KR100725211B1 - An apparatus for measuring a differential mode delay of a multimode waveguide and the measuring method thereof - Google Patents

Abstract

A multi-mode differential time delay measurement device of a multi-mode wave guide and a measurement method thereof are provided to measure interference patterns caused by displacement differences of light passing through the wave guide and a reference light path by configuring an interference system using a light source and a wavelength component photo detector, thereby measuring differential time delay between modes. A light source(10) is in certain width. A light distributor(20) inputs light emitted from the light source(10), and distributes the light to a multi-mode wave guide and a reference light path. A reflector(30) reflects an optical signal passing through the reference light path to the distributor(20). A wavelength component detector(40) detects signals by interference which are generated by a combination of an optical signal returning from a cut surface of the wave guide and the optical signal returning by being reflected from the reflector(30), according to each optical strength by wavelength component, and sends the detected signals to a computer(50). The computer(50) is mounted with a program consisting of a frequency component conversion process of converting the detected signals into frequency components, a process of analyzing interference patterns into differential time mode delay information, and a process of displaying measured results.

Description

An apparatus for measuring a differential time delay between multiple modes of a multimode waveguide and a method for measuring the differential mode delay of a multimode waveguide and the measuring method

1 to 5 are views showing the configuration of the differential time delay measuring device between modes of the multi-mode waveguide according to an embodiment of the present invention,

2 is a view showing an embodiment of an inter-mode differential time delay measurement apparatus of a multimode waveguide composed of an optical fiber interferometer of the present invention.

3 and 4 are schematic diagrams of a differential time delay measurement apparatus between modes in a multi-mode waveguide using transmitted light analysis using a Mahgender-type interferometer composed of optical fibers according to another embodiment of the present invention.

5 is a schematic diagram of a differential time delay measurement apparatus between modes in a multimode mode waveguide using transmitted light analysis using a Mahgender-type interferometer composed of an optical system in another embodiment of the present invention.

Figure 6a, 6b is a graph showing the light intensity for each wavelength component detected by the wavelength component photodetector measured in the differential time delay between modes of the multi-mode waveguide according to the present invention.

7A and 7B are waveform diagrams showing a mode differential delay time distribution in the present invention.

The present invention enables to measure the delay distribution between modes of a multimode optical fiber, and more specifically, the time difference between modes in a multimode waveguide simply and accurately by using an interferometer having a wide light source and a wavelength component photodetector. The present invention relates to a differential time delay measuring device between multimode optical waveguides for measuring delay.

Recently, many researches on next-generation optical networks in the local area network have been conducted.

Among them, optical transmission using an optimized vertical cavity surface emitting laser (VCSEL) in the 850 nm region is drawing attention.

In this optical transmission, there may be a problem that the optical signal is deformed according to the occurrence of the differential time delay between the waveguide modes, in which the mode between the modes in the characteristic analysis of the MMF (multimode optical fiber) which is the main medium of the optical transmission Differential mode delay (DMD) is an important factor in determining the characteristics of an optical fiber.

In addition, photonic crystal fiber (PCF), which has a multi-mode characteristic, is being applied to optical devices, and researches on 0-PCB (Optical printed circuit board) and polymer type optical pointed circuit boards are being actively conducted.

Differential time delay measurement method in multimode optical waveguide

(a). Measurement method in time domain using optical short pulse and sampling oscilloscope,

 (b). There is a measurement method in the frequency domain using the recently developed optical frequency domain reflectometry (OFDR).

The already standardized measurement method in the time domain first applies an optical short pulse to an optical fiber.

The width of the applied optical pulse is divided after passing through the optical fiber, and after passing through the measurement optical fiber using a sampling oscilloscope, the differential time delay between modes is measured by observing the spread of the optical pulse width.

This method is simple but uses expensive equipment such as expensive optical shoot pulses and sampling oscilloscopes, which leads to an increase in production cost during the fiber production process.

Light pulses, which are used as measurement light sources, are difficult to manufacture, and are difficult to obtain by the customers on the production site.

The device also has difficulty in improving resolution.

Reducing the width of the optical pulse, which determines the resolution of the device, increases the wavelength component of the optical pulse in the wavelength region, which means that the shorter the optical pulse in the time domain, the inverse of the time domain. This is because the frequency component, that is, the component of the wavelength component, becomes wider. The wider optical pulse thus increases the pulse spreading effect due to the color dispersion effect in the measurement optical waveguide, thereby reducing the resolution of the measurement system.

It is also impossible to measure the mode distribution of short length multimode optical waveguides.

    On the other hand, the measurement method using OFDR can measure the differential time delay of the optical fiber with a relatively higher resolution than the time domain measurement method, but it still requires the use of expensive frequency-converted lasers and the measurement of short optical waveguides and multiple measurements within a few meters. The mode distribution of the mode device cannot be measured. Since the inter-mode delay time should be within 0.2ps / m for commercially available multi-mode fiber, the minimum length to measure the inter-mode delay time is 100ps / (0.2ps / m) = 500m when using a typical 100ps laser. This is because the mode distribution measurement is not possible with multimode optical waveguides with short lengths of less than that.

Therefore, there is a need for a differential time delay measurement method that is inexpensive and easily used in a production site and that can be measured by a short length multimode waveguide.

The present invention relates to a method for measuring differential time delay in a multimode waveguide at a simple and low cost. The present invention relates to an apparatus capable of measuring differential time delay between modes in a short length multimode waveguide.

The present invention is to solve the above problems, to improve the resolution, low cost and to measure the differential time delay between modes in the multi-mode waveguide that is readily available in the production site,

The present invention constructs an interferometer using a light source having a wide light source and a wavelength component photodetector to measure the interference fringe caused by the displacement difference of the light passing through the reference optical path and the multimode waveguide, and Fourier transforms it through a simple numerical analysis on a computer. An object of the present invention is to provide a differential mode delay time measurement apparatus between multimode waveguides capable of measuring differential time delays.

The present invention,

A light source with a width,

Light distribution means for distributing the light emitted from the light source as a multimode waveguide and a reference optical path;

Reflecting means for reflecting the optical signal passing through the reference optical path to the light distribution means;

The optical signal returned from the cutting plane of the multi-mode waveguide and the optical signal reflected by the reflecting means after passing through the air path, which is the reference optical path, are combined by the optical distribution means. A wavelength component detector for detecting and transmitting to a computer

A frequency component conversion process for converting a detection signal according to the light intensity input from the wavelength component detector into a frequency component, a process for decomposing the interference fringe changed through the Fourier transform from the changed frequency component into differential time mode delay information, and the side thereof And a computer equipped with a program including a process for displaying predetermined results in various forms.

Hereinafter, a configuration and an operation according to an embodiment of the present invention will be described in detail with reference to the accompanying drawings.

FIG. 1 is a schematic diagram illustrating an apparatus for measuring differential time delay between modes in a multimode waveguide according to an exemplary embodiment of the present invention.

A light source 10 having a width,

An optical splitter 20 for distributing the light emitted from the light source as a multi-mode waveguide and a reference optical path;

A reflector 30 for reflecting the optical signal passing through the reference optical path to the optical splitter 20,

The optical signal returned from the cutting plane of the multi-mode waveguide and the optical signal reflected by the reflector 30 after passing through the air path, which is the reference optical path, are combined by the optical splitter 20 to generate signals of interference generated by wavelength components, respectively. A wavelength component detector 40 for detecting the light intensity of the light and transmitting the same to the computer 50;

A frequency component conversion process for converting a detection signal according to the light intensity input from the wavelength component detector 40 into a frequency component, a process for decomposing the interference fringe changed through the Fourier transform from the changed frequency component into differential time mode delay information; And a computer 50 equipped with a program including a process for displaying the measured results in various forms.

Such an embodiment of the present invention,

Light is emitted from the light source 10 having the width to the optical interferometer.

The emitted light is applied to the multimode waveguide and the reference optical path through the optical splitter 20.

The light applied in the two paths is reflected at the reflecting portions at the ends of the two paths. The light is reflected at the cutting surface of the multimode waveguide and the light is reflected by the reflector 30 after passing through the air path, which is the reference light path. The signals are then combined in the optical splitter 20 to cause interference.

The signal causing the interference is applied to the wavelength component photodetector 40, and the wavelength component detector 40 detects the optical signal according to each light intensity for each wavelength component.

The wavelength component photodetector 40 includes an optical spectrum analyzer, a spectrum meter, and an optical spectrometer.

The optical signal detected by the wavelength component photodetector 40 is sent to a computer and converted into frequency components through a simple numerical analysis process by the computer, and the changed interference pattern is decomposed into differential time mode delay information through Fourier transform.

Such measurement results are output to the display of the computer 50 in various forms.

In this case, in order to maximize the interference fringe, a PC (Polarization Controller) 60 may be included in the reference optical path.

Maximizing the interference fringe means that the interference phenomenon is maximized, and means the method of equalizing the polarization state of the light passing through the reference light path and the multi-mode light path.

It is also possible to install a transfer device to convert the relative length of the reference light path from the reference light path.

The reason for configuring the transfer device for moving the reference light path as described above is that the mode distribution measured by moving the reference light path can be relatively adjusted.

In the case of measuring objects with a relatively small mode distribution, for example, when measuring signals of about several ps / m or about 0.1 ps / m, the interference fringes have information of the DC region. The frequency component is zero when the Fourier transform is performed.

However, the information of the actual DC region is not only 0 but also a signal within a sub point order.

Therefore, when measuring the mode distribution in a very small area where the DC level signal and the current measurement signal are difficult to decompose, the mode distribution is relatively adjusted to measure in another mode distribution area.

Such methods have generally been used to measure the longitudinal distribution of properties of biological samples (tooth, skin epidermis, cells).

FIG. 2 is a diagram illustrating a mode difference time delay measuring apparatus of a multimode waveguide composed of the optical fiber interferometer of the present invention as shown in FIG.

In FIG. 2, a PC (Polarization Controller) and a transfer device (not shown) for adjusting the length of the reference optical path are described.

The light source 10 having the wavelength component outputs light.

The incident light is applied to the optical fiber splitter, and the applied light is transmitted through the optical fiber splitter 21 by dividing it into a multimode waveguide for measurement and a reference optical path.

The transmitted light is reflected at the end section of the multimode optical waveguide, and is reflected by the reflector of the reference optical path and concentrated again by the optical fiber distributor 21.

The collected light meets in the optical fiber splitter 21 to cause interference and is detected by the wavelength component of the wavelength component photodetector 40.

The detected optical signal is sent to the computer and shows the mode delay time information between the modes of measurement by the stored program.

In this case, the provided PC 60 allows the interference phenomenon of the interference light signal detected by the wavelength component photodetector 40 to occur to the maximum.

The reference path is movable and this movement is measured on the measured multimode waveguide.

An offset can be given to the entire time mode delay measurement.

However, even if an offset is given to the entire time mode delay measurement amount, the measurement amount between the time mode delay amounts between the measured modes does not change.

3 is a schematic diagram of an apparatus for measuring differential time delay between modes in a multi-mode waveguide using transmitted light analysis using a Mahzender interferometer composed of optical fibers according to another embodiment of the present invention.

The embodiment of the present invention shown in FIG. 3 configures two optical fiber splitters and distributes them to a reference optical path and a multimode waveguide, and receives signals passing through the reference optical path and the multimode waveguide through another optical fiber optical splitter. One configuration is shown.

A first optical fiber optical splitter 21 for distributing the light source 10 having a width and the light emitted from the light source 10 into a multimode waveguide and a reference optical path;

A second optical fiber optical splitter 22 which receives the optical signal passing through the multi-mode waveguide and the optical signal passing through the air path, the reference optical path, and optically couples the optical signal;

A wavelength component detector 40 which detects a signal due to interference generated by the second optical fiber optical splitter 22 according to each optical intensity and transmits the signal to a computer;

A frequency component conversion process for converting a detection signal according to the light intensity input from the wavelength component detector 40 into a frequency component, a process for decomposing the interference fringe changed through the Fourier transform from the changed frequency component into differential time mode delay information; A computer (50) equipped with a program including a process for displaying the measured results in various forms;

PC (Polarization controller) 60 included in the reference optical path to maximize the interference fringe,

And a conveying device for converting the relative lengths of the reference light paths.

Embodiment of the present invention shown in Figure 3 having such a configuration,

The light source 10 having the wavelength component outputs light.

Light incident on the first optical fiber optical splitter 21 is transmitted through two paths through the first optical fiber optical splitter 21.

This light passes through the multimode waveguide, a measurement sample, and into the air, the reference light path.

Light passing through the two paths similarly meets the second optical fiber optical splitter 22 to cause interference.

Interfering light is detected by the wavelength component photodetector 40.

The detected optical signal is sent to the computer 50 and shows mode delay time information between modes of the measurement target by the stored program.

At this time, the provided PC 60 causes the interference phenomenon of the interference light signal detected by the wavelength component photodetector to occur to the maximum.

In this case, a light source 10 having a width of a wavelength component is used.

The reference optical path can be moved by the feeder, and this movement can give an offset relative to the measured time mode delay measurement in the measured multimode waveguide.

However, as described above, the measured amount between the time mode delays between the measured modes does not change.

Figure 4 shows another embodiment of the present invention, and shows a schematic diagram of the differential time delay measuring device between modes in a multi-mode waveguide using the transmitted light analysis using the Mahgender-type interferometer consisting of optical fibers.

In this case, instead of the optical fiber optical splitter used in another embodiment of the present invention shown in FIG. 3, the optical optical splitter is used.

The light source 10 having the wavelength component outputs light.

Light incident on the optical splitter 23 splits into two paths through the optical splitter 23.

This light passes through the light path with the multimode waveguide as the measurement sample and into the air as the reference light path.

At this time, the light passing through the reference light path is incident to the optical splitter 24 through the reflector 31.

Both paths pass through the light splitter 24 equally and cause interference.

Interfering light is detected by the wavelength component photodetector 40.

The detected optical signal is sent to the computer and shows the mode delay time information between the modes of measurement by the stored program.

At this time, the provided PC 60 causes the interference phenomenon of the interference light signal detected by the wavelength component photodetector 40 to occur to the maximum.

At this time, the light source 10 used is a light source 10 having a wavelength component width.

The reference light path is movable and this movement can give an offset relative to the measured time mode delay measurement in the measured multimode waveguide.

However, the measurement amount between the time mode delays between the measured modes does not change.

FIG. 5 shows a schematic diagram of a differential time delay measurement apparatus between modes in a multimode mode waveguide using transmitted light analysis using a Mahzender interferometer composed of an optical system.

Such an embodiment of the present invention consists of using an optical splitter for an optical system instead of the optical splitter used in another embodiment of the present invention of FIG. 3.

The light source 10 having the wavelength component outputs light.

Light incident on the optical first splitter 25 splits into two paths through the first splitter 26.

Light is condensed by the lens and passed through the multimode waveguide, a measurement sample, and in the air, the reference light path.

The light passing through the two paths is similarly collected by the lens after passing through the second light splitter 26 and detected by the wavelength component photodetector 40.

Interfering light is detected by the wavelength component photodetector 40.

The detected optical signal is sent to the computer and shows the mode delay time information between the modes of measurement by the stored program.

In this case, the provided PC 60 maximizes the interference phenomenon of the interference light signal detected by the wavelength component photodetector.

At this time, the light source 10 used is a light source 10 having a wavelength component width.

The reference path is movable and this shift can give an offset relative to the measured time mode delay measurement in the measured multimode waveguide.

However, the measurand between time mode delays between the measured modes does not change.

Figure 6a is a graph showing the light intensity for each wavelength component detected by the wavelength component photodetector measured in the differential time delay between modes of the multi-mode waveguide according to the present invention.

Using the mathematical program created in the computer 50, the optical spectrometer displayed for each wavelength component converts the frequency-specific fractional light intensity and then outputs a differential time delay result value between modes of the waveguide through a Fourier transform.

The process of outputting the differential time delay result value of the waveguides formed by the computer's mathematical program is described with the following equation.

The excited modes in the optical waveguide pass through the optical fiber at different speeds in time, so the wavelength components are detected differently.

The light intensity of the signal of the interference light measured in the frequency domain may be expressed by Equation 1 below.

Where N is the number of optical fibers excited in the multimode waveguide,

는 측정에 사용된 폭이 넓은 광섬유의 스펙트럼,

Is the spectrum of the broad optical fiber used for the measurement,

는 m번째로 여기된 모드의 상대적인 광파워,

Is the relative optical power of the m th excited mode,

은 기준광신호와 m번째로 여기된 신호사이의 상대적인 위상,

Is the relative phase between the reference light signal and the m th excited signal,

<> Is the time domain average value.

Again, this phase can be expressed as Equation 2 below.

은 측정된 다중모드도파로의 길이, here,

Is the length of the measured multimode waveguide,

는 기준광경로의 시간지연,

Is the time delay of the reference light path,

은 m번째로 여기된 모드들의 전파속도이다.

Is the propagation velocity of the m th excited modes.

Here, the m th propagation speed can be expressed again by Taylor expansion (Equation 3).

고정된 주파수 영역에서 색분산(

)을 무시하면 다음의 수학식 4와 같이 표현된다.At this time,

Color dispersion in a fixed frequency domain

Ignoring) is expressed as Equation 4 below.

은 상수 ,

은 m 번째 여기된 모드의 그룹지연 속도이다. only,

Is a constant,

Is the group delay rate of the m th excited mode.

The Fourier transformed value is used as in Equation 5 below.

로 표현이 되며, 이 피크(peak)는 다중모드광도파로에서의 여기된 m번째의 시간차등지연에 해당하는 값이다. Where * is a standard convolution operator, G (t) is the Fourier transform of the measured light source, and each peak in Eq.

This peak is the value corresponding to the excited mth time difference delay in the multimode optical waveguide.

FIG. 6B is an enlarged graph of the graph of FIG. 6A and shows an enlarged view of 1550 nm to 1555 nm.

This graph shows a modulated graph in which the modulated width includes the differential time delay information between modes.

In order to facilitate the analysis, a multimode waveguide having only a few modes is fabricated and measured.

FIG. 6A is a graph measuring three modes of a multimode waveguide, and FIG. 6B is a graph measured after removing one higher-order mode with a value measured by the same measurement as that of FIG. 6A.

7A and 7B illustrate the mode differential delay time distribution according to the present invention. When the graph of the wavelength component of FIG. 6A is changed to frequency components and Fourier transform is performed, the waveform of FIG. 7A appears.

Here, the value of the x-axis corresponding to each peak (peak) in FIG. 7A is the differential delay time distribution of the mode.

The present invention is not limited to the embodiments, and it is possible to implement a differential time delay measuring apparatus between multiple modes of various multimode waveguides through an arrangement combination of an optical optical splitter or an optical optical splitter and a plurality of reflectors.

As described above, the present invention can not only measure the differential delay time between modes of the multimode waveguide using a low-cost light source and an interferometer, but also measure a short-length multimode waveguide.

In addition, this method is easy and simple, so anyone who produces a multimode waveguide can use it easily.

Claims (11)

A light distribution means for distributing the light source having a width, the light emitted from the light source to the multimode waveguide and the reference optical path; Reflecting means for reflecting the optical signal passing through the reference optical path to the light distribution means; The optical signal returned from the cutting plane of the multi-mode waveguide and the optical signal reflected by the reflecting means after passing through the air path, which is the reference optical path, are combined by the optical distribution means. A wavelength component detector for detecting and transmitting to a computer A frequency component conversion process for converting a detection signal according to the light intensity input from a wavelength component detector into a frequency component, a process for decomposing the interference fringe changed through the Fourier transform from the changed frequency component into differential time mode delay information, and the measurement An apparatus for measuring differential time delay between multiple modes of a multimode waveguide, comprising a computer equipped with a program including a process for displaying the results. 2. The differential mode between multimode waveguides according to claim 1, wherein the light distribution means is constituted by an optical fiber splitter so as to provide a distribution path between the light incident from the light source and the multimode optical waveguide and the reference optical path. Time delay measuring device. The method of claim 1, wherein the light distribution means, A first optical fiber distributor for providing a distribution path between the multimode optical waveguide and the reference optical path to the light incident from the light source; Differential time delay measurement between multi-mode waveguides comprising two optical fiber splitters of a second optical fiber splitter for generating interference by combining an optical signal passing through a multimode optical waveguide and an optical signal passing through a reference optical path Device. A light source with a width, An optical fiber optical splitter that provides light emitted from the light source as a multi-mode waveguide and a reference optical path, Reflecting means for reflecting the optical signal passing through the reference optical path to the light distribution means; Optical system for generating interference by condensing the optical signal through the multimode optical waveguide and the optical signal reflected by the reflecting means through the reference optical path, combining the optical signal through the multimode optical waveguide and the optical signal through the reference optical path Type optical splitter, A lens for collecting the interference light passing through the optical system splitter and providing the wavelength component detector to the wavelength component detector; A wavelength component detector which detects an optical signal focused through a lens and transmits it to a computer according to each optical intensity for each wavelength component; A frequency component conversion process for converting a detection signal according to the light intensity input from a wavelength component detector into a frequency component, a process for decomposing the interference fringe changed through the Fourier transform from the changed frequency component into differential time mode delay information, and the measurement An apparatus for measuring differential time delay between multiple modes of a multimode waveguide, comprising a computer equipped with a program including a process for displaying the results. A light source with a width, A lens that converts light from the light source into parallel light, An optical system type first optical splitter which receives light emitted from a light source through a lens and provides a multimode waveguide and a reference optical path; A lens for focusing the light passing through the optical system optical splitter to the multimode waveguide and a lens for focusing the optical light to the optical optical second optical splitter after passing through the multimode waveguide to make parallel light; One or more reflectors to redirect the light along the reference path; An optical type second optical splitter for generating interference by combining an optical signal passing through a multi-mode optical waveguide and an optical signal passing through a reference optical path; A lens for collecting the interference light passing through the optical system splitter and providing the wavelength component detector to the wavelength component detector; A wavelength component detector which detects an optical signal focused through a lens and transmits it to a computer according to each optical intensity for each wavelength component; A frequency component conversion process for converting a detection signal according to the light intensity input from a wavelength component detector into a frequency component, a process for decomposing the interference fringe changed through the Fourier transform from the changed frequency component into differential time mode delay information, and the measurement An apparatus for measuring differential time delay between multiple modes of a multimode waveguide, comprising a computer equipped with a program including a process for displaying the results. The method according to any one of claims 1 to 5, The differential time delay value between the multiple modes representing the differential time delay information is [Equation]

(Where * is a standard convolution operator, G (t) is the Fourier transform value of the measurement light source, and each maximum peak expressed in the above equation is

The peak is a value corresponding to the m th time difference delay excited in the multimode optical waveguide.) The differential time delay measurement between the multimode waveguides of the multimode waveguide is calculated as Device. The method of claim 6, wherein [Equation] [Equation 1]

[Equation 2]

[Equation 3]

[Equation 4]

 Where I (f) is the intensity of the interfering light signal, N is the number of optical fibers excited in the multimode waveguide,

Is the spectrum of the broad optical fiber used for the measurement,

Is the relative optical power of the m th excited mode,

Is the relative phase between the reference light signal and the m th excited signal, <> Is the time domain average,

Is the propagation velocity of the m th excited excitation, L is the length of the measured multimode waveguide) Differential time delay measurement apparatus between the multi-mode waveguide, characterized in that induced by. A light source having a width; A multimode waveguide; The differential time delay value between the multiple modes provided with the wavelength component detection means and representing the differential time delay information from the detection signal of the wavelength component detection means is [Equation]

(* Is a standard convolution operator, G (t) is the Fourier transform value of the measured light source, and each peak peak expressed in the above equation is

This peak is the value corresponding to the excited mth time difference delay in the multimode optical waveguide. here

Is the relative optical power of the m th excited mode, L denotes the length of the measured multimode waveguide), and the differential time delay measurement apparatus between the multimode waveguides of the multimode waveguide. The method of claim 8, wherein [Equation] [Equation 1]

[Equation 2]

[Equation 3]

[Equation 4]

 Where I (f) is the intensity of the interfering light signal,

Is the relative phase between the reference light signal and the m th excited signal,

Is the propagation velocity of the m th excited excitation,  L is the length of the measured multimode waveguide), the differential time delay measurement apparatus between the multimode waveguide of the multimode waveguide. Outputting light from a light source having a wavelength component to a light splitter; Distributing light into an optical path and a reference path with multiple waveguides; Light passing through the two paths causes interference; Detecting light for each wavelength component from the light causing the interference; And outputting differential time delay information from the detected optical signal, wherein the differential time delay value is [Equation]

(Where * is a standard convolution operator, G (t) is the Fourier transform value of the measurement light source, and each maximum peak expressed in the above equation is

The peak is a value corresponding to the mth time difference delay excited in the multimode optical waveguide.) The differential time delay measurement between the multimode waveguides of the multimode waveguide is calculated as Way. The method of claim 10, wherein [Equation] [Equation 1]

[Equation 2]

[Equation 3]

[Equation 4]

 Where I (f) is the intensity of the interfering light signal,

Is the relative phase between the reference light signal and the m th excited signal,

Is the propagation velocity of the m th excited excitation, L is the length of the measured multimode waveguide), the differential time delay measurement method between the multimode waveguide of the multimode waveguide.

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