JP3932030B2 - Nonlinear constant measuring method and apparatus for single mode optical fiber - Google Patents

Description

【数１０】

【数１１】

但し、Ｋ（λ _m ）は被測定単一モード光ファイバのガラス材料の前記測定波長λ _m における特定の添加物に対する屈折率の添加量依存性、ｎ ₀ （Ｍ ₀ ，λ _m ）は純石英に前記特定の添加物をＭ ₀ （単位： mol% ）添加したガラスの前記測定波長λ _m における屈折率、ｎ _0S （λ _m ）は前記測定波長λ _m における純石英の屈折率、Ｍ ₀ は純石英に対する前記特定の添加物の添加量 （単位： mol% ）、Ａ _i ，Ｂ _i （ｉ＝１，２，３）はガラス材料に固有の係数、
に基づき算出する第２のステップと、前記添加量分布Ｍ（ｒ）を用いて、被測定単一モード光ファイバの非線形屈折率分布ｎ ₂ （ｒ）を算出する第３のステップと、前記非線形屈折率分布ｎ ₂ （ｒ）と前記所望の波長λ _d での電界分布Ｅ（ｒ，λ _d ）との演算処理を行うことにより、被測定単一モード光ファイバの前記所望の波長λ _d における非線形屈折率及び非線形定数を算出する第４のステップとを有することを特徴とする単一モード光ファイバの非線形定数測定方法にある。
【００１１】
本発明によれば、従来技術のパルス光を用いた測定法における測定精度が光パルスの形状に強く依存したり、被測定光ファイバの長さ、波長分散、実効断面積に依存するといった課題を解決し、高精度な非線形定数を求めることが可能になる。
【００１２】
第２の発明は、第１の発明に記載された単一モード光ファイバの非線形定数測定方法であって、前記第３のステップが、前記添加量分布Ｍ（ｒ）を用いて、３つの基準波長λ ₁ ＝０．４８６１３μｍ、λ ₂ ＝０．５８７５６μｍ、λ ₃ ＝０．６５６２７μｍにおける屈折率分布を、
【数１２】

【数１３】

【数１４】

【数１５】

但し、ｋ＝１，２，３、Ｋ（λ _k ）は被測定単一モード光ファイバのガラス材料の前記基準波長λ _k における特定の添加物に対する屈折率の添加量依存性、ｎ ₀ （Ｍ ₀ ，λ _k ）は純石英に前記特定の添加物をＭ ₀ （単位： mol% ）添加したガラスの前記基準波長λ _k における屈折率、ｎ _0S （λ _k ）は前記基準波長λ _k における純石英の屈折率、Ｍ ₀ は純石英に対する前記特定の添加物の添加量 （単位： mol% ）、
に基づき算出するステップと、前記３つの基準波長λ _k における屈折率分布を用いて、被測定単一モード光ファイバの非線形屈折率分布ｎ ₂ （ｒ）を
【数１６】

【数１７】

但し、ｖ _D (r) はアッべ数、
に基づき算出するステップとを有することを特徴とする。
第３の発明は、第１の発明に記載された単一モード光ファイバの非線形定数測定方法であって、前記第４のステップが、前記被線形屈折率分布ｎ ₂ （ｒ）と前記所望の波長λ _d で の電界分布Ｅ（ｒ，λ _d ）を用いて、被測定単一モード光ファイバの前記所望の波長λ _d における非線形屈折率ｎ _2(eff) （λ _d ）を、
【数１８】

に基づき算出するステップと、
前記所望の波長λ _d での電界分布Ｅ（ｒ，λ _d ）を用いて、被測定単一モード光ファイバの実効断面積Ａ _eff （λ _d ）を、
【数１９】

に基づき算出するステップと、
被測定単一モード光ファイバの前記所望の波長λ _d における非線形屈折率ｎ _2(eff) （λ _d ）と前記実効断面積Ａ _eff （λ _d ）を用いて、被測定単一モード光ファイバの前記所望の波長λ _d における非線形定数を、
ｎ _2(eff) （λ _d ）／Ａ _eff （λ _d ）
に基づき算出するステップとを有することを特徴とする。
第４の発明は、任意の測定波長λ _m における測定光を被測定単一モード光ファイバに入射する手段と、
前記被測定単一モード光ファイバの任意の断面における前記測定波長λ _m での屈折率分布ｎ ₀ （ｒ，λ _m ）を測定する手段と、
前記被測定単一モード光ファイバの所望の波長λ _d における電界分布Ｅ（ｒ，λ _d ）を測定する手段と、
前記屈折率分布ｎ ₀ （ｒ，λ _m ）を用いて、被測定単一モード光ファイバ中におけるガラス材料の添加物量分布Ｍ（ｒ）を、
【数９】

【数１０】

【数１１】

但し、Ｋ（λ _m ）は被測定単一モード光ファイバのガラス材料の前記測定波長λ _m における特定の添加物に対する屈折率の添加量依存性、ｎ ₀ （Ｍ ₀ ，λ _m ）は純石英に前記特定の添加物をＭ ₀ （単位： mol% ）添加したガラスの前記測定波長λ _m における屈折率、ｎ _0S （λ _m ）は前記測定波長λ _m における純石英の屈折率、Ｍ ₀ は純石英に対する前記特定の添加物の添加量 （単位： mol% ）、Ａ _i ，Ｂ _i （ｉ＝１，２，３）はガラス材料に固有の係数、
に基づき計算し、
前記添加量分布Ｍ（ｒ）を用いて、被測定単一モード光ファイバの非線形屈折率分布ｎ ₂ （ｒ）を計算し、
前記非線形屈折率分布ｎ ₂ （ｒ）と前記所望の波長λ _d での電界分布Ｅ（ｒ，λ _d ）との演算処理を行うことにより、被測定単一モード光ファイバの前記所望の波長λ _d における非線形屈折率及び非線形定数を計算する演算手段と
を備えた
ことを特徴とする単一モード光ファイバの非線形定数測定装置にある。
【００１３】
すなわち、本発明では、単一モード光ファイバの任意の断面における屈折率分布、並びに所望の波長λでの電界分布を測定する機能を有し、屈折率分布と単一モード光ファイバ中のガラス材料に固有の非線形屈折率の添加物依存性を用いて非線形屈折率分布を求め、更に、電界分布との数値演算処理により、被測定単一モード光ファイバの非線形屈折率を算出するものである。
【００１４】
また、電界分布の数値演算により求められる実効断面積Ａ_eff を用いて被測定単一モード光ファイバの非線形定数を算出するものである。
【００１５】
【発明の実施の形態】
本発明による実施の形態を以下に説明するが、本発明はこれらの実施の形態に限定されるものではない。
【００１６】
本発明の実施の形態による単一モード光ファイバの非線形定数の評価方法は以下の通りである。
【００１７】
本実施形態の評価方法では、被測定単一モード光ファイバの任意の断面における半径方法ｒ、測定波長λでの屈折率分布ｎ₀(ｒ，λ) を、ＮＦＰ法またはＲＮＦＰ法等を用いて測定し、下記「数１」に示す式（２）で表される関係を用いて、被測定単一モード光ファイバ中におけるガラス材料の添加量分布Ｍ(r) を算出する。
ここで、上記ＮＦＰ法またはＲＮＦＰ法等を用いて測定することは、下記文献７及び文献８に開示されている。
文献７：D.Marcuse and H.M.Presby,"Automatic geometric measurement of single-mode and multimode optical fibers",Appl.Opt.,vol.18,No.3,pp.402-409,1979.
文献８：K.I.White,"Practical application of the refracted nearfield technique for the measurement of optical fiber refractive index profiles",Opt.Quantum Electron.,vol.11,p.185,1979.
【００１８】
【数１】

ここで、式中のｎ_os（λ）は測定波長λにおける純石英の屈折率を表す。また、Ｋ（λ）は測定波長λにおける特定の添加物に対する屈折率の添加量依存性を表し、純石英に特定の添加物がＭ₀ （単位：mol%）添加されたガラスの波長λにおける屈折率ｎ₀（Ｍ₀ ，λ）を知ることにより、下記「数２」に示す次式（３）を用いて決定できる。
【００１９】
【数２】

尚、純石英に特定の添加物がＭ₀ 添加されたガラスの任意の波長λにおける屈折率ｎ₀（Ｍ₀ ，λ）は、下記「数３」に示す式（４）により求めることができ、式中のＡ_i ，Ｂ_i （ｉ＝１，２，３）はガラス材料に固有の係数を表す。
【００２０】
純石英に特定の添加物がＭ₀ 添加されたガラスの任意の波長λにおける屈折率ｎ₀（Ｍ₀ ，λ）の測定は、例えば「文献９」（J.W.Fleming,"Material dispersion in lightguide glasses",Electron.Lett.,vol.14,No.11,pp.326-328,1978.）等の測定例から知ることができる。
【００２１】
【数３】

【００２２】
次に、上記「数１」に示す式（２）のＭ(r) を用い、３つの基準波長、0.48613 、0.58756 、及び0.65627 μｍにおける屈折率分布、それぞれｎ_F (r) 、ｎ_D (r) 、及びｎ_C (r) を、下記「数４」に示す次式（５）の関係を用いて求める。
【００２３】
【数４】

【００２４】
更に、下記「数５」に示す式（６）で表される経験式を用いて、被測定単一モード光ファイバの非線形屈折率分布ｎ₂(r) ［単位：×１０^-20 ｍ²／Ｗ］を算出する。
【００２５】
この下記「数５」に示す式（６）で表される経験式を用いて、石英ガラスの線形屈折率ｎ₀ から非線形屈折率ｎ₂を算出する文献として例えば「文献１０」（N.L.Boling et al,"Emprical relationships for predicting nonlinear refractive index changes in optical solids",J.Quantum Electron.,QE-14,pp.601-608,1978.）を挙げることができる。
【００２６】
【数５】

ここで、式中のｖ_D (r) は下記「数６」に示す式（７）で与えられるアッべ数を表す。
【００２７】
【数６】

【００２８】
次に、被測定単一モード光ファイバの所望の波長λにおけるニア・フィールド・パターンまたは、ファー・フィールド・パターンを、ＮＦＰ法、もしくはＦＦＰ法等（文献１１：Y.Murakami et al.,"Cut-off wavelength measurements for single-mode optical fibers",Appl.Opt.,vol.18,p.1101,1979.、文献１２：A.R.Tynes et al.,"Low v-number optical fiber:secondary maxims in the far-field radiation pattern",J.Opt,Soc.Am.,vol.69,No.11,pp.1587-1596,1979. ）により測定し、被測定ファイバの任意の断面における電界分布Ｅ（ｒ，λ）を算出する。
【００２９】
尚、ＦＦＰ法によりファー・フィールド・パターンを測定した場合、測定結果をハンケル変換することにより、被測定単一モード光ファイバの電界分布Ｅ（ｒ，λ）を算出することができる。
【００３０】
次に、前記の非線形屈折率分布ｎ₂(r) 、及び電界分布Ｅ（ｒ，λ）の測定結果を、下記「数７」に示す式（８）で表される関係式を用いて演算処理を行うことにより、被測定ファイバの非線形屈折率ｎ_2(eff)（λ) を算出する。
【００３１】
【数７】

【００３２】
また、上記「数７」に示す式（８）で得られたｎ_2(eff)（λ) を実効断面積Ａ_eff（λ）で割ることにより、被測定光ファイバの非線形定数ｎ_2(eff)（λ) ／Ａ_eff（λ）を算出する。尚、Ａ_eff（λ）は前述のＥ（ｒ，λ）を用いて、下記「数８」に示す次式（９）により算出される。
【００３３】
【数８】

【００３４】
このように本発明の測定方法では、線形の屈折率分布と所望の測定波長における電界分布の測定結果を用いて、被測定単一モード光ファイバの非線形屈折率、並びに非線形定数の評価を行うことができる。
【００３５】
また、線形の屈折率分布、並びに電界分布は、所望の測定波長を有する連続波光源と短尺な光ファイバを用いて測定可能なため、測定用光源の特性や被測定単一モード光ファイバの特性による測定精度の劣化を回避することができる。
【００３６】
【実施例】
以下、本発明の効果を確認する好適な実施例について説明するが、本発明はこれらに限定されるものではない。
【００３７】
本発明の実施例では、ＲＮＦＰ法とＦＦＰ法を用いて1.３μｍ帯零分散ファイバ（ＳＭＦ）の屈折率分布と所望の波長1.55μｍにおける電界分布を測定し、被測定ＳＭＦの非線形屈折率、並びに非線形定数を評価した。
【００３８】
図１は本発明の実施形態による、単一モード光ファイバの非線形定数測定方法の処理手順を示すフロー図である。
【００３９】
1)ステップ１：先ず、図１に示すように、本実施例における単一モード光ファイバの非線形定数測定では、被測定単一モード光ファイバの任意の断面における測定波長λでの屈折率分布ｎ₀(ｒ，λ) を、ＲＮＦＰ法もしくはＮＦＰ法を用いて測定する（Ｓ１０１）。
【００４０】
▲２▼ ステップ２：次に、同被測定単一モード光ファイバの任意の断面におけるフィールド・パターンを、所望の波長λを有する測定光源とＦＦＰ法もしくはＮＦＰ法を用いて測定する（Ｓ１０２）。
【００４１】
▲３▼ ステップ３： 次に、前記ステップ１（Ｓ１０１）で得られた屈折率分布ｎ₀(ｒ，λ) と式（２）〜式（４）の関係を用いて、被測定単一モード光ファイバの添加量分布Ｍ(r) を算出する（Ｓ１０３）。
尚、本実施例の測定で用いたＳＭＦは純石英にゲルマニウムを添加したコア部と、純石英のクラッド部により構成されるため、本実施例では式（４）の係数Ａ_i ，Ｂ_i （ｉ＝１，２，３）に文献９を参照した下記「表１」の値を用いて演算処理を行った。
【００４２】
また、このときの測定波長0.67μｍにおける純石英の屈折率ｎ_0s（0.67μｍ）は1.4563、屈折率のゲルマニウム添加量依存性Ｋ（0.67μｍ）は1.585 ×１０^-3（単位：１／mol%）となる。
【００４３】
【表１】

【００４４】
▲４▼ ステップ４：次に、前記ステップ３（Ｓ１０３）で得られた添加量分布Ｍ(r) と関係式（５）を用いて３つの基準波長における屈折率分布ｎ_F (r) 、ｎ_D (r) 、及びｎ_C (r) を算出し、式（６）並びに式（７）の関係を用いて非線形屈折率分布ｎ₂(r)を算出する（Ｓ１０４）。
【００４５】
▲５▼ ステップ５：更に、前記ステップ２（Ｓ１０２）で得られたファー・フィールド・パターンをハンケル変換し、所望の波長λにおける被測定単一モード光ファイバの電界分布Ｅ（ｒ，λ）を算出する（Ｓ１０５）。
尚、上記ステップ２（Ｓ１０２）においてＮＦＰ法によりニア・フィールド・パターンを測定した場合には、ステップ５（Ｓ１０５）の演算処理は不要となる。
【００４６】
6)ステップ６：次に、前記ステップ４（Ｓ１０４）の非線形屈折率分布ｎ₂(r)及び、ステップ５（Ｓ１０５）の電界分布Ｅ（ｒ，λ）を式（８）に代入し、所望の波長λにおける被測定単一モード光ファイバの非線形屈折率ｎ_2(eff)（λ）を評価する（Ｓ１０６）。
【００４７】
▲７▼ ステップ７：更に、前記ステップ５（Ｓ１０５）の電界分布Ｅ（ｒ，λ）と式（９）の関係を用いて、所望の波長λにおける被測定単一モード光ファイバの実効断面積Ａ_eff （λ）を算出する（Ｓ１０７）。
【００４８】
8)ステップ８：前記ステップ６（Ｓ１０６）の非線形屈折率ｎ_2(eff)（λ）とステップ７の実効断面積Ａ_eff（λ）を用いて、所望の波長λにおける被測定単一モード光ファイバの非線形定数ｎ_2(eff)（λ）／Ａ_eff（λ）を評価する（Ｓ１０８）。
【００４９】
図２は、本発明による実施形態の単一モード光ファイバの非線形定数測定方法を実施する装置の概略構成を示す模式図である。図２中、符号１１は屈折率分布測定装置、１２はフィールド・パターン測定装置、１３は演算処理部を各々図示する。
【００５０】
図３は被測定ＳＭＦの測定波長λ（＝0.67μｍ）での屈折率分布ｎ₀(ｒ，λ) の測定結果を示す図である。
ここで、図３において横軸は被測定ＳＭＦの任意の測定断面における半径ｒ、縦軸は線形の屈折率ｎ₀ を表している。
【００５１】
図４は被測定ＳＭＦの波長λ（＝1.55μｍ）におけるファー・フィールド・パターン測定結果を示す図である。
ここで、図４において横軸は被測定ＳＭＦの任意の測定断面におけるＦＦＰ受光素子の回転角度、縦軸は規格化された受光強度を示している。
【００５２】
図５は、前記図３の結果を用い上述の処理手順により計算された、被測定ＳＭＦのガラス材料の添加量分布Ｍ(r) の演算処理結果を示す図である。
ここで、図５において横軸は被測定ＳＭＦの任意の測定断面における半径ｒ、縦軸はゲルマニウムの添加量Ｍを表している。
【００５３】
図６は、前記図４、並びに図５の結果を用い上述の処理手順により計算された、被測定ＳＭＦの非線形屈折率分布ｎ₂(r)、及び波長1.55μｍにおける電界強度分布Ｅ²(ｒ，λ）の演算処理結果を示す図である。
ここで、図６において横軸は被測定ＳＭＦの任意の測定断面における半径ｒ、縦軸は非線形屈折率ｎ₂ 並びに規格化電界強度Ｅ² を表している。
【００５４】
図６の結果を式（８）及び（９）の関係を用いて演算処理することにより、被測定ＳＭＦの波長1.55μｍでの非線形屈折率ｎ_2(eff) (λ)及び非線形定数ｎ_2(eff)（λ）／Ａ_eff（λ）は、それぞれ以下のように評価できる。
【００５５】
実効非線形屈折率ｎ_2(eff)（λ） 2.66×１０^-20 ｍ² ／Ｗ
実効非線形定数ｎ_2(eff) (λ）／Ａ_eff（λ） 3.36×１０^-10 Ｗ^-1
【００５６】
【発明の効果】
以上説明したように、本発明によれば、被測定単一モード光ファイバの任意の断面で測定した屈折率分布及び、所望の測定波長におけるフィールド・パターンを演算処理することにより、被測定単一モード光ファイバの非線形屈折率、並びに非線形定数を、被測定単一モード光ファイバの特性に無依存に評価することができる。
【００５７】
本発明によれば、従来技術のパルス光を用いた測定法における測定精度が光パルスの形状に強く依存したり、被測定光ファイバの長さ、波長分散、実効断面積に依存するといった課題を解決し、高精度な非線形定数を求めることが可能になる。
【００５８】
また、屈折率分布及びフィールド・パターンの測定は、所望の波長を有する連続波光源を用いて行えるため、測定光源の特性により測定精度が変動するといった問題も生じない。
【図面の簡単な説明】
【図１】本発明の実施形態による単一モード光ファイバの非線形定数測定方法の処理手順を示すフロー図である。
【図２】本発明の実施形態による単一モード光ファイバの非線形定数測定方法を実施する測定装置の概略構成を示す図である。
【図３】本発明の実施例における被測定ＳＭＦの測定波長0.67μｍにおける屈折率分布ｎ₀(ｒ，λ)の測定結果を示す図である。
【図４】本発明の実施例における被測定ＳＭＦの所望の波長1.55μｍにおけるファー・フィールド・パターンの測定結果を示す図である。
【図５】本発明の実施例における被測定ＳＭＦのガラス材料の添加量分布Ｍ(r) の演算処理結果を表す図である。
【図６】本発明の実施例における被測定ＳＭＦの非線形屈折率分布ｎ₂(r)並びに所望の波長1.55μｍにおける電界強度分布Ｅ²(ｒ，λ)の演算処理結果を示す図である。[0001]
BACKGROUND OF THE INVENTION
The present invention is a non-linear refractive index of the single-mode optical fiber, and a method and apparatus for measuring nonlinear constants.
[0002]
[Prior art]
In an optical communication system using a recent optical amplifying apparatus, as the light intensity propagating in the single mode optical fiber increases, the deterioration of the propagation waveform due to the optical nonlinearity in the single mode optical fiber becomes a problem. The optical nonlinearity in the single mode optical fiber is caused by the fact that the refractive index n (P) of the single mode optical fiber changes according to the relationship expressed by the following formula (1) according to the light intensity P.
n (P) = n ₀ + n ₂ P (1)
Here, n ₀ in the formula represents a linear refractive index, and n ₂ represents a nonlinear refractive index.
[0003]
Moreover, the influence of various optical nonlinearities changes according to the nonlinear constant showing the optical nonlinearity of a single mode optical fiber. The nonlinear constant is given by n ₂ / A _eff using the nonlinear refractive index n ₂ of the single mode optical fiber and the effective area A _eff which is a parameter representing the energy density of light.
Therefore, in long-distance / large-capacity optical communication using an optical amplifier, it is necessary to accurately know the nonlinear refractive index and the nonlinear constant of the single-mode optical fiber to be used.
[0004]
The nonlinear constant of a single mode optical fiber can be measured by observing various optical nonlinear phenomena that occur in the single mode optical fiber with respect to changes in the input light intensity. Various proposals as shown in FIG. 5 have been made.
(1) Reference 1: Method using self-phase modulation effect (RHStolen and C. Lin, “Self-phase-modulation in silica optical fibers”, Phy. Rev., vol. 17, No. 4, pp. 1448- 1453,1978.
(2) Reference 2: Method using self-phase modulation effect (A. Boskovic et al., “Direct continuous-wave measurement of n2 in various types of telecommunication fiber at 1.55 μm”, Opt. Lett., Vol. 21, No.24, pp.1966-1968, 1996),
(3) Reference 3: Method using cross-phase modulation effect (A. Wada et al., “Measurement of nonlinear-index coefficients of optical fibers through the cross-phase modulation using delayed-self-heterodyne technique”, ECOC “93 MoB1.2, pp.45-48,1993.),
(4) Reference 4: Method using four-wave mixing (L. Prigent and JP Hamaiide, “Measurement of fiber nonlinear Kerr coefficient by four-wave mixing”, Photon. Technol. Lett., Vol. 5, No. 9, pp. .1092-1095, 1993.)
(5) Reference 5: Method using modulation instability (M. Artiglia et al., “Using modulation instability to determine Kerr coefficient in optical fibers”, Electron. Lett., Vol. 31, No. 12, pp. 1012 -1013, 1995.)
[0005]
Further, it is possible to evaluate the effective area A _{eff at} a desired wavelength λ of a single mode optical fiber by measuring the electric field distribution on the end surface of the single mode optical fiber using measurement light having the desired wavelength λ. Has been proposed.
(6) Reference 6: (GPAgrawal, “Nonlinear fiber optics”, Academic Press.)
[0006]
Therefore, the nonlinear refractive index difference of the single mode optical fiber can be obtained from the measurement result of the effective area A _eff and the nonlinear constant.
[0007]
[Problems to be solved by the invention]
However, the measurement method using pulsed light as the measurement light has a problem that the measurement accuracy of the nonlinear constant strongly depends on the pulse shape of the pulsed light.
[0008]
Even when the pulse shape is adjusted appropriately or when continuous light is used as the measurement light, the measurement accuracy of the nonlinear constant is the fiber length, chromatic dispersion, effective cross-sectional area, etc. of the single-mode optical fiber to be measured. There was a problem of changing depending on.
[0009]
The present invention uses a refractive index distribution in an arbitrary cross section of a single-mode optical fiber and an electric field distribution measurement result at a desired wavelength λ, and adds a nonlinear refractive index determined by a glass material used in the optical fiber. by performing numerical calculation that takes into account the object-dependent, non-linear constant measurement method of independent and highly accurate single mode optical fiber to the measurement conditions, and it is an object to provide a device.
[0010]
[Means for Solving the Problems]
The first invention of the present invention that solves the above-mentioned problems is a refractive index distribution n ₀ (r, λ _m ) at an arbitrary measurement wavelength λ _m in an arbitrary cross section of a single-mode optical fiber to be measured , and a desired wavelength. a first step of measuring the electric field distribution E (r, λ _d) at lambda _d, the refractive index distribution n ₀ (r, λ _m) using a glass material in a single mode optical fiber to be measured Additive amount distribution M (r)
[Equation 9]

[Expression 10]

## EQU11 ##

Where K (λ _m ) is the dependency of the refractive index on the specific additive at the measurement wavelength λ _m of the glass material of the single-mode optical fiber to be measured , and n ₀ (M ₀ , λ _m ) is pure quartz. The refractive index at the measurement wavelength λ _m of the glass added with M ₀ (unit: mol% ) of the specific additive , n _0S (λ _m ) is the refractive index of pure quartz at the measurement wavelength λ _m , and M ₀ is Addition amount of the specific additive to pure quartz (Unit: mol% ), A _i and B _i (i = 1, 2, 3) are coefficients inherent to the glass material,
A second step of calculating based on the additive amount distribution M (r) , a third step of calculating a nonlinear refractive index distribution n ₂ (r) of the measured single-mode optical fiber, and the nonlinearity the refractive index distribution n ₂ (r) and the electric field distribution E in the desired wavelength λ _d (r, λ _d) by performing arithmetic processing and, in the desired wavelength lambda _d of single-mode optical fiber to be measured in a non-linear constant measurement method of the single-mode optical fiber, characterized by a fourth step of calculating a non-linear refractive index and a non-linear constant.
[0011]
According to the present invention, the measurement accuracy in the conventional measurement method using pulsed light strongly depends on the shape of the optical pulse, and depends on the length, chromatic dispersion, and effective area of the optical fiber to be measured. It is possible to solve the problem and obtain a highly accurate nonlinear constant.
[0012]
A second invention is a method for measuring a nonlinear constant of a single mode optical fiber according to the first invention, wherein the third step uses the additive amount distribution M (r) to provide three criteria. Refractive index distribution at wavelengths λ ₁ = 0.48613 μm, λ ₂ = 0.58756 μm, λ ₃ = 0.65627 μm,
[Expression 12]

[Formula 13]

[Expression 14]

[Expression 15]

However, k = 1, 2, 3, and K (λ _k ) are dependency of the refractive index on the specific additive at the reference wavelength λ _k of the glass material of the single-mode optical fiber to be measured , n ₀ (M ₀ , λ _k ) is the refractive index at the reference wavelength λ _k of the glass obtained by adding the specific additive to pure quartz to M ₀ (unit: mol% ) , and n _0S (λ _k ) is the pure index at the reference wavelength λ _k . The refractive index of quartz, M ₀ is the amount of the specific additive added to pure quartz (Unit: mol% ),
And calculating the nonlinear refractive index distribution n ₂ (r) of the single-mode optical fiber to be measured using the refractive index distributions at the three reference wavelengths λ _k .

[Expression 17]

Where v _D (r) is the Abbe number,
And calculating based on the above.
A third invention is a method for measuring a nonlinear constant of a single mode optical fiber according to the first invention, wherein the fourth step includes the linear refractive index distribution n ₂ (r) and the desired refractive index distribution n ₂ (r). electric field distribution E (r, λ _d) at the wavelength lambda _d using a nonlinear refractive index n ₂ in the desired wavelength lambda _d of single-mode optical fiber to be measured _{(eff) (λ d),}
[Formula 18]

Calculating based on:
Using the electric field distribution E (r, λ _d ) at the desired wavelength λ _d , the effective area A _eff (λ _d ) of the single-mode optical fiber to be measured is
[Equation 19]

Calculating based on:
Using the nonlinear refractive index n _{2 (eff)} (λ _d ) and the effective area A _eff (λ _d ) at the desired wavelength λ _d of the single-mode optical fiber to be measured, the single-mode optical fiber to be measured A nonlinear constant at the desired wavelength λ _d ,
n _{2 (eff)} (λ _d ) / A _eff (λ _d )
And calculating based on the above.
The fourth invention comprises means for injecting measurement light at an arbitrary measurement wavelength λ _m into a single-mode optical fiber to be measured ,
Means for measuring a refractive index distribution n ₀ (r, λ _m ) at the measurement wavelength λ _m in an arbitrary cross section of the single-mode optical fiber to be measured ;
Means for measuring the electric field distribution E (r, λ _d) at the desired wavelength lambda _d of the measured single-mode optical fiber,
Using the refractive index distribution n ₀ (r, λ _m ), an additive amount distribution M (r) of the glass material in the single-mode optical fiber to be measured is
[Equation 9]

[Expression 10]

## EQU11 ##

Where K (λ _m ) is the dependency of the refractive index on the specific additive at the measurement wavelength λ _m of the glass material of the single-mode optical fiber to be measured , and n ₀ (M ₀ , λ _m ) is pure quartz. The refractive index at the measurement wavelength λ _m of the glass added with M ₀ (unit: mol% ) of the specific additive , n _0S (λ _m ) is the refractive index of pure quartz at the measurement wavelength λ _m , and M ₀ is Addition amount of the specific additive to pure quartz (Unit: mol% ), A _i and B _i (i = 1, 2, 3) are coefficients inherent to the glass material,
Calculated based on
Using the additive amount distribution M (r), a nonlinear refractive index distribution n ₂ (r) of the single-mode optical fiber to be measured is calculated ,
By calculating the nonlinear refractive index distribution n ₂ (r) and the electric field distribution E (r, λ _d ) at the desired wavelength λ _d , the desired wavelength λ of the single-mode optical fiber to be measured is obtained. in a non-linear measuring apparatus of the single-mode optical fiber, characterized by comprising calculating means for calculating a non-linear refractive index and non-linear constant in _d.
[0013]
That is, the present invention has a function of measuring the refractive index distribution in an arbitrary cross section of a single mode optical fiber and the electric field distribution at a desired wavelength λ, and the refractive index distribution and the glass material in the single mode optical fiber. obtains a nonlinear refractive index distribution using the additive dependence of intrinsic nonlinear refractive index, and further, by the numerical calculation of the electric field distribution, and calculates the nonlinear refractive index of the single-mode optical fiber to be measured .
[0014]
Further, it calculates a non-linear constant of the single-mode optical fiber to be measured using the effective area A _eff obtained by numerical calculation of the electric field distribution.
[0015]
DETAILED DESCRIPTION OF THE INVENTION
Embodiments according to the present invention will be described below, but the present invention is not limited to these embodiments.
[0016]
Evaluation method of non-linear constant of the single-mode optical fiber according to an embodiment of the present invention is as follows.
[0017]
In the evaluation method of the present embodiment, the radius method r and the refractive index distribution n ₀ (r, λ) at an arbitrary cross section of the single-mode optical fiber to be measured are measured using the NFP method, the RNFP method, or the like. Using the relationship expressed by the equation (2) shown in the following “Equation 1”, the additive amount distribution M (r) of the glass material in the single-mode optical fiber to be measured is calculated.
Here, the measurement using the NFP method or the RNFP method is disclosed in the following document 7 and document 8.
Reference 7: D. Marcuse and HMPresby, "Automatic geometric measurement of single-mode and multimode optical fibers", Appl. Opt., Vol. 18, No. 3, pp. 402-409, 1979.
Reference 8: KIWhite, “Practical application of the refracted nearfield technique for the measurement of optical fiber refractive index profiles”, Opt.Quantum Electron., Vol.11, p.185, 1979.
[0018]
[Expression 1]

Here, n _os (λ) in the formula represents the refractive index of pure quartz at the measurement wavelength λ. K (λ) represents the dependency of the refractive index on the specific additive at the measurement wavelength λ, and the specific additive M ₀ (unit: mol%) is added to pure quartz at the wavelength λ. Knowing the refractive index n ₀ (M ₀ , λ), it can be determined using the following equation (3) shown in the following “Equation 2”.
[0019]
[Expression 2]

Incidentally, the refractive index n ₀ (M ₀ , λ) at an arbitrary wavelength λ of a glass in which a specific additive is added to pure quartz to M ₀ can be obtained by the following equation (4). , A _i and B _i (i = 1, 2, 3) in the formulas represent coefficients specific to the glass material.
[0020]
Measurement of the refractive index n ₀ (M _0, λ) at an arbitrary wavelength lambda of the glass a particular additive is added M ₀ in pure silica, for example, "Document 9" (JWFleming, "Material dispersion in lightguide glasses", Electron. Lett., Vol. 14, No. 11, pp. 326-328, 1978).
[0021]
[Equation 3]

[0022]
Next, using M (r) in the equation (2) shown in the above “Equation 1”, refractive index distributions at three reference wavelengths, 0.48613, 0.58756, and 0.65627 μm, respectively, n _F (r) and n _D (r ) And n _C (r) are obtained using the relationship of the following equation (5) shown in the following “Equation 4”.
[0023]
[Expression 4]

[0024]
Furthermore, by using an empirical formula represented by Formula (6) shown in the following “Formula 5”, the nonlinear refractive index distribution n ₂ (r) of the single-mode optical fiber to be measured [unit: × 10 ⁻²⁰ m ² / W] is calculated.
[0025]
As a document for calculating the nonlinear refractive index n ₂ from the linear refractive index n ₀ of quartz glass using the empirical formula represented by the formula (6) shown in the following “Formula 5”, for example, “Reference 10” (NLBoling et al , “Emprical relationships for predicting nonlinear refractive index changes in optical solids”, J. Quantum Electron., QE-14, pp. 601-608, 1978.).
[0026]
[Equation 5]

Here, v _D (r) in the formula represents the Abbe number given by the formula (7) shown in the following “Formula 6”.
[0027]
[Formula 6]

[0028]
Next, a near field pattern or a far field pattern at a desired wavelength λ of the single-mode optical fiber to be measured is converted into an NFP method, an FFP method or the like (Reference 11: Y. Murakami et al., “Cut -off wavelength measurements for single-mode optical fibers ", Appl.Opt., vol.18, p.1101,1979., Reference 12: ARTynes et al.," Low v-number optical fiber: secondary maxims in the far- field radiation pattern ", J. Opt, Soc. Am., vol. 69, No. 11, pp. 1587-1596, 1979.), and the electric field distribution E (r, λ) in an arbitrary cross section of the measured fiber ) Is calculated.
[0029]
When the far field pattern is measured by the FFP method, the electric field distribution E (r, λ) of the single-mode optical fiber to be measured can be calculated by performing Hankel transformation on the measurement result.
[0030]
Next, the measurement results of the nonlinear refractive index distribution n ₂ (r) and the electric field distribution E (r, λ) are calculated using a relational expression represented by the following expression (8). by performing the processing to calculate the non-linear refractive index of a measured fiber _{n 2 (eff) (λ)} .
[0031]
[Expression 7]

[0032]
Further, by dividing by which the n ₂ obtained by the equation (8) shown in "Number 7" _(eff) (lambda) effective area A _eff (lambda), and non-linear constant n ₂ of the optical fiber to be measured _{( eff)} (λ) / A _eff (λ) is calculated. A _eff (λ) is calculated by the following equation (9) shown in the following “Equation 8” using E (r, λ) described above.
[0033]
[Equation 8]

[0034]
In the measurement method according to the present invention, using the measurement results of the electric field distribution and the linear refractive index distribution in the desired measurement wavelength, the non-linear refractive index of the single-mode optical fiber to be measured, and the evaluation of the non-linear constant It can be carried out.
[0035]
In addition, linear refractive index distribution and electric field distribution can be measured using a continuous wave light source having a desired measurement wavelength and a short optical fiber, so the characteristics of the measurement light source and the characteristics of the single-mode optical fiber to be measured It is possible to avoid the deterioration of measurement accuracy due to.
[0036]
【Example】
Hereinafter, although the suitable Example which confirms the effect of this invention is described, this invention is not limited to these.
[0037]
In an embodiment of the present invention, the electric field distribution is measured at the desired wavelength 1.55μm and the refractive index distribution of 1.3μm band zero-dispersion fiber (SMF) with RNFP method and FFP method, non-linear refractive index of the SMF to be measured , as well as evaluating the non-linear constant.
[0038]
1 according to an embodiment of the present invention, is a flowchart showing a processing procedure of a non-linear constant measurement method of the single-mode optical fiber.
[0039]
1) Step 1: First, as shown in FIG. 1, the non-linear constant measurement of the single-mode optical fiber in this embodiment, the refractive index distribution at a measurement wavelength λ at any cross-section of the single-mode optical fiber to be measured n ₀ (r, λ) is measured using the RNFP method or the NFP method (S101).
[0040]
{Circle around (2)} Step 2: Next, a field pattern in an arbitrary cross section of the measured single mode optical fiber is measured using a measurement light source having a desired wavelength λ and the FFP method or the NFP method (S102).
[0041]
(3) Step 3: Next, using the relationship between the refractive index distribution n ₀ (r, λ) obtained in Step 1 (S101) and Equations (2) to (4), a single mode to be measured An addition distribution M (r) of the optical fiber is calculated (S103).
The SMF used in the measurement of this example is composed of a core part obtained by adding germanium to pure quartz and a clad part of pure quartz. Therefore, in this example, the coefficients A _i and B _i ( The calculation process was performed using the values of the following “Table 1” referring to Document 9 for i = 1, 2, 3).
[0042]
Further, the refractive index n _0s (0.67 μm) of pure quartz at the measurement wavelength of 0.67 μm at this time is 1.4563, and the germanium addition amount dependency K (0.67 μm) of the refractive index is 1.585 × 10 ⁻³ (unit: 1 / mol%). )
[0043]
[Table 1]

[0044]
{Circle over (4)} Step 4: Next, the refractive index distributions n _F (r) and n at three reference wavelengths are calculated using the additive amount distribution M (r) obtained in Step 3 (S103) and the relational expression (5). _D (r) and n _C (r) are calculated, and the non-linear refractive index distribution n ₂ (r) is calculated using the relationship of the equations (6) and (7) (S104).
[0045]
(5) Step 5: Further, the far-field pattern obtained in Step 2 (S102) is subjected to Hankel conversion, and the electric field distribution E (r, λ) of the measured single mode optical fiber at the desired wavelength λ is obtained. Calculate (S105).
When the near field pattern is measured by the NFP method in the above step 2 (S102), the calculation process in step 5 (S105) becomes unnecessary.
[0046]
6) Step 6: Next, the nonlinear refractive index distribution n ₂ (r) in Step 4 (S104) and the electric field distribution E (r, λ) in Step 5 (S105) are substituted into Equation (8) to obtain the desired value. wavelength nonlinear refractive index of the single-mode optical fiber to be measured at _{λ n 2 (eff) (λ} ) assessing (S106).
[0047]
(7) Step 7: Furthermore, using the relationship between the electric field distribution E (r, λ) in Step 5 (S105) and the equation (9), the effective cross-sectional area of the single-mode optical fiber to be measured at the desired wavelength λ. A _eff (λ) is calculated (S107).
[0048]
8) Step 8: Using the non-linear refractive index n ₂ of the step _{6 (S106) (eff) (} λ) and the effective area A _eff of Step 7 (lambda), single-mode to be measured at the desired wavelength lambda nonlinear constants n ₂ of the optical fiber _{(eff) (λ) / a} eff (λ) assessing (S108).
[0049]
FIG. 2 is a schematic diagram showing a schematic configuration of an apparatus for carrying out a nonlinear constant measuring method for a single mode optical fiber according to an embodiment of the present invention. In FIG. 2, reference numeral 11 denotes a refractive index distribution measuring device, 12 denotes a field pattern measuring device, and 13 denotes an arithmetic processing unit.
[0050]
FIG. 3 is a diagram showing the measurement result of the refractive index distribution n ₀ (r, λ) at the measurement wavelength λ (= 0.67 μm) of the SMF to be measured.
Here, in FIG. 3, the horizontal axis represents the radius r of an arbitrary measurement cross section of the SMF to be measured, and the vertical axis represents the linear refractive index n ₀ .
[0051]
FIG. 4 is a diagram showing the far field pattern measurement result at the wavelength λ (= 1.55 μm) of the SMF to be measured.
Here, in FIG. 4, the horizontal axis represents the rotation angle of the FFP light receiving element in an arbitrary measurement cross section of the SMF to be measured, and the vertical axis represents the standardized light receiving intensity.
[0052]
FIG. 5 is a diagram showing a calculation processing result of the addition amount distribution M (r) of the glass material of the SMF to be measured, calculated by the above-described processing procedure using the result of FIG.
Here, in FIG. 5, the horizontal axis represents the radius r of an arbitrary measurement cross section of the SMF to be measured, and the vertical axis represents the amount M of germanium added.
[0053]
FIG. 6 shows the nonlinear refractive index distribution n ₂ (r) of the SMF to be measured and the electric field intensity distribution E ² (r) at a wavelength of 1.55 μm calculated by the above-described processing procedure using the results of FIG. 4 and FIG. , Λ) is a diagram illustrating a calculation processing result.
Here, in FIG. 6, the horizontal axis represents the radius r in an arbitrary measurement cross section of the SMF to be measured, and the vertical axis represents the nonlinear refractive index n _{2 and the} normalized electric field strength E ² .
[0054]
By processing using the result of the relationship of Equation (8) and (9) in FIG. 6, the non-linear refractive index n ₂ at a wavelength 1.55μm of SMF to be measured _(eff) (lambda), and nonlinear coefficient n _{2 (eff)} (λ) / A _eff (λ) can be evaluated as follows.
[0055]
Effective nonlinear refractive index n _{2 (eff)} (λ) 2.66 × 10 ⁻²⁰ m ² / W
Effective nonlinear constant n _{2 (eff)} (λ) / A _eff (λ) 3.36 × 10 ⁻¹⁰ W ⁻¹
[0056]
【The invention's effect】
As described above, according to the present invention, by calculating the refractive index distribution measured at an arbitrary cross section of the single-mode optical fiber to be measured and the field pattern at the desired measurement wavelength, nonlinear refractive index of the mode optical fiber, and a non-linear constant, it can be evaluated independent on the characteristics of single-mode optical fiber to be measured.
[0057]
According to the present invention, the measurement accuracy in the conventional measurement method using pulsed light strongly depends on the shape of the optical pulse, and depends on the length, chromatic dispersion, and effective area of the optical fiber to be measured. It is possible to solve the problem and obtain a highly accurate nonlinear constant.
[0058]
Further, since the refractive index distribution and the field pattern can be measured using a continuous wave light source having a desired wavelength, there is no problem that the measurement accuracy varies depending on the characteristics of the measurement light source.
[Brief description of the drawings]
Is a flowchart showing a processing procedure of a non-linear constant measurement method of the single-mode optical fiber according to embodiments of the present invention; FIG.
It is a diagram showing a schematic configuration of a non-linear constant measuring method implementing a measuring device of a single-mode optical fiber according to embodiments of the present invention; FIG.
FIG. 3 is a diagram showing a measurement result of a refractive index distribution n ₀ (r, λ) at a measurement wavelength of 0.67 μm of an SMF to be measured in the example of the present invention.
FIG. 4 is a diagram showing a measurement result of a far field pattern at a desired wavelength of 1.55 μm of an SMF to be measured in an example of the present invention.
FIG. 5 is a diagram showing a calculation processing result of an addition amount distribution M (r) of a glass material of an SMF to be measured in an example of the present invention.
FIG. 6 is a diagram showing the calculation processing result of the nonlinear refractive index distribution n ₂ (r) of the measured SMF and the electric field intensity distribution E ² (r, λ) at a desired wavelength of 1.55 μm in the example of the present invention.

Claims (4)

The refractive index distribution n ₀ (r, λ _m ) at an arbitrary measurement wavelength λ _m and an electric field distribution E (r, λ _d ) at a desired wavelength λ _d in an arbitrary cross section of the single-mode optical fiber to be measured. A first step of measuring;
Using the refractive index distribution n ₀ (r, λ _m ), an additive amount distribution M (r) of the glass material in the single-mode optical fiber to be measured is

Where K (λ _m ) is the dependency of the refractive index on the specific additive at the measurement wavelength λ _m of the glass material of the single-mode optical fiber to be measured , and n ₀ (M ₀ , λ _m ) is pure quartz. The refractive index at the measurement wavelength λ _m of the glass added with M ₀ (unit: mol% ) of the specific additive , n _0S (λ _m ) is the refractive index of pure quartz at the measurement wavelength λ _m , and M ₀ is Addition amount of the specific additive to pure quartz (Unit: mol% ), A _i and B _i (i = 1, 2, 3) are coefficients inherent to the glass material,
A second step of calculating based on:
A third step of calculating a nonlinear refractive index distribution n ₂ (r) of the single-mode optical fiber to be measured using the additive amount distribution M (r) ;
The nonlinear refractive index distribution n ₂ (r) and the electric field distribution at a desired wavelength _{λ d E (r, λ d} ) by performing the arithmetic processing of the desired wavelength of the single-mode optical fiber to be measured lambda a fourth step of calculating a non-linear refractive index and non-linear constant in _d
Nonlinear constant measurement method of the single-mode optical fiber according to claim <br/> to have. The third step includes
Using the additive amount distribution M (r), three reference wavelengths λ ₁ = 0.48613 μm, λ ₂ = 0.58756 μm, λ _Three = Refractive index distribution at 0.65627 μm,

However, k = 1, 2, 3, K (λ _k ) Is the reference wavelength λ of the glass material of the single-mode optical fiber to be measured _k Dependence of the refractive index on the specific additive in n, n ₀ (M ₀ , Λ _k ) Add the specific additive M to pure quartz ₀ (unit: mol% ) Reference wavelength λ of the added glass _k Refractive index at n _0S (Λ _k ) Is the reference wavelength λ _k Refractive index of pure quartz at M ₀ Is the amount of the specific additive added to pure quartz (unit: mol% ),
Calculating based on:
The three reference wavelengths λ _k Is used to determine the nonlinear refractive index distribution n of the single-mode optical fiber to be measured. ₂ (R)

However, v _D (r) Is the Abbe number,
Calculating based on
Have
The method for measuring a nonlinear constant of a single mode optical fiber according to claim 1. The fourth step includes
The linear refractive index distribution n ₂ (R) and the desired wavelength λ _d Field distribution E (r, λ _d The desired wavelength λ of the single-mode optical fiber to be measured _d Nonlinear refractive index n _{2 (eff)} (Λ _d )

Calculating based on:
The desired wavelength λ _d Field distribution E (r, λ _d ), The effective area A of the single-mode optical fiber to be measured _eff (Λ _d )

Calculating based on:
The desired wavelength λ of the single-mode optical fiber to be measured _d Nonlinear refractive index n _{2 (eff)} (Λ _d ) And the effective area A _eff (Λ _d The desired wavelength λ of the single-mode optical fiber to be measured _d The nonlinear constant at
n _{2 (eff)} (Λ _d ) / A _eff (Λ _d )
Calculating based on
Have
The method of measuring a nonlinear constant of a single mode optical fiber according to claim 1. Means for injecting measurement light at an arbitrary measurement wavelength λ _m into the single-mode optical fiber to be measured ;
Means for measuring a refractive index distribution n ₀ (r, λ _m ) at the measurement wavelength λ _m in an arbitrary cross section of the single-mode optical fiber to be measured ;
Means for measuring the electric field distribution E (r, λ _d) at the desired wavelength lambda _d of the measured single-mode optical fiber,
Using the refractive index distribution n ₀ (r, λ _m ), an additive amount distribution M (r) of the glass material in the single-mode optical fiber to be measured is

However, K (λ _m) additive amount dependency of the refractive index for a particular additive that put on the measurement wavelength lambda _m of the glass material of a single-mode optical fiber to be _{measured, n 0 (M 0, λ} m) are Refractive index at the measurement wavelength λ _m of glass obtained by adding M ₀ (unit: mol% ) of the specific additive to pure quartz , n _0S (λ _m ) is the refractive index of pure quartz at the measurement wavelength λ _m , M ₀ is the amount of the specific additive added to pure quartz (Unit: mol% ), A _i and B _i (i = 1, 2, 3) are coefficients inherent to the glass material,
Calculated based on
Using the additive amount distribution M (r), a nonlinear refractive index distribution n ₂ (r) of the single-mode optical fiber to be measured is calculated ,
By calculating the nonlinear refractive index distribution n ₂ (r) and the electric field distribution E (r, λ _d ) at the desired wavelength λ _d , the desired wavelength λ of the single-mode optical fiber to be measured is obtained. non linear measuring apparatus of the single-mode optical fiber, characterized by comprising calculating means for calculating a non-linear refractive index and non-linear constant in _d.

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