CN108803018B - Method for reconstructing longitudinal refractive index distribution of optical waveguide - Google Patents
Method for reconstructing longitudinal refractive index distribution of optical waveguide Download PDFInfo
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- CN108803018B CN108803018B CN201810930387.9A CN201810930387A CN108803018B CN 108803018 B CN108803018 B CN 108803018B CN 201810930387 A CN201810930387 A CN 201810930387A CN 108803018 B CN108803018 B CN 108803018B
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- G—PHYSICS
- G02—OPTICS
- G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
- G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
- G02B27/0012—Optical design, e.g. procedures, algorithms, optimisation routines
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- G—PHYSICS
- G02—OPTICS
- G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
- G02B6/00—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings
- G02B6/10—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings of the optical waveguide type
Abstract
The invention discloses a method for reconstructing the longitudinal refractive index distribution of an optical waveguide, which comprises the steps of firstly obtaining an amplitude spectrum and a phase spectrum of optical waveguide response from reflected light of the optical waveguide, and calculating intermediate quantity by using the amplitude spectrum and the phase spectrum; the intermediate quantity is sampled at equal intervals in space frequency and discretized, the discretized intermediate quantity is subjected to inverse Fourier transform, and the longitudinal refractive index distribution of the optical waveguide is calculated according to the result of the inverse Fourier transform. According to the mathematical relation of the optical waveguide response spectrum, the longitudinal refractive index distribution of the optical waveguide is reconstructed by using the amplitude spectrum, the phase spectrum and the Fourier transform of the optical waveguide response. The method has the advantages of high reconstruction precision, high speed and the like, and is suitable for reconstructing the optical waveguide with any complex refractive index distribution.
Description
Technical Field
The invention relates to the technical field of optical waveguides, in particular to a method for reconstructing the refractive index of an optical waveguide.
Background
The optical waveguide device can be widely applied to the fields of optical fiber communication, optical sensing, integrated optics, biochemical physical sensing, medical diagnosis and the like, and the optical waveguide device with excellent response spectrum performance, particularly used for micro-distribution sensing, is generally a non-uniform optical waveguide with a complex structure. Analyzing, designing, and reconfiguring optical waveguide structures is an important aspect of optical waveguide research and applications. The internal structure and characteristic information of the optical waveguide device can be obtained through the reconstruction of the longitudinal refractive index of the optical waveguide, and the method can be used for structural design, distributed micro-sensing and monitoring of the optical waveguide device. Therefore, the reconstruction method of the longitudinal refractive index distribution of the optical waveguide has important function and good application prospect.
In the related art, an Integral Layer-stripping (ILP), a Discrete Layer-stripping (DLP), a genetic algorithm, and the like reconstruct the refractive index distribution of the optical waveguide using the amplitude response spectrum of the optical waveguide. The methods lack the uniqueness of waveguide structure reconstruction (namely, a plurality of structures can be reconstructed without phase requirements), can be used for designing optical waveguides instead of reconstruction (the reconstruction needs to have uniqueness), and are difficult to be used for micro-distributed sensing. At present, the unique optical waveguide reconstruction method is mainly a digital holographic tomography method. The method is similar toIn Computed Tomography (CT), the device to be tested is rotated by 180 degrees, interference holograms at various angles are recorded by a two-dimensional CCD, and three-dimensional distribution (including longitudinal refractive index distribution) of the refractive index of an optical waveguide is reconstructed based on a filtering back projection method, wherein the precision can reach 10-4. The method has the defects that a measured device needs to be mechanically rotated and two-dimensional data based on CCD interference imaging are needed, the measuring and calculating processes are complex, the accumulated error is large, and the resolution ratio is not high enough.
Disclosure of Invention
In view of the above-mentioned deficiencies of the prior art, the present invention provides a method for reconstructing a longitudinal refractive index profile of an optical waveguide by combining an amplitude spectrum with a phase spectrum. The method does not need to rotate the measured device and two-dimensional CCD interference imaging, reduces the complexity of the measuring and calculating process, improves the resolution, overcomes the defects of the existing method, and is suitable for reconstructing the optical waveguide with any complex refractive index distribution.
In order to achieve the above objects and solve the related technical problems, the present invention adopts the following technical solutions: the method for reconstructing the longitudinal refractive index distribution of the optical waveguide comprises the following steps:
step 1: obtaining an amplitude spectrum and a phase spectrum of optical waveguide response by using reflected light of the optical waveguide;
step 2, calculating an intermediate quantity η (upsilon) by using the amplitude spectrum and the phase spectrum of the optical waveguide response according to the following formula:
wherein, k is the waveguide coupling coefficient,
arth is an inverse hyperbolic tangent function, e is a natural constant, and an argument υ is 2n0λ is the wavelength of light λ and the effective refractive index n of the optical waveguide0Determined spatial frequency, gamma and
respectively an amplitude spectrum and a phase spectrum;
step 3, sampling and discretizing the intermediate quantity η (upsilon) at equal intervals according to the spatial frequency to obtain a frequency domain sequence A (i),then, the frequency domain sequence A (i) is subjected to inverse discrete Fourier transform to obtain a spatial domain sequencen(i) Then using the spatial domain sequencen(i) Calculating the longitudinal refractive index distribution n (z) of the optical waveguide according to the following formula, wherein A (i) is η (i delta upsilon), and n (z) is n0+n(int (zN Δ ν)); in the formula, the number i is {0,1,2,3... times.n-1 }, N is a sequence length, Δ ν is a spatial frequency interval, z is a spatial position quantity in the longitudinal direction of the optical waveguide or in the light propagation direction, and int is an integer arithmetic operation.
Further, the amplitude spectrum and the phase spectrum of the optical waveguide response in the step 1 are an amplitude spectrum gamma (upsilon) and a phase spectrum which change along with the spatial frequency upsilon
Or an amplitude spectrum gamma (lambda) and a phase spectrum which vary with the wavelength lambda of the light
Further, in step 1, an optical waveguide response amplitude spectrum gamma (lambda) and a phase spectrum which change with the optical wavelength lambda are obtained
Then according to lambda being 2n0The relation of v converts the amplitude spectrum and the phase spectrum which change along with the optical wavelength lambda into an amplitude spectrum gamma (v) and a phase spectrum which change along with the spatial frequency v respectively
Further, in step 1, the spectrum measuring instrument is used for obtaining a spectrum containing an amplitude spectrum gamma and a phase spectrum
Complex response spectrum varying with spatial frequency upsilon or optical wavelength lambda
Or
As lightAmplitude spectrum and phase spectrum of the waveguide response.
Further, in the step 1, a power spectrum and a time delay spectrum of the optical waveguide response are obtained by a spectrum measuring instrument; and then, carrying out square-opening operation on the power spectrum to obtain an amplitude spectrum, and carrying out integral operation on the time delay spectrum to obtain a phase spectrum.
Further, step 2: using optical waveguide response amplitude spectrum gamma (lambda) and phase spectrum varying with optical wavelength lambda
Intermediate quantity η (ν) is calculated as follows:
preferably, the value of N.DELTA.v is not less than 5/μm.
Preferably, the spectrum measuring instrument is a fourier transform spectrometer or a radio frequency modulation spectrum measuring instrument.
Preferably, the optical waveguide is a planar optical waveguide, a strip optical waveguide or a cylindrical optical waveguide.
In summary, the present invention has the following advantages:
1. the method for reconstructing the longitudinal refractive index distribution of the optical waveguide simultaneously utilizes the amplitude spectrum and the phase spectrum in the response of the optical waveguide, can realize the inverse Fourier transform based on the fast Fourier transform algorithm, does not depend on image information, and does not generate accumulated errors, so the method has the advantages of high reconstruction precision and high speed, and is suitable for reconstructing the optical waveguide with any complex refractive index distribution.
2. The reconstruction method of the longitudinal refractive index distribution of the optical waveguide does not need to rotate a measured device and is based on two-dimensional CCD interference imaging, and has the characteristics of simple measurement and calculation processes and high resolution.
3. The method for reconstructing the longitudinal refractive index distribution of the optical waveguide can be used for designing and reconstructing an optical waveguide structure, precise micro-distribution sensing and the like.
Drawings
FIG. 1 is a flow chart of a method of reconstructing a longitudinal refractive index profile of an optical waveguide of the present invention;
fig. 2 is a schematic diagram of obtaining an amplitude spectrum and a phase spectrum of optical waveguide response in embodiment 7.
Fig. 3 is a schematic diagram of a radio frequency modulation spectrometer according to embodiment 8 (in the figure, dashed arrows indicate light and its transmission direction, and solid arrows indicate electrical signal connection and its flow direction).
Detailed Description
To illustrate the present invention more clearly, the following description will be made in conjunction with the method for reconstructing the longitudinal refractive index profile of an optical waveguide according to the present invention, preferred embodiments thereof, and the accompanying drawings. It is to be understood by persons skilled in the art that the following detailed description is illustrative and not restrictive, and is not to be taken as limiting the scope of the invention.
Example 1
In this embodiment, the optical waveguide is a Bragg grating structure in a single-mode cylindrical optical waveguide (i.e., a single-mode optical fiber), and the refractive index distribution of the Bragg grating along the axial direction of the optical fiber is reconstructed. The central wavelength of the Bragg grating reflected light is 1550nm, the 3dB bandwidth is 10nm, the reflectivity is more than 0.9, the waveguide coupling coefficient kappa is 2655 pi N/s, and the effective refractive index N of the fundamental mode01.55, taking a super-radiation light-emitting diode combined light source with the total power of 10mw and the spectral range of 1450-1650 nm as an incident light source, and taking N as 106A fourier transform spectrometer having a value of N Δ ν ═ 10/μm was used as a spectrometer.
The method for reconstructing the longitudinal refractive index distribution of the optical waveguide, as shown in fig. 1, comprises the following steps:
step 1: light emitted by the light source enters the Bragg grating in the optical fiber and is reflected by the Bragg grating; measuring the amplitude spectrum and the phase spectrum of the reflected light by a spectrum measuring instrument to acquire the amplitude spectrum gamma (upsilon) and the phase spectrum of the optical waveguide response changing with the spatial frequency upsilon
Step 2: amplitude spectrum gamma (upsilon) and phase spectrum responded by the optical waveguide
Intermediate quantity η (ν) is calculated as follows:
wherein the content of the first and second substances,
arth is an inverse hyperbolic tangent function, e is a natural constant, and an independent variable upsilon is 3.1/lambda and is composed of optical wavelength variables lambda and n0A determined spatial frequency;
step 3, sampling and discretizing the intermediate quantity η (upsilon) at equal intervals according to the space frequency to obtain a frequency domain sequence A (i), and then performing inverse discrete Fourier transform on the frequency domain sequence A (i) to obtain a space domain sequencen(i) Then using the spatial domain sequencen(i) Calculating the longitudinal refractive index distribution n (z) of the optical waveguide according to the following formula, wherein A (i) is η (i delta upsilon), and n (z) is n0+n(int (zN Δ ν)); in the formula, the sequence number i is {0,1,2,3.. times.n-1 }, and the sequence length N is 106Space frequency interval Δ ν 10-5And/mum, z is a space position variable in the longitudinal direction of the optical waveguide or the light propagation direction, and int is an integer operation. The calculated n (z) is the reconstructed optical waveguide longitudinal refractive index profile.
Example 2
This example differs from example 1 in that: in step 1, a spectrum measuring instrument is used for obtaining a spectrum containing an amplitude spectrum gamma and a phase spectrum
Complex response spectrum as a function of spatial frequency v
Amplitude spectrum and phase spectrum as response of the optical waveguide. The other steps were the same as in example 1.
Example 3
This example differs from example 1 or example 2 in that: in step 1, a waveguide response amplitude spectrum gamma (lambda) and a waveguide response phase spectrum which change along with the optical wavelength lambda are obtained
Then according to lambda being 2n0The amplitude spectrum and the phase spectrum which change along with the optical wavelength lambda are respectively converted into an amplitude spectrum and a phase spectrum which change along with the spatial frequency upsilon by the relation of/upsilon; and then zero filling is carried out on the amplitude spectrum and the phase spectrum outside the bandwidth of the light source, so that the data length of the amplitude spectrum and the phase spectrum is an integer power of 2, for example, N is 222(ii) a The other steps were the same as in example 1.
Example 4
This example differs from example 3 in that: in step 1, a composite response spectrum which varies with the wavelength of light lambda is used
Amplitude spectrum and phase spectrum as optical waveguide response; then according to lambda being 2n0The method comprises the steps of converting a composite response spectrum changing along with optical wavelength lambda into a composite response spectrum changing along with spatial frequency upsilon, and then performing zero filling on the composite response spectrum outside a light source bandwidth to enable the data length of the composite response spectrum to be an integer power of 2, such as N-221(ii) a The other steps were the same as in example 3.
Example 5
This example differs from example 3 or example 4 in that: in step 1, a waveguide response amplitude spectrum gamma (lambda) and a waveguide response phase spectrum which change along with the optical wavelength lambda are obtained
Step 2: using optical waveguide response amplitude spectrum gamma (lambda) and phase spectrum varying with optical wavelength lambda
Intermediate quantity η (ν) is calculated as follows:
the other steps were the same as in example 4.
Example 6
This example differs from example 5 in that: in step 1, a spectrum measuring instrument is used for acquiring a spectrum containing an amplitude spectrum gamma and a phase spectrum
Complex response spectrum varying with the wavelength of light lambda
Amplitude spectrum and phase spectrum as optical waveguide response; step 2: using composite response spectra varying with the wavelength of light lambda
Intermediate quantity η (ν) is calculated as follows:
the other steps were the same as in example 5.
Example 7
This example differs from example 1 in that: amplitude spectrum gamma (upsilon) and phase spectrum of the optical waveguide response are obtained as follows
The principle is shown in fig. 2: firstly, acquiring a power spectrum and a time delay spectrum of optical waveguide response by using a spectrum measuring instrument; then, the power spectrum is subjected to square operation to obtain an amplitude spectrum gamma (upsilon), and the time delay spectrum is subjected to integral operation to obtain a phase spectrum
The other steps were the same as in example 1.
Example 8
This example differs from example 1 in that: amplitude spectrum gamma (upsilon) and phase spectrum are obtained by adopting spectral measuring instrument based on radio frequency modulation method
A schematic diagram of a radio frequency modulation spectrometer is shown in fig. 3. In the radio frequency modulation method spectral measurement instrument, light output by a tunable laser is modulated by a radio frequency RF signal and is divided into two paths of light by a light splitter (or a coupler) C, and one path of light is converted into a reference electric signal by a photoelectric detector 1(PD1)And input to a vector network analyzer; the other path of light is incident to the optical waveguide to be reconstructed (to be measured) and is reflected, and the reflected light wave is converted into a measured electric signal through the photoelectric detector 2(PD2) and is input to the vector network analyzer; the vector network analyzer compares the phase of the reference electric signal with that of the measured electric signal, acquires the comparison result and phase spectrum of the optical waveguide response
And an amplitude spectrum γ (ν). The other steps were the same as in example 1.
The method for reconstructing the longitudinal refractive index distribution of the optical waveguide mainly solves the problem of reconstructing or designing the longitudinal (light transmission direction) refractive index distribution (namely, a waveguide structure) of any complex optical waveguide. The reconstruction method can acquire the internal structure and characteristic information of the optical waveguide device, and can be used for structural design, distributed micro-sensing and monitoring of the optical waveguide device.
The above-described embodiments are merely exemplary embodiments of the present invention, which should not be construed as limiting the invention, and any modifications, equivalents, improvements, etc. made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (9)
1. The method for reconstructing the longitudinal refractive index distribution of the optical waveguide is characterized in that: the method comprises the following steps:
step 1: obtaining an amplitude spectrum and a phase spectrum of optical waveguide response by using reflected light of the optical waveguide;
step 2, calculating an intermediate quantity η (upsilon) by using the amplitude spectrum and the phase spectrum of the optical waveguide response according to the following formula:
wherein, k is the waveguide coupling coefficient,
arth is an inverse hyperbolic tangent function, e is a natural constant, and an argument υ is 2n0λ is formed by optical wavelength λ and optical waveguideEffective refractive index n0Determined spatial frequency, gamma and
respectively an amplitude spectrum and a phase spectrum;
step 3, sampling and discretizing the intermediate quantity η (upsilon) at equal intervals according to the space frequency to obtain a frequency domain sequence A (i), and then performing inverse discrete Fourier transform on the frequency domain sequence A (i) to obtain a space domain sequencen(i) Then using the spatial domain sequencen(i) Calculating the longitudinal refractive index distribution n (z) of the optical waveguide according to the following formula, wherein A (i) is η (i delta upsilon), and n (z) is n0+n(int (zN Δ ν)); in the formula, the number i is {0,1,2,3... times.n-1 }, N is a sequence length, Δ ν is a spatial frequency interval, z is a spatial position quantity in the longitudinal direction of the optical waveguide or in the light propagation direction, and int is an integer arithmetic operation.
2. The method for reconstructing a longitudinal refractive index profile of an optical waveguide according to claim 1, wherein: the amplitude spectrum and the phase spectrum of the optical waveguide response in the step 1 are amplitude spectrum gamma (upsilon) and phase spectrum which change along with the spatial frequency upsilon
Or an amplitude spectrum gamma (lambda) and a phase spectrum which vary with the wavelength lambda of the light
3. The method for reconstructing a longitudinal refractive index profile of an optical waveguide according to claim 1, wherein: in step 1, an optical waveguide response amplitude spectrum gamma (lambda) and a phase spectrum which change along with the optical wavelength lambda are obtained
Then according to lambda being 2n0The relation of v converts the amplitude spectrum and the phase spectrum which change along with the optical wavelength lambda into an amplitude spectrum gamma (v) and a phase spectrum which change along with the spatial frequency v respectively
4. The method for reconstructing a longitudinal refractive index profile of an optical waveguide according to claim 1, wherein: in step 1, a spectrum measuring instrument is used for acquiring a spectrum containing an amplitude spectrum gamma and a phase spectrum
Complex response spectrum varying with spatial frequency upsilon or optical wavelength lambda
Or
Amplitude spectrum and phase spectrum as response of the optical waveguide.
5. The method for reconstructing a longitudinal refractive index profile of an optical waveguide according to claim 1, wherein: in the step 1, a spectrum measuring instrument is used for obtaining a power spectrum and a time delay spectrum of optical waveguide response; and then, carrying out square-opening operation on the power spectrum to obtain an amplitude spectrum, and carrying out integral operation on the time delay spectrum to obtain a phase spectrum.
6. The method for reconstructing a longitudinal refractive index profile of an optical waveguide according to claim 1, wherein: step 2: using optical waveguide response amplitude spectrum gamma (lambda) and phase spectrum varying with optical wavelength lambda
Intermediate quantity η (ν) is calculated as follows:
7. the method for reconstructing a longitudinal refractive index profile of an optical waveguide according to claim 1, wherein: the value of N [ Delta ] upsilon is not less than 5/mum.
8. The method for reconstructing a longitudinal refractive index profile of an optical waveguide according to claim 4 or 5, wherein: the spectrum measuring instrument is a Fourier transform spectrometer or a radio frequency modulation method spectrum measuring instrument.
9. The method for reconstructing a longitudinal refractive index profile of an optical waveguide according to claim 1, wherein: the optical waveguide is a planar optical waveguide, a strip optical waveguide or a cylindrical optical waveguide.
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| CN105829928A (en) * | 2014-01-31 | 2016-08-03 | Ofs菲特尔有限责任公司 | Design and manufacture of multi-mode optical fibers |
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| CN105829928A (en) * | 2014-01-31 | 2016-08-03 | Ofs菲特尔有限责任公司 | Design and manufacture of multi-mode optical fibers |
| CN107121916A (en) * | 2017-07-11 | 2017-09-01 | 重庆理工大学 | Fiber waveguide device holography spectrometry method and device |
| CN107479217A (en) * | 2017-09-11 | 2017-12-15 | 山东大学 | A kind of reconfigurable optical waveguide and its application based on lattice structure |
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