JP3696369B2 - Short optical pulse waveform regeneration method - Google Patents

Description

のように表される。本発明は、リアルタイムでは直接は測定することができない短光パルス電場波形ｅ(ｔ)を上述の２種類のスペクトラム（｜Ｅ₁(ω)｜²,｜Ｉ(ω)｜²）から計算して再生するものである。そして、ｅ(ｔ)が決定できれば、強度波形、位相波形、さらにはチャープ特性も決定される。
【００１８】
式(1)をフーリエ変換した結果は、
Ｅ₁(ω)＝Ｅ(ω−ω_o) (3)
ここで、Ｅ(ω),Ｅ₁(ω)は、それぞれ、ｅ(ｔ),ｅ₁(ｔ)のフーリエ変換を表す。
【００１９】
式(3)は、原理的に、ｅ(ｔ)のパワースペクトラム｜Ｅ(ω)｜²が、ｅ₁(ｔ)のパワースペクトラム｜Ｅ₁(ω)｜²をω_oだけ周波数軸の負の方向に移動させたものであり、すなわち、スペクトラム｜Ｅ₁(ω)｜²のω＝ω_oの点をあらためてω＝０としたものに等しいことを意味している。
【００２０】
ゆえにこのパワースペクトラム｜Ｅ(ω)｜²は、波長分解能が高い光スペクトラムアナライザを用いて測定した光電場スペクトラムデータ｜Ｅ₁(ω)｜²を周波数軸の負の方向にω_oだけシフトすれば、決定できる。
【００２１】
一方、時間分解能の高いオートコリレータを用いれば、短光パルスの自己相関波形データ
Ｉ(τ)＝∫ｉ(ｔ)・ｉ(ｔ−τ)・ｄｔ (4)
を測定できる。τは遅延時間であり、ｉ(ｔ)は入射した短光パルスの強度波形である。ｉ(ｔ)のフーリエ変換をＩ(ω)と表したとき、自己相関波形データＩ(τ)をフーリエ変換すれば数学的に｜Ｉ(ω)｜²となることから、強度パワースペクトラムデータ｜Ｉ(ω)｜²の値を決定できる。
【００２２】
データ｜Ｅ(ω)｜²と｜Ｉ(ω)｜²の値を決定したならば、｜Ｅ(ω)｜²の離散データ間の周波数分解幅Δｆ_Eと｜Ｉ(ω)｜²の周波数分解幅Δｆ_Iとが等しくなるように補間計算し（周波数分解幅が大きい方に合わせるのが妥当である）、かつ、高速フーリエ変換（ＦＦＴ）が可能なようにスペクトラムの離散データの総数ＮがＮ＝２^m（ｍは自然数）になるように、零値をもつデータを付加する。このようにして、強度パワースペクトラム｜Ｉ(ω)｜²の離散データ｜Ｉ(ｋ)｜²と電場パワースペクトラム｜Ｅ(ω)｜²の離散データ｜Ｅ(ｋ)｜²の値を決定する。
ここで、ｋは０,１,…,Ｎ−１の整数であり、ＮはＦＦＴでの演算点数である。
【００２３】
［波形再生計算］
上述のようにして離散データ｜Ｉ(ｋ)｜²と｜Ｅ(ｋ)｜²を決定したら、次に、波形再生計算を実行する。短光パルス電場波形ｅ(ｋ)を決定するためには、複素スペクトラムＥ(ω)の位相φ(ω)が分かればよい。しかしながら、オートコリレータによる測定はもちろん、光スペクトラムアナライザによる測定も基本的には自己相関測定であるため、φ(ω)の情報は失われている。そこで、本発明では、｜Ｅ(ω)｜²と｜Ｉ(ω)｜²のデータを同時に満足するようなφ(ω)を数値計算で求め、短光パルス電場波形ｅ(ｔ)、さらには、短光パルス電場波形ｉ(ｔ)やチャープ特性を求めることとする。以下に、この手順の概略を説明する。図１はこのこの手順の概略を説明する図である。
【００２４】
まず、(a)に示すように、周波数領域におけるＥ(ω)の位相変数φ(ω)に適切な初期値φ_i(ω)を代入する。そして、位相φ(ω)とスペクトラムデータ｜Ｅ(ω)｜から、複素スペクトラムＥ(ω)を算出する。次に、(b)に示すように、複素スペクトラムＥ(ω)に対して高速逆フーリエ変換を実施することにより、時間領域での電場波形ｅ(ｔ)を求め、このｅ(ｔ)の複素絶対値の２乗から強度波形ｉ(ｔ)を求める。続けて、ｉ(ｔ)を高速フーリエ変換して強度波形のフーリエ変換Ｉ'(ω)を求め、さらに、このフーリエ変換Ｉ'(ω)の複素絶対値｜Ｉ'(ω)｜を計算する。
【００２５】
そして、(c)に示すように、計算値｜Ｉ'(ω)｜と測定値｜Ｉ(ω)｜とを比較して両者間の誤差が小さくなるように位相φ(ω)を徐々に微少変化させながら、上述の高速フーリエ変換及び高速逆フーリエ変換を繰り返し、誤差が最小となるときの位相φ'(ω)を求める。
【００２６】
このようにして位相φ'(ω)が決定できたならば、スペクトラムデータ｜Ｅ(ω)｜と位相φ'(ω)から複素スペクトラムＥ'(ω)を計算し、この複素スペクトラムＥ'(ω)を高速逆フーリエ変換して、短光パルスの電場波形の解ｅ'(ｔ)を求める。そして、このｅ'(ｔ)の複素絶対値の２乗から短光パルスの強度波形ｉ'(ｔ)を計算し、また、ｅ'(ｔ)の位相成分から位相波形φ'(ｔ)を計算する。最後に、位相波形データφ'(ｔ)を時間で微分して２πで除算すれば、チャープ周波数の変化を求めることができる。
【００２７】
【発明の実施の形態】
次に、本発明の実施の形態について図面を参照して説明する。図２は本発明の実施の一形態の短光パルスの波形再生方法の実施に用いられる測定系の概略を示すブロック図である。
【００２８】
この測定系は、被測定短光パルス発生源１からの短光パルスの波形を再生するものであって、光スペクトラムアナライザ２と、オートコリレータ３と、コンピュータ４とから構成されている。被測定短光パルス発生源１からの短光パルスは、光スペクトラムアナライザ２とオートコリレータ３の両方に入力する。オートコリレータ３としては、ＳＨＧ結晶を内部に有するものが使用される。ここで光スペクトラムアナライザ２は、短光パルスの電場パワースペクトラム｜Ｅ(ω)｜²を求めるのに使用され、オートコリレータ３は、短光パルスの強度自己相関波形Ｉ(τ)＝∫ｉ(ｔ)・ｉ(ｔ−τ)・ｄｔを求めるのに使用されている。コンピュータ４には、電場パワースペクトラム｜Ｅ(ω)｜²と強度自己相関波形Ｉ(τ)とから波形再生を行う波形再生計算部５と、再生された波形等を表示するためのデータ表示部６とが設けられている。
【００２９】
次に、オートコリレータ３により測定した自己相関波形データＩ(τ)と光スペクトラムアナライザ２を用いて測定した電場パワースペクトラムデータ｜Ｅ(ω)｜²とから、短光パルスの波形を再生するための具体的手順について、図３を用いて説明する。短光パルスの光としての中心周波数をω_oとする。
【００３０】
まず、内部にＳＨＧ結晶を具備したオートコリレータ３を用いて測定した短光パルス強度自己相関波形の離散データＩ(τ)に対して高速フーリエ変換（ＦＦＴ）を行い、強度パワースペクトラム｜Ｉ(ｋ)｜²の平方根｜Ｉ(ｋ)｜を求める（ステップ１０１）。ここで、ＦＦＴでのデータ点数をＮとして、ｋは、ｋ＝０,１,…,Ｎ−１の整数である（以下、Ｎ,ｋについて、同様である）。また、光スペクトラムアナライザ２で測定した電場パワースペクトラムデータ｜Ｅ₁(ω)｜²を光中心周波数ω_oだけ周波数軸の負の方向にシフトさせた離散データ｜Ｅ(ｋ)｜²の平方根｜Ｅ(ｋ)｜の値を計算する（ステップ１０２）。
【００３１】
次に、ステップ１０３において、データ｜Ｅ(ｋ)｜の周波数分解能Δｆ_Eとデータ｜Ｉ(ｋ)｜の周波数分解能ｆ_Iとが等しくなるように補間計算を行い、引き続いて、｜Ｅ(ｋ)｜のデータ個数及び｜Ｉ(ｋ)｜のデータ個数がともにＮ（ｍを自然数としてＮ＝２^m）になるように、各々のデータ｜Ｅ(ｋ)｜,｜Ｉ(ｋ)｜に零値を有するデータを付加する。この結果をあらためて｜Ｅ(ｋ)｜,｜Ｉ(ｋ)｜（測定値）と表記する。
【００３２】
次に、｜Ｅ(ｋ)｜と｜Ｉ(０)｜の間に成立する関係式
【００３３】
【数２】

にしたがって、｜Ｅ(ｋ)｜と｜Ｉ(ｋ)｜の大きさを互いに規格化する（ステップ１０４）。そして、求めようとしているＥ(ｋ)の位相φ(ｋ)に、適切な初期値φ_i(ｋ)を代入する（ステップ１０５）。
【００３４】
次に、｜Ｅ(ｋ)｜（測定値）と位相φ(ｋ)とから、複素データＥ(ｋ)を計算し（ステップ１０６）、計算されたＥ(ｋ)に対して高速逆フーリエ変換（ＩＦＦＴ）を実行して時間領域での電界波形ｅ(ｋ)を求め、このｅ(ｋ)の複素絶対値の２乗、すなわち、時間領域での強度波形ｉ(ｋ)を計算する（ステップ１０７）。時間領域での強度波形ｉ(ｋ)が求められたら、このｉ(ｋ)に対して高速フーリエ変換を実行して強度波形の周波数スペクトラムの計算値Ｉ'(ｋ)を求め、さらにこの計算値Ｉ'(ｋ)の複素絶対値｜Ｉ'(ｋ)｜を求める（ステップ１０８）。
【００３５】
次に、ステップ１０４においてすでに規格化ずみの｜Ｉ(ｋ)｜（測定値）とステップ１０８での計算値｜Ｉ'(ｋ)｜との間の誤差を次の誤差評価関数Ｓ₁を用いて評価する（ステップ１０９）。
【００３６】
【数３】

【００３７】
そして、この誤差評価関数Ｓ₁の値が所定のしきい値Ｔ（例えば、０.０００５〜０.００５程度の値）よりも大きいかどうかを判断し（ステップ１１０）、Ｓ₁≧Ｔであるときには、ステップ１１１に移行して周波数領域における位相波形φ(ｋ)を微少変化させたものをあらためてφ(ｋ)とし、ステップ１０６に戻って処理を繰り返す。ステップ１１０は、所定の収束条件を満足しているかどうかを判断するためのステップである。
【００３８】
一方、ステップ１１０においてＳ₁＜Ｔであるときには、このときの周波数領域での位相φ(ｋ)を、｜Ｅ(ｋ)｜と｜Ｉ(ｋ)｜を同時に満たす近似解φ'(ｋ)とする（ステップ１１２）。この近似解φ'(ｋ)は、誤差が最小となったときの位相である。周波数領域におけるＥ(ｋ)の位相解（上述の近似解）φ'(ｋ)が求められたら、ステップ１１３において、データ｜Ｅ(ｋ)｜（測定値）とこの位相解φ'(ｋ)とから複素データＥ(ｋ)を求め、このＥ(ｋ)に対して高速逆フーリエ変換を実行することにより、時間領域における短光パルス電場波形の解ｅ'(ｋ)を計算する。また、短光パルス強度波形の解ｉ(ｋ)は、ｅ(ｋ)の複素絶対値の２乗で計算する。時間領域の位相φ'_t(ｋ)は、ｅ(ｋ)の複素位相から求める。さらに、チャープ周波数変化は、φ'_t(ｋ)を時間微分して２πで除算することにより求める。
【００３９】
以上のようにして、短光パルスの波形再生が行われる。この波形再生演算は、コンピュータ４の波形再生計算部５で行われ、その計算結果は、所望の表示形式によって、データ表示部６に表示される。
【００４０】
ところで、被測定短光パルスがソリトンパルスである場合には、図４に示すように、｜Ｅ(ω)｜²や｜Ｉ(ω)｜²の各光スペクトラムデータに、被測定短光パルスの繰返し周波数に対応した周波数間隔をもった離散的なピークが出現するようになる。
【００４１】
上述の図３に示す波形再生計算手順は、基本的には、滑らかに変化するスペクトラムデータに対して適用できるものであるが、ソリトンパルスのように離散的なピーク構造をもつ光スペクトラムに対して本発明による波形再生計算方法を適用する場合には、各々のスペクトラムでの離散ピークの最大値をとるところのデータのみを抽出して、その抽出したデータのみを用いればよい。
【００４２】
図５は、被測定短光パルスがソリトンパルスであるときの波形再生計算手順を示すフローチャートである。この手順は、図３に示すフローチャートにおいて、ステップ１０３の代わりに、測定したデータ｜Ｅ(ｋ)｜と｜Ｉ(ｋ)｜に出現している離散的ピーク１個１個の最大位置のデータ値のみを抽出して、これらの抽出データの総数がともにＮ（Ｎ＝２^m：ｍは自然数）となるように零値をもつデータを付加し、このような処理を施した結果をあらためて｜Ｅ(ｋ)｜,｜Ｉ(ｋ)｜（測定値）とするステップ１１４を設けた構成のものである。ステップ１０３をこのステップ１１４によって置き換えたこと以外は、図５に示す手順と図３に示す手順は同一である。
【００４３】
なお、離散的ピークからデータを抽出するときに測定スペクトラムデータの周波数分解能が粗くてピーク最大値の位置がよく分からない場合には、スプライン補間等の補間計算を行って、ピーク最大位置ならびにピーク値を補間すればよい。このような補間を施すことにより、ソリトンパルスの波形のより正確な再生が可能になる。
【００４４】
【発明の効果】
以上説明したように本発明は、光スペクトラムアナライザなどによって得られる光電場パワースペクトラム｜Ｅ(ω)｜²と、ＳＨＧ結晶を内部に有するオートコリレータなどによって得られる強度自己相関波形Ｉ(τ)と用いて、フーリエ変換演算及び逆フーリエ変換演算を繰り返すことにより、複雑な測定系を用いることなく、短光パルスの強度波形やチャープ特性を簡単に再生することができるようになるという効果がある。
【図面の簡単な説明】
【図１】短光パルスの波形再生の手順の概略を説明する図である。
【図２】本発明の実施の一形態の短光パルスの波形再生方法の実施に用いられる測定系の概略を示すブロック図である。
【図３】本発明の実施の一形態の短光パルスの波形再生方法の具体的手順を示すフローチャートである。
【図４】ソリトンパルスに対する光スペクトラムの一例を示す図である。
【図５】ソリトンパルスに対する波形再生方法の具体的手順を示すフローチャートである。
【図６】短光パルス波形を評価するための従来の評価システムの構成の一例を示すブロック図である。
【図７】ＳＨＧ自己相関法による従来の波形再生方法を説明するブロック図である。
【符号の説明】
１ 被測定短光パルス発生源
２ 光スペクトラムアナライザ
３ オートコリレータ
４ コンピュータ
５ 波形再生計算部
６ データ表示部
１０１〜１１４ ステップ[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a method for reproducing a waveform of an optical pulse having a short duration, that is, a short optical pulse, and more particularly to a waveform reproducing method capable of reproducing an intensity waveform and chirp characteristics in a time domain of a short optical pulse including a soliton pulse.
[0002]
[Prior art]
As ultra-high speed optical communication develops, there is an increasing demand for measuring the intensity waveform and chirp characteristics of short light pulses.
[0003]
Autocorrelator (Short Light Pulse Intensity Autocorrelation Measurement) with a Second Harmonic Generation (SHG) Crystal as a Method to Evaluate the Approximate Half-Time Width and Chirp Size of Short Light Pulses And a high-resolution optical spectrum analyzer. FIG. 6 shows an example of the configuration of a system for implementing this conventional evaluation method. The short light pulse to be measured from the short light pulse source 71 to be measured is input to both the optical spectrum analyzer 72 and the autocorrelator 73. The optical spectrum analyzer 72 measures the electric field spectrum | E (ω) | ^{2 of} the short light pulse. ω represents an angular frequency. In the autocorrelator 73, the intensity autocorrelation waveform I (τ) is measured by the SHG crystal. τ represents the delay time,
I (τ) = ∫i (t) · i (t−τ) dt
It is. Then, by a computer 75 having a data display unit 74, the half-width and the electric field spectrum intensity autocorrelation waveform I (τ) | E (ω ) | ² of the half-width, approximate half width and chirp magnitudes of the short optical pulse Can be estimated.
[0004]
There is also a method of reproducing a short optical pulse waveform by the SHG autocorrelation method. FIG. 7 is a block diagram showing the configuration of a conventional measurement system for reproducing an optical pulse waveform by the SHG autocorrelation method. This system is roughly divided into an optical unit 76 including a Michelson interferometer 80 and an optical detection unit on which an optical pulse is incident, a signal processing unit 77 that processes and stores an electrical signal from the optical unit 76, and The signal processing unit 77 and an arithmetic processing unit 78 connected to the signal processing unit 77 and performing various calculations are configured. As the arithmetic processing unit 78, for example, a workstation is used.
[0005]
The Michelson interferometer 80 includes a beam splitter 81, a fixed mirror 82, and a moving mirror 83. The light pulse incident on the Michelson interferometer 80 from the outside is divided into two by the beam splitter 81, one is reflected by the fixed mirror 82, the other is reflected by the moving mirror 83, and reaches the beam splitter 81 again and is multiplexed. Then, it is emitted from the Michelson interferometer 80 and divided again into two by the beam splitter 86. One light divided by the beam splitter 86 is incident on a photodetector 87 formed of a photodiode, and the other light passes through a second harmonic generation element 89 made of an SHG crystal, and a second harmonic component. The light passes through a filter 90 that passes only the light and enters a photodetector 91 constituted by a photomultiplier tube. Further, the optical unit 76 is also provided with a He—Ne laser 84 for generating a reference signal, and laser light (broken line in the figure) from the He—Ne laser 84 is also incident on the Michelson interferometer. This laser light emitted from the light is detected by a photodetector 85 formed of a photodiode. The output of the photodetector 85 is incident on a sampling signal generation circuit 88. The sampling signal generation circuit 88 multiplies the frequency of the interference fringes of He-Ne laser light by the Michelson interferometer by 2 ⁿ to obtain a sampling signal. To do.
[0006]
The signal processing unit 77 includes A / D converters 92 and 93 for analog / digital conversion of the detection signals from the photodetectors 87 and 91 in accordance with the sampling signal from the sampling signal generation circuit 88, and each A A data memory 94 for storing data for each sampling from the / D converters 92 and 93 is provided.
[0007]
When reproducing the waveform of the short optical pulse using such a system, the short optical pulse to be measured is incident on the optical unit 76 and divided into two by the beam splitter 81, and the delay time τ is given by the moving mirror 83 to cause interference. This short optical pulse interference light is divided into two by the beam splitter 86, and one of the short optical pulses enters the photodetector 87 as it is, and the interference waveform S ₁ (τ) is measured. The other half is incident on the SHG crystal (second harmonic generation element 89), and the SH (second harmonic) light output from the SHG crystal is detected by the photodetector 91, whereby the SH interference waveform S ₂ is detected. (τ) is measured.
[0008]
When the electric field waveform of the short optical pulse to be measured is e (t), the electric field power spectrum | E (ω) | ² of e (t) is extracted from the frequency component analysis of the interference waveform S ₁ (τ). Also, S ₂ short light pulse intensity waveform from the frequency component analysis (τ) i (t) = | e (t) | 2 of the power spectrum | I (ω) | and ^{2, u (t) = e} (t) ² of the power spectrum | to extract ² | U ^(ω). In this measurement, only spectrum amplitude component data can be measured.
[0009]
When each power spectrum is obtained in this way, the phase component φ _E (ω) of the electric field spectrum E (ω) and these power spectra | E (ω) | ² , | I (ω) | ² , | U (ω ) | Repeat the Fast Fourier Transform (FFT) and Fast Inverse Fourier Transform (IFFT) calculations to find one that satisfies ² . As a result, the electric field waveform e (t) of the short light pulse can be finally obtained.
[0010]
As a method for directly obtaining a short light pulse intensity waveform in real time, the method having the highest time resolution is a method using a streak camera. However, the time resolution of the streak camera is about several ps at most, and the streak camera is not sufficient for the measurement of short light pulses used in ultrahigh-speed optical communication.
[0011]
[Problems to be solved by the invention]
The short light pulse evaluation system that uses only an optical spectrum analyzer and an autocorrelator can, at best, evaluate the approximate half-width of short light pulses and the magnitude of chirp changes. You cannot ask yourself.
[0012]
On the other hand, the SHG autocorrelation method measures | I (ω) | ² and | U (ω) | ² in addition to | E (ω) | ² to measure the intensity waveform and chirp characteristics of short light pulses. A short light pulse waveform that satisfies these three types of data is obtained by numerical calculation. Of these three types of data, | I (ω) | ² is the autocorrelator for autocorrelation I (τ) = ∫i (t) · i (t−τ) dt of the short optical pulse intensity waveform i (t). The autocorrelation I (τ) can be determined relatively easily by performing Fourier transform.
As an autocorrelator for measuring the autocorrelation I (τ), for example, various types such as those using a Michelson interferometer can be used. However, in order to measure | U (ω) | ² , the measurement system shown in FIG. 7 must be used.
However, the measurement system shown in FIG. 7 requires a special skill to realize because the phase matching of the SHG crystal is difficult and the configuration of the measurement system itself is complicated.
[0013]
An object of the present invention is to provide a short optical pulse waveform reproduction method capable of easily reproducing the intensity waveform and chirp characteristics of a short optical pulse without using a complicated measurement system.
[0014]
[Means for Solving the Problems]
The short optical pulse waveform reproduction method of the present invention is a method of reproducing the waveform of a short optical pulse to be measured,
The photoelectric field power spectrum | E ₁ (ω) | ² of the short optical pulse to be measured is measured, and the photoelectric field power spectrum | E ₁ (ω) | ² is negative on the frequency axis by the optical center frequency ω ₀ of the short optical pulse. A first step of shifting in the direction to determine the electric field power spectrum | E (ω) | ² ;
A second step of measuring intensity autocorrelation waveform data of a short optical pulse to be measured, performing Fourier transform on the data, and obtaining an intensity power spectrum | I (ω) | ² ;
Assuming the phase φ (ω) of the complex spectrum E (ω), the electric field is obtained by inverse Fourier transform from the assumed phase φ (ω) of the square root of the electric field power spectrum | E (ω) | ² | E (ω) | A third step of temporarily calculating the waveform e (t) and calculating the calculated value i (t) of the intensity waveform in the time domain from the temporarily calculated electric field waveform e (t);
A fourth step of obtaining a calculated value | I ′ (ω) | of the intensity waveform in the frequency domain by Fourier-transforming the calculated value i (t);
The calculated value | I ′ (ω) | obtained in the fourth step is compared with the measured value | I (ω) | obtained from the intensity power spectrum | I (ω) | ² obtained in the first step. And a fifth step for obtaining an error,
The third step, the fourth step, and the fifth step are repeated while changing the phase φ (ω) so as to reduce the error, and the phase φ (ω) when the error satisfies a predetermined convergence condition is changed to φ As' (ω), a true electric field waveform e ′ (t) is calculated by inverse Fourier transform from the square root | E (ω) | of the electric field power spectrum | E (ω) | ² and the phase φ ′ (ω).
[0015]
That is, in the present invention, first, the photoelectric field spectrum | E ₁ (ω) | ² of the short optical pulse to be measured is measured using an optical spectrum analyzer or the like, and an autocorrelator (short optical pulse intensity autocorrelation measuring device) is installed. The intensity autocorrelation waveform data I (τ) of the short optical pulse to be measured is measured. Then, the power spectrum | I (ω) | ² of the short optical pulse intensity waveform i (t) = | e (t) | ² is obtained from the autocorrelation data I (τ) by Fourier transform. The short optical pulse intensity waveform is determined from | E ₁ (ω) | ² and | I (ω) | ² as described in detail below, and the chirp characteristics are also determined as necessary. Hereinafter, the principle of the present invention will be described.
[0016]
[Measurement of spectrum data]
The electric field waveform e ₁ (t) of the short optical pulse to be measured is
e ₁ (t) = e (t) · exp {j · ω _o · t} (1)
It expresses. Here, ω _o is the center frequency of the short light pulse, and e (t) is an amplitude including a slowly changing phase. Of course, t is a variable representing time. When e (t) is expressed using the short light pulse intensity i (t) and the phase change amount φ _t (t),
[0017]
[Expression 1]

It is expressed as In the present invention, a short optical pulse electric field waveform e (t) that cannot be directly measured in real time is calculated from the above two types of spectra (| E ₁ (ω) | ² , | I (ω) | ² ). To play. If e (t) can be determined, the intensity waveform, phase waveform, and chirp characteristic are also determined.
[0018]
The result of Fourier transform of equation (1) is
E ₁ (ω) = E (ω−ω _o ) (3)
Here, E (ω) and E ₁ (ω) represent Fourier transforms of e (t) and e ₁ (t), respectively.
[0019]
Equation (3) can in principle, the power spectrum of e (t) | E (ω ) | 2 is the power spectrum of _{e 1 (t) | E 1} (ω) | only ² omega _o negative frequency axis That is, it means that the point of ω = ω _o of the spectrum | E ₁ (ω) | ² is set to ω = 0 again.
[0020]
Therefore, the power spectrum | E (ω) | ² is obtained by shifting the photoelectric field spectrum data | E ₁ (ω) | ² measured using an optical spectrum analyzer with high wavelength resolution by ω _{o in} the negative direction of the frequency axis. Can be determined.
[0021]
On the other hand, if an autocorrelator with high time resolution is used, the autocorrelation waveform data I (τ) = ∫i (t) · i (t−τ) · dt (4) of the short optical pulse.
Can be measured. τ is a delay time, and i (t) is an intensity waveform of an incident short light pulse. When the Fourier transform of i (t) is expressed as I (ω), if the autocorrelation waveform data I (τ) is Fourier transformed, it becomes mathematically | I (ω) | ^2. The value of I (ω) | ² can be determined.
[0022]
Data | E (ω) | ² and | I (ω) | Once determined a value of ^2, | E (ω) | and frequency resolution width Delta] f _E between ^two discrete data | I (ω) | ² of The total number N of discrete data in the spectrum is calculated so that the frequency resolution width Δf _I is equal to the frequency resolution width Δf _I (it is appropriate to adjust to the larger frequency resolution width) and fast Fourier transform (FFT) is possible. N = 0 ^m (m is a natural number) is added with data having a zero value. In this way, the intensity power spectrum | determine the value of ² | I (omega) | ² of the discrete data | I (k) | ² and the electric field power spectrum | E (omega) | ² of the discrete data | E (k) To do.
Here, k is an integer of 0, 1,..., N−1, and N is the number of calculation points in FFT.
[0023]
[Waveform playback calculation]
After the discrete data | I (k) | ² and | E (k) | ² are determined as described above, the waveform reproduction calculation is executed next. In order to determine the short optical pulse electric field waveform e (k), it is only necessary to know the phase φ (ω) of the complex spectrum E (ω). However, not only the measurement by the autocorrelator, but also the measurement by the optical spectrum analyzer is basically an autocorrelation measurement, information on φ (ω) is lost. Therefore, in the present invention, φ (ω) that satisfies the data | E (ω) | ² and | I (ω) | ² at the same time is obtained by numerical calculation, the short optical pulse electric field waveform e (t), Is to obtain the short optical pulse electric field waveform i (t) and chirp characteristics. Below, the outline of this procedure is demonstrated. FIG. 1 is a diagram for explaining the outline of this procedure.
[0024]
First, as shown in (a), an appropriate initial value φ _i (ω) is substituted into the phase variable φ (ω) of E (ω) in the frequency domain. Then, a complex spectrum E (ω) is calculated from the phase φ (ω) and the spectrum data | E (ω) |. Next, as shown in (b), a fast inverse Fourier transform is performed on the complex spectrum E (ω) to obtain an electric field waveform e (t) in the time domain, and the complex of this e (t) The intensity waveform i (t) is obtained from the square of the absolute value. Subsequently, i (t) is subjected to fast Fourier transform to obtain a Fourier transform I ′ (ω) of the intensity waveform, and a complex absolute value | I ′ (ω) | of the Fourier transform I ′ (ω) is calculated. .
[0025]
Then, as shown in (c), the calculated value | I ′ (ω) | and the measured value | I (ω) | are compared, and the phase φ (ω) is gradually increased so that the error between the two becomes small. While slightly changing, the above-mentioned fast Fourier transform and fast inverse Fourier transform are repeated to obtain the phase φ ′ (ω) when the error is minimized.
[0026]
If the phase φ ′ (ω) can be determined in this way, a complex spectrum E ′ (ω) is calculated from the spectrum data | E (ω) | and the phase φ ′ (ω), and this complex spectrum E ′ ( ω) is subjected to a fast inverse Fourier transform to obtain an electric field waveform solution e ′ (t) of the short optical pulse. Then, the intensity waveform i ′ (t) of the short optical pulse is calculated from the square of the complex absolute value of e ′ (t), and the phase waveform φ ′ (t) is calculated from the phase component of e ′ (t). calculate. Finally, if the phase waveform data φ ′ (t) is differentiated by time and divided by 2π, a change in chirp frequency can be obtained.
[0027]
DETAILED DESCRIPTION OF THE INVENTION
Next, embodiments of the present invention will be described with reference to the drawings. FIG. 2 is a block diagram showing an outline of a measurement system used for carrying out the short optical pulse waveform reproducing method according to the embodiment of the present invention.
[0028]
This measurement system reproduces the waveform of a short light pulse from the short light pulse generation source 1 to be measured, and comprises an optical spectrum analyzer 2, an autocorrelator 3, and a computer 4. A short light pulse from the short light pulse source 1 to be measured is input to both the optical spectrum analyzer 2 and the autocorrelator 3. As the autocorrelator 3, one having an SHG crystal inside is used. Here, the optical spectrum analyzer 2 is used to obtain the electric field power spectrum | E (ω) | ² of the short optical pulse, and the autocorrelator 3 is the intensity autocorrelation waveform I (τ) = ∫i ( t) · i (t−τ) · dt. The computer 4 includes a waveform reproduction calculation unit 5 that performs waveform reproduction from the electric field power spectrum | E (ω) | ² and the intensity autocorrelation waveform I (τ), and a data display unit that displays the reproduced waveform and the like. 6 are provided.
[0029]
Next, in order to reproduce the waveform of the short optical pulse from the autocorrelation waveform data I (τ) measured by the autocorrelator 3 and the electric field power spectrum data | E (ω) | ² measured using the optical spectrum analyzer 2. A specific procedure will be described with reference to FIG. The center frequency as light of a short light pulse is ω _o .
[0030]
First, fast Fourier transform (FFT) is performed on discrete data I (τ) of a short optical pulse intensity autocorrelation waveform measured using an autocorrelator 3 having an SHG crystal inside, and an intensity power spectrum | I (k ) | The square root | I (k) | of ² is obtained (step 101). Here, assuming that the number of data points in FFT is N, k is an integer of k = 0, 1,..., N−1 (hereinafter, the same applies to N and k). Further, the electric field power spectrum data measured by the optical spectrum analyzer _{2 | E 1 (ω) |} 2 of the optical center frequency omega _o discrete data were negative shift in the direction of the frequency axis by | E (k) | ² of the square root of | The value of E (k) | is calculated (step 102).
[0031]
Next, in step 103, interpolation calculation is performed so that the frequency resolution Δf _E of the data | _E (k) | is equal to the frequency resolution f _{I of the} data | I (k) |, and then | E (k ) | And the number of data of | I (k) | are both N (m = 2 as a natural number, N = 2 ^m ), and each data | E (k) |, | I (k) | Append data with zero value. This result is rewritten as | E (k) |, | I (k) | (measured value).
[0032]
Next, a relational expression established between | E (k) | and | I (0) |
[Expression 2]

Accordingly, the sizes of | E (k) | and | I (k) | are normalized to each other (step 104). Then, an appropriate initial value φ _i (k) is substituted into the phase φ (k) of E (k) to be obtained (step 105).
[0034]
Next, complex data E (k) is calculated from | E (k) | (measured value) and phase φ (k) (step 106), and fast inverse Fourier transform is performed on the calculated E (k). (IFFT) is performed to obtain the electric field waveform e (k) in the time domain, and the square of the complex absolute value of e (k), that is, the intensity waveform i (k) in the time domain is calculated (step) 107). When the intensity waveform i (k) in the time domain is obtained, fast Fourier transform is performed on this i (k) to obtain the calculated value I ′ (k) of the frequency spectrum of the intensity waveform, and this calculated value The complex absolute value | I ′ (k) | of I ′ (k) is obtained (step 108).
[0035]
Then, already Zumi normalized in step 104 | using the error evaluation function S ₁ the error of the next between | and (measured) Calculated in step 108 | | I (k) I '(k) (Step 109).
[0036]
[Equation 3]

[0037]
Then, it is determined whether or not the value of the error evaluation function S ₁ is larger than a predetermined threshold T (for example, a value of about 0.0005 to 0.005) (step 110), and S ₁ ≧ T. In some cases, the process proceeds to step 111, where a slight change in the phase waveform φ (k) in the frequency domain is changed to φ (k), and the process returns to step 106 and the process is repeated. Step 110 is a step for determining whether or not a predetermined convergence condition is satisfied.
[0038]
On the other hand, when S ₁ <T in step 110, the phase φ (k) in the frequency domain at this time satisfies the approximate solution φ ′ (k) satisfying | E (k) | and | I (k) | (Step 112). This approximate solution φ ′ (k) is the phase when the error is minimized. When the phase solution of E (k) in the frequency domain (the above approximate solution) φ ′ (k) is obtained, in step 113, the data | E (k) | (measured value) and the phase solution φ ′ (k) The complex data E (k) is obtained from the above, and a fast inverse Fourier transform is performed on the E (k), thereby calculating a solution e ′ (k) of the short optical pulse electric field waveform in the time domain. The solution i (k) of the short optical pulse intensity waveform is calculated by the square of the complex absolute value of e (k). The time domain phase φ ′ _t (k) is obtained from the complex phase of e (k). Further, the chirp frequency change is obtained by time-differentiating φ ′ _t (k) and dividing by 2π.
[0039]
As described above, the waveform reproduction of the short light pulse is performed. This waveform reproduction calculation is performed by the waveform reproduction calculation unit 5 of the computer 4 and the calculation result is displayed on the data display unit 6 in a desired display format.
[0040]
When the short optical pulse to be measured is a soliton pulse, the short optical pulse to be measured is included in each optical spectrum data of | E (ω) | ² and | I (ω) | ² as shown in FIG. Discrete peaks having frequency intervals corresponding to the repetition frequency of appear.
[0041]
The waveform reproduction calculation procedure shown in FIG. 3 described above is basically applicable to smoothly changing spectrum data, but for an optical spectrum having a discrete peak structure such as a soliton pulse. When applying the waveform reproduction calculation method according to the present invention, it is only necessary to extract only the data that takes the maximum value of the discrete peaks in each spectrum and use only the extracted data.
[0042]
FIG. 5 is a flowchart showing a waveform reproduction calculation procedure when the short optical pulse to be measured is a soliton pulse. In this flowchart, instead of step 103, the maximum position data of each discrete peak appearing in the measured data | E (k) | and | I (k) | Extracting only the values, adding data having zero values so that the total number of these extracted data is N (N = 2 ^m : m is a natural number), and re-applying the result of such processing | In this configuration, step 114 is provided for setting E (k) |, | I (k) | (measured value). The procedure shown in FIG. 5 is the same as the procedure shown in FIG. 3 except that step 103 is replaced by step 114.
[0043]
When extracting data from discrete peaks, if the frequency resolution of the measured spectrum data is rough and the position of the peak maximum value is not well understood, interpolation calculation such as spline interpolation is performed, and the peak maximum position and peak value are calculated. Can be interpolated. By performing such interpolation, it is possible to reproduce the waveform of the soliton pulse more accurately.
[0044]
【The invention's effect】
As described above, the present invention provides the photoelectric field power spectrum | E (ω) | ² obtained by an optical spectrum analyzer and the like, and the intensity autocorrelation waveform I (τ) obtained by an autocorrelator having an SHG crystal inside. By using and repeating the Fourier transform operation and the inverse Fourier transform operation, there is an effect that the intensity waveform and chirp characteristic of the short optical pulse can be easily reproduced without using a complicated measurement system.
[Brief description of the drawings]
FIG. 1 is a diagram for explaining an outline of a procedure for reproducing a waveform of a short optical pulse.
FIG. 2 is a block diagram showing an outline of a measurement system used for implementing the short optical pulse waveform reproduction method according to the embodiment of the present invention.
FIG. 3 is a flowchart showing a specific procedure of a method for reproducing a waveform of a short optical pulse according to an embodiment of the present invention.
FIG. 4 is a diagram showing an example of an optical spectrum with respect to a soliton pulse.
FIG. 5 is a flowchart showing a specific procedure of a waveform reproduction method for soliton pulses.
FIG. 6 is a block diagram showing an example of a configuration of a conventional evaluation system for evaluating a short optical pulse waveform.
FIG. 7 is a block diagram for explaining a conventional waveform reproduction method by the SHG autocorrelation method.
[Explanation of symbols]
DESCRIPTION OF SYMBOLS 1 Short optical pulse generation source to be measured 2 Optical spectrum analyzer 3 Autocorrelator 4 Computer 5 Waveform reproduction calculation part 6 Data display part 101-114 Step

Claims (3)

A method for reproducing a waveform of a short optical pulse to be measured,
The photoelectric field power spectrum | E ₁ (ω) | ² of the short light pulse to be measured is measured, and the photoelectric field power spectrum | E ₁ (ω) | ² is the frequency axis by the optical center frequency ω ₀ of the short light pulse. A first step of determining the electric field power spectrum | E (ω) | ² by shifting in the negative direction of
A second step of measuring intensity autocorrelation waveform data of the short optical pulse to be measured, performing Fourier transform on the waveform data, and obtaining an intensity power spectrum | I (ω) | ² ;
Assuming the phase φ (ω) of the complex spectrum E (ω), an inverse Fourier transform is performed from the square root | E (ω) | of the electric field power spectrum | E (ω) | ² and the assumed phase φ (ω). A third step of temporarily calculating an electric field waveform e (t) by calculating a calculated value i (t) of an intensity waveform in the time domain from the temporarily calculated electric field waveform e (t);
A fourth step of obtaining a calculated value | I ′ (ω) | of the intensity waveform in the frequency domain by Fourier-transforming the calculated value i (t);
The calculated value | I ′ (ω) | obtained in the fourth step and the measured value | I (ω) | obtained from the intensity power spectrum | I (ω) | ² obtained in the first step. A fifth step of comparing and determining an error,
The third step, the fourth step and the fifth step are repeated while changing the phase φ (ω) so as to reduce the error, and the error when the error satisfies a predetermined convergence condition. With the phase φ (ω) as φ ′ (ω), the true electric field waveform is obtained by inverse Fourier transform from the square root | E (ω) | of the electric field power spectrum | E (ω) | ² and the phase φ ′ (ω). A method of reproducing a waveform of a short optical pulse, which calculates e ′ (t). ^2. The short light according to claim 1, wherein the photoelectric field power spectrum | E ₁ (ω) | ² is measured by an optical spectrum analyzer, and the intensity autocorrelation waveform data is measured by an autocorrelator having a second harmonic generation crystal therein. Pulse waveform reproduction method. When the electric field power spectrum | E (ω) | ² and the intensity power spectrum | I (ω) | ² are spectrums having a plurality of discrete peaks, data of discrete peak positions from the respective power spectra. The method of reproducing a waveform of a short optical pulse according to claim 1 or 2, wherein the third step, the fourth step, and the fifth step are performed only on the extracted data.

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