CN110459941B - 8-shaped cavity orbital angular momentum mode-locked fiber laser - Google Patents

8-shaped cavity orbital angular momentum mode-locked fiber laser Download PDF

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CN110459941B
CN110459941B CN201910697355.3A CN201910697355A CN110459941B CN 110459941 B CN110459941 B CN 110459941B CN 201910697355 A CN201910697355 A CN 201910697355A CN 110459941 B CN110459941 B CN 110459941B
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angular momentum
orbital angular
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甘久林
衡小波
杨中民
张智深
林巍
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South China University of Technology SCUT
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    • H01SDEVICES USING THE PROCESS OF LIGHT AMPLIFICATION BY STIMULATED EMISSION OF RADIATION [LASER] TO AMPLIFY OR GENERATE LIGHT; DEVICES USING STIMULATED EMISSION OF ELECTROMAGNETIC RADIATION IN WAVE RANGES OTHER THAN OPTICAL
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    • H01S3/06Construction or shape of active medium
    • H01S3/063Waveguide lasers, i.e. whereby the dimensions of the waveguide are of the order of the light wavelength
    • H01S3/067Fibre lasers
    • H01S3/0675Resonators including a grating structure, e.g. distributed Bragg reflectors [DBR] or distributed feedback [DFB] fibre lasers
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    • H01S3/091Processes or apparatus for excitation, e.g. pumping using optical pumping
    • H01S3/094Processes or apparatus for excitation, e.g. pumping using optical pumping by coherent light
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    • H01S3/10Controlling the intensity, frequency, phase, polarisation or direction of the emitted radiation, e.g. switching, gating, modulating or demodulating
    • H01S3/11Mode locking; Q-switching; Other giant-pulse techniques, e.g. cavity dumping
    • H01S3/1106Mode locking
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Abstract

The invention discloses an 8-shaped cavity orbital angular momentum mode-locked fiber laser which comprises a fundamental mode pumping source, a first polarization controller, an orbital angular momentum mode generator, a wavelength division multiplexer, a vortex gain fiber, a second polarization controller, a first fiber coupler, a second fiber coupler, a polarization isolator, a third polarization controller and a vortex fiber. The invention is based on mode separation and optimization design of optical fibers, and can ensure the generation and stable transmission of a specific order orbital angular momentum mode in a resonant cavity and at an output end by adopting a vortex optical fiber device. Based on a same-order mode pumping mechanism and a resonant cavity mode filtering effect, the gain of signal light in a same-order orbital angular momentum mode in the cavity is maximized, and then orbital angular momentum mode-locked laser output is obtained under the nonlinear amplification ring mirror mode-locked technology. Based on a single-mode direct resonance mechanism in the 8-shaped cavity, the output orbital angular momentum mode-locked laser has the advantages of high mode purity, good beam quality and the like.

Description

8-shaped cavity orbital angular momentum mode-locked fiber laser
Technical Field
The invention relates to the technical field of laser, in particular to an 8-shaped cavity orbital angular momentum mode-locked fiber laser.
Background
Vortex beam is field distributed with a helical phase term exp: (ilφ) Of a light beam in which each photon carrieslhOrbital angular momentum of (lIn order to be the number of topological charges,φin order to be the azimuth angle,hplanck constant), has the characteristics of annular light field distribution and helical phase singularities. These unique properties make it widely used in material processing,Optical tweezers, high-resolution imaging, optical fiber sensing, optical fiber communication and other fields. However, these application prospects put higher demands on the output peak power, stability, mode purity, bandwidth and the like of the vortex beam. Mode-locked pulsed laser can satisfy such requirements because of its advantages such as narrow pulse width, high peak power, wide spectrum width, etc. Meanwhile, the mode-locked pulse laser also has important application in the fields of material fine processing, interaction of high-field laser and substances and the like, and is also one of the key technologies for realizing future large-capacity high-speed optical fiber communication by being applied to wavelength division multiplexing and optical time division multiplexing. The mode-locked pulse vortex laser is formed by combining the mode-locked pulse laser and the vortex laser, and the application field is wider. Therefore, the research on the vortex optical mode-locked laser is of great significance.
There are two common architectures for mode-locked lasers: a spatial structure based on bulk optical elements and a fiber architecture based on fiber optic devices. Compared with the former, the mode-locking fiber laser has obvious advantages, and the cavity structure of the fiber laser is flexible (a linear cavity or an annular cavity), and the adjustable parameters in the cavity are more, so that mode-locking pulses can be generated conveniently. On the other hand, the mode-locked fiber laser has an all-fiber cavity, and the fiber has a plurality of special characteristics such as self-phase modulation, cross-phase modulation, nonlinear polarization rotation and the like, and the pulse quality can be effectively improved by reasonably utilizing the characteristics. Many researches on mode-locked fiber lasers have been made, and patent CN105428976A discloses a mode-locked fiber laser and a pulse laser generating method, which generate mode-locked pulses by adopting a linear cavity structure. Patent CN106785842A discloses a passive mode-locked fiber laser based on cadmium arsenide thin film, which adopts a ring cavity structure to realize high pulse energy mode-locked pulse output. In fact, when light waves are transmitted in an optical fiber, due to the limitation of the fiber core boundary, solving the helmholtz equation of light wave transmission results in a discontinuous electromagnetic field solution, which is called a mode and includes a fundamental transverse mode and a high-order transverse mode. The mode of stable transmission in the conventional single mode fiber is the fundamental transverse mode. The vortex light in the optical fiber is formed by overlapping odd mode and even mode of high-order vector transverse mode (HE or EH) with pi/2 phase difference, and is also called orbital angular momentum mode. It is obvious that the mode-locked fiber laser disclosed in the above patent outputs a fundamental transverse mode-locked pulse, and is not capable of directly generating an eddy optical mode-locked pulse.
At present, the method of generating the eddy optical mode-locking pulse is to add an orbital angular momentum mode generator or converter at the output end of the conventional mode-locking fiber laser, that is, to convert the fundamental transverse mode-locking pulse into an orbital angular momentum mode-locking pulse, for example, patent nos. CN105870768A, CN108963734A and CN 108988112A. Although the method can also generate orbital angular momentum mode-locked laser, the laser performance is heavily dependent on the performance of an orbital angular momentum mode generator or converter, the mode purity of the output laser is low, and the beam quality is poor. In addition, most of the fiber type orbital angular momentum mode generators or converters are made based on single mode fibers and conventional few mode fibers or multimode fibers. The traditional single-mode fiber only supports the transmission of a fundamental transverse mode, and the traditional few-mode fiber or the traditional multi-mode fiber can not meet the requirement of stable transmission of an orbital angular momentum mode in the fiber because a high-order vector transverse mode close to a propagation constant is degenerated into a linear polarization mode due to the approximation of weak waveguide. Therefore, the transmission of the mode-locked pulse in the orbital angular momentum mode converted from the output end of the conventional mode-locked fiber laser is unstable. Therefore, it is very important to design a mode-locked fiber laser to obtain stable and high-mode-purity mode-locked laser in orbital angular momentum mode.
Disclosure of Invention
In view of the above problems in the prior art, an object of the present invention is to provide an 8-shaped cavity mode-locked fiber laser in orbital angular momentum mode. The method has the advantages of low cost, easy integration of an optical fiber system, high purity of an output laser orbital angular momentum mode and good stability.
The purpose of the invention can be achieved by the following technical scheme.
An 8-shaped cavity orbital angular momentum mode-locked fiber laser comprises a fundamental mode pumping source, a first polarization controller, an orbital angular momentum mode generator, a wavelength division multiplexer, a vortex gain fiber, a second polarization controller, a first fiber coupler, a second fiber coupler, a polarization isolator, a third polarization controller and a vortex fiber;
the orbital angular momentum mode generator has a first port and a second port;
the wavelength division multiplexer has a first port, a second port and a third port;
the first fiber coupler has a first port, a second port, a third port, and a fourth port;
the second fiber coupler has a first port, a second port, and a third port;
the fundamental mode pump source is connected to a first port of an orbital angular momentum mode generator through a single mode fiber, the first polarization controller is applied to the single mode fiber, a second port of the orbital angular momentum mode generator is connected to a first port of a wavelength division multiplexer, a second port of the wavelength division multiplexer is connected to a first port of a first fiber coupler through a second polarization controller and a vortex gain fiber, a third port of the wavelength division multiplexer is connected to a second port of the first fiber coupler, a third port of the first fiber coupler is connected to a first port of a second fiber coupler, a second port of the second fiber coupler is connected to a fourth port of the first fiber coupler through a polarization isolator and a third polarization controller, and a third port of the second fiber coupler outputs orbital angular momentum mode laser.
The mode-locked fiber laser provided by the invention is of an 8-shaped cavity structure and comprises a nonlinear amplification ring mirror and a linear ring. The 8-shaped cavity is formed by connecting vortex optical fibers and devices based on the vortex optical fibers. Compared with the traditional few-mode fiber or multimode fiber, the vortex fiber is designed by increasing the refractive index contrast of the fiber core and the cladding so as to break the degeneracy of vector modes with similar propagation constants, namely the effective refractive index difference of each vector mode supported by the fiber is larger than 1 multiplied by 10-4And further realize the stable transmission of the orbital angular momentum mode in the cavity. The wavelength division multiplexer, the second polarization controller, the vortex gain fiber and the first fiber coupler form a nonlinear amplification ring mirror, and the first fiber coupler, the second fiber coupler, the polarization isolator and the third polarization controller form a linear ring. The polarization isolator is used for suppressing nonlinearityThe second polarization controller and the third polarization controller are used for adjusting the polarization state of the transmission light in the optical fiber. And the fundamental mode pump light output by the fundamental mode pump source is converted into specific orbital angular momentum mode pump light through a polarization controller and an orbital angular momentum mode generator. The pumping light in the orbital angular momentum mode enters the nonlinear amplification ring mirror through the wavelength division multiplexer, and a gain medium in the vortex gain fiber is excited to generate spontaneous radiation light carrying the same orbital angular momentum. The spontaneous radiation light in the orbital angular momentum mode enters the linear ring through the first optical fiber coupler and then runs in a single direction, and then is divided into two light beams which are transmitted in opposite directions through the first optical fiber coupler. Light in one direction is amplified upon entering the non-linear amplification ring mirror, and light in the other direction is amplified upon exiting the non-linear amplification ring mirror. Two light waves with opposite propagation directions obtain different nonlinear phase shifts when completing one-time annular in the nonlinear amplification annular mirror, and the phase difference is not constant but changes along with the pulse shape. The energy at the center of the pulse is stronger, more nonlinear phase shift is obtained, and the transmittance is larger, while the energy at the two sides of the pulse is weaker, and the nonlinear phase shift is accumulated less and is reflected more. When the pulse is circulated to the first fiber coupler, the center of the pulse is transmitted and two sides of the pulse are reflected, which is equivalent to the function of a saturable absorber, and finally the pulse output from the nonlinear amplification ring mirror is narrower than the pulse input by the nonlinear amplification ring mirror. The mode locking of the laser can be stabilized by adjusting the second polarization controller and the third polarization controller. This 8-shaped cavity design ensures stable existence of orbital angular momentum modes within the cavity and direct resonant lasing. Finally, the orbital angular momentum mode-locked pulse is output through a third port of the second fiber coupler.
Preferably, the orbital angular momentum mode generator is a fusion type optical fiber mode selection coupler, a long-period optical fiber grating or a chiral optical fiber grating, the mode conversion efficiency is greater than 70%, the mode purity is greater than 80%, the first port adopts a single-mode optical fiber, and the second port adopts a vortex optical fiber.
Preferably, the first port, the second port and the third port of the wavelength division multiplexer are all vortex optical fibers.
Preferably, the vortex gain fiber is a vortex fiber which is formed by annularly doping one or more combinations of lanthanide rare earth luminescent ions, transition metal ions or alkaline earth metal ions with high concentration in a fiber core.
Preferably, the first optical fiber coupler is a 2 × 2 coupler made by fusion tapering of a vortex optical fiber and a vortex optical fiber, the splitting ratio of the first port to the second port is 50:50, and the vortex optical fibers are adopted for the first port, the second port, the third port and the fourth port.
Preferably, the second optical fiber coupler is a 1 × 2 coupler made by melting and tapering a vortex optical fiber and the vortex optical fiber, and the vortex optical fiber is adopted for the first port, the second port and the third port.
Preferably, the vortex optical fiber is a step-index ring-core optical fiber, a gradient-index optical fiber or an inverse parabolic-index optical fiber supporting stable transmission of orbital angular momentum mode, and the difference of effective refractive index of each transmitted vector mode is larger than 1 × 10-4
Compared with the prior art, the invention has the following beneficial effects:
1. based on a same-order mode pumping mechanism and a resonant cavity filtering effect, pumping is carried out on a resonant cavity by utilizing specific-order orbital angular momentum mode pumping light, so that signal light in the same-order orbital angular momentum mode in the cavity is directly resonated, and the obtained laser mode has high purity and good beam quality;
2. the passive mode locking technology of the nonlinear amplification ring mirror is utilized, the regulation and control are simple, and the stability of the output laser pulse is good;
3. the invention adopts an all-fiber structure, has the advantages of low cost, easy integration of a fiber system and the like, and improves the practicability of the orbital angular momentum mode laser.
Drawings
Fig. 1 is a schematic diagram of an 8-shaped cavity orbital angular momentum mode-locked fiber laser in example 1.
In the figure, a 1-base mode pump source, a 2-first polarization controller, a 3-orbital angular momentum mode generator, a 301-orbital angular momentum mode generator first port, a 302-orbital angular momentum mode generator second port, a 4-wavelength division multiplexer, a 401-wavelength division multiplexer first port, a 402-wavelength division multiplexer second port, a 403-wavelength division multiplexer third port, a 5-second polarization controller, a 6-vortex gain fiber, a 7-first fiber coupler, a 701-first fiber coupler first port, a 702-first fiber coupler second port, a 703-first fiber coupler third port, a 704-first fiber coupler fourth port, an 8-second fiber coupler, a 801-second fiber coupler first port, 802-second fiber coupler second port, 803-second fiber coupler third port, 9-polarization isolator, 10-third polarization controller, 11-vortex fiber.
Detailed Description
The present invention will be described in further detail with reference to examples and drawings, but the present invention is not limited thereto.
Example 1
Fig. 1 shows an 8-shaped cavity orbital angular momentum mode-locked fiber laser in this embodiment, which includes a fundamental mode pump source 1, a first polarization controller 2, an orbital angular momentum mode generator 3, a wavelength division multiplexer 4, a second polarization controller 5, a vortex gain fiber 6, a first fiber coupler 7, a second fiber coupler 8, a polarization isolator 9, and a third polarization controller 10. Wherein the orbital angular momentum mode generator 3 has a first port 301 and a second port 302; the wavelength division multiplexer 4 has a first port 401, a second port 402 and a third port 403; the first fiber coupler 7 has a first port 701, a second port 702, a third port 703 and a fourth port 704; the second fiber coupler 8 has a first port 801, a second port 802, and a third port 803; the fundamental mode pump source 1 is connected to a first port 301 of an orbital angular momentum mode generator 3 through a single mode fiber, a first polarization controller 2 is applied on the single mode fiber, a second port 302 of the orbital angular momentum mode generator 3 is connected to a first port 401 of a wavelength division multiplexer 4, a second port 402 of the wavelength division multiplexer 4 is connected to a first port 701 of a first fiber coupler 7 through a second polarization controller 5 and a vortex gain fiber 6, a third port 403 of the wavelength division multiplexer 4 is connected to a second port 702 of the first fiber coupler 7, a third port 703 of the first fiber coupler 7 is connected to a first port 801 of a second fiber coupler 8, a second port 802 of the second fiber coupler 8 is connected through a polarization isolator 9, the third polarization controller 10 is connected to the fourth port 704 of the first fiber coupler 7, and the third port 803 of the second fiber coupler 8 outputs the orbital angular momentum mode-locked laser.
In this embodiment, 980nm semiconductor laser is selected as the fundamental mode pump source 1; the orbital angular momentum mode generator 3 is a fused fiber mode selection coupler and is made by fusion tapering of a conventional single-mode fiber and a gradient refractive index fiber supporting stable transmission of an orbital angular momentum mode with topological charge number of 1, the diameter ratio of the single-mode fiber and the gradient refractive index fiber is determined according to phase matching conditions of an HE11 mode in the single-mode fiber and an HE21 mode in the gradient refractive index fiber before the fusion tapering, a base mode is injected into the single-mode fiber during the tapering, the tapering is stopped when the maximum optical power and a circular ring light spot are observed in the gradient refractive index fiber, namely, the directional selection coupling between the base mode in the single-mode fiber and the orbital angular momentum mode with the topological charge number of 1 in the gradient refractive index fiber is realized, the mode conversion efficiency is 80%, the mode purity is 90%, the first port 301 is the single-mode fiber, and the second port 302 is the gradient refractive index fiber; the first port 401, the second port 402 and the third port 403 of the wavelength division multiplexer 4 are gradient refractive index optical fibers, so that 980nm pump light with the topological charge number of 1 can be efficiently injected into the nonlinear amplification ring mirror, and 1550nm signal light with the topological charge number of 1 can pass through with low loss; the vortex gain optical fiber 6 is a gradient refractive index optical fiber with erbium ions doped in the fiber core in a ring shape; the first optical fiber coupler 7 is a 2 x 2 coupler made by fusion tapering of a gradient refractive index optical fiber and a gradient refractive index optical fiber, can realize the coupling of an orbital angular momentum mode with topological charge number of 1 at 1550nm between the gradient refractive index optical fibers, the first port 701, the second port 702, the third port 703 and the fourth port 704 are all gradient refractive index optical fibers, and the splitting ratio of the first port 701 to the second port 702 is 50: 50; the second optical fiber coupler 8 is a 1 × 2 coupler made by fusion tapering of gradient index optical fiber and gradient index optical fiber, and can realize the coupling between gradient index optical fibers in the orbital angular momentum mode with topological charge number of 1 at 1550nmThe first port 801, the second port 802 and the third port 803 are all gradient index optical fibers, and the splitting ratio of the second port 802 and the third port 803 is 90: 10; the vortex optical fiber 11 is a gradient refractive index optical fiber supporting stable transmission of an orbital angular momentum mode with topological charge numbers of 1 at 980nm and 1550nm, and the minimum effective refractive index difference between the transmitted vector modes is 1.5 multiplied by 10-4It can be understood that the gradient index optical fiber used in the present embodiment is the same, and further reduces the loss in the optical path when ensuring the stable transmission of the orbital angular momentum mode.
In the present embodiment, the wavelength division multiplexer 4, the second polarization controller 5, the vortex gain fiber 6, and the first fiber coupler 7 constitute a nonlinear amplification ring mirror, and the first fiber coupler 7, the second fiber coupler 8, the polarization isolator 9, and the third polarization controller 10 constitute a linear loop. The polarization isolator 9 is used for suppressing the reflected light of the nonlinear amplification ring mirror and ensuring that the light runs in a linear ring in a single direction, and the second polarization controller 5 and the third polarization controller 10 are used for adjusting the polarization state of the transmitted light in the optical fiber. The fundamental mode pump source 1 outputs 980nm fundamental mode pump light, and the fundamental mode pump light is converted into orbital angular momentum mode pump light with topological charge number of 1 through the polarization controller 2 and the orbital angular momentum mode generator 3. Pumping light in an orbital angular momentum mode with the topological charge number of 1 enters the nonlinear amplification ring mirror through the wavelength division multiplexer 4, and a gain medium in the vortex gain fiber 6 is excited to generate spontaneous radiation light in the orbital angular momentum mode with the topological charge number of 1. The spontaneous radiation light in the orbital angular momentum mode enters the linear ring through the first optical fiber coupler 7 and then runs in a single direction, and then is divided into two light beams which are transmitted in opposite directions through the first optical fiber coupler 7. The light at the 701 port is amplified when entering the nonlinear amplification ring mirror, and the light at the 702 port is amplified when exiting the nonlinear amplification ring mirror. The two light waves with opposite propagation directions obtain different nonlinear phase shifts when completing one-time loop in the nonlinear amplification loop mirror, and the phase difference is not constant but changes along with the pulse shape. The energy at the center of the pulse is stronger, more nonlinear phase shift is obtained, and the transmittance is larger, while the energy at the two sides of the pulse is weaker, and the nonlinear phase shift is accumulated less and is reflected more. When the pulse is circulated to the first fiber coupler 7, the center of the pulse is transmitted and both sides of the pulse are reflected, which is equivalent to the function of a saturable absorber, and finally the pulse output from the nonlinear amplification ring mirror is narrower than the pulse input by the nonlinear amplification ring mirror. The laser can be stably mode-locked by adjusting the second polarization controller 5 and the third polarization controller 10, and the orbital angular momentum mode-locked pulse is output through the third port 803 of the second fiber coupler 8.
The above embodiments are preferred embodiments of the present invention, but the present invention is not limited to the above embodiments, and any other changes, modifications, substitutions, combinations, and simplifications which do not depart from the spirit and principle of the present invention should be construed as equivalents thereof, and all such changes, modifications, substitutions, combinations, and simplifications are intended to be included in the scope of the present invention.

Claims (5)

1. An 8-shaped cavity orbital angular momentum mode-locked fiber laser is characterized by comprising a fundamental mode pumping source, a first polarization controller, an orbital angular momentum mode generator, a wavelength division multiplexer, a vortex gain fiber, a second polarization controller, a first fiber coupler, a second fiber coupler, a polarization isolator, a third polarization controller and a vortex fiber;
the orbital angular momentum mode generator has a first port and a second port;
the wavelength division multiplexer has a first port, a second port and a third port;
the first fiber coupler has a first port, a second port, a third port, and a fourth port;
the second fiber coupler has a first port, a second port, and a third port;
the fundamental mode pump source is connected to a first port of an orbital angular momentum mode generator through a single mode fiber, the first polarization controller is applied to the single mode fiber, a second port of the orbital angular momentum mode generator is connected to a first port of a wavelength division multiplexer, a second port of the wavelength division multiplexer is connected to a first port of a first fiber coupler through a second polarization controller and a vortex gain fiber, a third port of the wavelength division multiplexer is connected to a second port of the first fiber coupler, a third port of the first fiber coupler is connected to a first port of a second fiber coupler, a second port of the second fiber coupler is connected to a fourth port of the first fiber coupler through a polarization isolator and a third polarization controller, and a third port of the second fiber coupler outputs orbital angular momentum mode laser;
the refractive index of the fiber core and the refractive index of the cladding of the vortex optical fiber meet high refractive index contrast so that the difference of effective refractive index of each vector mode supported in the vortex optical fiber is larger than 1 multiplied by 10-4The optical fiber further supports stable transmission of an orbital angular momentum mode; the orbital angular momentum mode generator is a fusion type optical fiber mode selection coupler, a long-period optical fiber grating or a chiral optical fiber grating, the mode conversion efficiency is more than 70%, the mode purity is more than 80%, the first port adopts a single-mode optical fiber, and the second port adopts a vortex optical fiber;
the orbital angular momentum mode generator, the wavelength division multiplexer, the vortex gain fiber, the first fiber coupler, the second fiber coupler and the polarization isolator are all vortex fiber devices and support generation and stable transmission of an orbital angular momentum mode in the resonant cavity and at the output end; the second optical fiber coupler is a 1 x 2 coupler made by melting and tapering a vortex optical fiber and the vortex optical fiber, and the first port, the second port and the third port all adopt vortex optical fibers;
the wavelength division multiplexer, the second polarization controller, the vortex gain fiber and the first fiber coupler form a nonlinear amplification ring mirror, the first fiber coupler, the second fiber coupler, the polarization isolator and the third polarization controller form a linear ring, the nonlinear amplification ring mirror and the linear ring form an 8-shaped resonant cavity, and based on a same-order mode pumping mechanism and a mode filtering effect of the resonant cavity, the same-order orbital angular momentum mode in the cavity directly resonates, so that high-purity orbital angular momentum mode-locked laser output is obtained under a nonlinear amplification ring mirror mode-locked technology.
2. The 8-shaped cavity orbital angular momentum mode-locked fiber laser according to claim 1, wherein the first port, the second port and the third port of the wavelength division multiplexer are all vortex fibers.
3. The 8-shaped cavity orbital angular momentum mode-locked fiber laser according to claim 1, wherein the vortex gain fiber is a vortex fiber which is annularly doped with one or more of lanthanide rare earth luminescent ions, transition metal ions or alkaline earth metal ions in a fiber core.
4. The 8-shaped cavity orbital angular momentum mode-locked fiber laser device according to claim 1, wherein the first fiber coupler is a 2 x 2 coupler made of a vortex fiber and a vortex fiber fused biconical taper, the splitting ratio of the first port to the second port is 50:50, and the vortex fibers are adopted for the first port, the second port, the third port and the fourth port.
5. The 8-shaped cavity orbital angular momentum mode-locked fiber laser according to claim 1, wherein the vortex fiber is a step-index ring-core fiber, a gradient-index fiber or an inverse parabolic-index fiber supporting stable transmission of an orbital angular momentum mode.
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