JP2004205646A

JP2004205646A - Optical thin film filter

Info

Publication number: JP2004205646A
Application number: JP2002372372A
Authority: JP
Inventors: Shigeki Takeda; 重喜武田
Original assignee: Kyocera Corp
Current assignee: Kyocera Corp
Priority date: 2002-12-24
Filing date: 2002-12-24
Publication date: 2004-07-22

Abstract

<P>PROBLEM TO BE SOLVED: To realize an optical filter having target characteristics by using optical thin film materials which are actually available. <P>SOLUTION: In a band pass optical thin film filter, a cavity layer is formed of a reflecting mirror in which a plurality of optical thin films having different refractive indexes are layered and spacer layers, the plurality of cavity layers are made into a multistage structure through connecting layers and the constitution of the layer is determined in accordance with the transmission characteristics and reflection characteristics obtained from a denominator polynomial and a numerator polynomials which represent transmission characteristics and a denominator polynomial and a numerator polynomials which represent reflection characteristics in a Hurwitz polynomial of a complex frequency s. A polynomial for a reflection coefficient is newly determined by using a new transmission coefficient which is obtained by multiplying a constant that is less than 1 and larger than 0.95 by the transmission coefficient for the combination of the original numerator and denominator having the absolute value of a transmission coefficient at the center frequency of a pass band to be 1 and the constitution of the layer is determined from these new polynomials. <P>COPYRIGHT: (C)2004,JPO&NCIPI

Description

【０００１】
【発明の属する技術分野】
本発明は波長多重（ＷＤＭ）方式の光ファイバー通信網等に用いるフィルタに関し、特に反射される信号に対し直線歪みを軽減した光学薄膜フィルタの実現を容易にする技術に関する。
【０００２】
【従来の技術】
波長多重方式（ＷＤＭ）の光ファイバー通信網では、それぞれの波長の光信号を分離抽出あるいは合波するため光学的な挿入分岐器（ＡＤＭ：add/drop multiplexer）が用いられ、その機能を実現するために波長分離用光学フィルタが用いられる。
【０００３】
従来、その為のフィルタとしては、主に図１０に示すＦＢＧ（Fiber Bragg Grating）、図１１に示すＡＷＧ(Arrayed, Waveguide Grating)、図１２示す光学薄膜フィルタの３種類の光学フィルタが用いられている。
【０００４】
図１０に示すＦＢＧにおいては、フィルタ端面２１からの入射光はグレイティング部１５で波長選択されて反射して反射光としてフィルタ端面２１より取り出される。図１１に示すＡＷＧにおいては、入射波は分波部１６で分波されて移相部１７を通り、波長選択部１８で波長分離されて取り出される。図１２に示す光学薄膜フィルタにおいては、多層の薄膜からなる反射鏡１９、スペーサ１４、反射鏡２０を積層して構成され、各層に垂直に光が入射、透過する。
【０００５】
【特許文献１】特開２００２−２５８０３６号公報
【０００６】
【発明が解決しようとする課題】
これらのフィルタを使用した場合、透過する光信号の伝送速度が上がった場合、おもに群遅延の偏差により透過信号の波形歪みを受けることが問題にされ始めている。
【０００７】
従来例の図１０、１１に示すＦＢＧやＡＷＧでは、透過特性の群遅延の偏差までは考慮されておらず、もっぱら透過の振幅特性のみを考慮するか、あるいは一部のＡＷＧでは透過の振幅特性をあまり考慮せずに、透過位相の単純な傾斜の位相補正に利用するのみであった。
【０００８】
一方、図１２に示す光学薄膜フィルタは、現実の屈折率や膜構成で構成しなければならない。即ち、光学薄膜材料や基板ガラスの屈折率は固定されており、また層数は整数である。このため、任意の帯域幅、減衰、群遅延などの特性のフィルタが実現出来る訳ではなく、いかに目標に近い特性の層構成にするかが課題であった。
【０００９】
そこで本発明者は透過特性の群遅延の偏差が少ない帯域通過特性の光学薄膜フィルタを提案している（特許文献１）が、実際に上記の制約までを緩和する手段には触れていない。
【００１０】
【課題を解決するための手段】
そこで、本発明では理想の条件で設計し、それに通過帯域の中心周波数において僅かに反射を許して設計値の素子感度を緩和し、実際の製造誤差の許容範囲が大きく製造しやすい設計値とすることで理想特性に近い光学薄膜フィルタを実現する。
【００１１】
その為に、屈折率の異なる複数の光学薄膜を多層化した反射鏡層とスペーサ層からキャビティ層を形成し、複数のキャビティ層を連絡層を介して多段化し、複素周波数ｓのフルビッツ多項式における透過特性を表す分母多項式と分子多項式、及び反射特性を表す分母多項式と分子多項式から、求める透過特性及び反射特性に応じて層構成を定めた帯域通過型光学薄膜フィルタであって、上記透過特性、反射特性を示すフルビッツ多項式に絶対値が１より小さく０．９５よりも大きい定数の逆数を乗じ、これらの新多項式から層構成を定めたことを特徴とする。
【００１２】
【作用】
本発明の光学薄膜フィルタにより、既存の材料と成膜プロセスで目標の設計値に近い光学薄膜フィルタを実現することが出来る。この結果、波形歪みを抑えたＡＤＭなどの波長選択機能を実現できる。
【００１３】
【発明の実施の形態】
以下、図面に基づいて本発明を詳細に説明する。なお、本発明は以下の例に限定されるものではなく以下、本発明の主旨を逸脱しない範囲で変更・改良を施すことは何ら差し支えない。
【００１４】
まず、図１に本発明の光学薄膜フィルタの具体例を示す。ガラス基板１上に反射鏡層２、３、４、５、６、７、８とスペーサ層９からなる複数のキャビティ層１０、１１、１２、１３を連絡層１４を介して多重化してある。上記反射鏡層２、３、４、５、６、７、８、スペーサ層９、連絡層１４はそれぞれ屈折率の異なる複数の光学薄膜を多層化して形成したものである。図２、図３、図４に本発明による光学薄膜フィルタの透過群遅延特性、透過振幅特性および反射振幅特性を示す。
【００１５】
以下に本発明の原理を説明する。電気回路のフィルタ理論における複素周波数ｓのフルビッツ多項式より、求めるフィルターの透過特性及び反射特性が定まるものとすると、このフルビッツ多項式より基準化低域通過型フィルタの素子値が定まり、該基準化低域通過型フィルタを周波数変換、等価変換することにより、図１に示す本発明の多重薄膜光学フィルタの層構成を定めることができる（詳細は特許文献１参照）。
【００１６】
即ち、光学薄膜フィルタの特性は数１に示されるＳパラメータにより表現できる。数２、数３に示すように、透過特性を表すｓ２１の分母多項式のｇ（ｓ）はフルビッツの多項式を示し、分子多項式のｆ（ｓ）は数４に示すように、この場合１である。透過特性はこのフルビッツの多項式のみで決まることから、群遅延偏差の少ないフルビッツの多項式を選ぶことで目的の透過特性のフィルタを実現することができる。
【００１７】
【数１】

【００１８】
【数２】

【００１９】
【数３】

【００２０】
【数４】

【００２１】
図５と図６に通過帯域で群遅延が最大平坦である基準化低域通過型の４次のベッセルフィルタの振幅特性と群遅延特性を示す。通常は通過帯域の中心周波数での透過係数は１、反射係数は０となるように各多項式の係数は選ばれる。即ち数３のrの値は１としてある。なおrは図９の等価回路の負荷抵抗８１に相当する。
【００２２】
光学薄膜フィルタの反射特性は数５のようにｓ１１の分母多項式ｇ（ｓ）と分子多項式ｈ（ｓ）とで定まる。分母多項式ｇ（ｓ）はｓ２１の分母多項式と同じである。一方、分子多項式はユニタリ条件の数６よりｇ（ｓ）とｆ（ｓ）が与えられればそれに伴い決められる。
【００２３】
【数５】

【００２４】
【数６】

【００２５】
透過特性の群遅延時間は数７で与えられる。
【００２６】
【数７】

【００２７】
またポート１の反射特性の群遅延時間は数８で与えられる。またｈ（ｓ）が定まるとポート２の反射係数は数９に示すように、分子多項式の複素周波数を異符号にすることで与えられる。
【００２８】
【数８】

【００２９】
【数９】

【００３０】
１によれば、これらの多項式を用いれば、与えられた光学薄膜材料とガラス基板材料を用いて、目標の中心周波数、通過帯域幅の光学薄膜フィルタの膜構成を設計できた。
【００３１】
しかし、その膜構成の層数は計算上は任意の数となるが、実際は整数でしか実現できず、それを補う幾つかの手法を用いても目標の設計値に対していくらかの偏差が残る。特に群遅延時間の偏差はクリティカルである。
【００３２】
図７と図８に従来の特許文献１の設計法による４次のベッセルフィルタの振幅特性と群遅延特性を示す。膜構成と屈折率の制約で、図５と図６の基準化低域通過型フィルタの特性と比べると、透過振幅特性と透過群遅延時間に偏差が生じ、特に群遅延時間の偏差が大きい。
【００３３】
そこで本発明はベッセルフィルタのフルビッツ多項式の各係数に僅かに１より大きい定数を乗じると透過群遅延特性は変化せずに、透過振幅特性は１より僅かに小さい値にシフトし、その分反射振幅特性は僅かに増加することを利用すれば偏差の緩和が可能なことを見出した。
【００３４】
透過振幅特性が１の設計値では、現実の素子値に誤差がある場合には受動素子であるために透過振幅特性は必ず１より小さくなる特性偏差となり、また予め１より大きな値で補う設計も出来ず、設計した値は不安定な定数になりやすい。しかし、透過振幅を１より僅かに小さい値としておくと、プラスマイナスの透過振幅の補正が出来、また素子誤差に対してトレランスが大きくなり、実現しやすい。
【００３５】
透過振幅特性、透過群遅延特性を変化させずにこの操作を行うには、透過特性、反射特性を示すフルビッツ多項式に絶対値が１より小さく０．９５よりも大きい定数の逆数を乗じたものとすれば良い。そのためには数３のrの値を１からずらして、数３の定数項である(r+1)/2√rが０．９５から１の間の値の逆数となるようにする。そのためにはrは０．５２４１から１．９０８０の間の値とすればよい。
【００３６】
以上より、実際のベッセルフィルタのフルビッツの多項式を修正して、再度特許文献１による設計を行うことで、元の目標に近い特性の光学薄膜フィルタを実際の光学薄膜材料とガラス基板で安定に実現できる。
【００３７】
以上の説明で示される回路網関数から導かれた等価回路を図９に示す。終端抵抗８０、８１の間に、キャビティ６７、６８、６９が虚ジャイレータ６６を介して接続されている。それぞれのキャビティは共振器７６、７７、７８とその前後に接続された理想トランス７０、７１、７２、７３、７４、７５から成り立つ。図１の実施例の各部と図９の等価回路の各部との関係は連絡層１４が虚ジャイレータ６６に、反射鏡層２〜８が理想トランス７０〜７５に、スペーサ層９が共振器７６〜７８にキャビティ層１０〜１３がキャビティ６７〜６９に対応する。
【００３８】
【実施例】
本発明の実施例として、数３のｒを０．７として分母多項式g(s)に乗ずる定数(r+1)/2√rを１．０１６とする。即ちｓ_１１、ｓ_２１のフルビッツ多項式に乗ずる定数を０．９８４とする。この等価回路から特許文献１による設計を行い光学薄膜フィルタを実現しその特性を図２〜図４に示す。この結果、中心周波数の透過振幅は０．１３ｄD悪化し、反射特性は−１５ｄDに増加するが、群遅延特性は目標どおりに実現できる。透過振幅の悪化は実用上問題ないレベルである。
【００３９】
【発明の効果】
本発明によれば、屈折率の異なる複数の光学薄膜を多層化した反射鏡層とスペーサ層からキャビティ層を形成し、複数のキャビティー層を連絡層を介して多段化し、複素周波数ｓのフルビッツ多項式における透過特性を表す分母多項式と分子多項式、及び反射特性を表す分母多項式と分子多項式から、求める透過特性及び反射特性に応じて層構成を定めた帯域通過型光学薄膜フィルタであって、通過帯域の中心周波数における透過係数の絶対値が１である元の分子多項式と分母多項式の組み合わせに対し、透過係数に１より小さく０．９５よりも大きい定数を乗じた透過係数をあらたな透過係数として、反射係数の多項式を新たに定め、これらのあらたな多項式から層構成を定めたことで、目標の特性に近い特性のフィルタを現有の材料で実現できる。
【図面の簡単な説明】
【図１】本発明の光学薄膜フィルタの構成を示す図である。
【図２】本発明の光学薄膜フィルタの透過振幅特性を示す図である。
【図３】本発明の光学薄膜フィルタの透過群遅延特性を示す図である。
【図４】本発明の光学薄膜フィルタの反射振幅特性を示す図である。
【図５】ベッセルフィルタの多項式による透過群遅延特性を示す図である。
【図６】ベッセルフィルタの多項式による透過振幅特性を示す図である。
【図７】従来の設計による光学薄膜フィルタの透過群遅延特性を示す図である。
【図８】従来の設計による光学薄膜フィルタの透過振幅特性を示す図である。
【図９】光学薄膜フィルタの等価回路を示す図である。
【図１０】従来のＦＢＧを示す図である。
【図１１】従来のＡＷＧを示す図である。
【図１２】従来の光学薄膜のフィルタを示す図である。
【符号の説明】
１：ガラス基板
２、３、４、５、６、７、８、１９、２０：反射鏡層
９：スペーサ層
１０、１１、１２、１３：キャビティ層
１４：連絡層
１５：グレーティング部
１６：分波部
１７：移相部
１８：波長選択部
２１：フィルタ端面
５１、５２、５３、５４、５５：群遅延特性
６６：虚ジャイレータ
６７、６８、６９：キャビティ
７０、７１、７２、７３、７４、７５：理想トランス
７６、７７、７８：共振器
８０、８１：終端抵抗[0001]
TECHNICAL FIELD OF THE INVENTION
The present invention relates to a filter used in a wavelength division multiplexing (WDM) type optical fiber communication network or the like, and more particularly to a technique for facilitating the realization of an optical thin film filter that reduces linear distortion with respect to a reflected signal.
[0002]
[Prior art]
In a wavelength division multiplexing (WDM) optical fiber communication network, an optical add / drop multiplexer (ADM) is used to separate and extract or combine optical signals of respective wavelengths. An optical filter for wavelength separation is used.
[0003]
Conventionally, three types of optical filters have been used as filters for this purpose: an FBG (Fiber Bragg Grating) shown in FIG. 10, an AWG (Arrayed, Waveguide Grating) shown in FIG. 11, and an optical thin film filter shown in FIG. I have.
[0004]
In the FBG shown in FIG. 10, the incident light from the filter end face 21 is selected in wavelength by the grating section 15, reflected, and extracted from the filter end face 21 as reflected light. In the AWG shown in FIG. 11, an incident wave is split by a splitter 16, passes through a phase shifter 17, is wavelength-separated by a wavelength selector 18, and is extracted. The optical thin film filter shown in FIG. 12 is configured by stacking a reflecting mirror 19, a spacer 14, and a reflecting mirror 20 each formed of a multilayer thin film, and light is incident on and transmitted through each layer vertically.
[0005]
[Patent Document 1] Japanese Patent Application Laid-Open No. 2002-258036
[Problems to be solved by the invention]
When these filters are used, when the transmission speed of the transmitted optical signal is increased, the problem that the waveform of the transmitted signal is distorted mainly due to the deviation of the group delay has begun to be a problem.
[0007]
In the conventional FBGs and AWGs shown in FIGS. 10 and 11, the deviation of the group delay of the transmission characteristics is not considered, and only the transmission amplitude characteristics are considered, or the transmission amplitude characteristics are used in some AWGs. Is used only for phase correction of a simple inclination of the transmission phase without much consideration.
[0008]
On the other hand, the optical thin-film filter shown in FIG. 12 must be configured with the actual refractive index and film configuration. That is, the refractive index of the optical thin film material or the substrate glass is fixed, and the number of layers is an integer. For this reason, it is not always possible to realize a filter having characteristics such as an arbitrary bandwidth, attenuation, and group delay, and it has been a problem how to make a layer configuration having characteristics close to a target.
[0009]
The present inventor has proposed an optical thin-film filter having a band-pass characteristic in which the deviation of the group delay of the transmission characteristic is small (Patent Document 1), but does not mention means for actually reducing the above-mentioned restrictions.
[0010]
[Means for Solving the Problems]
Therefore, in the present invention, the design is performed under ideal conditions, the device sensitivity of the design value is relaxed by allowing a slight reflection at the center frequency of the pass band, and the design value has a large allowable range of the actual manufacturing error and is easy to manufacture. This realizes an optical thin-film filter having almost ideal characteristics.
[0011]
For this purpose, a cavity layer is formed from a reflector layer and a spacer layer in which a plurality of optical thin films having different refractive indices are multi-layered, and a plurality of cavity layers are multistaged via a communication layer, and the transmission in the Hurwitz polynomial of the complex frequency s is performed. From the denominator polynomial and the numerator polynomial representing the characteristic, and the denominator polynomial and the numerator polynomial representing the reflection characteristic, a band-pass optical thin-film filter having a layer configuration determined according to transmission characteristics and reflection characteristics to be obtained. It is characterized in that a layer configuration is determined from these new polynomials by multiplying a Hurwitz polynomial exhibiting characteristics by a reciprocal of a constant whose absolute value is smaller than 1 and larger than 0.95.
[0012]
[Action]
With the optical thin film filter of the present invention, it is possible to realize an optical thin film filter close to a target design value with existing materials and a film forming process. As a result, a wavelength selection function such as ADM with suppressed waveform distortion can be realized.
[0013]
BEST MODE FOR CARRYING OUT THE INVENTION
Hereinafter, the present invention will be described in detail with reference to the drawings. It should be noted that the present invention is not limited to the following examples, and modifications and improvements can be made without departing from the scope of the present invention.
[0014]
First, FIG. 1 shows a specific example of the optical thin film filter of the present invention. A plurality of

cavity layers

10, 11, 12, 13 each comprising a

reflector layer

2, 3, 4, 5, 6, 7, 8 and a spacer layer 9 are multiplexed on a glass substrate 1 via a connecting layer 14. The reflecting

mirror layers

2, 3, 4, 5, 6, 7, 8, the spacer layer 9, and the connecting layer 14 are each formed by forming a plurality of optical thin films having different refractive indices into multiple layers. 2, 3 and 4 show transmission group delay characteristics, transmission amplitude characteristics and reflection amplitude characteristics of the optical thin film filter according to the present invention.
[0015]
Hereinafter, the principle of the present invention will be described. Assuming that the transmission characteristic and the reflection characteristic of the filter to be obtained are determined from the Hurwitz polynomial of the complex frequency s in the filter theory of the electric circuit, the element value of the standardized low-pass filter is determined from this Hurwitz polynomial, and By performing frequency conversion and equivalent conversion of the pass-type filter, the layer configuration of the multiple thin film optical filter of the present invention shown in FIG. 1 can be determined (for details, see Patent Document 1).
[0016]
That is, the characteristics of the optical thin film filter can be expressed by the S parameter shown in Expression 1. As shown in

Equations

2 and 3, g (s) of the denominator polynomial of s21 representing the transmission characteristic represents a Hurwitz polynomial, and f (s) of the numerator polynomial is 1 in this case as shown in Equation 4. . Since the transmission characteristics are determined only by the Hurwitz polynomial, a filter having the desired transmission characteristics can be realized by selecting a Hurwitz polynomial having a small group delay deviation.
[0017]
(Equation 1)

[0018]
(Equation 2)

[0019]
[Equation 3]

[0020]
(Equation 4)

[0021]
FIGS. 5 and 6 show the amplitude characteristic and the group delay characteristic of the normalized low-pass type fourth-order Bessel filter having the maximum flat group delay in the pass band. Normally, the coefficients of each polynomial are selected so that the transmission coefficient at the center frequency of the pass band is 1 and the reflection coefficient is 0. That is, the value of r in Equation 3 is 1. Note that r corresponds to the load resistance 81 in the equivalent circuit of FIG.
[0022]
The reflection characteristic of the optical thin film filter is determined by the denominator polynomial g (s) of s11 and the numerator polynomial h (s) as shown in Expression 5. The denominator polynomial g (s) is the same as the denominator polynomial of s21. On the other hand, the numerator polynomial is determined from g (s) and f (s) according to the unitary condition (Equation 6).
[0023]
(Equation 5)

[0024]
(Equation 6)

[0025]
The group delay time of the transmission characteristic is given by Expression 7.
[0026]
(Equation 7)

[0027]
The group delay time of the reflection characteristic of the port 1 is given by Expression 8. When h (s) is determined, the reflection coefficient of port 2 is given by changing the complex frequency of the numerator polynomial to a different sign as shown in Expression 9.
[0028]
(Equation 8)

[0029]
(Equation 9)

[0030]
According to No. 1, by using these polynomials, it was possible to design a film configuration of an optical thin-film filter having a target center frequency and a passband using a given optical thin-film material and glass substrate material.
[0031]
However, although the number of layers of the film configuration is an arbitrary number in the calculation, it can be actually realized only with an integer, and some deviation from the target design value remains even if some methods for complementing it are used . Especially, the deviation of the group delay time is critical.
[0032]
7 and 8 show amplitude characteristics and group delay characteristics of a fourth-order Bessel filter according to the conventional design method of Patent Document 1. FIG. Due to the restrictions of the film configuration and the refractive index, compared with the characteristics of the normalized low-pass filter shown in FIGS. 5 and 6, there is a deviation between the transmission amplitude characteristic and the transmission group delay time, and the deviation of the group delay time is particularly large.
[0033]
Therefore, according to the present invention, when each coefficient of the Hurwitz polynomial of the Bessel filter is multiplied by a constant slightly larger than 1, the transmission group delay characteristic is not changed, and the transmission amplitude characteristic is shifted to a value slightly smaller than 1, and the reflection amplitude is accordingly reduced. It has been found that the deviation can be alleviated by utilizing the fact that the characteristic slightly increases.
[0034]
If the transmission amplitude characteristic has a design value of 1, if there is an error in the actual element value, the transmission amplitude characteristic always becomes a characteristic deviation that becomes smaller than 1 because it is a passive element. No, the designed value is likely to be an unstable constant. However, if the transmission amplitude is set to a value slightly smaller than 1, the transmission amplitude can be corrected in plus and minus, and the tolerance for the element error increases, which is easy to realize.
[0035]
To perform this operation without changing the transmission amplitude characteristic and the transmission group delay characteristic, it is necessary to multiply the Fulbitz polynomial representing the transmission characteristic and the reflection characteristic by the reciprocal of a constant whose absolute value is smaller than 1 and larger than 0.95. Just do it. For this purpose, the value of r in Equation 3 is shifted from 1, so that the constant term (r + 1) / 2√r in Equation 3 is the reciprocal of a value between 0.95 and 1. For that purpose, r may be set to a value between 0.5241 and 1.9080.
[0036]
As described above, by correcting the Hurwitz polynomial of the actual Bessel filter and performing the design according to Patent Document 1 again, an optical thin film filter having characteristics close to the original target can be stably realized using the actual optical thin film material and the glass substrate. it can.
[0037]
FIG. 9 shows an equivalent circuit derived from the circuit network function shown in the above description. The

cavities

67, 68, 69 are connected via the imaginary gyrator 66 between the terminating

resistors

80, 81. Each cavity consists of

resonators

76, 77, 78 and

ideal transformers

70, 71, 72, 73, 74, 75 connected before and after the resonators. The relationship between the components of the embodiment of FIG. 1 and the components of the equivalent circuit of FIG. 9 is as follows: the communication layer 14 is an imaginary gyrator 66; the reflecting mirror layers 2 to 8 are ideal transformers 70 to 75; At 78, the cavity layers 10 to 13 correspond to the cavities 67 to 69.
[0038]
【Example】
As an embodiment of the present invention, the constant (r + 1) / 2√r multiplied by the denominator polynomial g (s) is set to 1.016, where r in Equation 3 is set to 0.7. That constant multiplied to Hurwitz polynomial of _s _{11, s 21} and 0.984. From this equivalent circuit, the design according to Patent Document 1 is performed to realize an optical thin film filter, and the characteristics thereof are shown in FIGS. As a result, the transmission amplitude at the center frequency is deteriorated by 0.13 dD and the reflection characteristic is increased to -15 dD, but the group delay characteristic can be realized as intended. The deterioration of the transmission amplitude is at a level that causes no practical problem.
[0039]
【The invention's effect】
According to the present invention, a cavity layer is formed from a reflector layer and a spacer layer in which a plurality of optical thin films having different refractive indices are multilayered, and the plurality of cavity layers are multistaged via a communication layer, and a Hurwitz of complex frequency s is formed. From the denominator polynomial and the numerator polynomial representing the transmission characteristic in the polynomial, and the denominator polynomial and the numerator polynomial representing the reflection characteristic, a band-pass optical thin film filter having a layer configuration determined according to the transmission characteristic and the reflection characteristic to be obtained, For the combination of the original numerator polynomial and the denominator polynomial in which the absolute value of the transmission coefficient at the center frequency is 1, the transmission coefficient obtained by multiplying the transmission coefficient by a constant smaller than 1 and larger than 0.95 is defined as a new transmission coefficient. By defining a new polynomial for the reflection coefficient and defining the layer configuration from these new polynomials, a filter with characteristics close to the target characteristics can be implemented using existing materials. It can be.
[Brief description of the drawings]
FIG. 1 is a diagram showing a configuration of an optical thin film filter of the present invention.
FIG. 2 is a diagram showing transmission amplitude characteristics of the optical thin film filter of the present invention.
FIG. 3 is a diagram showing transmission group delay characteristics of the optical thin film filter of the present invention.
FIG. 4 is a diagram showing a reflection amplitude characteristic of the optical thin film filter of the present invention.
FIG. 5 is a diagram showing a transmission group delay characteristic of a Bessel filter by a polynomial.
FIG. 6 is a diagram illustrating a transmission amplitude characteristic of a Bessel filter using a polynomial.
FIG. 7 is a diagram showing transmission group delay characteristics of an optical thin film filter according to a conventional design.
FIG. 8 is a diagram showing transmission amplitude characteristics of an optical thin film filter according to a conventional design.
FIG. 9 is a diagram showing an equivalent circuit of the optical thin film filter.
FIG. 10 is a diagram showing a conventional FBG.
FIG. 11 is a diagram showing a conventional AWG.
FIG. 12 is a diagram showing a conventional optical thin film filter.
[Explanation of symbols]
1:

glass substrate

2, 3, 4, 5, 6, 7, 8, 19, 20: reflecting mirror layer 9:

spacer layer

10, 11, 12, 13: cavity layer 14: communication layer 15: grating portion 16: minute Wave part 17: Phase shift part 18: Wavelength selection part 21: Filter end face 51, 52, 53, 54, 55: Group delay characteristic 66: Imaginary gyrator 67, 68, 69:

Cavity

70, 71, 72, 73, 74, 75: Ideal transformer 76, 77, 78: Resonator 80, 81: Terminating resistor

Claims

A cavity layer is formed from a reflector layer and a spacer layer in which a plurality of optical thin films having different refractive indices are multilayered, and a plurality of cavity layers are multistaged via a communication layer, and a denominator representing a transmission characteristic in a Hurwitz polynomial of a complex frequency s. From a polynomial and a numerator polynomial, and a denominator polynomial and a numerator polynomial representing a reflection characteristic, a band-pass optical thin-film filter in which a layer configuration is determined in accordance with a desired transmission characteristic and a reflection characteristic,
An optical thin-film filter characterized by multiplying a Hurwitz polynomial representing the transmission characteristics and reflection characteristics by a reciprocal of a constant having an absolute value smaller than 1 and larger than 0.95, and determining a layer configuration from these new polynomials.