JP5470320B2 - Laser light coherence length measuring method and measuring apparatus - Google Patents

Description

  The present invention relates to a laser beam coherence length measuring method and a measuring apparatus for measuring the coherence length of a laser beam.

  As a conventional method for measuring the coherence length of laser light, the laser light spectrum measuring method described in Non-Patent Document 1 is known. In this method, the laser to be measured is split into two, and is transmitted by a sufficiently long optical fiber prepared for one, and the other is passed through an acoustooptic device or the like to shift the frequency by a certain amount. Thereafter, both are combined, received by the light receiving element, and the beat spectrum width of the received light signal is measured. It is known that 1 / √2 of the beat spectrum width is an oscillation spectrum line width of the laser beam (hereinafter referred to as a laser beam spectrum line width), and the laser beam spectrum line width is measured from the measured beat spectrum width. be able to. If this laser beam spectral line width is Δν, the coherence time of the laser beam is 1 / Δν. Also, the coherence length can be obtained by multiplying the coherence time by the light velocity constant.

  However, in the above method, it is necessary to pass one of the branched laser beams through a sufficiently long optical fiber to give a sufficient time delay and then combine the other with the other, which is longer than the coherence length of the laser beam to be measured. A sufficiently long delay is required. For this reason, it is a precondition that a delay longer than the coherence length of the laser beam, which is unknown at the time of measurement, is obtained. Therefore, although the measurement result enables a constant estimation of the spectral line width of the laser beam, the measurement result has to be uncertain. This concern is particularly noticeable when laser light with a narrow spectral line width (long coherence time) is measured. In recent years, lasers having a spectral line width of about several kilohertz, such as fiber lasers, have been commercialized. Then, the ambiguity of the measurement is a problem.

T. Okoshi, K. Kikuchi, and A. Nakayama, “Novel method for high resolution measurement of laser output spectrum,” Electronics Letters, Vol. 16, No. 16, pp. 630-631, 1980 Y. Koshikiya, X. Fan, and F. Ito, “Long range and cm-level spatial resolution measurement using coherent optical frequency domain reflectmetry with SSB-SC modulator and narrow linewidth fiber laser”, IEEE / OSA J. Lightwave Technol. Vol 26, No. 18, pp. 3287-3294, 2008

As described above, the conventional laser beam coherence length measurement technique is premised on that a delay longer than the coherence length of the laser beam is obtained. There are uncertainties in the measurement results.
The present invention has been made paying attention to the above circumstances, and a laser beam coherence length measuring method capable of more accurately measuring the coherence time of a laser beam having a narrow spectral line width of the laser beam and a long coherence time, and It aims at providing a measuring device.

The laser beam coherence measurement method according to the present invention has the following configuration.
(1) A laser light coherence measuring method for measuring a coherence function γ (τ) of a laser beam to be measured that is a function of a delay time τ, wherein the frequency of the laser beam to be measured is linearly swept and the frequency sweep is performed. The laser beam is branched into two systems, one of the branched laser beams is incident on an optical fiber, the Rayleigh scattered light generated in the optical fiber is captured, and the Rayleigh scattered light and the other branched laser beam are And the photocurrent generated by the multiplexing is detected, the current value of the detected photocurrent is Fourier transformed to calculate its power spectrum, and the photocurrent is detected and the power spectrum is analyzed multiple times. The ensemble average of the power spectrum is obtained as a function of the delay τ by repeating, and the standard deviation of the ensemble average delay τ of the power spectrum is obtained. It is calculated and the manner of obtaining the absolute value of the coherence function by utilizing the fact that the standard deviation is proportional to the absolute value of the coherence function in the delay tau.

(2) In the method of (1), the coherence time is obtained with a delay τ in which the absolute value of the coherence function is 1 / e.
The laser beam coherence measuring apparatus according to the present invention has the following configuration.
(3) A laser light coherence measuring apparatus for measuring a coherence function γ (τ) of a laser beam to be measured that is a function of the delay time τ, a frequency sweeping means for linearly sweeping the frequency of the laser beam to be measured; Optical branching means for branching the frequency-swept laser light into two systems, Rayleigh scattered light acquisition means for entering the one of the branched laser lights into an optical fiber and capturing Rayleigh scattered light generated in the optical fiber, and Optical multiplexing means for combining Rayleigh scattered light generated in the optical fiber and the other laser beam branched by the optical branching means, photocurrent detection means for detecting a photocurrent generated by the multiplexing, and the detected A power spectrum calculating means for calculating a power spectrum by Fourier-transforming a current value of the photocurrent, the photocurrent detecting means and the power spectrum calculating means; Analysis means for obtaining an absolute value of the coherence function of the laser beam based on the detection result and the calculation result, and the analysis means repeatedly detects the photocurrent and analyzes the power spectrum thereof a plurality of times. To obtain an ensemble average of the power spectrum as a function of delay τ, calculate a standard deviation in the delay τ of the ensemble average of the power spectrum, and use that the standard deviation is proportional to the absolute value of the coherence function in the delay τ. In this manner, the absolute value of the coherence function is obtained.

  (4) In the apparatus of (3), the analyzing means obtains the coherence time with a delay τ at which the absolute value of the coherence function is 1 / e.

  As described above, the present invention is characterized in that the reliability is improved as compared with the prior art by performing statistical processing on the measured value. Specifically, the Rayleigh scattering intensity of the laser beam to be measured, frequency-swept using C-OFDR, is measured, the standard deviation of the absolute value of the Rayleigh scattering intensity obtained by this measurement is calculated, and τ (coherence time) ) To obtain the absolute value of the coherence function. Thus, according to the present invention, the absolute value of the coherence function can be obtained even when τ is smaller than the round-trip time of the light of the full length of the prepared optical fiber. Further, by obtaining τ whose value is reduced to 1 / e, it is possible to obtain the coherence time of the laser beam.

The laser light coherence measurement according to the present invention has the following advantages over the prior art.
First, according to the present invention, measurement can be performed with an optical fiber length comparable to the coherence time, and if the coherence time is much longer than that, the measurement itself becomes clear by measurement. Therefore, it is possible to take measures such as re-measurement by replacing with a longer optical fiber. Therefore, it can be said that the present invention provides a measurement result that is more reliable than the prior art.

Secondly, according to the present invention, not only is the coherence time measured, but the entire absolute value of the coherence function is grasped as a function of the delay time τ. Thereby, the property of the laser beam can be investigated in more detail.
Therefore, according to the present invention, it is possible to provide a laser beam coherence length measurement method and a measurement apparatus that can more accurately measure the coherence time of a laser beam with a narrow spectral line width of the laser beam and a long coherence time. .

It is a block diagram which shows the structure of the measuring apparatus to which the laser beam coherence measuring method which concerns on this embodiment is applied. It is a figure showing the waveform of the frequency modulation provided by the frequency sweep apparatus of the measuring apparatus shown in FIG.

Embodiments of the present invention will be described with reference to the accompanying drawings. The embodiment described below is an example of the configuration of the present invention, and the present invention is not limited to the following embodiment.
FIG. 1 is a block diagram showing a configuration of a laser beam coherence measuring apparatus according to the present embodiment. In FIG. 1, reference numeral 1 denotes a laser light source to be measured, and the laser light to be measured generated here is subjected to a frequency sweep of a specified width within a predetermined period as shown in FIG. The light is branched into two systems by the optical branching device 3-1. The branched transmission light of one system is guided to the optical fiber 5 by the optical circulator 4, and the transmission light of the other system is guided to the optical multiplexer 3-2. Subsequently, the backward Rayleigh scattered light generated in the optical fiber 5 is guided to the optical multiplexer 3-2 through the optical circulator 4, and is combined with the other transmission light, and then received by the balance type light receiving element 6. The

  The light reception signal obtained by the balance type light receiving element 6 is converted into data at a predetermined sampling period by the data acquisition device 7, and then the beat spectrum width is analyzed by the power spectrum analysis device 8 and sequentially stored in the memory device 9. . The coherence function analyzer 10 reads beat spectrum width data stored in the memory device 9 at a predetermined period, analyzes the coherence function of the laser beam to be measured, and obtains the coherence length of the laser beam from the analysis result. Both the sweep period of the frequency sweep device 2 and the data acquisition period of the data acquisition device 7 are determined according to instructions issued from the control device 11.

In the above configuration, the measurement method and procedure will be described below.
First, the electric field amplitude E ′ (t) of the laser beam of time length T emitted from the laser light source 1 to be measured is expressed as follows.

ここで、

here,

すなわち、式（１）はレーザ１から取り出される電界振幅のｉ番目のアンサンブルを意味している。以下に説明する本発明の実施形態において測定されるレーザ光のコヒーレンス関数γ(τ)は、

That is, Equation (1) means the i-th ensemble of the electric field amplitude extracted from the laser 1. The coherence function γ (τ) of the laser beam measured in the embodiment of the present invention described below is

で与えられる量である。かっこ記号の＜ ＞はアンサンブル平均を意味し、多くのアンサンブルに対する平均を表す。尚、＊は位相共役を意味する。
ここで、式（２）で表される量が持つ意味を考察しておく。もともとのレーザ光の電界は式（１）で表わされるが、これは中心周波数ω_iを中心として位相揺らぎθ_i(t)を持っている。しかるに、式（２）においては、中心周波数ω_iは現われておらず、位相揺らぎθ_i(t)のみに関係する量であることがわかる。すなわち、電界振幅のいくつかのアンサンブルを集めたときに、仮にそのアンサンブル間で中心周波数ω_iが変化（ドリフト）していたとしても、その効果は式（２）には現れず、１つのアンサンブルの中で観測される位相揺らぎθ_i(t)（すなわち発振周波数の揺らぎ）が測定されることになる。よって本発明で測量されるものは、レーザ光が一定時間Ｔだけ発振した時の位相もしくは周波数の揺らぎ幅を意味しており、これはレーザ光のスペクトルの広がりを評価する際には極めて有用な尺度になると考えられる。

Is the amount given by. The parenthesis <> means an ensemble average, which represents the average for many ensembles. Note that * means phase conjugation.
Here, the meaning of the quantity represented by the formula (2) will be considered. The original electric field of the laser beam is expressed by equation (1), which has a phase fluctuation θ _i (t) with the center frequency ω _i as the center. However, in the equation (2), it can be seen that the center frequency ω _i does not appear and is an amount related only to the phase fluctuation θ _i (t). That is, even if several ensembles of electric field amplitude are collected, even if the center frequency ω _i changes (drifts) between the ensembles, the effect does not appear in the equation (2), and one ensemble The phase fluctuation θ _i (t) (that is, fluctuation of the oscillation frequency) observed in is measured. Therefore, what is measured in the present invention means the fluctuation width of the phase or frequency when the laser beam oscillates for a certain time T, which is extremely useful for evaluating the spread of the spectrum of the laser beam. It is considered to be a scale.

  The frequency of the light emitted from the laser light source 1 to be measured is swept linearly for T seconds with respect to time by the frequency sweep device 2 as shown in FIG. The frequency sweep width is represented by ΔF. The frequency sweep device 2 can be realized by using, for example, a single sideband modulator described in Non-Patent Document 2. That is, the electric field amplitude of the light wave swept by the frequency sweeping device 2 is expressed by Expression (4).

周波数掃引されたレーザ光は、光分岐器３−１により２分岐され、一方は光サーキュレータ４を介して光ファイバに入射される。光ファイバ５内ではレイリー散乱と呼ばれる光散乱が生じ、その散乱光は光ファイバを逆方向に伝搬してサーキュレータ４に戻り、光合波器３−２に向かって進行する。分岐されたもう一方のレーザ光は、そのまま光合波器３−２に向かって進行する。光合波器３−２ではこれらのレーザ光が合波される。

The frequency-swept laser light is branched into two by an optical branching device 3-1, and one is incident on an optical fiber via an optical circulator 4. Light scattering called Rayleigh scattering occurs in the optical fiber 5, and the scattered light propagates in the opposite direction through the optical fiber, returns to the circulator 4, and travels toward the optical multiplexer 3-2. The other branched laser light travels toward the optical multiplexer 3-2 as it is. In the optical multiplexer 3-2, these laser beams are multiplexed.

This configuration is an application of the configuration of a reflection distribution measuring device called a coherent optical frequency domain reflectometer (hereinafter referred to as C-OFDR), which is also described in Non-Patent Document 2. If the round-trip time of light up to one reflection point z _m is τ _m , the ensemble E ″ _i (t) of the i-th optical electric field is scattered from this reflection point and is generated in the balance light receiving element 6 The current is expressed by the equation (5).

ここで複素数r_mは反射点z_mのレイリー反射係数であり、ランダムな値をとる確率変数である。
式（２）より、

Here, the complex number r _m is the Rayleigh reflection coefficient of the reflection point z _m and is a random variable that takes a random value.
From equation (2)

実際の光電流は反射点z_mの近傍の多数の反射点からの散乱光の和によって生じるから、観測される光電流の大きさは、

Since the actual photocurrent is generated by the sum of scattered light from a number of reflection points near the reflection point z _m , the magnitude of the observed photocurrent is

と表される。データ取得装置７は、式（７）で表される光電流を数値化して取得し、データとして格納する。
C-OFDRでは、光ファイバの距離z_mからの散乱光の強度は、式（７）で表現される光電流のパワースペクトルにより算出される。C-OFDRの距離分解能は、遅延時間τ_mに換算して1/ΔFであり、典型値として例えばΔF＝10GHzと仮定すると、距離分解能に相当する遅延時間差は100psとなり、これは今考えているレーザのコヒーレンス時間（典型的には１μsまたはそれ以上）と比べて非常に小さいものである。C-OFDRが観測する距離z_mにおける散乱光強度は、式（７）において、この距離分解能に相当する遅延時間差1/ΔFにわたる範囲で、ｍについて和を取ったものである。

It is expressed. The data acquisition device 7 obtains the photocurrent expressed by the equation (7) in numerical form and stores it as data.
In C-OFDR, the intensity of scattered light from the optical fiber distance z _m is calculated from the power spectrum of the photocurrent expressed by Equation (7). The distance resolution of C-OFDR is 1 / ΔF in terms of delay time τ _m. Assuming that ΔF = 10 GHz as a typical value, for example, the delay time difference corresponding to the distance resolution is 100 ps. It is very small compared to the laser coherence time (typically 1 μs or more). The scattered light intensity at the distance z _m observed by C-OFDR is the sum of m in the range over the delay time difference 1 / ΔF corresponding to this distance resolution in the equation (7).

  The power spectrum analyzer 8 calculates the power spectrum of the photocurrent. That is,

とすると、

Then,

式（７）の光電流のパワースペクトルは、式（１０）で表される。

The power spectrum of the photocurrent of Expression (7) is expressed by Expression (10).

制御装置１１により、上記の一連の測定は繰り返し行われる。この繰り返し測定の目的は、上記のパワースペクトルを多数取得することによって、そのアンサンブル平均

The control device 11 repeatedly performs the above series of measurements. The purpose of this repeated measurement is to obtain the ensemble average by acquiring a number of the above power spectra.

を求めることにある。よって繰り返しの回数は大きければ大きいほど精度よくアンサンブル平均を求めることができるが、現実的には測定回数には限度があり、許容される測定時間等の制約から決定されるものである。メモリ装置９には繰り返し測定されたパワースペクトラムが格納される。

Is to seek. Therefore, the larger the number of repetitions, the more accurately the ensemble average can be obtained. However, in practice, there is a limit to the number of measurements, and it is determined based on restrictions such as an allowable measurement time. The memory device 9 stores a power spectrum measured repeatedly.

Here, the relationship between the ensemble average of the power spectrum obtained in the above and the coherence function of the light source measured in the present invention will be considered.
First, from equation (9):

であることがわかる。よって、それらのアンサンブル平均は、適当な比例係数を除きお互いに等しい。すなわち、

It can be seen that it is. Thus, their ensemble averages are equal to each other except for an appropriate proportionality factor. That is,

Ｋは適当な比例係数であるが、以下の説明には影響しないため、以後１とおくことにする。このことより、光電流のアンサンブル平均は式（１３）のように表すことができる。

K is an appropriate proportional coefficient, but does not affect the following explanation, so it will be set to 1 hereinafter. From this, the ensemble average of the photocurrent can be expressed as in equation (13).

ここで、n_i,mはそのアンサンブル平均（ｉについての平均）が０であるような、相関をもたない複素数、すなわち

Where n _{i, m} is an uncorrelated complex number whose ensemble average (average for i) is 0, ie

である。
一方、γ(τ_m)はｉには依存しない、すなわち繰り返し測定の間で一定の値をとる複素数である。式（１３）を式（１１）に代入し、Ａの値は何であっても以下の説明に影響しないため、Ａを１とおくと、

It is.
On the other hand, γ (τ _m ) is a complex number that does not depend on i, that is, takes a constant value between repeated measurements. Substituting equation (13) into equation (11) and whatever the value of A does not affect the following description, if A is set to 1,

となる。そして、式（１４）より、

It becomes. And from equation (14),

であるから

Because

考えているτ_mの範囲ではコヒーレンス関数の絶対値はほとんど変化しないので、

Since the absolute value of the coherence function hardly changes in the range of τ _m we are thinking about,

となる。したがって、

It becomes. Therefore,

である。これを式（１５）に代入すると、

It is. Substituting this into equation (15) gives

となる。
次に、遅延τ_m＝０、すなわち距離０におけるパワースペクトルを計算する。遅延０においては完全にコヒーレントであるので、繰り返し測定の間に観測されるパワースペクトルは常に同じでｉには依存しない。従って、この場合はｉによらず、

It becomes.
Next, the power spectrum at delay τ _m = 0, that is, distance 0 is calculated. Since it is completely coherent at delay 0, the power spectrum observed during repeated measurements is always the same and does not depend on i. Therefore, in this case, regardless of i,

とおいてよい。したがって、式（１１）より、

It ’s okay. Therefore, from equation (11):

となる。
ここで式（１６）と式（１８）により求められた<a_i(τ_m)>と<a_i(0)>を比較する。これらのパワースペクトルは、ランダムな確率変数であるレイリー散乱係数r_mの関数である。すなわち、光ファイバの観測点近傍の複数のランダムな反射の干渉によって与えられ、その結果このパワースペクトルは遅延τ_mによりランダムに変動する。この変動は、いわゆるスペックルと呼ばれて知られている現象であり、式（１８）における右辺はこの変動を含むパワースペクトルを与えている。

It becomes.
Here, <a _i (τ _m )> and <a _i (0)> obtained by the equations (16) and (18) are compared. These power spectrum is a function of the Rayleigh scattering coefficient r _m is a random random variable. That is, it is given by interference of a plurality of random reflections in the vicinity of the observation point of the optical fiber, and as a result, this power spectrum varies randomly with the delay τ _m . This variation is a phenomenon known as so-called speckle, and the right side in the equation (18) gives a power spectrum including this variation.

  Next, looking at equation (16), the first term

は、式（１８）に類似していることがわかる。相違点は、まず全体が|γ(τ_m)|²倍になっている。次に括弧｛ ｝内の第２項にexp(jφ_mn)が付加されているが、これはr_mがもともとランダムな確率変数であるから、変動の統計量を変えるものではない。

Is similar to equation (18). The difference is that the entire first is | γ (τ _m) | is ^doubled. Then exp paragraph 2 in brackets {} (jφ _mn) but is added, this is because there is r _m is originally random random variables, does not change the statistic fluctuation.

  Also, the second term of equation (16)

については、完全にインコヒーレントな成分であり、干渉によるスペックルを生じることはなく、τ_mには依存しない均一なパワースペクトルを与えるだけである。
以上のことから、式（１６）の変動の振幅を見る限り、式（１８）の|γ(τ_m)|²倍になっていることがわかる。よって、両者の標準偏差を、σ₀とσ_τとすると、

Is a completely incoherent component, does not cause speckle due to interference, and only gives a uniform power spectrum independent of τ _m .
From the above, as far as the amplitude of the variation of formula (16), formula _{(18) | γ (τ m} ) | it can be seen that the ^doubled. Therefore, if the standard deviation of both is σ ₀ and σ _τ ,

または

Or

の関係があることがわかる。
以上の考察により、コヒーレンス関数解析装置１０は、遅延０の近傍のパワースペクトルの標準偏差と遅延τの付近での標準偏差とを解析する。これより式（１９）または式（２０）を用いて、任意の遅延τにおけるコヒーレンス関数の絶対値|γ(τ)|を求めることができる。さらに、その値が1/eに減ずるτを求めることにより、レーザ光のコヒーレンス時間を求めることも可能となる。

It can be seen that there is a relationship.
Based on the above consideration, the coherence function analysis apparatus 10 analyzes the standard deviation of the power spectrum near the delay 0 and the standard deviation near the delay τ. From this, the absolute value | γ (τ) | of the coherence function at an arbitrary delay τ can be obtained using Expression (19) or Expression (20). Further, by obtaining τ whose value is reduced to 1 / e, it is possible to obtain the coherence time of the laser beam.

As described above, the coherence function and the coherence time measuring method according to the present invention have the following advantages over the prior art.
First, it is possible to measure with an optical fiber length comparable to the coherence time, and if the coherence time is much longer than that, the measurement itself will be revealed by the measurement. It is possible to take measures such as replacing the fiber with another measurement. Therefore, the present invention can provide measurement results that are more reliable than the prior art.

Second, not only is the coherence time measured, but the entire absolute value of the coherence function is captured as a function of the delay time τ. Thereby, the property of the laser beam can be investigated in more detail.
Note that the present invention is not limited to the above-described embodiment as it is, and can be embodied by modifying the constituent elements without departing from the scope of the invention in the implementation stage. In addition, various inventions can be formed by appropriately combining a plurality of components disclosed in the embodiment. For example, some configurations may be deleted from all the components shown in the embodiment. Furthermore, constituent elements over different example embodiments may be combined as appropriate.

  DESCRIPTION OF SYMBOLS 1 ... Measuring laser light source, 2 ... Frequency sweep apparatus, 3-1 ... Optical branching device, 3-2 ... Optical multiplexer, 4 ... Optical circulator, 5 ... Optical fiber, 6 ... Balance type light receiving element, 7 ... Data acquisition Device: 8 ... Power spectrum analysis device, 9 ... Memory device, 10 ... Coherence function analysis device, 11 ... Control device.

Claims (4)

A laser beam coherence measurement method for measuring a coherence function γ (τ) of a laser beam to be measured which is a function of a delay time τ,
The frequency of the laser beam to be measured is swept linearly,
Branching the frequency-swept laser light into two systems;
One of the branched laser beams is incident on an optical fiber, and Rayleigh scattered light generated in the optical fiber is captured.
Combining the Rayleigh scattered light and the other branched laser light;
Detecting the photocurrent generated by the multiplexing;
Fourier transform the current value of the detected photocurrent to calculate its power spectrum,
Obtaining the ensemble average of the power spectrum as a function of the delay τ by repeatedly detecting the photocurrent and analyzing the power spectrum multiple times,
Calculating the standard deviation of the ensemble average delay τ of the power spectrum;
An optical laser coherence measurement method characterized in that an absolute value of a coherence function is obtained by utilizing the fact that this standard deviation is proportional to the absolute value of a coherence function at a delay τ.   2. The laser light coherence measurement method according to claim 1, wherein the coherence time is obtained with a delay τ at which the absolute value of the coherence function is 1 / e. A laser beam coherence measuring apparatus for measuring a coherence function γ (τ) of a laser beam to be measured which is a function of a delay time τ,
Frequency sweeping means for linearly sweeping the frequency of the laser beam to be measured;
Optical branching means for branching the frequency-swept laser light into two systems;
Rayleigh scattered light acquisition means for entering one of the branched laser lights into an optical fiber and taking in Rayleigh scattered light generated in the optical fiber;
Optical multiplexing means for multiplexing Rayleigh scattered light generated in the optical fiber and the other laser beam branched by the light branching means;
Photocurrent detection means for detecting a photocurrent generated by the multiplexing;
A power spectrum calculation means for calculating a power spectrum by Fourier-transforming a current value of the detected photocurrent;
Analyzing means for obtaining the absolute value of the coherence function of the laser beam based on the detection results and the calculation results of the photocurrent detection means and the power spectrum calculation means, respectively.
The analysis means obtains an ensemble average of the power spectrum as a function of the delay τ by repeatedly detecting the photocurrent and analyzing the power spectrum thereof, and calculates a standard deviation in the delay τ of the ensemble average of the power spectrum. An optical laser coherence measuring apparatus, characterized in that the absolute value of the coherence function is calculated by utilizing the fact that the standard deviation is proportional to the absolute value of the coherence function at the delay τ.   4. The laser light coherence measuring apparatus according to claim 3, wherein the analyzing unit obtains a coherence time with a delay τ in which an absolute value of the coherence function is 1 / e.

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