JP2004333336A - Polarization mode dispersion measuring device of optical fiber and measuring method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To measure PMD of an optical fiber by a small amount of measurement data and operation processing. <P>SOLUTION: A linearly polarized optical pulse having a prescribed wavelength is allowed to enter one end side of the optical fiber 1, and its back-scattering light is received by a polarized light receiving part 26, to thereby acquire a Stokes parameter in each section of the optical fiber 1. A parameter calculation means 32 calculates parameters of each matrix in each section based on a model formula of the optical fiber 1 defined by a transfer function matrix and a scattering Meuller matrix and the acquired Stokes parameter. The first Jones matrix calculation means 33 determines the first Jones matrix in each section based on the calculated parameters, and the second Jones matrix calculation means 34 determines the second Jones matrix in each section having a different wavelength from the prescribed wavelength based on the calculated parameters. A polarization mode dispersion calculation means 35 calculates the polarization mode dispersion in an optional section of the optical fiber 1 based on the acquired two pairs of Jones matrices. <P>COPYRIGHT: (C)2005,JPO&NCIPI

Description

【００２９】
即ち、伝達関数行列Ｔ（ω）は、３つのパラメータΦ、Θ、Ψの自由度をもつ伝達関数で表現される。
【００３０】
ここで、パラメータΦは伝搬する光の直交２偏波間の初期位相差を表し、パラメータΘは伝搬する光の直交２偏波の主軸に対する回転角を表し、パラメータΨは、伝搬する光の直交２偏波間の位相差を表している。
【００３１】
また、レーリー散乱行列Ｒは、散乱体が対称面を持った粒子の集合体であると仮定すると、次式（３）のミュラー行列で表される。
【００３２】
【数２】

【００３３】
したがって、散乱行列（ミュラー）は、２つのパラメータａ_１、ａ_２の自由度を持っている（ただし、後述するようにパラメータａ_１は、測定データから既知となる）。
【００３４】
散乱行列は、入射光の４つのストークスパラメータ（Ｉ，Ｑ，Ｕ，Ｖ）と出射光のストークスパラメータ（Ｉ′，Ｑ′，Ｕ′，Ｖ′）で表現され、観測によって得られた波形と比較することができる。そのときの関係式は次式（４）となる。
【００３５】
【数３】

【００３６】
また、ストークスパラメータ（Ｉ，Ｑ，Ｕ，Ｖ）と、各偏波成分の強度Ｉ_０〜Ｉ_Ｃとは、次式（５）のように関係付けられる。ただし、Ｅｘ、Ｅｙは直交成分の振幅、記号＊は共役を示す。
【００３７】
【数４】

【００３８】
また、式（４）により、次式（６）、（７）が得られる。
【００３９】
Ｉ′＝ａ_１・Ｉ， Ｑ′＝ａ_２・Ｑ ……（６）
【００４０】

【００４１】
上記式（７）の関係から、前記式（４）は、次式（８）のように表すことができる（Ｒ′は散乱行列）。
【００４２】
【数５】

【００４３】
ここで、入射光は直線偏光なので、Ｉ_０＝１、Ｉ_９０＝Ｉ_４５＝Ｉ_Ｃ＝０となり、式（７）から、ａ_１＝Ｉ_０′＋Ｉ_９０′で測定データから既知となり、散乱行列Ｒ′は、結局ａ_２の自由度となる。
【００４４】
以上により、４種類の偏波成分の測定データのうち、入射端から距離Ｚだけ離れた地点から戻る散乱光についての測定データに対して、伝達関数行列Ｔの３つのパラメータ（Φ，Θ，Ψ）と散乱ミュラー行列Ｍの１つのパラメータａ_２が決定できれば、前記した伝達関数行列Ｔ（ω）を計算できる。
【００４５】
ただし、伝達関数行列Ｔ（ω）は２行２列であるのに対し、散乱行列Ｒ′は４行４列であるため、このままの形では計算できない。
【００４６】
そこで、次式（９）のように、伝達関数行列Ｔを４行４列のミュラー行列Ｍに置き換える。
【００４７】
【数６】

【００４８】
このように置き換えた場合、伝達関数行列Ｔと散乱ミュラー行列Ｍの要素は、次の各式（１０−１）〜（１０−１６）の関係を満たす。
【００４９】
Ｍ１１＝（｜Ｔ１１｜^２＋｜Ｔ１２｜^２＋｜Ｔ２１｜^２＋｜Ｔ２２｜^２）／２……（１０−１）
【００５０】
Ｍ１２＝（｜Ｔ１１｜^２−｜Ｔ１２｜^２＋｜Ｔ２１｜^２−｜Ｔ２２｜^２）／２……（１０−２）
【００５１】
Ｍ１３＝−Ｒｅ（Ｔ１１・Ｔ１２^＊＋Ｔ２２・Ｔ２１^＊） ……（１０−３）
【００５２】
Ｍ１４＝−Ｉｍ（Ｔ１１・Ｔ１２^＊−Ｔ２２・Ｔ２１^＊） ……（１０−４）
【００５３】
Ｍ２１＝（｜Ｔ１１｜^２＋｜Ｔ１２｜^２−｜Ｔ２１｜^２−｜Ｔ２２｜^２）／２……（１０−５）
【００５４】
Ｍ２２＝（｜Ｔ１１｜^２−｜Ｔ１２｜^２−｜Ｔ２１｜^２＋｜Ｔ２２｜^２）／２……（１０−６）
【００５５】
Ｍ２３＝−Ｒｅ（Ｔ１１・Ｔ１２^＊−Ｔ２２・Ｔ２１^＊） ……（１０−７）
【００５６】
Ｍ２４＝−Ｉｍ（Ｔ１１・Ｔ１２^＊＋Ｔ２２・Ｔ２１^＊） ……（１０−８）
【００５７】
Ｍ３１＝−Ｒｅ（Ｔ１１・Ｔ２１^＊＋Ｔ２２・Ｔ１２^＊） ……（１０−９）
【００５８】
Ｍ３２＝−Ｒｅ（Ｔ１１・Ｔ２１^＊−Ｔ２２・Ｔ１２^＊） ……（１０−１０）
【００５９】
Ｍ３３＝Ｒｅ（Ｔ１１・Ｔ２２^＊＋Ｔ１２・Ｔ２１^＊） ……（１０−１１）
【００６０】
Ｍ３４＝−Ｉｍ（Ｔ１１・Ｔ２２^＊＋Ｔ２１・Ｔ２１^＊） ……（１０−１２）
【００６１】
Ｍ４１＝−Ｉｍ（Ｔ２１・Ｔ１１^＊＋Ｔ２２・Ｔ１２^＊） ……（１０−１３）
【００６２】
Ｍ４２＝−Ｉｍ（Ｔ２１・Ｔ１１^＊−Ｔ２２・Ｔ１２^＊） ……（１０−１４）
【００６３】
Ｍ４３＝Ｉｍ（Ｔ２２・Ｔ１１^＊−Ｔ１２・Ｔ１２^＊） ……（１０−１５）
【００６４】
Ｍ４４＝Ｒｅ（Ｔ２２・Ｔ１１^＊−Ｔ１２・Ｔ２１^＊） ……（１０−１６）
【００６５】
この行列Ｍを用いて前記式（１）を表せば、次式（１１）のようになる。
【００６６】
Ｆｚ＝Ｍｚ′・Ｒｚ′・Ｍｚ ……（１１）
【００６７】
この式（１１）を、前記式（８）、（９）を用いて書き直すと、以下の式（１２）となる。
【００６８】
【数７】

【００６９】
上記式（１２）が、被測定光ファイバ１について定義されたモデル式となり、これを計算することで、４つの未知のパラメータ（Φ，Θ，Ψ，ａ_２）を算出することができる。なお、詳述しないが、このパラメータの算出にはマーカット（ｍａｒｑｕａｔｄ）法を用いている。
【００７０】
これにより、被測定光ファイバ１の区間１′における片道の伝達関数行列Ｔの３つのパラメータと散乱行列Ｒ′の１つのパラメータが決定する。
【００７１】
また、図３に示すように、被測定光ファイバ１の全長を単位長区間に分け、入力端からｍ−１番目の区間までの伝達関数行列をＴ_ｍ−１、ｍ番目の区間までの伝達関数行列をＴ_ｍとし、ｍ番目の区間の伝達関数行列をｔ_ｍとすれば、次の関係が成り立つ。
【００７２】
Ｔ_ｍ＝ｔ_ｍ・Ｔ_ｍ−１， ｔ_ｍ＝Ｔ_ｍ・Ｔ_ｍ−１ ^−１ ……（１３）
【００７３】
つまり、ｍ−１番目までの伝達関数行列Ｔ_ｍ−１と、ｍ番目までの伝達関数行列Ｔ_ｍとが求まれば、上記式（１３）からｍ番目の区間の伝達関数行列ｔ_ｍを算出できる。
【００７４】
ｍ番目の区間のパラーメータをΦ_ｍ、Θ_ｍ、Ψ_ｍを用いて伝達関数行列ｔを表すと以下の式（１４）となる。
【００７５】
【数８】

【００７６】
したがって、任意のｎ番目の区間までの伝達関数行列Ｔ_ｎは、次式（１５）で表すことができる。
【００７７】
【数９】

【００７８】
上記演算により、被測定ファイバ１の任意の区間の伝達関数行列および任意の区画までの伝達関数行列を計算することができる。
【００７９】
次に、波長が異なる光に対する伝達関数行列の要素に含まれるパラメータを演算によって求める（Ｓ３）。
【００８０】
即ち、伝達関数行列Ｔの要素を決定する３種類のパラメータΦ_ｍ、Ψ_ｍ、Θ_ｍのうち、Θ_ｍ以外の２つのパラメータΦ_ｍ、Ψ_ｍは波長依存性を持っており、入射光の角周波数ωについて、それぞれ以下のように表されることが知られている。
【００８１】
Φ_ｍ＝ｋ_１，ｍ・ω， Ψ_ｍ＝ｋ_２，ｍ・ω ……（１６）
ただし、ｋ_１、ｋ_２は、位相と角周波数とを関係付ける係数
【００８２】
したがって、ｍ番目の第１ジョーンズマトリクスＴｍ（ω）は、以下の式（１７）のように表される。
【００８３】
【数１０】

【００８４】
また、ωをΔω変化させたω＋Δωを用いて式（１７）により、第２ジョーンズマトリクスＴ（ω＋Δω）を各区間毎に算出する（Ｓ４）。
【００８５】
そして、ＰＭＤを前記非特許文献１と同様に、次式（１８）で示すＰＭＤ演算子Ｄ（ω）を用いて算出する（Ｓ５）。
【００８６】
【数１１】

【００８７】
なお、被測定光ファイバ１の全長にわたるＰＭＤの分布を求める場合には、全ての区間毎のＰＭＤを求める。
【００８８】
次に、上記方法に基づくＰＭＤ測定装置の実施形態について説明する。
図４は、本発明を適用したＰＭＤ測定装置２０の構成を示している。
【００８９】
図４において、光パルス発生部２１は、半導体レーザ２２をパルス発生器２３から出力されるパルス信号Ｅｐによって励起して、波長および幅が一定の光パルスＰを出射させ、その光パルスＰを偏光子２４に入射して、偏波方向が一定の直線偏光の光パルスＰ′を出射する。
【００９０】
方向生結合器２５は、光パルス発生部２１から出射された光パルスＰ′を端子２０ａを介して被測定光ファイバ１の一端側に入射し、その入射した光パルスＰ′に対して被測定光ファイバ１の一端側から出射される後方散乱光Ｐｓを光パルスＰ′の入射光路と異なる光路から出射させる。
【００９１】
この後方散乱光Ｐｓは、例えば、図５に示すように、時間（光パルスの進行距離）の経過とともに減衰（一部で反射して強度が増大する場合もある）し、光ファイバの遠端で大きく減衰する。
【００９２】
偏波受光部２６は、後述するストークスパラメータ取得手段３１とともにこの実施形態のストークスパラメータ測定手段を構成するものであり、方向性結合器２５から出射された後方散乱光Ｐｓを受けて、その後方散乱光Ｐｓに含まれる異なる複数の偏波成分を抽出し、各偏波成分の時間毎の強度をそれぞれ測定する。
【００９３】
この偏波受光部２６は、例えば図６に示しているように、方向性結合器２２から出射された後方散乱光Ｐｓを偏波分離器２７で受けて前記した４種類の偏波成分Ｉ_０〜Ｉ_Ｃを光学的に分離抽出し、その各偏波成分Ｉ_０〜Ｉ_Ｃをそれぞれ受光器２８ａ〜２８ｄで受光して、その受光信号をそれぞれＡ／Ｄ変換器２９ａ〜２９ｄによって所定周期でサンプリングしてディジタル値に変換し、これを各偏波成分の強度を表す信号Ｉ_０（ｋ）〜Ｉ_Ｃ（ｋ）（都合上偏波成分と同一記号を用いる）として演算処理部３０に時系列に出力する（ｋ＝１，２，…）。
【００９４】
コンピュータ構成の演算処理部３０は、ストークスパラメータ取得手段３１、、パラメータ算出手段３２、第１のジョーンズマトリクス算出手段３３、第２のジョーンズマトリクス算出手段３４およびＰＭＤ算出手段３５を有している。
【００９５】
ストークスパラメータ取得手段３１は、光パルス発生部２１が光パルスＰ′を出射したタイミングから所定時間が経過するまでの間に、偏波受光部２６から出力される偏波成分毎の強度信号Ｉ_０（ｋ）〜Ｉ_Ｃ（ｋ）を取得して、取得した信号から、前記式（５）にしたがって、被測定光ファイバ１の各区間（前記サンプリング周期に対応した長さを最小とする区間）毎のストークスパラメータ（Ｉ，Ｑ，Ｕ，Ｖ）を求める。
【００９６】
なお、実際の演算で必要なパラメータは、前記式（８）、（１２）で示しているように、測定値Ｉ_０、Ｉ_９０を含む４つのパラメータ（Ｉ_０，Ｉ_９０，Ｕ，Ｖ）であり、ここでは、この測定値を含む４つのパラメータもストークスパラメータと呼ぶ。
【００９７】
また、この信号取得時間は測定対象区間に応じて任意であるが、被測定光ファイバ１の全長にわたるＰＭＤを測定する場合には、被測定光ファイバ１に入射された光パルスが遠端に到達し、その遠端からの後方散乱光が入射端に到達するのに必要な時間までとする。
【００９８】
パラメータ算出手段３２は、波長依存性を有するパラメータを含み３つのパラメータ（Φ，Ψ，Θ）からなる伝達関数行列Ｍと少なくとも１つのパラメータ（ａ_２）からなる散乱ミュラー行列Ｒ′とで定義される被測定光ファイバの前記モデル式（１２）と、ストクースパラメータ取得手段３１によって取得された４つのストークスパラメータとに基づいて、伝達関数行列Ｔの３つのパラメータと散乱ミュラー行列の少なくとも１つのパラメータとを区間毎に算出する。
【００９９】
即ち、前記したＰＭＤの測定方法で示したモデル式（１２）に関わる計算を行なって、４つのパラメータ（Φ，Ψ，Θ，ａ_２）を各区間毎に求める。
【０１００】
第１のジョーンズマトリクス算出手段３３は、パラメータ算出手段３２によって得られたパラメータに基づいて、所定波長λ、つまり角周波数ωについての第１ジョーンズマトリクスＴｍ（ω）を前記式（１７）にしたがって、区間毎に算出する。
【０１０１】
また、第２のジョーンズマトリクス算出手段３４は、パラメータ算出手段３２によって算出されたパラメータのうち、前記式（１６）で示した波長依存性をもつパラメータの角周波数ω＋Δωにおける値を求めて、そのパラメータについての第２ジョーンズマトリクスＴｍ（ω＋Δω）を前記式（１７）にしたがって区間毎に算出する。
【０１０２】
ＰＭＤ算出手段３５は、第１のジョーンズマトリクス算出手段３３および第２のジョーンズマトリクス算出手段３４によって得られた第１のジョーンズマトリクスＴｍ（ω）と第２ジョーンズマトリクスＴｍ（ω＋Δω）について、例えば、前記非特許文献１と同様に、前記式（１８）で示したＰＭＤ演算子Ｄ（ω）を用いて、被測定光ファイバの任意の区間あるいは任意の区間までの偏波モード分散ＰＭＤ（Δτ）を算出する。なお、このＰＭＤの算出方法は上記のようにＰＭＤ演算子Ｄ（ω）を用いた方法以外に他の周知の方法を用いることもできる。
【０１０３】
このように、実施形態のＰＭＤ測定装置および測定方法では、光ファイバについて散乱体のデポーラリゼーションを考慮するとともに、単一波長で且つ単一の入射偏光に対する後方散乱光から得られる４種類のストークスパラメータと関連付けされたモデル式を定義し、そのモデル式と測定データから得られたストークスパラメータとに基づいて、光の角周波数ωにおける光ファイバ１の伝達関数行列を決定するパラメータを算出し、その算出されたパラメータに基づいて角周波数ωにおける第１のジョーンズマトリクスＴｍ（ω）を求め、光の角周波数ω＋Δωについてのパラメータを演算で求めて、それについての第２のジョーンズマトリクスＴｍ（ω＋Δω）を求め、得られた２つのジョーンズマトリクスから光ファイバのＰＭＤを算出している。
【０１０４】
つまり、光ファイバ１を、散乱体のデポーラリゼーションを考慮して正確にモデル化しているので、単一波長で且つ単一の入射偏光で必要なパラメータを算出することができ、測定のための時間が従来（特許文献１）の１／６で済み、短時間に且つ精度よく光ファイバの任意の区間のＰＭＤを測定することができる。
【０１０５】
【発明の効果】
以上説明したように、本発明の偏波モード分散測定装置および測定方法では、光ファイバについて散乱体のデポーラリゼーションを考慮するとともに、単一波長で且つ単一の入射偏光に対する後方散乱光から得られる４種類のストークスパラメータと関連付けされたモデル式を定義し、そのモデル式と測定データから得られたストークスパラメータとに基づいて、光の角周波数ωにおける光ファイバの伝達関数行列を決定するパラメータを区間毎に算出し、その算出されたパラメータに基づいて角周波数ωにおける第１のジョーンズマトリクスを区間毎に求め、光の角周波数ω＋Δωについてのパラメータを演算で求めて、それについての第２のジョーンズマトリクスを区間毎に求め、得られた２つのジョーンズマトリクスから光ファイバの任意の区間のＰＭＤを算出している。
【０１０６】
このように散乱体のデポーラリゼーションを考慮して光ファイバを正確にモデル化しているので、単一波長で且つ単一の入射偏光のみで必要なパラメータを算出することができ、このため、光ファイバの任意の区間の偏波モード分散を短時間に且つ精度よく測定することができる。
【図面の簡単な説明】
【図１】本発明の実施形態の偏波モード分散測定方法の手順を示すフローチャート
【図２】光ファイバをモデル化した図
【図３】任意区間の偏波モード分散を求める方法を説明するための図
【図４】本発明の実施形態の偏波モード分散測定装置の構成を示す図
【図５】後方散乱光の時間に対する強度変化の一例を示す図
【図６】実施形態の要部の構成例を示す図
【図７】偏波モード分散の影響を説明するための図
【符号の説明】
１……被測定光ファイバ、２０……偏波モード分散（ＰＭＤ）測定装置、２１……光パルス発生部、２５……方向性結合器、２６……偏波受光部、３０……演算処理部、３１……ストークスパラメータ取得手段、３２……パラメータ算出手段、３３……第１のジョーンズマトリクス算出手段、３４……第２のジョーンズマトリクス算出手段、３５……偏波モード分散（ＰＭＤ）算出手段[0001]
TECHNICAL FIELD OF THE INVENTION
The present invention relates to a technique for measuring polarization mode dispersion of an optical fiber in a short time with a simple configuration.
[0002]
[Prior art]
An optical fiber is used as a medium for transmitting information at high speed. In recent years, however, a rapid increase in the number of Internet users and the like has further demanded a higher communication speed.
[0003]
In response to such a demand for high speed, the polarization mode dispersion (hereinafter referred to as PMD) of an optical fiber cannot be ignored.
[0004]
The PMD is generated due to the fact that the cross-sectional shape of the core portion for transmitting light of the optical fiber is not completely round at the time of manufacturing, or is distorted by pressure from the outside, and propagates inside. This is a phenomenon in which the refractive index differs in the polarization direction of light, and the propagation time differs for each polarization component.
[0005]
Due to the influence of the PMD, for example, as shown in FIG. 7, when the optical pulse P is incident on one end of the optical fiber 1, the waveform of the optical pulse P ′ emitted from the other end of the optical fiber 1 is bimodal. The pulse width becomes wider, and the upper limit of the communication speed is determined by the spread of the pulse width.
[0006]
Therefore, when manufacturing an optical fiber or performing maintenance on an optical fiber that has already been laid, it is necessary to measure the PMD of the optical fiber.
[0007]
Many methods of measuring the PMD have been proposed so far, and among them, the method using the Jones matrix method is well known as having high measurement accuracy and capable of automating the measurement.
[0008]
The Jones matrix method is a measurement method for obtaining an average value Δτ of group delay of orthogonal two polarization components for an arbitrary wavelength as PMD of an optical device, in which linearly polarized light of a predetermined wavelength is incident on one end side of a device to be measured, The process of determining the intensity of light emitted from the other end of the device under measurement in different polarization directions is performed by changing the wavelength of the incident light and further changing the polarization direction to 0 degree (reference), 45 degrees, and 90 degrees. A Jones matrix representing input / output characteristics between both ends of the optical fiber is calculated for the two wavelengths from the obtained intensity data, and the PMD is calculated using the PMD operator (for example, see Non-Patent Document 1). ).
[0009]
[Non-patent document 1]
Teruhiko Kudo, Midori Iguchi, Masaru Masada, and Takeshi Ozeki “Theoretical Basis of Polarization Mode of Disp. 18 NO. 4 APRIL 2000 pp. 614-617.
[0010]
However, in the method of measuring the polarization component of the light emitted from one end of the optical fiber and measuring the intensity of the polarization component of the light emitted from the other end of the optical fiber to obtain the PMD, for example, When measuring an already-used optical fiber as an object to be measured, instruments for measurement must be installed at both ends, which is inconvenient.
[0011]
Further, only the PMD value for the entire length from one end to the other end of the optical fiber can be obtained, and the PMD during that period cannot be known.
[0012]
In order to solve this, the applicant of the present application incident a linearly polarized light pulse on one end of an optical fiber, and received backscattered light of the optical fiber for the incident light pulse on one end of the optical fiber, A method and an apparatus for measuring PMD, that is, a PMD distribution for each section of an optical fiber from an intensity change characteristic of each polarization component of the backward scattered light have been proposed (Patent Document 1).
[0013]
According to this method, the distribution of the PMD of the optical fiber can be obtained by measurement from one end of the optical fiber to be measured, and for example, the PMD for each position with respect to the installed optical fiber can be accurately grasped.
[0014]
[Patent Document 1] Japanese Patent Application Laid-Open No. 2002-48680
[Problems to be solved by the invention]
However, the PMD measurement method and apparatus proposed in Patent Document 1 described above do not take scatterers into consideration, so that accurate measurement for each section cannot be performed. Further, since the above-described Jones matrix method is used, two types of incident light wavelengths and three types of polarization states of the incident light are required for each wavelength, and four types of polarization component measurement data are required for each combination. Had to get.
[0016]
That is, acquisition of 2.times.3.times.4 = 24 types of measurement data and calculation processing on the data are required.
[0017]
In consideration of this point, the present invention can measure the PMD of the optical fiber with less waveform data and arithmetic processing. In other words, taking into account the depolarization of the scatterer, the conventional three incident linearly polarized lights are converted into one incident linearly polarized light, and the wavelength component is taken into account in the fiber model. It is an object of the present invention to provide an optical fiber PMD measuring apparatus and a measuring method which can be measured by the above method.
[0018]
[Means for Solving the Problems]
In order to achieve the above object, an optical fiber polarization mode dispersion measuring apparatus according to claim 1 of the present invention,
An optical pulse generator (21) for emitting a linearly polarized optical pulse at a predetermined wavelength;
The light pulse is incident on one end of the optical fiber to be measured, and backscattered light emitted from one end of the optical fiber to be measured is emitted from an optical path different from the incident optical path of the optical pulse with respect to the incident optical pulse. A directional coupler (25) for causing
Stokes parameter measuring means (26, 31) for receiving backscattered light emitted from the directional coupler and measuring four Stokes parameters for each section of the measured optical fiber;
Based on a model equation of the measured optical fiber defined by a transfer function matrix including three parameters including a parameter having wavelength dependence and a scattering Mueller matrix including at least one parameter, and based on the four Stokes parameters Parameter calculating means (32) for calculating, for each section, three parameters included in the elements of the transfer function matrix and at least one parameter included in the elements of the scattering Mueller matrix;
First Jones matrix calculating means (33) for obtaining a first Jones matrix for each section based on the parameters calculated by the parameter calculating means;
A second Jones matrix calculating means (34) for obtaining a second Jones matrix for each section at a wavelength different from the predetermined wavelength based on the parameters calculated by the parameter calculating means;
A polarization mode dispersion calculating means (35) for calculating a polarization mode dispersion of an arbitrary section of the measured optical fiber based on the first Jones matrix and the second Jones matrix.
[0019]
Further, the method for measuring the polarization mode dispersion of an optical fiber according to claim 2 of the present invention comprises:
A linearly polarized optical pulse having a predetermined wavelength is incident on one end of an optical fiber to be measured, and four Stokes parameters for each section from the backscattered light emitted from the one end by the optical fiber to be measured with respect to the optical pulse. Measuring (S1);
Based on a model equation of the measured optical fiber defined by a transfer function matrix including three parameters including a parameter having wavelength dependence and a scattering Mueller matrix including at least one parameter, and based on the four Stokes parameters Calculating three parameters included in the elements of the transfer function matrix and at least one parameter included in the elements of the scattering Mueller matrix at the predetermined wavelength in an arbitrary section of the measured optical fiber (S2);
Obtaining a first Jones matrix for each section based on the calculated parameters (S3);
Obtaining a second Jones matrix for each section at a wavelength different from the predetermined wavelength based on the calculated parameters (S4);
Calculating a polarization mode dispersion of an arbitrary section of the measured optical fiber based on the first Jones matrix and the second Jones matrix (S5).
[0020]
BEST MODE FOR CARRYING OUT THE INVENTION
Hereinafter, embodiments of the present invention will be described with reference to the drawings.
First, a PMD measurement method according to an embodiment of the present invention will be described with reference to FIG.
[0021]
The flowchart of FIG. 1 shows a procedure for measuring the PMD of the optical fiber to be measured by one-end measurement using an optical pulse, as in Patent Document 1 described above. A linearly polarized optical pulse P is incident on one end of the optical fiber to be measured, and the optical fiber to be measured uses the polarization component contained in the backscattered light emitted from one end of the optical fiber to measure the optical pulse. Four Stokes parameters are obtained for each section (S1).
[0022]
Here, the Stokes parameters for each section, 45 relative to the polarization component _I 90, _{I 0} the relative polarization component _I 0, _{I 0} of 0 degree as a reference from the back-scattered light having an angle of 90 degrees The polarization component I ₄₅ and the circular polarization component I _C having an angle of degree are converted from the timing at which the optical pulse P is incident on the optical fiber to be measured, for example, when the optical pulse reaches the far end of the optical fiber to be measured. Then, observation is performed until the time required for the backscattered light from the far end to return to the incident end elapses, and calculation is performed based on the observation result.
[0023]
Then, based on the obtained Stokes parameter for each section, an optical fiber model formula defined by a transfer function matrix including three parameters including a parameter having wavelength dependence and a scattering Mueller matrix including at least one parameter. Then, three parameters of the transfer function matrix and at least one parameter of the scattering Mueller matrix at a predetermined wavelength λ in an arbitrary section of the measured optical fiber are calculated (S2).
[0024]
Note that a plurality of parameters of the scattering Mueller matrix can be calculated by increasing the accuracy of the Stokes parameter. Here, the case where there is one parameter will be described, but a plurality of parameters may be calculated and used.
[0025]
Hereinafter, the processes S1 and S2 will be described.
As shown in FIG. 2, assuming a section 1 'of a certain length Z of the optical fiber 1 to be measured, and a one-way transfer function matrix from the incident end (left end in FIG. 2) to the scattering point (right end) is Tz. If the matrix obtained by converting this into a Muller matrix is Mz, the Muller matrix corresponding to the transposed matrix Tz ^t is Mz ′, and the scattering matrix is Rz, the round-trip Muller matrix Fz is expressed as follows: be able to.
[0026]
Fz = Mz ′ · Rz · Mz (1)
[0027]
Here, the transfer function matrix T (ω) at the angular frequency ω of light is represented by the following equation (2) using three parameters Φ, Θ, and Ψ.
[0028]
(Equation 1)

[0029]
That is, the transfer function matrix T (ω) is represented by a transfer function having three parameters Φ, Θ, and 自由.
[0030]
Here, the parameter Φ represents the initial phase difference between the two orthogonal polarizations of the propagating light, the parameter 表 し represents the rotation angle of the orthogonal two polarizations of the propagating light with respect to the main axis, and the parameter Ψ represents the orthogonal 2 polarization of the propagating light. It represents the phase difference between the polarized waves.
[0031]
The Rayleigh scattering matrix R is represented by the following Mueller matrix assuming that the scatterer is an aggregate of particles having a symmetry plane.
[0032]
(Equation 2)

[0033]
Therefore, the scattering matrix (Muller) has two degrees of freedom of parameters a ₁ and a ₂ (however, as will be described later, the parameter a ₁ is known from measurement data).
[0034]
The scattering matrix is expressed by four Stokes parameters (I, Q, U, V) of the incident light and Stokes parameters (I ', Q', U ', V') of the outgoing light. Can be compared. The relational expression at that time is the following expression (4).
[0035]
[Equation 3]

[0036]
Further, the Stokes parameters (I, Q, U, V) and the intensities I _{0 to} I _C of the respective polarization components are related as in the following equation (5). Here, Ex and Ey indicate the amplitude of the orthogonal component, and the symbol * indicates conjugate.
[0037]
(Equation 4)

[0038]
Further, the following equations (6) and (7) are obtained from the equation (4).
[0039]
I ′ = a ₁ · I, Q ′ = a ₂ · Q (6)
[0040]

[0041]
From the relationship of the above equation (7), the above equation (4) can be expressed as the following equation (8) (R ′ is a scattering matrix).
[0042]
(Equation 5)

[0043]
Here, since the incident light is linearly polarized light, I ₀ = 1, I ₉₀ = I ₄₅ = I _C = 0, and from equation (7), a ₁ = I ₀ ′ + I ₉₀ ′, which is known from the measured data, and is scattered. matrix R 'is, after all the freedom of _{a 2.}
[0044]
As described above, of the four types of polarization component measurement data, three parameters (Φ, Θ, Ψ) of the transfer function matrix T are used for the measurement data of the scattered light returning from the point away from the incident end by the distance Z. ) and if one parameter a ₂ is determined in the scattered Mueller matrix M, it can be calculated the the transfer function matrix T (omega).
[0045]
However, while the transfer function matrix T (ω) has 2 rows and 2 columns, the scattering matrix R ′ has 4 rows and 4 columns, and therefore cannot be calculated as it is.
[0046]
Therefore, as shown in the following equation (9), the transfer function matrix T is replaced with a 4-by-4 Mueller matrix M.
[0047]
(Equation 6)

[0048]
When replaced in this way, the elements of the transfer function matrix T and the scattering Mueller matrix M satisfy the following equations (10-1) to (10-16).
[0049]
^{M11 = (| T11 | 2 +} | T12 | 2 + | T21 | 2 + | T22 | 2) / 2 ...... (10-1)
[0050]
M12 = (| T11 | ² − | T12 | ² + | T21 | ² − | T22 | ² ) / 2 (10-2)
[0051]
M13 = −Re (T11 · T12 ^* + T22 · T21 ^* ) (10-3)
[0052]
M14 = −Im (T11 · T12 ^* −T22 · T21 ^* ) (10-4)
[0053]
^{M21 = (| T11 | 2 +} | T12 | 2 - | T21 | 2 - | T22 | 2) / 2 ...... (10-5)
[0054]
^{M22 = (| T11 | 2 -} | T12 | 2 - | T21 | 2 + | T22 | 2) / 2 ...... (10-6)
[0055]
M23 = −Re (T11 · T12 ^* −T22 · T21 ^* ) (10-7)
[0056]
M24 = −Im (T11 · T12 ^* + T22 · T21 ^* ) (10-8)
[0057]
M31 = −Re (T11 · T21 ^* + T22 · T12 ^* ) (10-9)
[0058]
M32 = −Re (T11 · T21 ^* −T22 · T12 ^* ) (10-10)
[0059]
M33 = Re (T11 · T22 ^* + T12 · T21 ^* ) (10-11)
[0060]
M34 = −Im (T11 · T22 ^* + T21 · T21 ^* ) (10-12)
[0061]
M41 = −Im (T21 · T11 ^* + T22 · T12 ^* ) (10-13)
[0062]
M42 = −Im (T21 · T11 ^* −T22 · T12 ^* ) (10-14)
[0063]
M43 = Im (T22 · T11 ^* −T12 · T12 ^* ) (10-15)
[0064]
M44 = Re (T22 · T11 ^* −T12 · T21 ^* ) (10-16)
[0065]
If the above equation (1) is expressed using this matrix M, the following equation (11) is obtained.
[0066]
Fz = Mz ′ · Rz ′ · Mz (11)
[0067]
When this equation (11) is rewritten using the above equations (8) and (9), the following equation (12) is obtained.
[0068]
(Equation 7)

[0069]
The above equation (12) is a model equation defined for the optical fiber 1 to be measured, and by calculating this, four unknown parameters (Φ, Θ, Ψ, a ₂ ) can be calculated. Although not described in detail, the parameter is calculated using a marquatd method.
[0070]
Thus, three parameters of the one-way transfer function matrix T and one parameter of the scattering matrix R 'in the section 1' of the measured optical fiber 1 are determined.
[0071]
Further, as shown in FIG. 3, the total length of the optical fiber under test 1 is divided into unit length sections, and the transfer function matrix from the input end to the (m-1) th section is represented by T _m-1 , the function matrix and T _m, the m-th transfer function matrix of the section if t _m, the following relation holds.
[0072]
_{T m = t m · T m} -1, t m = T m · T m-1 -1 ...... (13)
[0073]
That is, if the transfer function matrix T _{m-1 up} to the m-1th and the transfer function matrix T _{m up} to the _mth are obtained, the transfer function matrix tm of the _mth section is calculated from the above equation (13). it can.
[0074]
The parameter contains the m th interval [Phi _m, theta _m, the following equation to represent the transfer function matrix t using [psi _m (14).
[0075]
(Equation 8)

[0076]
Therefore, the transfer function matrix T _n up to an arbitrary n-th section can be expressed by the following equation (15).
[0077]
(Equation 9)

[0078]
By the above calculation, a transfer function matrix of an arbitrary section of the measured fiber 1 and a transfer function matrix up to an arbitrary section can be calculated.
[0079]
Next, parameters included in the elements of the transfer function matrix for light having different wavelengths are obtained by calculation (S3).
[0080]
That is, the transfer function matrix T 3 kinds of determining the elements of the parameter [Phi _m, [psi _m, among theta _m, 2 one parameter [Phi _m other than theta _m, [psi _m is has a wavelength dependence, the incident light It is known that the angular frequency ω is expressed as follows.
[0081]
Φ _m = k _{1, m} · ω, _{ｍ m} = k _{2, m} · ω (16)
Here, k ₁ and k ₂ are coefficients relating the phase and the angular frequency.
Therefore, the m-th first Jones matrix Tm (ω) is represented by the following equation (17).
[0083]
(Equation 10)

[0084]
Further, the second Jones matrix T (ω + Δω) is calculated for each section by the equation (17) using ω + Δω obtained by changing ω by Δω (S4).
[0085]
Then, similarly to Non-Patent Document 1, the PMD is calculated using a PMD operator D (ω) expressed by the following equation (18) (S5).
[0086]
(Equation 11)

[0087]
When the distribution of PMD over the entire length of the optical fiber 1 to be measured is obtained, the PMD for each section is obtained.
[0088]
Next, an embodiment of a PMD measuring apparatus based on the above method will be described.
FIG. 4 shows a configuration of a PMD measuring apparatus 20 to which the present invention is applied.
[0089]
In FIG. 4, an optical pulse generator 21 excites a semiconductor laser 22 by a pulse signal Ep output from a pulse generator 23, emits an optical pulse P having a constant wavelength and width, and polarizes the optical pulse P. Incident on the element 24 and emits a linearly polarized light pulse P ′ having a constant polarization direction.
[0090]
The directional coupler 25 inputs the optical pulse P ′ emitted from the optical pulse generator 21 to one end of the optical fiber 1 to be measured via the terminal 20a, and measures the measured optical pulse P ′ with respect to the incident optical pulse P ′. The backscattered light Ps emitted from one end of the optical fiber 1 is emitted from an optical path different from the incident optical path of the optical pulse P ′.
[0091]
For example, as shown in FIG. 5, the backscattered light Ps is attenuated (in some cases, the intensity is increased due to partial reflection) with the passage of time (the traveling distance of the light pulse), and the far end of the optical fiber Greatly attenuates at
[0092]
The polarization receiving unit 26 constitutes a Stokes parameter measuring unit of this embodiment together with a Stokes parameter acquiring unit 31 described later, receives the backscattered light Ps emitted from the directional coupler 25, and receives the backscattered light Ps. A plurality of different polarization components included in the light Ps are extracted, and the intensity of each polarization component at each time is measured.
[0093]
For example, as shown in FIG. 6, the polarization light receiving unit 26 receives the backscattered light Ps emitted from the directional coupler 22 by the polarization separator 27 and receives the four types of polarization components I _{0 described above.} the ~I _C optically separated and extracted, and receives its each polarization component _I 0 ~I _C at each light receiver 28a to 28d, the light reception signal at a predetermined period by the a / D converter 29a~29d respectively The digital signal is sampled and converted to a digital value, which is then sent to the arithmetic processing unit 30 as signals I ₀ (k) to I _C (k) (for the sake of convenience, using the same symbol as the polarization component) representing the intensity of each polarization component. Output to the series (k = 1, 2,...).
[0094]
The arithmetic processing unit 30 having a computer configuration includes a Stokes parameter acquisition unit 31, a parameter calculation unit 32, a first Jones matrix calculation unit 33, a second Jones matrix calculation unit 34, and a PMD calculation unit 35.
[0095]
The Stokes parameter acquiring unit 31 outputs the intensity signal I _{0 for} each polarization component output from the polarization light receiving unit 26 until a predetermined time elapses from the timing when the optical pulse generation unit 21 emits the optical pulse P ′. (K) to I _C (k) are acquired, and from the acquired signal, each section of the optical fiber 1 to be measured (a section that minimizes the length corresponding to the sampling period) according to the above equation (5). The Stokes parameters (I, Q, U, V) are obtained for each.
[0096]
The parameters required for the actual calculation are four parameters (I ₀ , I ₉₀ , U, V) including the measured values I ₀ , I ₉₀ as shown in the equations (8) and (12). Here, the four parameters including the measured value are also called Stokes parameters.
[0097]
The signal acquisition time is arbitrary depending on the section to be measured. However, when measuring the PMD over the entire length of the optical fiber 1 to be measured, the optical pulse incident on the optical fiber 1 reaches the far end. And the time required for the backscattered light from the far end to reach the incident end.
[0098]
The parameter calculating means 32 is defined by a transfer function matrix M including three parameters (Φ, Ψ, Θ) including a parameter having a wavelength dependence, and a scattering Mueller matrix R ′ including at least one parameter (a ₂ ). Based on the model equation (12) of the optical fiber to be measured and the four Stokes parameters acquired by the Stokes parameter acquisition means 31, at least one parameter of the transfer function matrix T and at least one parameter of the scattering Mueller matrix Is calculated for each section.
[0099]
That is, the calculation relating to the model equation (12) shown in the above-described PMD measurement method is performed, and four parameters (Φ, Ψ, Θ, a ₂ ) are obtained for each section.
[0100]
The first Jones matrix calculating unit 33 calculates the first Jones matrix Tm (ω) for the predetermined wavelength λ, that is, the angular frequency ω, based on the parameters obtained by the parameter calculating unit 32 according to the above equation (17). It is calculated for each section.
[0101]
Further, the second Jones matrix calculating means 34 calculates a value at the angular frequency ω + Δω of the parameter having the wavelength dependence shown in the equation (16) among the parameters calculated by the parameter calculating means 32, and calculates the parameter. The second Jones matrix Tm (ω + Δω) is calculated for each section according to the equation (17).
[0102]
The PMD calculator 35 calculates the first Jones matrix Tm (ω) and the second Jones matrix Tm (ω + Δω) obtained by the first Jones matrix calculator 33 and the second Jones matrix calculator 34. Similarly to Non-Patent Document 1, the polarization mode dispersion PMD (Δτ) in an arbitrary section or up to an arbitrary section of the optical fiber to be measured is calculated using the PMD operator D (ω) shown in the above equation (18). calculate. It should be noted that other known methods can be used for this PMD calculation method other than the method using the PMD operator D (ω) as described above.
[0103]
As described above, in the PMD measuring apparatus and the measuring method of the embodiment, while considering the depolarization of the scatterer in the optical fiber, the four types of Stokes obtained from the backscattered light at a single wavelength and for a single incident polarized light are used. Define a model equation associated with the parameter, calculate a parameter for determining a transfer function matrix of the optical fiber 1 at an angular frequency ω of light based on the model equation and Stokes parameters obtained from measurement data, The first Jones matrix Tm (ω) at the angular frequency ω is obtained based on the calculated parameters, the parameter about the angular frequency ω + Δω of light is obtained by calculation, and the second Jones matrix Tm (ω + Δω) for that is obtained. From the obtained two Jones matrices to calculate the PMD of the optical fiber That.
[0104]
That is, since the optical fiber 1 is accurately modeled in consideration of the depolarization of the scatterer, the necessary parameters can be calculated at a single wavelength and with a single incident polarization, and the measurement can be performed. The time is only 1/6 of the conventional case (Patent Document 1), and the PMD of an arbitrary section of the optical fiber can be measured in a short time and with high accuracy.
[0105]
【The invention's effect】
As described above, in the polarization mode dispersion measuring apparatus and the measuring method of the present invention, the depolarization of the scatterer in the optical fiber is taken into consideration, and the optical fiber is obtained from the backscattered light at a single wavelength and for a single incident polarization. A model expression associated with the four types of Stokes parameters is defined, and a parameter for determining a transfer function matrix of the optical fiber at the angular frequency ω of light is defined based on the model expression and a Stokes parameter obtained from measurement data. The first Jones matrix at the angular frequency ω is calculated for each section based on the calculated parameters, the parameter for the angular frequency ω + Δω of light is calculated, and the second Jones for the matrix is calculated. A matrix is obtained for each section, and an arbitrary optical fiber is obtained from the two Jones matrices obtained. PMD of the section is calculated.
[0106]
Since the optical fiber is accurately modeled in consideration of the depolarization of the scatterer, necessary parameters can be calculated with only a single wavelength and only a single incident polarization. The polarization mode dispersion in an arbitrary section of the fiber can be accurately measured in a short time.
[Brief description of the drawings]
FIG. 1 is a flowchart showing a procedure of a polarization mode dispersion measuring method according to an embodiment of the present invention. FIG. 2 is a diagram modeling an optical fiber. FIG. 3 is a diagram for explaining a method for obtaining polarization mode dispersion in an arbitrary section. FIG. 4 is a diagram illustrating a configuration of a polarization mode dispersion measuring apparatus according to an embodiment of the present invention. FIG. 5 is a diagram illustrating an example of a change in intensity of backscattered light with respect to time. FIG. FIG. 7 is a diagram showing a configuration example. FIG. 7 is a diagram for explaining the influence of polarization mode dispersion.
DESCRIPTION OF SYMBOLS 1 ... Optical fiber to be measured, 20 ... Polarization mode dispersion (PMD) measuring device, 21 ... Optical pulse generator, 25 ... Directional coupler, 26 ... Polarized light receiver, 30 ... Calculation processing , 31... Stokes parameter acquisition means, 32... Parameter calculation means, 33... First Jones matrix calculation means, 34... Second Jones matrix calculation means, 35. means

Claims (2)

An optical pulse generator (21) for emitting a linearly polarized optical pulse at a predetermined wavelength;
The light pulse is incident on one end of the optical fiber to be measured, and backscattered light emitted from one end of the optical fiber to be measured is emitted from an optical path different from the incident optical path of the optical pulse with respect to the incident optical pulse. A directional coupler (25) for causing
Stokes parameter measuring means (26, 31) for receiving backscattered light emitted from the directional coupler and measuring four Stokes parameters for each section of the measured optical fiber;
Based on a model equation of the measured optical fiber defined by a transfer function matrix including three parameters including a parameter having wavelength dependence and a scattering Mueller matrix including at least one parameter, and based on the four Stokes parameters Parameter calculating means (32) for calculating, for each section, three parameters included in the elements of the transfer function matrix and at least one parameter included in the elements of the scattering Mueller matrix;
First Jones matrix calculating means (33) for obtaining a first Jones matrix for each section based on the parameters calculated by the parameter calculating means;
A second Jones matrix calculating means (34) for obtaining a second Jones matrix for each section at a wavelength different from the predetermined wavelength based on the parameters calculated by the parameter calculating means;
An optical fiber comprising: a polarization mode dispersion calculating means (35) for calculating a polarization mode dispersion of an arbitrary section of the measured optical fiber based on the first Jones matrix and the second Jones matrix. Polarization mode dispersion measuring device. A linearly polarized optical pulse having a predetermined wavelength is incident on one end of an optical fiber to be measured, and four Stokes parameters for each section from the backscattered light emitted from the one end by the optical fiber to be measured with respect to the optical pulse. Measuring (S1);
Based on a model equation of the measured optical fiber defined by a transfer function matrix including three parameters including a parameter having wavelength dependence and a scattering Mueller matrix including at least one parameter, and based on the four Stokes parameters Calculating three parameters included in the elements of the transfer function matrix and at least one parameter included in the elements of the scattering Mueller matrix at the predetermined wavelength in an arbitrary section of the measured optical fiber (S2);
Obtaining a first Jones matrix for each section based on the calculated parameters (S3);
Obtaining a second Jones matrix for each section at a wavelength different from the predetermined wavelength based on the calculated parameters (S4);
Calculating a polarization mode dispersion of an arbitrary section of the optical fiber under test based on the first Jones matrix and the second Jones matrix (S5). Method.

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