JP2008096147A - Apparatus and method for measuring polarization mode dispersion of optical fiber - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To accurately measure the polarization mode dispersion of even long optical fibers. <P>SOLUTION: The Stokes parameters are determined on the basis of back-scattered light to single incident polarized light having a single wavelength (S1). Parameters which determine a transfer function matrix of an optical fiber at a light angular frequency ω are computed for every section on the basis of a model expression taking into consideration the Stoke parameters and the depolarization of scattering body (S2). A first Jones matrix at the angular frequency ω and a second Jones matrix at an angular frequency ω+Δω are each determined for every section on the basis of the computed parameters (S3 and S4). The determined first Jones matrix and the determined second Jones matrix are corrected through the use of Jones matrices of adjacent sections and coefficients of correlation (S5). The PMD of any section of the optical fiber is computed on the basis of two Jones matrices acquired by the correction (S6). <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  The present invention relates to a technique for measuring polarization mode dispersion of an optical fiber, and relates to a technique for enabling accurate measurement even in an optical fiber having a simple configuration in a short time and a long distance.

  An optical fiber is used as a medium for transmitting information at high speed. However, in recent years, an increase in communication speed has been further demanded due to a rapid increase in Internet users and the like.

  In response to such a demand for higher speed, polarization mode dispersion (hereinafter referred to as PMD) of optical fibers cannot be ignored.

  PMD is caused by the fact that the cross-sectional shape of the core part for transmitting the light of the optical fiber is not a perfect circle at the time of manufacturing, or is distorted by receiving pressure from the outside, and propagates inside. This is a phenomenon in which the refractive index differs with respect to the polarization direction of light, and the propagation time differs for each polarization component.

  Due to the influence of PMD, for example, as shown in FIG. 12, when the optical pulse P is incident on one end of the optical fiber 1, the waveform of the optical pulse P ′ emitted from the other end of the optical fiber 1 is bimodal. The pulse width becomes wide, and the upper limit of the communication speed is determined by the spread of the pulse width.

  For this reason, when manufacturing an optical fiber or performing maintenance of an installed optical fiber, it is necessary to measure the PMD of the optical fiber.

  Many methods for measuring PMD have been proposed so far. Among them, the method based on the Jones matrix method is well known as one having high measurement accuracy and capable of automatic measurement.

  The Jones matrix method is a measurement method for obtaining an average value Δτ of group delay of orthogonal two polarization components with respect to an arbitrary wavelength as PMD of an optical device, and linearly polarized light having a predetermined wavelength is incident on one end side of the device under measurement. The process of obtaining the intensity of the polarization direction of the light emitted from the other end of the device under test is changed, the wavelength of the incident light is changed, and the polarization direction is changed to 0 degrees (reference), 45 degrees, and 90 degrees. The Jones matrix representing the input / output characteristics between both ends of the optical fiber is calculated for two wavelengths from the obtained intensity data, and the PMD is calculated using the PMD operator (see, for example, Non-Patent Document 1). ).

Teruhiko Kudo, Midori Iguchi, Masaru Masuda, and Takeshi Ozeki “Theoretical Basis of Polarization Mode Dispersion Equalization up to the Second Order.” Journal of LIGHTWAVE TECHNOLOGY, VOL.18 NO.4 APRIL 2000 pp.614-617.

  However, in this method for measuring PMD by measuring light incident on one end of an optical fiber and measuring the intensity of the polarization component of the light emitted from the other end of the optical fiber, for example, laying When measuring a used optical fiber, measurement equipment must be installed at both ends, which is inconvenient.

  Further, only the PMD value for the entire length from one end side to the other end side of the optical fiber can be obtained, and the PMD during that time cannot be known.

  In order to solve this, the applicant of the present invention enters a linearly polarized light pulse on one end side of the optical fiber, receives backscattered light of the optical fiber with respect to the incident light pulse on one end side of the optical fiber, Patent Document 1 proposes a method and an apparatus for measuring PMD for every section of an optical fiber, that is, PMD distribution, from intensity change characteristics of each polarization component of backward scattered light.

JP 2002-48680 A

  According to this method, the PMD distribution of the optical fiber can be obtained by measurement from one end of the optical fiber to be measured. For example, the PMD at each position with respect to the installed optical fiber can be accurately grasped.

  Further, in the following patent document 2, the applicant of the present application takes into account the depolarization of the scatterer, converts the conventional three incident linearly polarized light into one incident linearly polarized light, and considers the wavelength component in the fiber model. In other words, an optical fiber PMD measuring apparatus and a measuring method have been proposed which enable easy and more accurate measurement at one wavelength from the conventional measurement of two or more wavelengths.

JP 2004-333336 A

  However, as a result of actually measuring various optical fibers with the technique of Patent Document 2, a new problem has been found that, depending on the type of optical fiber, the measurement error increases as the distance increases.

  An object of the present invention is to improve this point and provide a polarization mode dispersion measuring apparatus and a measurement method capable of accurately measuring polarization mode dispersion even with an optical fiber having a long distance.

In order to achieve the above object, a polarization mode dispersion measuring apparatus for an optical fiber according to claim 1 of the present invention comprises:
An optical pulse generator (21) for emitting linearly polarized optical pulses at a predetermined wavelength;
The light pulse is incident on one end of the optical fiber to be measured, and backscattered light emitted from one end of the optical fiber to be measured is emitted from an optical path different from the incident optical path of the optical pulse. A directional coupler (25),
Stokes parameter measuring means (26, 31) for receiving four back-scattered light emitted from the directional coupler and measuring four Stokes parameters for each section of the measured optical fiber;
Based on the model equation of the measured optical fiber defined using a transfer function matrix including three parameters including a wavelength-dependent parameter and the four Stokes parameters, at least the elements of the transfer function matrix Parameter calculation means (32, 32 ') for calculating three included parameters for each section;
First Jones matrix calculating means (33, 33 ') for obtaining a first Jones matrix for each section based on the parameter calculated by the parameter calculating means;
First correction means (40) for correcting the first Jones matrix of each section calculated by the first Jones matrix calculation means using a first Jones matrix of a neighboring section and a correlation coefficient;
Second Jones matrix calculating means (34, 34 ') for obtaining a second Jones matrix for each section in a wavelength different from the predetermined wavelength based on the parameter calculated by the parameter calculating means;
Second correction means (41) for correcting the second Jones matrix of each section calculated by the second Jones matrix calculation means using a second Jones matrix of a neighboring section and a correlation coefficient;
Based on the first Jones matrix corrected by the first correction unit and the second Jones matrix corrected by the second correction unit, the polarization mode dispersion in an arbitrary section of the optical fiber to be measured Polarization mode dispersion calculating means (35) for calculating

An optical fiber polarization mode dispersion measuring apparatus according to claim 2 of the present invention is the optical fiber polarization mode dispersion measuring apparatus according to claim 1,
The parameter calculation means includes
Based on the model equation of the optical fiber to be measured defined by a transfer function matrix including three parameters and a scattering Mueller matrix including at least one parameter, and the four Stokes parameters. Thus, three parameters included in the elements of the transfer function matrix and at least one parameter included in the elements of the scattering Mueller matrix are calculated for each section.

An optical fiber polarization mode dispersion measuring apparatus according to claim 3 of the present invention is the optical fiber polarization mode dispersion measuring apparatus according to claim 1,
The parameter calculation means includes
Based on a model equation of the optical fiber to be measured defined by a transfer function matrix including three parameters including the wavelength dependency and one parameter representing suppression of the degree of polarization, and the four Stokes parameters. Thus, three parameters included in the elements of the transfer function matrix and one parameter representing the suppression of the polarization degree are calculated for each section.

The optical fiber polarization mode dispersion measuring method according to claim 4 of the present invention is
A linearly polarized optical pulse having a predetermined wavelength is incident on one end side of the optical fiber to be measured, and four Stokes parameters for each section from backscattered light emitted from the one end side by the optical fiber to be measured with respect to the optical pulse. Measuring (S1),
Based on the model equation of the measured optical fiber defined using a transfer function matrix including three parameters including a wavelength-dependent parameter and the four Stokes parameters, at least the elements of the transfer function matrix Calculating three included parameters for each section (S2);
Obtaining a first Jones matrix for each section based on the calculated parameters (S3);
Obtaining a second Jones matrix for each section at a wavelength different from the predetermined wavelength based on the calculated parameter (S4);
Correcting the determined first Jones matrix and second Jones matrix of each section using a Jones matrix and a correlation coefficient of neighboring sections (S5);
Calculating polarization mode dispersion in an arbitrary section of the measured optical fiber based on the corrected first Jones matrix and second Jones matrix (S6).

The optical fiber polarization mode dispersion measuring method according to claim 5 of the present invention is the optical fiber polarization mode dispersion measuring method according to claim 4,
Calculating the parameter comprises:
Based on the model equation of the optical fiber to be measured defined by a transfer function matrix including three parameters and a scattering Mueller matrix including at least one parameter, and the four Stokes parameters. Thus, three parameters included in the elements of the transfer function matrix and at least one parameter included in the elements of the scattering Mueller matrix are calculated for each section.

Moreover, the polarization mode dispersion measuring method for an optical fiber according to claim 6 of the present invention is the polarization mode dispersion measuring method for an optical fiber according to claim 4,
Calculating the parameter comprises:
Based on a model equation of the optical fiber to be measured defined by a transfer function matrix including three parameters including the wavelength dependency and one parameter representing suppression of the degree of polarization, and the four Stokes parameters. Thus, three parameters included in the elements of the transfer function matrix and one parameter representing the suppression of the polarization degree are calculated for each section.

  As described above, in the polarization mode dispersion measuring apparatus and measuring method of the present invention, a Stokes parameter is obtained from backscattered light with a single wavelength and a single incident polarized light, and the depolarization of the Stokes parameter and the scatterer is performed. The parameters for determining the transfer function matrix of the optical fiber at a predetermined frequency are calculated for each section on the basis of the model formula that takes into account the first Jones matrix at the predetermined frequency and the predetermined frequency based on the calculated parameter. The second Jones matrix at a different frequency from each other is obtained for each section, and the obtained first Jones matrix and second Jones matrix are corrected using the Jones matrix and the correlation coefficient of the neighboring sections, and From two Jones matrices obtained by correction of And calculates the PMD of any section of the Aiba.

  In this way, the optical fiber is accurately modeled in consideration of the depolarization of the scatterer, so that necessary parameters can be calculated only with a single wavelength and with a single incident polarization. Since the Jones matrix is corrected with the Jones matrix of the neighboring section and the correlation coefficient, the polarization mode dispersion of the arbitrary section can be measured in a short time and accurately even with a long optical fiber.

(First embodiment)
Hereinafter, embodiments of the present invention will be described with reference to the drawings.
First, a PMD measurement method according to an embodiment of the present invention will be described with reference to FIG.

  The flowchart of FIG. 1 shows a procedure for measuring PMD of an optical fiber to be measured by one-end measurement using an optical pulse, similar to the above-described Patent Document 1, and first, at a predetermined wavelength λ. A linearly polarized optical pulse P is incident on one end of the optical fiber to be measured, and the optical fiber to be measured is derived from the polarization component contained in the backscattered light emitted from the one end by the optical fiber to be measured. Four Stokes parameters for each section are obtained (S1).

Here, the Stokes parameter for each section is 45 for the polarization components I ₉₀ and I ₀ having an angle of 90 degrees with respect to the polarization components I ₀ and I _{0 of} 0 degrees as the reference from the backscattered light. the polarization component I ₄₅ and a circularly polarized wave component I _C having an angle in degrees, from the timing of the optical pulse P is incident on the measured optical fiber, for example, the light pulse reaches the far end of the optical fiber under test Thus, the observation is performed until the time necessary for the backscattered light from the far end to return to the incident end passes, and the calculation is performed based on the observation result.

  Then, based on the Stokes parameter for each obtained section, and an optical fiber model equation defined by a transfer function matrix including three parameters including a wavelength-dependent parameter and a scattering Mueller matrix including at least one parameter. Then, at least one parameter of the transfer function matrix and the scattering Mueller matrix at a predetermined wavelength λ in an arbitrary section of the optical fiber to be measured is calculated (S2).

  Note that a plurality of parameters can be calculated as the parameters of the scattering Mueller matrix by increasing the accuracy of the Stokes parameters. Here, although the case where there is one parameter will be described, a plurality of parameters may be calculated and used.

Hereinafter, the processes S1 and S2 will be described.
As shown in FIG. 2, assuming a section 1 ′ of a certain length Z of the optical fiber 1 to be measured, assuming that the one-way transfer function matrix from the incident end (left end in FIG. 2) to the scattering point (right end) is Tz. If the matrix obtained by converting this into a Mueller matrix is Mz, the Mueller matrix corresponding to the transposed matrix Tz ^t is Mz ′, and the scattering matrix is Rz, the round-trip Mueller matrix Fz is expressed as follows: be able to.

  Fz = Mz ′ · Rz · Mz (1)

  Here, the transfer function matrix T (ω) at the angular frequency ω of light is expressed by the following equation (2) using three parameters Φ, Θ, and Ψ.

  That is, the transfer function matrix T (ω) is expressed by a transfer function having three parameters Φ, Θ, and Ψ.

  Here, the parameter Φ represents the initial phase difference between the two orthogonal polarizations of the propagating light, the parameter Θ represents the rotation angle with respect to the main axis of the two orthogonal polarizations of the propagating light, and the parameter Ψ is the orthogonal 2 of the propagating light. It represents the phase difference between the polarized waves.

  The Rayleigh scattering matrix R is represented by the Mueller matrix of the following equation (3), assuming that the scatterer is an aggregate of particles having a symmetric surface.

Therefore, the scattering matrix (Müller) has the freedom of _two parameters a ₁ and a ₂ (however, as will be described later, the parameter a ₁ is known from the measurement data).

  The scattering matrix is expressed by the four Stokes parameters (I, Q, U, V) of the incident light and the Stokes parameters (I ', Q', U ', V') of the outgoing light, and the waveform obtained by observation. Can be compared. The relational expression at that time becomes the following expression (4).

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

  Moreover, following Formula (6) and (7) is obtained by Formula (4).

I ′ = a ₁ · I, Q ′ = a ₂ · Q (6)

I ₀ '+ I ₉₀ ' = a ₁ (I ₀ + I ₉₀ )
_{I 0 '-I 90' = a} 2 (I 0 -I 90)
...... (7)

  From the relationship of the above formula (7), the formula (4) can be expressed as the following formula (8) (R ′ is a scattering matrix).

Here, since the incident light is linearly polarized light, I ₀ = 1, I ₉₀ = I ₄₅ = I _C = 0, and from equation (7), it becomes known from the measurement data as a ₁ = I ₀ ′ + I ₉₀ ′, and is scattered The matrix R ′ eventually has a ₂ degrees of freedom.

As described above, the three parameters (Φ, Θ, Ψ) of the transfer function matrix T with respect to the measurement data of the scattered light returning from the point separated from the incident end by the distance Z among the measurement data of the four types of polarization components. ) And one parameter a _{2 of the} scattering Mueller matrix M can be determined, the transfer function matrix T (ω) described above can be calculated.

  However, since the transfer function matrix T (ω) has 2 rows and 2 columns, the scattering matrix R ′ has 4 rows and 4 columns, and thus cannot be calculated as it is.

  Therefore, the transfer function matrix T is replaced with a 4 × 4 Mueller matrix M as shown in the following equation (9).

  When replaced in this way, the elements of the transfer function matrix T and the scattering Mueller matrix M satisfy the following relationships (10-1) to (10-16).

M11
= (| T11 | ² + | T12 | ² + | T21 | ² + | T22 | ² ) / 2
(10-1)

M12
= (| T11 | ² − | T12 | ² + | T21 | ² − | T22 | ² ) / 2
(10-2)

M13
= −Re (T11 · T12 ^* + T22 · T21 ^* ) (10-3)

M14
= −Im (T11 · T12 ^* −T22 · T21 ^* ) (10-4)

M21
= (| T11 | ² + | T12 | ² − | T21 | ² − | T22 | ² ) / 2
...... (10-5)

M22
= (| T11 | ² − | T12 | ² − | T21 | ² + | T22 | ² ) / 2
...... (10-6)

M23
= -Re (T11 ^* T12 ^* -T22 ^* T21 ^* ) (10-7)

M24
= −Im (T11 · T12 ^* + T22 · T21 ^* ) (10-8)

M31
= -Re (T11 ^* T21 ^* + T22 ^* T12 ^* ) (10-9)

M32
= -Re (T11 ^* T21 ^* -T22 ^* T12 ^* ) (10-10)

M33
= Re (T11 · T22 ^* + T12 · T21 ^* ) (10-11)

M34
= −Im (T11 · T22 ^* + T21 · T21 ^* ) (10-12)

M41
= −Im (T21 · T11 ^* + T22 · T12 ^* ) (10-13)

M42
= −Im (T21 · T11 ^* −T22 · T12 ^* ) (10-14)

M43
= Im (T22 ^* T11 ^* -T12 ^* T12 ^* ) (10-15)

M44
= Re (T22 ^* T11 ^* -T12 ^* T21 ^* ) (10-16)

  When Expression (1) is expressed using this matrix M, the following Expression (11) is obtained.

  Fz = Mz ′ · Rz ′ · Mz (11)

  When this formula (11) is rewritten using the formulas (8) and (9), the following formula (12) is obtained.

The above equation (12) is a model equation defined for the optical fiber 1 to be measured, and by calculating this, four unknown parameters (Φ, Θ, Ψ, a ₂ ) can be calculated. Although not described in detail, the Marquatd method is used to calculate this parameter.

  Thereby, three parameters of the one-way transfer function matrix T and one parameter of the scattering matrix R ′ in the section 1 ′ of the measured optical fiber 1 are determined.

Also, as shown in FIG. 3, the entire length of the optical fiber 1 to be measured is divided into unit length sections, and the transfer function matrix from the input end to the (m−1) th section is T _m−1 , and the transmission to the mth section is performed. If the function matrix is T _m and the transfer function matrix in the m-th interval is t _m , the following relationship holds.

T _m = t _m · T _m−1 , t _m = T _m · T _m−1 ⁻¹ (13)

In other words, calculated to the transfer function matrix T _m-1 to m-1 th, if Motomare and the transfer function matrix T _m of a to m-th, the transfer function matrix t _m of the m-th interval from the above equation (13) it can.

When the transfer function matrix t is expressed using Φ _m , Θ _m , and Ψ _m as parameters of the m-th section, the following equation (14) is obtained.

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

  Next, parameters included in the elements of the transfer function matrix for light having different wavelengths are obtained by calculation.

That is, of the three parameters Φ _m , Ψ _m , and Θ _m that determine the elements of the transfer function matrix T, the two parameters Φ _m and Ψ _m other than Θ _m have wavelength dependence, and the incident light It is known that the angular frequency ω is expressed as follows.

Φ _m = k _{1, m} · ω, Ψ _m = k _{2, m} · ω (16)
Here, k ₁ and k ₂ are coefficients that relate the phase and the angular frequency.

  Therefore, the m-th first Jones matrix Tm (ω) is expressed as the following Expression (17) (S3).

  Further, the second Jones matrix T (ω + Δω) is calculated for each section by using equation (17) using ω + Δω obtained by changing ω by Δω (S4).

  By the above calculation, the transfer function matrix of an arbitrary section of the measured fiber 1 and the transfer function matrix up to an arbitrary section can be calculated, and the polarization mode dispersion of the arbitrary section can be calculated using these. .

  However, as a result of actually measuring various optical fibers, the applicant of the present application has found a new problem that a relatively large error occurs in a measurement result obtained for an optical fiber having a long distance.

  This error is expected to be due to the result of not considering the correlation of the transfer function matrix of the adjacent section, and in the present invention, by performing a correction calculation considering the correlation, an optical fiber having a long distance can be obtained. The polarization mode dispersion can be calculated with high accuracy (S5).

The Jones matrix T _m (ω) obtained from the parameters Φ _m , Ψ _m , and Θ _m obtained for each section by the above calculation has two solutions for Θ _m due to the difference in sign. At this time, using the Jones matrix up to the m + 1, m, m−1, and m−2nd sections and the correlation coefficient g representing the strength of correlation, ε is minimum in the following correction model equation (18). Θ _m ′ is determined as follows.

ε = | T _m (ω) −t _m (ω) T _m−1 (ω) | ²
+ G | T _{m + 1} (ω) −t _m (ω) T _m (ω) | ²
+ G | T _m−1 (ω) −t _m (ω) T _m−2 (ω) | ² (18)

Using the parameter Θ _m ′ determined in this way and the above-mentioned parameters Φ _m and Ψ _m in the above equation (17), the corrected first Jones matrix T _m as in the following equation (17 ′) is used. (Ω) ′ is sought.

Similarly, for the second Jones matrix T _m (ω + Δω), Θ _m ′ that minimizes ε is determined by the following correction model equation (19).

ε = | T _m (ω + Δω) −t _m (ω + Δω) T _m−1 (ω + Δω) | ²
+ G | T _{m + 1} (ω + Δω) −t _m (ω + Δω) T _m (ω + Δω) | ²
+ G | T _m−1 (ω + Δω) −t _m (ω + Δω) T _m−2 (ω + Δω) | ²
...... (19)

Using the parameter Θ _m ′ determined in this way and the above-mentioned parameters Φ _m and Ψ _m in the above equation (17), the corrected second Jones matrix T _m as in the following equation (17 ″) is used. (Ω + Δω) ′ is obtained.

  Here, the correlation coefficient g is a value determined by measuring a long optical fiber whose polarization mode dispersion value is known, and by correcting the Jones matrix of each section using this correction model formula, It has been confirmed that a long optical fiber whose polarization mode dispersion value is unknown can be accurately measured.

  And PMD is calculated using PMD operator D ((omega)) shown by following Formula (20) similarly to the said nonpatent literature 1 (S6).

  In addition, when calculating | requiring PMD distribution over the full length of the to-be-measured optical fiber 1, PMD for every area is calculated | required.

Next, an embodiment of a PMD measuring apparatus based on the above method will be described.
FIG. 4 shows the configuration of a PMD measuring apparatus 20 to which the present invention is applied.

  In FIG. 4, an optical pulse generator 21 excites a semiconductor laser 22 by a pulse signal Ep output from a pulse generator 23, emits an optical pulse P having a constant wavelength and width, and polarizes the optical pulse P. It enters the optical element 24 and emits a linearly polarized light pulse P ′ having a constant polarization direction.

  The direction biocoupler 25 makes the optical pulse P ′ emitted from the optical pulse generator 21 incident on one end side of the optical fiber 1 to be measured via the terminal 20a, and the optical pulse P ′ to be measured is measured. The backscattered light Ps emitted from one end side of the optical fiber 1 is emitted from an optical path different from the incident optical path of the optical pulse P ′.

  For example, as shown in FIG. 5, the backscattered light Ps attenuates (may be reflected in part and increases in intensity) with the passage of time (travel distance of the optical pulse), and the far end of the optical fiber. It attenuates greatly at.

  The polarization light receiving unit 26 constitutes the Stokes parameter measurement means of this embodiment together with the Stokes parameter acquisition means 31 described later, receives the backscattered light Ps emitted from the directional coupler 25, and backscatters it. A plurality of different polarization components included in the light Ps are extracted, and the intensity of each polarization component for each time is measured.

For example, as shown in FIG. 6, the polarization receiving unit 26 receives the backscattered light Ps emitted from the directional coupler 22 by the polarization separator 27 and receives the four types of polarization components I _{0 described above.} the ~I _C optically separated and extracted, and receives its each polarization component _I 0 ~I _C at each light receiver 28a to 28d, the light reception signal at a predetermined period by the a / D converter 29a~29d respectively It is sampled and converted into a digital value, and this is sent to the arithmetic processing unit 30 as signals I ₀ (k) to I _C (k) representing the intensity of each polarization component (for convenience, the same symbol as the polarization component is used). Output to series (k = 1, 2,...).

  The computer processing unit 30 includes a Stokes parameter acquisition unit 31, a parameter calculation unit 32, a first Jones matrix calculation unit 33, a second Jones matrix calculation unit 34, a first correction unit 40, and a second correction. Means 41 and PMD calculation means 35 are provided.

The Stokes parameter acquisition means 31 is an intensity signal I _{0 for} each polarization component output from the polarization receiving unit 26 until a predetermined time elapses from the timing when the optical pulse generation unit 21 emits the optical pulse P ′. (K) to I _C (k) are acquired, and from the acquired signal, each section of the optical fiber 1 to be measured (a section in which the length corresponding to the sampling period is minimized) according to the equation (5). Each Stokes parameter (I, Q, U, V) is obtained.

The parameters necessary for actual calculation are four parameters (I ₀ , I ₉₀ , U, V) including measured values I ₀ , I ₉₀ , as shown in the equations (8), (12). Here, the four parameters including the measured values are also referred to as Stokes parameters.

  The signal acquisition time is arbitrary depending on the section to be measured, but when measuring PMD over the entire length of the optical fiber 1 to be measured, the light pulse incident on the optical fiber 1 to be measured reaches the far end. The time required for the backscattered light from the far end to reach the incident end.

The parameter calculation means 32 is defined by a transfer function matrix M including three parameters (Φ, Ψ, Θ) and a scattering Mueller matrix R ′ including at least one parameter (a ₂ ), including parameters having wavelength dependency. Three parameters of the transfer function matrix T and at least one parameter of the scattering Mueller matrix based on the model equation (12) of the optical fiber to be measured and the four Stokes parameters acquired by the Stokes parameter acquisition means 31. Is calculated for each section.

That is, the calculation related to the model equation (12) shown in the PMD measurement method is performed to obtain four parameters (Φ, Ψ, Θ, a ₂ ) for each section.

  Based on the parameter obtained by the parameter calculation unit 32, the first Jones matrix calculation unit 33 calculates the first Jones matrix Tm (ω) for the predetermined wavelength λ, that is, the angular frequency ω, according to the equation (17). Calculate for each section.

  Further, the second Jones matrix calculating means 34 obtains the value at the angular frequency ω + Δω of the parameter having the wavelength dependence shown in the equation (16) among the parameters calculated by the parameter calculating means 32, and the parameter The second Jones matrix Tm (ω + Δω) for is calculated for each section according to the equation (17).

  Then, the first correction means 40 uses the first Jones matrix of each section calculated by the first Jones matrix calculation means 33 as a parameter using the first Jones matrix of the neighboring section and the correlation coefficient g. The second correction unit 41 determines the second Jones matrix of each section calculated by the second Jones matrix calculation unit 34, and calculates the second Jones matrix of the neighboring section. Correction is performed by determining and again calculating the parameter Θ ′ using the Jones matrix and the correlation coefficient g.

  The PMD calculating unit 35 uses the first Jones matrix Tm (ω) ′ and the second Jones matrix Tm (ω + Δω) ′ corrected by the first correcting unit 40 and the second correcting unit 41, for example, the non-patent document. As in the literature 1, using the PMD operator D (ω) shown in the equation (20), the polarization mode dispersion PMD (Δτ) up to an arbitrary section of the measured optical fiber or an arbitrary section is calculated. . In addition to the method using PMD operator D (ω) as described above, another known method can be used as the PMD calculation method.

Next, an example of the measurement result will be described. FIG. 7 shows an object to be measured by connecting an optical fiber A having a length of 500 m and a PMD value of 0.05 ps, an optical fiber B having a length of 500 m and a PMD value of 0.07 ps, and an optical fiber C having a length of 1000 m and a PMD value of 0.02 ps. The measurement results of PMD obtained from the above calculation from the optical fiber A side are shown. Note that the value of the correlation coefficient g used at this time is 10 ^−19.5 (= 3.162 × 10 ⁻²⁰ ).

  The dotted line in the figure is the theoretical value, and the broken line is the calculation result when the correction process is not performed. From this figure, it can be seen that the measurement result using the correction process has sufficient accuracy.

  FIG. 8 shows a measurement result when an optical fiber D having a length of 2000 m and a PMD value of 0.12 ps is added to the measurement target of FIG. 7, and the accuracy of the measurement result is sufficiently high even if the distance is further increased. I understand that.

  As described above, in the PMD measuring apparatus and the measuring method according to the first embodiment, the depolarization of the scatterer is taken into consideration for the optical fiber, and obtained from the backscattered light with a single wavelength and a single incident polarization 4. A model equation associated with various types of Stokes parameters is defined, and a parameter for determining a transfer function matrix of the optical fiber 1 at the angular frequency ω of light is calculated based on the model equation and the Stokes parameters obtained from the measurement data. The first Jones matrix Tm (ω) at the angular frequency ω is obtained based on the calculated parameters, the parameter for the angular frequency ω + Δω of the light is obtained by calculation, and the second Jones matrix Tm ( ω + Δω), and each Jones matrix is corrected in consideration of the correlation between neighboring sections , And it calculates the PMD of the optical fiber from the corrected Jones matrix.

  In other words, since the optical fiber 1 is accurately modeled in consideration of the depolarization of the scatterer, it is possible to calculate necessary parameters at a single wavelength and a single incident polarization. The time is only 1/6 of the conventional (Patent Document 1), and the Jones matrix is corrected in consideration of the correlation between neighboring sections. Therefore, the PMD in an arbitrary section of the optical fiber can be changed regardless of its length. Can be measured in a short time and with high accuracy.

(Second Embodiment)
In the above-described embodiment, it is assumed that the scatterer is an aggregate of particles having a plane of symmetry, but the scatterer can also be considered as an aggregate of particles having a spherical surface. At this time, a ₁ = a ₂ in the scattering matrix represented by the above-described equation (3), and can be represented by the Mueller matrix of the following equation (21).

Since the incident light as previously described linearly polarized light, a ₁ consists of measurement data and known. Therefore, the Mueller matrix R ″ of the above equation (21) is known.

Therefore, when the above equation (21) is applied to the above equation (12), the Stokes parameters (I ₀ ′, I ₉₀ ′, U ′, V ′) of the emitted light are the four Stokes parameters (I ₀ ) of the incident light. , I ₉₀ , U, V) and can be compared with the waveform obtained by observation. The relational expression at that time becomes the following expression (22).

  In the above equation (22), the Stokes parameter of the emitted light can be calculated by the following equation (23) using a parameter δ representing suppression of DOP (Degree of Polarization) (* indicates a conjugate complex number).

  A1, A2, A3, and A4 in the above equation (23) are elements of the Jones matrix J, and are expressed as a transfer function matrix T (ω) as shown in the following equation (24).

  Accordingly, when the scatterer is considered to be an aggregate of particles having a spherical surface, four parameters (Φ, Θ, Ψ, δ) including a parameter δ representing suppression of DOP are expressed by the Markut ( Marquatd) method can be applied and calculated.

  Here, in the first embodiment described above, the total length of the optical fiber 1 to be measured is the unit length, as described with respect to the expressions (13), (14), (15), (16), and (17) described above. When divided into sections, the m-th first Jones matrix Tm (ω) and the second Jones matrix Tm (ω + Δω) can be calculated using the parameters Φm, Θm, and Ψm of the m-th section from the input end. .

  Therefore, the parameters Φm, Θm, and Ψm of the mth section from the input end are obtained by the above-described equation (22). Similarly to the first embodiment described above, the m-th first Jones matrix Tm (ω) and the second Jones matrix Tm (ω + Δω) are calculated, and the corrected first Jones matrix Tm ( ω) ′ and the corrected second Jones matrix Tm (ω + Δω) ′ are obtained to calculate PMD. Since this part is the same as that of the first embodiment described above, description thereof is omitted.

  The flowchart of FIG. 9 shows the procedure for measuring the PMD of the optical fiber under measurement in the second embodiment of the present invention. The same steps as those in the flowchart of FIG. 1 are denoted by the same reference numerals, and description thereof is omitted.

  When the Stokes parameter for each section is obtained in step S1, the Stokes parameter, a transfer function matrix including three parameters (Φ, Ψ, Θ) including parameters having wavelength dependence, and one parameter representing suppression of the polarization degree. Based on the model equation (22) of the optical fiber to be measured defined by δ, three parameters of the transfer function matrix T in an arbitrary section of the optical fiber to be measured and one parameter representing suppression of the degree of polarization are obtained. Calculate (S2 ').

  Based on these calculated parameters, the first Jones matrix T (ω) for the predetermined wavelength λ, that is, the angular frequency ω, is calculated for each section according to the equation (17) (S3 ′).

  Further, based on these calculated parameters, the second Jones matrix T (ω + Δω) is calculated for each section according to the equation (17) using ω + Δω obtained by changing ω by Δω (S4 ′). . Since the subsequent procedure is the same as that of the first embodiment, description thereof is omitted.

  FIG. 10 shows a configuration of a PMD measuring apparatus 20 ′ to which the second embodiment of the present invention is applied. Parts having the same functions as those of the PMD measuring apparatus 20 shown in FIG.

  The parameter calculating means 32 'includes the light to be measured defined by a transfer function matrix including parameters having wavelength dependency and including three parameters (Φ, Ψ, Θ) and one parameter δ representing suppression of polarization degree. Based on the fiber model equation (22) and the four Stokes parameters acquired by the Stokes parameter acquisition means 31, three parameters of the transfer function matrix T and one parameter representing the suppression of the degree of polarization are obtained for each section. calculate.

  Based on the parameter obtained by the parameter calculation means 32 ′, the first Jones matrix calculation means 33 ′ obtains the first Jones matrix Tm (ω) for the predetermined wavelength λ, that is, the angular frequency ω, by the above equation (17). The calculation is performed for each section.

  The second Jones matrix calculating means 34 ′ obtains the value at the angular frequency ω + Δω of the parameter having the wavelength dependence shown in the equation (16) among the parameters obtained by the parameter calculating means 32 ′, and the parameter The second Jones matrix Tm (ω + Δω) for is calculated for each section according to the equation (17). Since the configuration of other parts is the same as that of the first embodiment, description thereof is omitted.

  FIG. 11 shows an example of the measurement result of the second embodiment. FIG. 11 shows an optical fiber E having a length of 2000 m and a PMD value of 0.16 ps, an optical fiber D having a length of 2000 m and a PMD value of 0.12 ps, an optical fiber A having a length of 500 m and a PMD value of 0.14 ps, a length of 500 m, The measurement result of PMD obtained by the above calculation from the optical fiber E side is shown by connecting an optical fiber B having a PMD value of 0.1 ps and an optical fiber C having a length of 1000 m and a PMD value of 0.02 ps.

  The dotted line in the figure is a theoretical value, and it can be seen from this figure that the measurement result of the second embodiment has sufficient accuracy.

  As described above, in the PMD measuring apparatus and the measuring method according to the second embodiment, the scatterer is considered as an aggregate of particles having a spherical surface, and four parameters including the parameter δ representing suppression of DOP are calculated. The m-th interval parameter is obtained from the first m-th interval, the m-th first Jones matrix Tm (ω) and the second Jones matrix Tm (ω + Δω) are calculated, and the corrected first Jones matrix Tm (ω) ′ is calculated. And the corrected second Jones matrix Tm (ω + Δω) ′, and PMD is calculated.

  This makes it possible to calculate the necessary parameters for a single wavelength and a single incident polarization. The time required for the measurement can be shorter than before, and the Jones matrix can be calculated in consideration of the correlation of neighboring intervals. Since the correction is performed, PMD in an arbitrary section of the optical fiber can be measured accurately in a short time regardless of the length.

  The correction model equations (18) and (19) of the above embodiment are merely examples, and do not limit the present invention.

  In each of the above embodiments, the front and rear two sections are used for correction. However, it may be possible to perform correction using two or more neighboring sections before and after. In that case, a smaller correlation coefficient may be used for a section that is separated from the section to be obtained.

The flowchart which shows the procedure of the polarization mode dispersion | distribution measuring method of the 1st Embodiment of this invention. Diagram of optical fiber model The figure for explaining the method of obtaining the polarization mode dispersion of the arbitrary section The figure which shows the structure of the polarization mode dispersion measuring apparatus of embodiment of this invention. The figure which shows an example of the intensity | strength change with respect to time of backscattered light The figure which shows the structural example of the principal part of embodiment. The figure which shows an example of the measurement result of embodiment The figure which shows another example of the measurement result of embodiment The flowchart which shows the procedure of the polarization mode dispersion | distribution measuring method of another embodiment. The figure which shows the structure of the polarization mode dispersion measuring apparatus of another embodiment. The figure which shows an example of the measurement result of another embodiment Diagram for explaining the effect of polarization mode dispersion

Explanation of symbols

  DESCRIPTION OF SYMBOLS 1 ... Optical fiber to be measured, 20, 20 '... Polarization mode dispersion (PMD) measuring device, 21 ... Optical pulse generator, 25 ... Directional coupler, 26 ... Polarization receiver, 30 ... Arithmetic processing unit 31 ... Stokes parameter acquisition means 32, 32 '... parameter calculation means 33, 33' ... first Jones matrix calculation means 34, 34 '... second Jones matrix calculation means 35... Polarization mode dispersion (PMD) calculation means 40... First correction means 41.

Claims (6)

An optical pulse generator (21) for emitting linearly polarized optical pulses at a predetermined wavelength;
The light pulse is incident on one end of the optical fiber to be measured, and backscattered light emitted from one end of the optical fiber to be measured is emitted from an optical path different from the incident optical path of the optical pulse. A directional coupler (25),
Stokes parameter measuring means (26, 31) for receiving four back-scattered light emitted from the directional coupler and measuring four Stokes parameters for each section of the measured optical fiber;
Based on the model equation of the measured optical fiber defined using a transfer function matrix including three parameters including a wavelength-dependent parameter and the four Stokes parameters, at least the elements of the transfer function matrix Parameter calculation means (32, 32 ') for calculating three included parameters for each section;
First Jones matrix calculating means (33, 33 ') for obtaining a first Jones matrix for each section based on the parameter calculated by the parameter calculating means;
First correction means (40) for correcting the first Jones matrix of each section calculated by the first Jones matrix calculation means using a first Jones matrix of a neighboring section and a correlation coefficient;
Second Jones matrix calculating means (34, 34 ') for obtaining a second Jones matrix for each section in a wavelength different from the predetermined wavelength based on the parameter calculated by the parameter calculating means;
Second correction means (41) for correcting the second Jones matrix of each section calculated by the second Jones matrix calculation means using a second Jones matrix of a neighboring section and a correlation coefficient;
Based on the first Jones matrix corrected by the first correction unit and the second Jones matrix corrected by the second correction unit, the polarization mode dispersion in an arbitrary section of the optical fiber to be measured Polarization mode dispersion measuring device for optical fiber, comprising polarization mode dispersion calculating means (35) for calculating. The parameter calculation means includes
Based on the model equation of the optical fiber to be measured defined by a transfer function matrix including three parameters and a scattering Mueller matrix including at least one parameter, and the four Stokes parameters. The polarization of an optical fiber according to claim 1, wherein three parameters included in the elements of the transfer function matrix and at least one parameter included in the elements of the scattering Mueller matrix are calculated for each section. Modal dispersion measuring device. The parameter calculation means includes
Based on a model equation of the optical fiber to be measured defined by a transfer function matrix including three parameters including the wavelength dependency and one parameter representing suppression of the degree of polarization, and the four Stokes parameters. The polarization mode dispersion of an optical fiber according to claim 1, wherein three parameters included in the elements of the transfer function matrix and one parameter representing suppression of the polarization degree are calculated for each section. measuring device. A linearly polarized optical pulse having a predetermined wavelength is incident on one end side of the optical fiber to be measured, and four Stokes parameters for each section from backscattered light emitted from the one end side by the optical fiber to be measured with respect to the optical pulse. Measuring (S1),
Based on the model equation of the measured optical fiber defined using a transfer function matrix including three parameters including a wavelength-dependent parameter and the four Stokes parameters, at least the elements of the transfer function matrix Calculating three included parameters for each section (S2);
Obtaining a first Jones matrix for each section based on the calculated parameters (S3);
Obtaining a second Jones matrix for each section at a wavelength different from the predetermined wavelength based on the calculated parameter (S4);
Correcting the determined first Jones matrix and second Jones matrix of each section using a Jones matrix and a correlation coefficient of neighboring sections (S5);
Calculating polarization mode dispersion of an arbitrary section of the measured optical fiber based on the corrected first Jones matrix and second Jones matrix (S6). Measuring method. Calculating the parameter comprises:
Based on the model equation of the optical fiber to be measured defined by a transfer function matrix including three parameters and a scattering Mueller matrix including at least one parameter, and the four Stokes parameters. 5. The polarization mode of an optical fiber according to claim 4, wherein three parameters included in the elements of the transfer function matrix and at least one parameter included in the elements of the scattering Mueller matrix are calculated for each section. Dispersion measurement method. Calculating the parameter comprises:
Based on a model equation of the optical fiber to be measured defined by a transfer function matrix including three parameters including the wavelength dependency and one parameter representing suppression of the degree of polarization, and the four Stokes parameters. 5. The polarization mode dispersion measurement of an optical fiber according to claim 4, wherein three parameters included in the elements of the transfer function matrix and one parameter representing suppression of the polarization degree are calculated for each section. Method.

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