JP3932030B2 - Nonlinear constant measuring method and apparatus for single mode optical fiber - Google Patents
Nonlinear constant measuring method and apparatus for single mode optical fiber Download PDFInfo
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Description
【0001】
【発明の属する技術分野】
本発明は単一モード光ファイバの非線形屈折率、及び非線形定数を測定するための方法及び装置に関する。
【0002】
【従来の技術】
近年の光増幅装置を用いた光通信システムでは、単一モード光ファイバ中を伝搬する光強度の増大に伴い、単一モード光ファイバ中の光非線形性による伝搬波形の劣化等が問題となる。単一モード光ファイバ中における光非線形性は、単一モード光ファイバの屈折率n(P)が光の強度Pに応じ、下記式(1)で表される関係により変化することに起因する。
n(P)=n0 +n2P (1)
ここで、式中のn0 は線形の屈折率、n2 は非線形屈折率を表す。
【0003】
また、各種光非線形性の影響は、単一モード光ファイバの光非線形性を表す非線形定数に応じて変化する。非線形定数は、単一モード光ファイバの非線形屈折率n2 と光のエネルギー密度を表すパラメータである実効断面積Aeff を用いて、n2/Aeff により与えられる。
従って、光増幅装置を用いた長距離・大容量光通信では、使用する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正確に知る必要がある。
【0004】
単一モード光ファイバの非線形定数は、単一モード光ファイバ中で生じる各種光非線形現象を、入力光強度の変化に対して観測することにより測定することができ、これまでに、下記文献1乃至5に示すようなのような種々の提案がなされている。
▲1▼文献1:自己位相変調効果を用いた方法(R.H.Stolen and C.Lin,"Self-phase-modulation in silica optical fibers",Phy.Rev.,vol.17,No.4,pp.1448-1453,1978. 、
▲2▼文献2:自己位相変調効果を用いた方法(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▼文献3:相互位相変調効果を用いた方法(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▼文献4:4光波混合を用いた方法(L.Prigent and J.P.Hamaide,"Measurement of fiber nonlinear Kerr coefficient by four-wave mixing",Photon.Technol.Lett.,vol.5,No.9,pp.1092-1095,1993.)
▲5▼文献5:変調不安定性を用いた方法(M.Artiglia et al.,"Using modulation instability to determine Kerr coefficient in optical fibres",Electron.Lett.,vol.31,No.12,pp.1012-1013,1995.)
【0005】
また、単一モード光ファイバの所望の波長λにおける実効断面積Aeff は、単一モード光ファイバ端面の電界分布を所望の波長λの測定光を用いて測定することにより評価できることが下記文献6に提案されている。
▲6▼文献6:(G.P.Agrawal,"Nonlinear fiber optics",Academic Press.)
【0006】
従って、実効断面積Aeff と非線形定数の測定結果から、単一モード光ファイバの非線形屈折率差を求めることができる。
【0007】
【発明が解決しようとする課題】
しかし、測定光にパルス光を用いる測定法では、非線形定数の測定精度はパルス光のパルス形状に強く依存するという問題があった。
【0008】
また、パルスの形状を適切に調整した場合や、測定光に連続光を用いた場合においても、非線形定数の測定精度は被測定単一モード光ファイバのファイバ長、波長分散、並びに実効断面積等に依存して変化するという問題があった。
【0009】
本発明は、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と、所望の波長λでの電界分布の測定結果を用い、光ファイバ中に用いられるガラス材料により決定される非線形屈折率の添加物依存性を考慮に入れた数値演算を行うことにより、測定条件に無依存かつ高精度な単一モード光ファイバの非線形定数測定方法、並びに装置を提供することを課題とする。
【0010】
【課題を解決するための手段】
上記課題を解決する本発明の第1の発明は、被測定単一モード光ファイバの任意の断面における任意の測定波長λ m での屈折率分布n 0 (r,λ m )、並びに所望の波長λ d での電界分布E(r,λ d )を測定する第1のステップと、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Aeff 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nos(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Ai ,Bi (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nF (r) 、nD (r) 、及びnC (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vD (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n2(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n2(eff)(λ) を実効断面積Aeff(λ)で割ることにより、被測定光ファイバの非線形定数n2(eff)(λ) /Aeff(λ)を算出する。尚、Aeff(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Ai ,Bi (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n0s(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nF (r) 、nD (r) 、及びnC (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n2(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Aeff (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n2(eff)(λ)とステップ7の実効断面積Aeff(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n2(eff)(λ)/Aeff(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n2(eff) (λ)及び非線形定数n2(eff)(λ)/Aeff(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n2(eff)(λ) 2.66×10-20 m2 /W
実効非線形定数n2(eff) (λ)/Aeff(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
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 “
[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 “
[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, “
[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 “
[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,
[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)
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、
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。 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
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.
前記添加量分布M(r)を用いて、3つの基準波長λUsing the additive amount distribution M (r), three reference wavelengths λ 11 =0.48613μm、λ= 0.48613 μm, λ 22 =0.58756μm、λ= 0.58756 μm, λ 3Three =0.65627μmにおける屈折率分布を、= Refractive index distribution at 0.65627 μm,
に基づき算出するステップと、Calculating based on:
前記3つの基準波長λThe three reference wavelengths λ kk 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nIs used to determine the nonlinear refractive index distribution n of the single-mode optical fiber to be measured. 22 (r)を(R)
に基づき算出するステップとCalculating based on
を有するHave
ことを特徴とする請求項1に記載の単一モード光ファイバの非線形定数測定方法。The method for measuring a nonlinear constant of a single mode optical fiber according to claim 1.
前記被線形屈折率分布nThe linear refractive index distribution n 22 (r)と前記所望の波長λ(R) and the desired wavelength λ dd での電界分布E(r,λField distribution E (r, λ dd )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λThe desired wavelength λ of the single-mode optical fiber to be measured dd における非線形屈折率nNonlinear refractive index n 2(eff)2 (eff) (λ(Λ dd )を、)
前記所望の波長λThe desired wavelength λ dd での電界分布E(r,λField distribution E (r, λ dd )を用いて、被測定単一モード光ファイバの実効断面積A), The effective area A of the single-mode optical fiber to be measured effeff (λ(Λ dd )を、)
被測定単一モード光ファイバの前記所望の波長λThe desired wavelength λ of the single-mode optical fiber to be measured dd における非線形屈折率nNonlinear refractive index n 2(eff)2 (eff) (λ(Λ dd )と前記実効断面積A) And the effective area A effeff (λ(Λ dd )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λThe desired wavelength λ of the single-mode optical fiber to be measured dd における非線形定数を、The nonlinear constant at
nn 2(eff)2 (eff) (λ(Λ dd )/A) / A effeff (λ(Λ dd ))
に基づき算出するステップとCalculating based on
を有するHave
ことを特徴とする請求項1に記載の単一モード光ファイバの非線形定数測定方法。The method of measuring a nonlinear constant of a single mode optical fiber according to claim 1.
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、
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。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
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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