively large due to the number of layers Lo being 343 which is relatively small.

FIG.48is a graph showing a discrete Fourier transform spectrum of a film thickness number sequence of Example 17 and a period corresponding to a number m.

According toFIG.48, the discrete Fourier transform spectrum of Example 17 is different from that of Example 3, but there are peaks in the discrete Fourier transform spectrum corresponding to the basic period p and the period Λ1, respectively (Λ′35=(343−1)/35=9.8≈p, Λ′9=(343−1)/9=38.0≈Λ1). However, the period Λ1of the modulation corresponds more to the period Λ1of the modulation=35 for setting the center wavelength of the stopband to 1550 nm in the third basic filter repeat structure (basic period p=10) by a relatively large adjustment.

Even when adjustment is performed to a relatively great extent from the basic filter repeat structure as in the film structure of Example 17, if peaks corresponding to the basic period p and the period Λ1, respectively, appear in the discrete Fourier transform spectrum, the periodicities of the basic period p and the period Λ1of the modulation are maintained, so that the characteristics required for notch filters are obtained.

If the notch filter satisfies the following conditions, better characteristics are obtained.(1-1) The free filter region includes a wavelength range of 400 nm or more and 1200 nm or less.(1-2) A stopband is formed in a wavelength range of 600 nm or more and 1200 nm or less.(1-3) The average transmittance in the free filter region is 85% or more. The transmittance in the stopband is not considered in the calculation of the average transmittance in the free filter region. The wavelength range of the stopband may be a wavelength range between adjacent ripples (minimum values of the transmittance) on both sides thereof.(1-4) In the discrete Fourier transform spectrum of the film thickness number sequence, the following peak exists for each basic period p of the first basic filter structure (basic period p=6), the second basic filter structure (basic period p=14), and the third basic filter structure (basic period p=10). That is, a peak exists at least at any of a spectral number mf1corresponding best to a period of 6, spectral numbers mf1−2, mf1−1, mf1+1, and mf1+2, which are two before, one before, one after, and two after the number mf1, a spectral number mf corresponding best to a period of 14, spectral numbers mf2−2, mf2−1, mf2+1, and mf2+2, which are two before, one before, one after, and two after the number mf, and a spectral number m-corresponding best to a period of 10, and spectral numbers mf3−2, mf3−1, mf3+1, and mf3+2 which are two before, one before, one after, and two after the number mf3. As for the spectral intensity of this peak, an additional condition may be that the spectral intensity of this peak is larger than the spectral intensity at the spectral number m=1, i.e., when oscillations over all layer numbers are shown and no periodicity is exhibited. Hereinafter, “mf1−1 and mf1+1” are sometimes represented as “mf1±1”, “mf1−2 and mf1±2” are sometimes represented as “mf1±2”, and other spectral numbers are sometimes represented in the same manner.(1-5) In the discrete Fourier transform spectrum of the film thickness number sequence, the following peak exists for the period Λkof the modulation. That is, a peak exists at a spectral number between a minimum number mminand a maximum number mmaxamong spectral numbers mm1, mm2, and mm3corresponding best to the periods Λkof the modulation determined according to the periods (three types of 6, 14, and 10) and the center wavelength of the stopband and spectral numbers mm1±1, mm2±1, and mm3±1 which are one before and one after the respective numbers mm1, mm2, and mm3. As for the spectral intensity of this peak, an additional condition may be that the spectral intensity of this peak is larger than the spectral intensity at the spectral number m=1.

The application of these conditions to the above-described examples is shown in Table 1 below. The application of these conditions to the above-described comparative examples is shown in Table 2 below. In Table 2, (1-1) is omitted, and conditions (1-2) to (1-5) are listed as (2) to (5) in that order. Hereinafter, the values observed in the examples and the comparative examples are shown as OK when conditions (1-2) to (1-5) or conditions (2) to (5) are satisfied, as × when these conditions are not satisfied, and as A when these values are slightly less than those of these conditions.

First, (1-1) the free filter region includes a wavelength range of 400 nm or more and 1200 nm or less in Examples 1 and 2 and Comparative Examples 1 and 2. The case where the free filter region includes a wavelength range of 400 nm or more and 1800 nm or less, will be described later.

Next, in each of Examples 1 and 2 and Comparative Examples 1 and 2, (1-2) a stopband is formed in a wavelength range of 600 nm or more and 1200 nm or less (OK).

Then, in each of Examples 1 and 2 and Comparative Examples 1 and 2, (1-3) the average transmittance in the free filter region is 85% or more (OK).

On the other hand, in Examples 1 and 2, (1-4) a peak exists for the basic period p (OK), and (1-5) a peak exists for the period Λkof the modulation (OK). The spectral intensities of these peaks are both larger than the spectral intensity at the number m=1 (each additional condition is OK). In contrast, in Comparative Examples 1 and 2, (1-4) no peak exists for the basic period p (×), and (1-5) no peak exists for the period Λkof the modulation (×).

In Comparative Example 2, there are two stopbands, and there are two periods Λ1and Λ2of the modulation corresponding thereto, so that there can be two spectral numbers mm2(mm2aand mm2b), and there can be two spectral numbers mm3(mm3aand mm3b).

If the notch filter satisfies the following conditions, better characteristics are obtained.(2-1) The free filter region includes a wavelength range of 400 nm or more and 1800 nm or less.(2-2) A stopband is formed in a wavelength range of 600 nm or more and 1800 nm or less.(2-3) The average transmittance in the free filter region is 85% or more. The transmittance in the stopband is not considered in the calculation of the average transmittance in the free filter region. The wavelength range of the stopband may be a wavelength range between adjacent ripples (minimum values of the transmittance) on both sides thereof.(2-4) In the discrete Fourier transform spectrum of the film thickness number sequence, the following peak exists for each basic period p of the second basic filter structure (basic period p=14) and the third basic filter structure (basic period p=10). That is, a peak exists at least at any of the spectral number ma corresponding best to a period of 14, the spectral numbers mf2+1 and mf2+2, which are ±1 and ±2 of the number mf2, the spectral number mf3corresponding best to a period of 10, and the spectral numbers mf3±1 and mf3±2 which are ±1 and ±2 of the number m3. As for the spectral intensity of this peak, an additional condition may be that the spectral intensity of this peak is larger than the spectral intensity at the spectral number m=1.(2-5) In the discrete Fourier transform spectrum of the film thickness number sequence, the following peak exists for the period Λkof the modulation. That is, a peak exists at a spectral number between the minimum number mminand the maximum number mmaxamong the spectral numbers mm2and mm3corresponding to the periods Λkof the modulation determined according to the basic periods p (=two types of 14 and 10) and the center wavelength of the stopband and the spectral numbers mm2±1 or mm3±1 which are ±1 of the numbers mm2and mm3, respectively. As for the spectral intensity of this peak, an additional condition may be that the spectral intensity of this peak is larger than the spectral intensity at the spectral number m=1.

The application of these conditions to the above-described examples is shown in Tables 3 to 5 below.

First, (2-1) the free filter region includes a wavelength range of 400 nm or more and 1800 nm or less in Examples 3 to 17.

Next, in each of Examples 3 to 17, (2-2) a stopband is formed in a wavelength range of 600 nm or more and 1800 nm or less (OK).

Then, in Examples 3 to 17, (2-3) the average transmittance in the free filter region is 8500 or more (OK), except in Example 14. In Example 14, the average transmittance in the free filter region is 84.7% o, which is slightly less than 850% (Δ).

On the other hand, in Examples 3 to 17, (2-4) a peak exists for the basic period p (OK), and (2-5) a peak exists for the period Λkof the modulation (OK). The spectral intensities of these peaks are both larger than the spectral intensity at the number m=1 except in Example 17 (each additional condition is OK). In Example 17, the spectral intensity of the peak at the number m=8 is smaller than the spectral intensity at the number m=1 (the additional condition in (2-5) is ×).

In Examples 8 and 9, there are two stopbands, and there are two periods Λ1and Λ2of the modulation corresponding thereto, so that there can be two spectral numbers mm2(mm2aand mm2b), and there can be two spectral numbers mm3(mm3aand mm3b). The minimum number mminand the maximum number mmaxare determined by considering all mm*(* is an arbitrary symbol) including mm2a, mm2b, mm3a, and mm3b.

For reference, the application of the conditions to Example 16 will be described in more detail.

When the center wavelength of the stopband is set to 1550 nm as in Example 16, modulation with a period of 50 is performed for the second basic filter repeat structure (basic period p=14), and modulation with a period of 35 is performed for the third basic filter repeat structure (basic period p=10).

Thus, in Example 16, first, as in (2-4), at any of the number mf2=31 (Λ′31=(433−1)/31=13.9) corresponding best to the basic period p=14 and the spectral numbers29,30,32, and33, which are ±1 and ±2 of the number mf2, a spectral intensity peak exists (there is a peak at the number m=29; Λ′29=(433−1)/29=14.9), and the periodicity of the basic period p=14 is maintained, which is preferable for improving the characteristics of the notch filter.

Also, in Example 16, as in (2-5), between the minimum number mmin=8 (=mm2−1) and the maximum number mmax=13(=mm3+1) among the spectral number mm2=9 (Λ′9=(433−1)/9=48) corresponding best to the modulation period of 50 and mm2±1=8 and 10 adjacent thereto, and the spectral number mm3=12 corresponding to the modulation period of 35 and mm3±1=11 and 13 adjacent thereto, a spectral intensity peak exists (there are peaks at the number m=8, 10, and 12; Λ′8=(433−1)/8=54.0, Λ′10=(433−1)/10=43.2, Λ′12=(433−1)/12=36.0), which is preferable since better periodicity of the film thickness number sequence is obtained.

In Example 16, because of the presence of the periodicity for the modulation period of 50, the periodicity for the modulation period of 35 may be small or may be absent. In fact, in Example 16, the condition of (2-5) for the modulation period of 35 is satisfied, that is, among the spectral number mm3=12 corresponding to the modulation period of 35 and mm3±1=11 and 13 adjacent thereto, a spectral intensity peak exists at the number m=12, but the spectral intensity is smaller than the spectral intensity at the number m=1. Only the periodicity for the modulation period of 35 may be found, or both of the periodicities for the modulation periods of 50 and 35 may be found strongly.

Examples 1 to 17 are each a notch filter having a free filter region which is a wavelength range in which light is transmitted, and one or more stopbands which are located between the lower and upper limits of the free filter region and in which transmission of light in a predetermined wavelength range is suppressed, and including a base material2and an optical multilayer film4formed directly or indirectly on a base material surface M which is the surface of the base material2. The optical multilayer film4is formed on the basis of a basic filter repeat structure in which a basic filter structure in which low refractive index layers L made of a low refractive index material and high refractive index layers H made of a high refractive index material are alternately arranged is repeated a plurality of times, and the film thickness of each layer in the optical multilayer film4corresponds to a modulation film thickness number sequence obtained by performing modulation at a period different from a basic period based on the number of layers of the basic filter structure, for a basic film thickness number sequence in which the film thickness of each layer in the basic filter repeat structure is arranged in order from the base material2side.

Therefore, Examples 1 to 17 have a wider free filter region. Also, Examples 1 to 17 have a stopband having a narrower wavelength width.

In addition, in Examples 8 and 9, there are a plurality of periods of the modulation. Therefore, Examples 8 and 9 have a plurality of stopbands having narrower wavelength widths.

Furthermore, in Examples 1 to 17, a value dnof the nth term in the modulation film thickness number sequence corresponding to the film thickness of the nth layer counting from the base material2side in the optical multilayer film4is expressed by the above Expression (2) when the nth term of the basic film thickness number sequence corresponding to the film thickness of the nth layer counting from the base material2side in the basic filter repeat structure is denoted by Dn(n=1, 2, . . . , L0, where L0is the total number of terms) and the amplitude, period, and phase of the modulation for the kth stopband are denoted by ak, Λk, and φk, respectively (k=1, 2, . . . , u, where u is the number of stopbands to be formed). Thus, the modulation is more appropriately performed.

In addition, in Examples 2, 4, 7, 9, 11, 13, and 15 to 17, the film thickness of each layer in the optical multilayer film4is in accordance with an adjusted modulation film thickness number sequence obtained by adjusting the values of one or more terms in the modulation film thickness number sequence. Thus, a notch filter for which adjustment for reduction of the ripple in the free filter region, etc., is performed is provided.

Also, in Examples 1 to 17, the period of the modulation corresponds to the center wavelength of the stopband. Therefore, the period of the modulation is set more appropriately, and the design becomes easier.

Furthermore, in Examples 1 and 2, the free filter region includes a wavelength range of 400 nm or more and 1200 nm or less, and the basic filter repeat structure is any of a first basic filter repeat structure in which a basic filter structure in which the basic period is 6 is repeated, a second basic filter repeat structure in which a basic filter structure in which the basic period is 14 is repeated, and a third basic filter repeat structure in which a basic filter structure in which the basic period is 10 is repeated. The basic filter structure in which the basic period is 6 has optical film thicknesses that are 0.25 times “1.17 0.32 0.32 2.31 0.32 0.32 1.17”, with the first layer as a low refractive index layer in order from the base material2side. Furthermore, the basic filter structure in which the basic period is 14 has optical film thicknesses that are 0.25 times “1.10 0.14 0.48 0.30 0.28 0.50 0.12 2.16 0.12 0.50 0.28 0.30 0.48 0.14 1.10”, with the first layer as a low refractive index layer, in order from the base material2side. Moreover, the basic filter structure in which the basic period is 10 has optical film thicknesses that are 0.25 times “1.26 0.22 0.51 0.52 0.21 2.53 0.21 0.52 0.51 0.22 1.26”, with the first layer as a low refractive index layer, in order from the base material2side.

Thus, it becomes easier to design the notch filter.

Furthermore, in Examples 3 to 17, the free filter region includes a wavelength range of 400 nm or more and 1800 nm or less, and the basic filter repeat structure is any of a second basic filter repeat structure in which a basic filter structure in which the basic period is 14 is repeated and a third basic filter repeat structure in which a basic filter structure in which the basic period is 10 is repeated. The basic filter structure in which the basic period is 14 has optical film thicknesses that are 0.25 times “1.10 0.14 0.48 0.30 0.28 0.50 0.12 2.16 0.12 0.50 0.28 0.30 0.48 0.14 1.10”, with the first layer as a low refractive index layer, in order from the base material2side. Furthermore, the basic filter structure in which the basic period is 10 has optical film thicknesses that are 0.25 times “1.26 0.22 0.51 0.52 0.21 2.53 0.21 0.52 0.51 0.22 1.26”, with the first layer as a low refractive index layer, in order from the base material2side.

Thus, it becomes easier to design the notch filter.

In addition, Examples 1 and 2 each have a free filter region which is a wavelength range in which light is transmitted, and one or more stopbands which are located between the lower and upper limits of the free filter region and in which transmission of light in a predetermined wavelength range is suppressed, and include a base material2and an optical multilayer film4formed directly or indirectly on a base material surface M which is the surface of the base material2. The optical multilayer film4has low refractive index layers L made of a low refractive index material and high refractive index layers H made of a high refractive index material which are alternated, and satisfies all of the following conditions.(1-1) The free filter region includes a wavelength range of 400 nm or more and 1200 nm or less.(1-2) A stopband is formed in a wavelength range of 600 nm or more and 1200 nm or less.(1-3) The average transmittance in the free filter region is 85% or more.(1-4) In a discrete Fourier transform spectrum of a film thickness number sequence in which the film thickness of each layer in the optical multilayer film4is arranged in order from the base material2side, a peak exists at least at any of a spectral number mf1corresponding best to a period of 6, spectral numbers mf1−2, mf1−1, mf1+1, and mf1+2, which are two before, one before, one after, and two after the number mf1, a spectral number mf2corresponding best to a period of 14, spectral numbers mf2−2, mf2−1, mf2+1, and mf2+2, which are two before, one before, one after, and two after the number mf, a spectral number m-corresponding best to a period of 10, and spectral numbers mf3−2, mf3−1, mf2+1, and mf3+2 which are two before, one before, one after, and two after the number mf3.(1-5) In the discrete Fourier transform spectrum, a peak exists at a spectral number between a minimum number mminand a maximum number mmaxamong spectral numbers mm1, mm2, and mm3corresponding best to periods of the modulation determined according to the three types of periods of 6, 14, and 10 and the center wavelength of the stopband, and spectral numbers mm1−1, mm1+1, mm2−1, mm2+1, mm3−1, and mm3+1 which are one before and one after the respective numbers mm1, mm2, and mm3.

Therefore, Examples 1 and 2 have a wider free filter region. Also, Examples 1 and 2 have a stopband having a narrower wavelength width.

Furthermore, in Examples 1 and 2, the additional condition that the spectral intensity of the peak is larger than the spectral intensity at the spectral number m=1 is also satisfied in each of the conditions of (1−4) and (1−5). Therefore, better periodicity of the film thickness number sequence is obtained, and at least one of a wider free filter region and a stopband having a narrower wavelength width is obtained.

Examples 3 to 13 and 15 to 17 each have a free filter region which is a wavelength range in which light is transmitted, and one or more stopbands which are located between the lower and upper limits of the free filter region and in which transmission of light in a predetermined wavelength range is suppressed, and include a base material2and an optical multilayer film4formed directly or indirectly on a base material surface M which is the surface of the base material2. The optical multilayer film4has low refractive index layers L made of a low refractive index material and high refractive index layers H made of a high refractive index material which are alternated, and satisfies all of the following conditions.(2−1) The free filter region includes a wavelength range of 400 nm or more and 1800 nm or less.(2−2) A stopband is formed in a wavelength range of 600 nm or more and 1800 nm or less.(2−3) The average transmittance in the free filter region is 85% or more.(2−4) In a discrete Fourier transform spectrum of a film thickness number sequence in which the film thickness of each layer in the optical multilayer film4is arranged in order from the base material2side, a peak exists at least at any of a spectral number mf2corresponding best to a period of 14, spectral numbers mf2−2, mf2−1, mf2+1, and mf2+2, which are two before, one before, one after, and two after the number mf2, a spectral number mf3corresponding best to a period of 10, and spectral numbers mf3−2, mf3−1, mf3+1, and mf3+2 which are two before, one before, one after, and two after the number mf3.(2−5) In the discrete Fourier transform spectrum, a peak exists at a spectral number between a minimum number mminand a maximum number mmaxamong spectral numbers mm2and mm3corresponding best to periods of the modulation determined according to the two types of periods of 14 and 10 and the center wavelength of the stopband, and spectral numbers mm2−1, mm2+1, mm3−1, and mm3+1 which are one before and one after the respective numbers mm2and mm3.

Therefore, Examples 3 to 13 and 15 to 17 have a wider free filter region. Also, Examples 3 to 13 and 15 to 17 have a stopband having a narrower wavelength width.

Furthermore, in Examples 3 to 16, the additional condition that the spectral intensity of the peak is larger than the spectral intensity at the spectral number m=1 is also satisfied in each of the conditions of (2-4) and (2-5). In Example 17, the additional condition that the spectral intensity of the peak is larger than the spectral intensity at the spectral number m=1 is also satisfied in the condition of (2-4). Therefore, better periodicity of the film thickness number sequence is obtained, and at least one of a wider free filter region and a stopband having a narrower wavelength width is obtained.