CN111679453A - Microwave photon filter based on few-mode fiber Bragg grating - Google Patents

Microwave photon filter based on few-mode fiber Bragg grating Download PDF

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CN111679453A
CN111679453A CN202010504935.9A CN202010504935A CN111679453A CN 111679453 A CN111679453 A CN 111679453A CN 202010504935 A CN202010504935 A CN 202010504935A CN 111679453 A CN111679453 A CN 111679453A
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few
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bragg grating
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CN111679453B (en
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胡贵军
庞睿
张美玲
刘晓
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Jilin University
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    • GPHYSICS
    • G02OPTICS
    • G02FOPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
    • G02F1/00Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics
    • G02F1/01Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour 
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    • GPHYSICS
    • G02OPTICS
    • G02BOPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B6/00Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings
    • G02B6/02Optical fibres with cladding with or without a coating
    • G02B6/02057Optical fibres with cladding with or without a coating comprising gratings
    • G02B6/02076Refractive index modulation gratings, e.g. Bragg gratings
    • GPHYSICS
    • G02OPTICS
    • G02BOPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B6/00Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings
    • G02B6/24Coupling light guides
    • G02B6/26Optical coupling means
    • GPHYSICS
    • G02OPTICS
    • G02BOPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B6/00Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings
    • G02B6/24Coupling light guides
    • G02B6/26Optical coupling means
    • G02B6/28Optical coupling means having data bus means, i.e. plural waveguides interconnected and providing an inherently bidirectional system by mixing and splitting signals
    • G02B6/2804Optical coupling means having data bus means, i.e. plural waveguides interconnected and providing an inherently bidirectional system by mixing and splitting signals forming multipart couplers without wavelength selective elements, e.g. "T" couplers, star couplers
    • G02B6/2861Optical coupling means having data bus means, i.e. plural waveguides interconnected and providing an inherently bidirectional system by mixing and splitting signals forming multipart couplers without wavelength selective elements, e.g. "T" couplers, star couplers using fibre optic delay lines and optical elements associated with them, e.g. for use in signal processing, e.g. filtering

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Abstract

The invention discloses a microwave photon filter based on a few-mode fiber Bragg grating, which belongs to the field of microwave photonics and comprises a laser, an electro-optical modulator, a few-mode fiber Bragg grating delay line module, a few-mode fiber circulator, a photon lantern, a beam combiner, a photoelectric detector and a vector network analyzer. The few-mode fiber Bragg grating delay line module is the core part of the filter. The delay line adopts a mode division multiplexing technology, the mode dimension is used as a multiplexing channel under a single signal wavelength, different modes are excited by a few-mode optical fiber superior Bragg grating, and the delay line is formed by controlling the distance between the gratings. The invention utilizes few-mode optical fiber Bragg grating delay lines to realize a multi-tap, high-frequency, large-bandwidth, low-loss and high-stability filter, overcomes the defect that the traditional microwave photon filter needs a multi-wavelength light source and a laser array by utilizing a wavelength division multiplexing technology and has high cost, greatly improves the integration level of a system and reduces the cost of the system.

Description

Microwave photon filter based on few-mode fiber Bragg grating
Technical Field
The invention belongs to the field of microwave photonics, and particularly relates to a microwave photonic filter based on a few-mode fiber Bragg grating.
Background
With the continuous development of communication technologies and communication modes such as real-time audio and video, the requirement for channel bandwidth is continuously increased, and carrier frequency has evolved from microwave to millimeter wave. The increase of the signal frequency increases the transmission loss of the link, and limits the transmission distance of the signal. Microwave photonics combines a microwave system and an optical system, modulates signals of millimeter wave bands onto optical signals, processes the microwave signals in an optical domain, and has the advantages of low loss, strong anti-electromagnetic interference capability and the like.
In a signal processing subsystem of microwave photonics, a microwave photon filter is one of key technologies, and is widely researched and applied in the fields of radar, millimeter wave communication and the like. The microwave photon filter overcomes the defects of inflexible operation, electronic bottleneck and frequency-related loss and the like of the traditional electronic filter, and has the advantages of low loss, low cost, large bandwidth, small volume, electromagnetic interference suppression and the like.
Microwave photonic filters fall into two categories, coherent and incoherent. The optical coherent filter is sensitive in phase, has large coherent noise, is greatly influenced by the environment, and is greatly limited in practical application. In addition, as the quality of optical fibers has been improved, incoherent microwave photonic filters based on fiber delay lines have become important to research. The incoherent microwave photonic filter with the optical fiber structure usually adopts a high-dispersion optical fiber or a Bragg optical fiber grating, and realizes multiple taps of the filter based on a laser array or a multi-wavelength laser of multiple optical wavelength light sources, so that the system is large in size, high in complexity and high in cost; the method for cutting the broadband light source is utilized to realize a plurality of taps of the microwave photonic filter based on a plurality of optical wavelength light sources, and the system is low in stability and low in signal-to-noise ratio. The few-mode optical fiber can simultaneously transmit different modes, can greatly improve the transmission capacity of an optical fiber communication system, and has the characteristics of low nonlinearity of a multimode optical fiber and low loss transmission of a single-mode optical fiber. In addition, the fiber grating has the advantages of small volume, low insertion loss, low cost, mode conversion and the like. In the microwave photon filter structure, mode dimensionality is introduced under single wavelength, different modes are excited by using few-mode fiber Bragg gratings to form a fiber delay line, the system structure is simplified, and the system cost is reduced. Therefore, the microwave photonic filter based on the few-mode fiber bragg grating has a great development prospect in the fields of radar and wireless communication.
Disclosure of Invention
The invention aims to introduce mode dimensionality aiming at the problems of complex system structure, large volume and high cost caused by applying a laser array or a multi-wavelength laser when a microwave photon filter based on a wavelength division multiplexing technology is used, and provides a microwave photon filter based on a few-mode fiber Bragg grating, which has the advantages of high stability, simple structure, low cost, high resolution and the like.
In order to achieve the purpose, the invention adopts the following technical scheme:
the structure diagram of the system of the microwave photon filter based on the few-mode fiber Bragg grating is shown in figure 1 and consists of a laser 1, an electro-optical modulator 2, a few-mode fiber Bragg grating delay line module 3, a few-mode fiber circulator 4, a photon lantern 5, a beam combiner 6, a photoelectric detector 7 and a vector network analyzer 8; wherein, the output port of the laser 1 is connected with one input port of the electro-optical modulator 2, and the output port of the vector network analyzer 8 is connected with the other input port of the electro-optical modulator 2; the output port of the electro-optical modulator 2 is connected with the first port 41 of the few-mode optical fiber circulator 4; a second port 42 of the few-mode optical fiber circulator 4 is connected with an input port of the few-mode optical fiber Bragg grating delay line module 3, and a third port 43 of the few-mode optical fiber circulator 4 is connected with a tail fiber input port of the photon lantern 5; the output port of the photon lantern 5 is connected with the input port of the beam combiner 6; the output port of the beam combiner 6 is connected with the input port of the photoelectric detector 7; the output port of the photodetector 7 is finally connected to the input port of the vector network analyzer 8.
Preferably, the laser 1 generates a continuous single wavelength light wave having a wavelength of 1550.51 nm.
Preferably, the vector network analyzer 8 generates a frequency sweep signal, which is input into the electro-optic modulator 2 via a cable.
Preferably, the few-mode fiber bragg grating delay line 3 is formed by cascading N few-mode fiber bragg gratings, excites N modes, and has equal energy.
Preferably, the number of modes that can be transmitted by the few-mode fiber circulator 4 is greater than or equal to the number of excitation modes of the few-mode fiber bragg grating delay line module 3.
Preferably, the photonic lantern 5 acts as a mode demultiplexer, supporting N mode separations.
Preferably, the beam combiner 6 is an N:1 equal splitting beam combiner.
Preferably, the vector network analyzer 8 measures the frequency response of the filter.
The working principle of the invention is as follows:
the laser emits continuous single-wavelength laser, the mode of the light wave is a fundamental mode, and the wavelength is lambda. When the light waves are transmitted to the electro-optical modulator, the radio-frequency signals are loaded on the optical carrier through electro-optical conversion. The modulated optical carrier signal is input into the few-mode fiber Bragg grating delay line module through the few-mode fiber circulator, and signal delay is realized by an optical method.
The few-mode fiber Bragg grating delay line module is a key part of a microwave photonic filter and is formed by cascading N few-mode Fiber Bragg Gratings (FBGs), namely FBG1, FBG2, FBG3 and FBGN. The few-mode fiber Bragg grating can convert a forward transmission mode propagating in a fiber core into a reverse transmission mode, and the two fiber core modes are in mode coupling, namely, a specific mode is reflected under specific wavelength. The coupling mode equation of the fiber bragg grating is as follows:
Figure BDA0002526189640000031
in the formula (1), Ak,AjSlowly varying amplitudes for mode k and mode j, respectively;
Figure BDA0002526189640000032
self-coupling coefficients for mode k and mode j, respectively;
Figure BDA0002526189640000033
mutual coupling coefficient for mode k and mode j, βk,βjPropagation constants for mode k and mode j, respectively, and Λ is the grating period.
The few-mode fiber Bragg grating meets the phase matching condition, and
Figure BDA0002526189640000034
mode coupling can only be performed because of the propagation constant of the mode in the fiber
Figure BDA0002526189640000035
neffIs the effective index of the mode, it can be seen that in a grating with a period of Λ, the effective index is neff,k,neff,jWhen the modes (a) and (b) are coupled, the corresponding resonance wavelengths are:
λ=(neff,k+neff,j)Λ (2)
from the equation (2), it can be known that the few-mode fiber bragg gratings with different periods can excite and reflect different core modes at λ wavelength. Based on the method, the specific mode conversion can be carried out by using the few-mode fiber Bragg grating with the specific period.
And the few-mode fiber circulator inputs the basic mode signal modulated by the modulator into the few-mode fiber Bragg grating delay line module. The primary mode is converted and reflected in mode 1 after FBG1, the unconverted primary mode is converted and reflected in mode 2 after FBG2, and the unconverted primary mode is converted and reflected in mode 3 after FBG 3. In this way, after the fundamental mode passes through the few-mode fiber bragg grating delay line module, the mode 1, the mode 2, the mode. The reflected N modes are made equal in power by varying the grating parameters.
FBG1, FBG2, FBG3, FBGN, to the second port 42 of the few-mode fiber circulator in the few-mode fiber bragg grating delay line module, i.e. the few-mode fiber bragg grating delay line moduleThe length of the optical fiber at the head end is l1、l2、l3、...、lN. Due to the dispersion effect, different modes have different propagation paths, so that different modes can generate different time delays after passing through a section of few-mode optical fiber, namely, the few-mode optical fiber has mode differential group time delay. The group delay per unit length of the mode 1, the mode 2, the mode 3, the mode N is tau1、τ2、τ3、...、τN. The fundamental mode signal is converted into N modes with equal energy after passing through N Bragg gratings, and is reflected back to the head end of the few-mode fiber Bragg grating delay line module. The delay after the N modes through the delay line is expressed as follows:
Figure BDA0002526189640000041
wherein, t2-t1=t3-t2=…=tN-tN-1Δ τ. A few-mode fiber bragg grating delay line with a delay difference of delta tau is formed.
And the optical carrier signal is reflected back to the few-mode optical fiber circulator after passing through the few-mode optical fiber Bragg grating delay line module. Optical signals are input to the photon lantern through the few-mode optical fiber circulator, and the photon lantern separates N modes to form N taps. The optical signal is then input to a combiner, which weights each branch to form a transfer function. And the combined optical signal is incident into a photoelectric detector, the optical signal is converted into an electric signal to obtain a band-pass microwave photon filter, and then the band-pass microwave photon filter is connected with a vector network analyzer to detect the signal, measure a spectrogram of the filter and analyze the filtering effect.
Compared with the prior art, the invention has the following advantages:
the invention relates to a microwave photon filter based on a few-mode fiber Bragg grating, wherein a few-mode fiber Bragg grating delay line module is the core part of the filter. By adopting a mode division multiplexing technology, the mode dimension is taken as a multiplexing channel under a single signal wavelength, few-mode fiber Bragg gratings are cascaded to excite a mode, and meanwhile, the equal-difference time delay is generated among different modes by controlling the distance among the gratings, so that the filter with multiple taps, high frequency, large bandwidth, low loss and high stability can be realized. The defect that the traditional microwave photon filter needs a multi-wavelength light source and a laser array by utilizing a wavelength division multiplexing technology and has high cost is overcome, the integration level of a system is greatly improved, and the cost of the system is reduced.
Drawings
FIG. 1: the invention relates to a structural schematic diagram of a microwave photon filter based on a few-mode fiber Bragg grating;
FIG. 2: the curve diagram of the effective refractive index of the few-mode optical fiber in four modes along with the change of the wavelength in the specific embodiment of the invention;
FIG. 3: in the specific embodiment of the invention, a reflection spectrum curve chart of four Bragg gratings in a few-mode fiber Bragg grating delay line module is provided. FIG. (a) shows a reflection spectrum plot of an FBG 1; FIG. (b) shows a reflection spectrum plot of the FBG 2; FIG. (c) shows a reflection spectrum plot of the FBG 3; FIG. (d) shows a reflection spectrum plot of the FBG 4;
FIG. 4: the frequency response curve of the microwave photon filter in the specific embodiment of the invention;
in the figure:
1. laser 2, electro-optical modulator 3 and few-mode fiber Bragg grating delay line module
4. Few-mode optical fiber circulator 5, photon lantern 6 and beam combiner
7. A photoelectric detector 8 and a vector network analyzer.
Detailed Description
The following detailed description of specific example embodiments of the invention is made with reference to the accompanying drawings.
The invention establishes a microwave photon filter based on a few-mode fiber Bragg grating, the structural block diagram of which is shown in figure 1 and comprises a laser 1, an electro-optical modulator 2, a few-mode fiber Bragg grating delay line module 3, a few-mode fiber circulator 4, a photon lantern 5, a beam combiner 6, a photoelectric detector 7 and a vector network analyzer 8; the output port of the laser 1 is connected with one input port of the electro-optical modulator 2, and the output port of the vector network analyzer 8 is connected with the other input port of the electro-optical modulator 2; the output port of the electro-optical modulator 2 is connected with the first port 41 of the few-mode optical fiber circulator 4; a second port 42 of the few-mode optical fiber circulator 4 is connected with an input port of the few-mode optical fiber Bragg grating delay line module 3, and a third port 43 of the few-mode optical fiber circulator 4 is connected with a tail fiber input port of the photon lantern 5; the output port of the photon lantern 5 is connected with the input port of the beam combiner 6; the output port of the beam combiner 6 is connected with the input port of the photoelectric detector 7; the output port of the photodetector 7 is finally connected to the input port of the vector network analyzer 8.
In the example of the present disclosure, the laser 1 is a narrow linewidth laser, and outputs a single wavelength light wave with a wavelength of 1550.51nm, and the output light wave is a fundamental mode. The line width of the selected laser is small, the coherent length of the light source is short, the microwave photon filter works in an incoherent region, and the influence of the performance along with environmental factors and polarization is small. The vector network analyzer 8 generates a sweep frequency signal, and the signal is connected with the electro-optic modulator 2 through a cable and loaded on an optical carrier. After passing through the few-mode fiber circulator 4, the optical carrier signal is input to the few-mode fiber bragg grating delay line module 3 through the second port 42 of the few-mode fiber circulator 4.
The few-mode optical fiber used by the few-mode fiber Bragg grating delay line module 3 is a large-delay four-mode step optical fiber, the diameter of a fiber core is 18.5 mu m, the refractive index of the fiber core is 1.44979, the diameter of a cladding is 125 mu m, the refractive index of the cladding is 1.44402, and the simultaneous transmission of four modes of LP01, LP11, LP02 and LP21 can be supported. Wherein, at the wavelength of 1550.51nm, the propagation time of the LP01 mode is 4.829ns for 1m, the differential mode group delay between the LP01 mode and the LP11 mode is 6.003ps/m, the differential mode group delay between the LP01 mode and the LP02 mode is 10.13ps/m, and the differential mode group delay between the LP01 mode and the LP21 mode is 11.68 ps/m. According to calculation, at the wavelength of 1550.51nm, the effective refractive index of the few-mode optical fiber is 1.4488 in the LP01 mode, 1.4474 in the LP11 mode, 1.4456 in the LP21 mode, and 1.4451 in the LP02 mode.
The few-mode fiber bragg grating delay line module 3 comprises four few-mode fiber bragg gratings, namely an FBG1, an FBG2, an FBG3 and an FBG 4. The laser generates a fundamental mode signal with the wavelength of 1550.51nm, the signal is input into the FBG1 through the few-mode optical fiber circulator after being modulated by the modulator, the grating period of the FBG1 is 535.10nm, the LP01 mode is converted into the LP01 mode, and the conversion efficiency is 25%; the unconverted LP01 mode is input into the FBG2, the grating period is 535.36nm, the FBG2 converts the LP01 mode into the LP11 mode, and the conversion efficiency is 33.3%; the unconverted LP01 mode passes through FBG3, the grating period is 535.79nm, the FBG3 converts the LP01 mode into the LP02 mode, and the conversion efficiency is 50%; the unconverted LP01 mode passes through FBG4 with a grating period of 535.69nm, FBG4 converts the LP01 mode to LP21 mode with a conversion efficiency of 100%. Different mode conversion efficiencies can be realized by controlling the mutual coupling coefficient and the grating length of the grating. The LP01 mode is converted into four modes of LP01, LP11, LP02 and LP21 with equal energy after passing through four few-mode fiber Bragg gratings, and is reflected back to a few-mode fiber circulator. The distance between the FBG1 and the head end of the few-mode fiber Bragg grating delay line module 3 is 1m, and the time of reflecting the converted LP01 mode to the second port 42 of the few-mode fiber circulator 4 is 9.658 ns; the distance between FBG1 and FBG2 was 10.285cm, and the time for the converted LP11 mode to reach the second port 42 was 10.658 ns; the distance between FBG2 and FBG3 was 10.297cm, and the time for the converted LP02 mode to reach the second port 42 was 11.658 ns; the distance between FBG3 and FBG4 was 10.322cm, and the time for the converted LP21 mode to reach the second port 42 was 12.658 ns. The time delay difference between the adjacent modes is 1ns, and a few-mode fiber Bragg grating delay line with the time delay of 1ns is formed.
The four modes are reflected by the few-mode fiber bragg grating delay line module 3, input into the few-mode fiber circulator 4, and input into the photon lantern 5 through the third port 43 of the few-mode fiber circulator 4 for mode separation. Among them, the photon lantern can support the separation of the four modes of LP01, LP11, LP02 and LP 21. The four modes separated by the photon lantern are used as four taps of the microwave photon filter and input into a 4:1 equal beam splitter for weighting to form a transmission function. And the combined optical signal is incident into a photoelectric detector, the optical signal is converted into an electric signal to obtain a microwave photon filter, and then the microwave photon filter is connected with a vector network analyzer to detect the signal, measure a spectrogram of the filter and analyze the filtering effect.
Fig. 2 is a curve of effective refractive index of the few-mode fiber in the LP01 mode, LP11 mode, LP02 mode, and LP21 mode as a function of wavelength, and it can be seen from the graph that effective refractive indexes of different modes are different, and conversion of different modes can be achieved by changing the period of the few-mode fiber bragg grating under a single wavelength. Fig. 3 shows reflection spectra of FBGs 1, 2, 3 and 4 in the few-mode fiber bragg grating delay line module. FBG1 has a grating mutual coupling coefficient of 800m-1The period is 535.10nm, the length is 1283 periods, LP01 mode conversion can be realized, and the conversion efficiency is 25%; FBG2 has a grating mutual coupling coefficient of 800m-1The period is 535.36nm, the length is 1537 periods, LP11 mode conversion can be realized, and the conversion efficiency is 33.3%; FBG3 has a grating mutual coupling coefficient of 800m-1The period is 535.79nm, the length is 2056 periods, LP02 mode conversion can be realized, and the conversion efficiency is 50%; FBG4 with a grating mutual coupling coefficient of 1600m-1The period is 535.69nm, the length is 5000 periods, LP21 mode conversion can be realized, and the conversion efficiency is 100%. The mode conversion efficiency of the few-mode fiber Bragg grating can be controlled by changing the mutual coupling coefficient and the grating length of the grating. The reflected four modes have equal energy, and the time delay is distributed in an equal difference mode, so that the few-mode optical fiber Bragg grating delay line is formed. The four modes are used as four taps of the microwave photon filter, and the tap coefficients are equal. Fig. 4 is a frequency response of a microwave photonic filter of an example of the present invention, which can be seen to achieve bandpass filtering.
The microwave photonic filter based on the few-mode optical fiber is introduced in detail, and the introduction is mainly used for further understanding the method and the core idea of the method; while the invention has been described with reference to specific embodiments and applications, it will be apparent to those skilled in the art that various changes in form and detail may be made therein without departing from the spirit and scope of the invention.

Claims (8)

1. The microwave photon filter based on the few-mode fiber Bragg grating is characterized by comprising a laser (1), an electro-optic modulator (2), a few-mode fiber Bragg grating delay line module (3), a few-mode fiber circulator (4), a photon lantern (5), a beam combiner (6), a photoelectric detector (7) and a vector network analyzer (8); the output port of the laser (1) is connected with one input port of the electro-optical modulator (2), and the output port of the vector network analyzer (8) is connected with the other input port of the electro-optical modulator (2); the output port of the electro-optical modulator (2) is connected with the 41 port of the few-mode optical fiber circulator (4); a 42 port of the few-mode optical fiber circulator (4) is connected with an input port of the few-mode optical fiber Bragg grating delay line module (3), and a 43 port of the few-mode optical fiber circulator (4) is connected with a tail fiber input port of the photon lantern (5); the output port of the photon lantern (5) is connected with the input port of the beam combiner (6); the output port of the beam combiner (6) is connected with the input port of the photoelectric detector (7); the output port of the photoelectric detector (7) is finally connected with the input port of the vector network analyzer (8).
2. The few-mode fiber bragg grating based microwave photonic filter according to claim 1, wherein the laser (1) generates a continuous single wavelength lightwave having a wavelength of 1550.51nm, which is a communication band wavelength.
3. The few-mode fiber bragg grating based microwave photonic filter according to claim 1, wherein the vector network analyzer (8) generates a frequency sweep signal, which is input into the electro-optical modulator (2) through a cable.
4. The few-mode fiber bragg grating based microwave photonic filter of claim 1, wherein the few-mode fiber bragg grating delay line module(3) The optical fiber Bragg gratings with the small modes are formed by cascading N few-mode optical fiber Bragg gratings, namely FBG1, FBG2, FBG3, mode. FBGs 1, 2, 3, 9, 3, 42, FBGN to the second port 42 of the few-mode fiber circulator (4), i.e. the fiber length of the head end of the few-mode fiber Bragg grating delay line module (3) is l1、l2、l3、...、lNAnd forming a few-mode fiber Bragg grating delay line with the delay difference delta tau.
5. The few-mode fiber bragg grating based microwave photonic filter according to claim 1, wherein the few-mode fiber circulator (4) can transmit a number of modes equal to or greater than the number of excitation modes of the few-mode fiber bragg grating delay line module (3).
6. The few-mode fiber bragg grating based microwave photonic filter according to claim 1, wherein the photonic lantern (5) is a mode demultiplexer capable of supporting N mode separations.
7. The few-mode fiber bragg grating based microwave photonic filter according to claim 1, wherein the beam combiner (6) is an N:1 equal splitting beam combiner.
8. The few-mode fiber bragg grating based microwave photonic filter according to claim 1, wherein the vector network analyzer (8) measures a swept frequency signal collected by the photodetector (7), the vector network analyzer (8) measuring a frequency response of the filter.
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