Abstract

We experimentally investigate high-order modes (HOMs) generating at the wavelength of 1.0 μm in all-fiber Yb-doped lasers based on mode-selective couplers (MSCs). Broadband MSCs for HOMs conversion are achieved by optimizing the phase-matching condition at 1.0 μm. Efficient generation of HOMs is demonstrated with the MSCs inserted both into continuous-wave and mode-locked fiber lasers. The slope efficiencies of HOMs (LP11, LP02 and LP21) are presented and discussed. Additionally, cylindrical vector and orbital angular momentum beams are produced out of the MSCs by controlling the polarization states. The results show proof-of-concept implementation of the MSCs, which enables high efficiency of HOMs generation especially in pulsed fiber lasers and holds promising applications in laser material processing.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Multimode fiber laser opens a new platform for nonlinear wave propagation researching in multimode optical fibers [1–3]. High-order modes (HOMs) in a few-mode fiber (FMF) cannot only propagate over a much broader area enabling more available energy level in the fiber lasers, but also have attracted rapid attentions in the applications, such as the generation of orbital angular momentum (OAM) due to the unique spatial intensity and polarization distribution properties of HOMs. OAM beams are spatially structured beams with helical phase front and a phase singularity in the doughnut-shaped spatial intensity [4,5]. On the other hand, degenerated linear polarization (LP11) mode is one of the most popular HOMs in the fiber, which consists of four vector eigenmodes. These eigenmodes, also called as cylindrical vector beams (CVBs) in the field of guided wave, are characterized by an axially symmetrical distribution of spatial polarization and field amplitude, including radially polarized, azimuthally polarized and hybrid polarized beams. Such HOM beams attract much attention in the applications, e.g. high-resolution measurement [6], optical trapping and manipulation of particles [7], quantum information technology [8–10], remote sensing [11], mode-division multiplexing optical communications [12], ultraviolet lithography [13] as well as laser material processing [14], etc.

Various kinds of methods have been demonstrated to generate HOMs in fiber lasers, where spatial mode-selective elements such as birefringence crystal [15], q-plate [16] and spatial light modulator [17] are used. However, those elements are normally designed for a specific laser wavelength, which lead to the inherently constrains of wavelength versatility consequently. Furthermore, all of these aforementioned mode conversions require careful alignment of free-space optics and suffer from the damage risks in high power lasers [18]. To pursue a convenient, stable and integrated device to generating HOMs, different types of optical-fiber based mode converters, such as few-mode fiber Bragg grating (FM-FBG) and long period grating (LPG) methods have been proposed. FM-FBG method has been reported to be an effective way to select one of the HOMs in the FMF [19–21]. However, the spectrum bandwidth of HOMs may be limited by the narrow reflective response of FM-FBG. Recently, an efficient solution of realizing high power HOMs has been reported by using a cladding-pumped all-fiber oscillator configuration [22]. The LPG method couples light from a fundamental core mode into forward propagating cladding HOMs in a FMF. A picosecond fiber laser with hundreds of Watt output power and over 50 W supercontinuum output in LP11 modes are demonstrated based on mechanical LPGs [23,24]. There is still a challenge to efficiently separate HOMs from the fundamental mode (LP01) in the long period gratings.

On the other hand, a mode-selective coupler (MSC) composed of a single-mode fiber (SMF) and a FMF has been proposed to be used in the femtosecond mode-locked fiber laser at 1.5 μm [25,26], which provides an effective method to break the limitation of conversion bandwidth. Furthermore, all-fiber structure of the MSC presents excellent integration with the fiber lasers. Since then, many fiber lasers based on high-order MSCs have been reported [27,28]. Intra-cavity and extra-cavity methods are seen as two kinds of ways to adopt MSCs in and outside the fiber laser. Though the extra-cavity method provides an independent and convenient mode conversion process, it requires high-efficiency of mode-conversion to ensure efficient output. However, it is still a challenge to fabricate the MSCs of higher-order modes, such as LP21 and LP31 modes. Based on the intra-cavity method, a MSC with a low coupling ratio directly converts some amount of LP01 mode beams to HOMs and the uncoupled LP01 mode output from the SMF port continues to circle in the resonant cavity. Therefore, the intra-cavity method has the advantage of high efficiency to generate and separate HOMs from LP01 mode lasing in the cavity. As we know, these studies are mainly focused at the wavelength of 1.5 μm currently. For many applications, such as material process of cutting and bio-photonics, high-power HOMs generation at 1.0 μm is extremely preferred [29]. Up to now, only few studies of generating high-efficiency HOMs at 1.0 μm are reported [30]. As a result, high power HOMs from fiber lasers at near-infrared region still deserves a detailed investigation, especially in pulsed HOMs.

In this paper, we demonstrate a promising method of generating HOMs (LP11, LP02 and LP21) by using diversified kinds of broadband fused MSCs, respectively. The LP-MSCs with different output coupling ratios (CRs) are spliced both into continuous wave (CW) and mode-locked fiber laser cavities to pursue efficient generation of HOMs. The slope efficiencies of LP11, LP02 and LP21 outputs are experimentally investigated and discussed. The proof-of-concept implementation of the MSCs demonstrates high efficiency of HOMs generation both in CW and pulsed Yb-doped fiber lasers.

2. Fabrication and characteristics of the MSCs

A high-efficient MSC at the wavelength of 1.0 μm is presented which directly converts the fundamental (LP01) mode to HOMs as well as plays the role of a power splitter. The schematic of the MSC is shown in Fig. 1(a), which composes of a SMF (core/cladding diameter = 6.2/125 μm, NA = 0.14, HI1060) and a FMF (core/cladding diameter = 20/125 μm NA = 0.14). Mode conversion is completed in the coupling region which is marked as depicted in Fig. 1(a). Microscopic images of the coupling region are also displayed with a microscope. The two parallel optical fibers are fused together using an oxyhydrogen flame to keep their fiber cores very close to each other.

 

Fig. 1 (a) Schematic of the MSC. The LP01 mode at 1.0 μm is lunched into the SMF input port (blue) and one of HOMs is excited at the FMF output port (red). The microscopic images of the coupling region are inserted. (b) Mode conversion evolution of LP01 to LP11, LP21, LP02 and LP31 modes in the simulation and the experimental intensity profiles of corresponding high-order modes.

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Coupled-mode theory has been proposed to be the basic principle of fiber MSCs [31–33]. Two closed optical waveguides change their energy based on phase matching conditions. The power distributions in a mode-selective coupler are given by

|A(z)|2=1ksin2(Dz)
|B(z)|2=ksin2(Dz)
where A(z) and B(z) represent the slowly-varying field amplitudes of SMF and FMF as a function of the coupling length z, and D is given as D=c/k. The power of LP01 mode can be completely transferred into a certain HOM, when the coupling length z equals to the periodic value zc
z=zc=(2n1)π2ck
Here, n can take any positive integer value. The power transfer coefficient k is defined as:
k[1+(βAβB)24c2]1
Here, βAand βBare modal propagation constants of the corresponding fibers, and c represents the coupling coefficient between the two fibers, which depends on the length and width of coupling region. When the two fibers are perfectly phase-matched, i.e.,βA=βB, the power exchanges periodically in the coupling region. The modal propagation constant is defined as 2πneff/λ. The neff represents the effective refractive index, which is dependent on the refractive indices and the diameters of fiber core and claddings. In practice, the effective coupling can be realized by pre-tapering SMF fibers to the optimum-diameter proportion of two fibers [25].

The perfect agreements between numerical simulations and experimental results are obtained at the wavelength of 1.5 and 1 μm, respectively. Mode effective refractive indices are calculated in the different fiber diameters for step-index fiber profiles to find the phase matching condition. Then, a commercial simulation software (Rsoft) is used to solve the phase-matching condition in the MSCs numerically, as detailed in the previous work [25,26]. The simulation and experiment results are shown in Fig. 1(b). The propagating modes both in the SMF and the FMF are guided in silica microfibers by assuming the silica-air interface under weakly fused condition. In order to achieve complete conversion in first half period of power exchange, the SMF need to be pre-tapered to different optimum diameters for HOMs (LP11, LP21, LP02 and LP31). Then, the pre-tapered SMF is fused together with the un-tapered FMF. This suggests that one can achieve mode selective excitation of any HOMs transmitted in the FMF by satisfying the peculiar phase-matching condition.

Optimum pre-tapering diameters for the MSCs are ascertained by iterating the fusing process, so as to pursue high conversion efficiency and low insert loss. The first-half period of mode conversion is preferred and high-order mode purity may be deteriorated if the coupling length is several periods of the optimal coupling length. The longer the coupling regime is, the thinner the cross-section diameters are, but it would suffer more destabilization. With the increase of coupling region length, the exchange period gets shorter and maximum conversion efficiency is obtained.

The coupling efficiency is defined as the ratio of output HOM power from a FMF to the total input power and the insert loss is the ratio of both output powers to the input power. The coupling efficiency and the insert loss are measured when the converted HOM powers reach the peak value at the first half period. The coupling efficiency of the LP11 MSC is up to 94.2% and the total insert loss is 0.26 dB when the optimum pre-tapered diameter of a SMF is 102 μm as presented in Fig. 2(a). The coupling efficiency of LP02 MSC is more than 86%, and the insert loss is 1.3 dB at the wavelength of 1060 nm when the pre-tapered diameter of the SMF is around 79 μm as shown in Fig. 2(c). The transmission spectra of LP11 and LP02 MSCs at 1060 nm are presented in Figs. 2(b) and 2(d), respectively. The inset pictures show the mode patterns of LP01 and the corresponding HOMs at the SMF and FMF output ports. The maximum power transmission of LP11 mode is close to 0 dB and the corresponding LP01 mode is attenuated to lower than −23 dB. The coupling ratio (CR) is defined as a HOM power over the total output power. High-contrast transmissions for LP01 conversion to LP11 modes indicate that the CR is up to 98% with the insert loss below 0.3 dB. Furthermore, the purity of the corresponding optical HOMs is estimated to be higher than 97.5% (LP11) and 93% (LP02) by bending the FMF tightly to attenuate HOMs [34].

 

Fig. 2 Coupling efficiency (CE) and insert loss (IL) of (a) LP11 and (c) LP02 MSCs as a function of the diameter of the pre-tapered SMF. The corresponding transmission spectra of (b) LP11 and (d) LP02 MSCs at the wavelength of 1.0 μm.

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3. Generating HOMs in a continuous-wave fiber laser

In order to investigate the characteristics of the MSCs with different CR in the laser cavity, LP11 MSCs with different output CRs of 17%, 33%, 55%, 70%, 89%, 96% and 98% are spliced into the laser resonator. The insert losses of the MSCs are lower than 0.3 dB. The experimental setup of a CW fiber laser with HOMs output is shown in Fig. 3(a). A 980-nm laser diode which provides the pump power is connected to a 980/1064 nm wavelength division multiplexer. A section of 0.2 m Ytterbium-doped fiber (YDF: LIEKKI Yb1200-4/125) is pumped to provide power gain. A single-mode fiber Bragg grating (FBG) at 1064 nm is used to be a resonator reflector as well as a narrow band filter to increase the purity of the HOMs. The reflect mirror set in the cavity is made by a commercial coupler with coupling ratio of 50:50, whose two output ports are connected together. The fused SMF-FMF fiber coupler is inserted in the laser cavity to act as an efficient converter of single-wavelength HOMs as well as an output splitter. The intra-cavity PC1 is used to control the polarization state of the fiber laser cavity. The PC2 is used to adjust the polarization state and eliminate the mode degeneracy of the output beam. The output mode intensity profiles are collimated through a focus lens and recorded by two kinds of CCD cameras (monochrome picture: InGaAs camera, Model C10633-23 from Hamamatsu Photonics; colorized picture: commercial USB-CCD laser camera). The output spectrum is analyzed by an optical spectrum analyzer (YOKOGAWA, AQ6370C), and the output power is measured by a power meter.

 

Fig. 3 (a) Experimental setup of a continuous-wave HOMs laser. (b) Output spectra for different CRs (17%, 33%, 55%, 70% and 89%). (c) Output power (green point) and the corresponding SBR (blue point) of LP11 MSCs inside a CW laser cavity for different CR. (d) Spectrum from a LP11 MSC with the CR of 89% after attenuation. FBG: Fiber Bragg grating; WDM: Wavelength Division Multiplexing coupler; PC: Polarization Controller; YDF: ytterbium-doped Fiber; CCD: Charge Coupled Device, infrared camera.

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Output laser spectra are measured as shown in Fig. 3(b). The center wavelength of the laser is around 1064 nm. When the pump power of the CW laser is 600 mW, the output power and the signal-to-background ratio (SBR) as a function of different CR are presented in Fig. 3(c). The output power increases with the CR of the MSCs until the CR is up to 89% at the cost of lower SBR. Further increasing of output CR changes the threshold condition of laser cavity and no obvious spectra at 1064 nm are observed. The maximum output power of 305 mW is obtained when the CR is selected to be 89% and the slope efficiency (SE) of the CW fiber laser is about 57%. The corresponding output spectrum after power attenuation is presented in Fig. 3(d), which has a wavelength bandwidth about 0.22 nm, narrower than the reflective bandwidth of 1064 nm FBG (0.38 nm).

With the increase of the output CR, background signals around 1030 nm get stronger and the largest signal-to-background ratio (SBR) of 65 dB is achieved with the output CR of 17%, which means the lower output CR have the higher SBR of the output spectrum. The output powers of HOMs as a function of pump power are shown in Fig. 4, which present a linear relationship. The slope efficiency of the CW laser cavity is also increased with the increase of CR. The LP02 (LP21) MSC with the insert loss of 1.3 dB (3.1 dB) and the output CR of 21% (15.4%) is fabricated and inserted in the CW laser to obtain high-quality LP02 (LP21) mode beams. The inserted figures represent the intensity profiles of their corresponding modes. The slope efficiencies of HOMs (LP11, LP02 and LP21) output powers are 9.38%, 5.04% and 3.03%, respectively. The decreasing slope efficiency of HOMs is caused by higher insert loss.

 

Fig. 4 HOMs (LP11, LP02 and LP21) output power and slope efficiency (SE) versus the pump power for different CRs of the MSCs. Insert figures are near-field intensity distribution of HOMs.

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Intensity profiles and polarization states of HOMs are recorded by using CCD devices. Note that linear polarization (LP) mode is a degenerated mode composed of vector eigenmodes, i.e., four vector modes with approximately identical effective refractive indices. The LP11 mode beams are composed ofTM01, TE01andHE21even/oddmodes. Efficient mode coupling occurs in the MSC and different eigenmodes can be excited by adjusting the PCs on the FMF output, which induce the rotation and extrusion to eliminate the mode degeneracy. As shown in Fig. 5, near-field distributions of degenerated vector modes are doughnut-like shapes. A polarizer before CCD is used to characterize vector beams and the polarizer directions are marked with double-headed black arrows. The intensity evolutions of the transmitted beam with the rotation of the polarizer are measured, as shown in Fig. 5(a). TM01 and TE01 modes are also known as the cylindrical vector beams, which are characterized by the axial of polarization distribution and field amplitudes, and they are two orthogonal modes as shown in the first and second rows of Fig. 5(a). The third and fourth rows are the even and odd HE21 modes, respectively.

 

Fig. 5 Near-field distribution of (a) CVBs and (b) OAMs output from the CW laser. The first column of (a): the vector modes with donut-shape intensity profiles. The second, third, fourth and fifth columns are the near-field distributions of each vector modes with a polarizer placed in front of the CCD. (b): Near-field distribution of LP modes, donut-shape OAM patterns and spiral interferograms of OAM+1, OAM-1, OAM+2 and OAM-2.

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Optical vortex beams (OVBs) are characterized by a helical phase front with OAM quantities, which provide unique materials processing technology [35,36]. The OAM modes are composed of two orthogonal vector modes with ±π/2 phase shift. As mentioned above, we can obtain two pairs of orthogonal vector modes (TM01, TE01) and (HE21even, HE21odd) by adjusting the PCs carefully. A simple method to produce a ±π/2 phase difference between two orthogonal vector modes has been proposed by stress the fiber [37]. Stress changes the effective dimensions of the FMF and the phase velocities of the two modes are changed as well. We use the PC2 to give a stress on the FMF. The output OAM1, 2 beams with a circularly symmetric intensity profile carrying OAM are shown in Fig. 5(b). Here, the linearly polarized modes, donut-shaped modes and their spiral intensity patterns are presented. The spiral intensity patterns are the interferences between a donut-shaped mode beam and a synchronous Gauss beam. The clockwise and anticlockwise spiral interferograms represent the negative and positive OAM of 1 and 2, respectively.

4. Generating HOMs in a mode-locked fiber laser

Nonlinear polarization rotation effect is employed in our experiment, which has been widely used to generate ultrafast pluses in a passively mode-locked fiber laser. Schematic setup of a mode-locked fiber laser (MLFL) with a HOM output is shown in Fig. 6. Pump source of 980nm is injected in the laser cavity by a wavelength division multiplexer and about 0.25 m YDF is inserted in fiber resonant cavity to provide power gain at the wavelength of 1.0 μm. The nonlinear polarization rotation mode-locking technique is implemented by two PCs and a polarization dependent isolator. A fused SMF-FMF high-order fiber MSC is located in the resonant cavity, acting as a power splitter and mode converter. All the devices in the cavity are connected by a SMF (HI-1060 fiber of Corning) with group velocity dispersion of 23 ps2/km at 1060 nm. The total length of MLFL cavity is measured about 7.9 meters. The output spectrum of HOM mode-locked pulse from the MSC is measured by an optical spectrum analyzer and the time-domain pulse is detected by a 1-GHz oscilloscope (Tektronix, MSO 4104). The intensity profiles of the output beam are recorded by CCD cameras as explained before.

 

Fig. 6 Experimental setup of mode-locked HOM laser. PD-ISO: Polarization dependent Isolator; OSC: Oscilloscope; OSA: Optical Spectrum Analyzer.

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Mode-locking is achieved in the fiber laser by adjusting the polarization states inside the cavity. Together with a polarization dependent isolator, two PCs work as an effective ultra-fast saturation absorber. Mode-locked LP11 mode can be obtained when a LP11 MSC with the CR of 17% is used as the output splitter of laser cavity. The pump power varies from 350 mW to 410 mW to maintain a stable mode-locking state. Output spectrum of LP11 mode is presented in Fig. 7(a), the 3-dB spectral bandwidth is measured to be 14 nm. The pulse train is recorded at the same time as shown in Fig. 7(b). The max output power of LP11 mode is measured to be 75 mW when the pump power is set as 410 mW. The slope efficiency of the MLFL is measured to be 31% shown in Fig. 7(c), which is much higher than the previous proposed HOMs mode-locked laser due to high gain of Yb-doped fiber.

 

Fig. 7 Characteristics of HOMs output from Yb-doped MLFL. The output spectra, mode-locked pulse trains and output power versus pump power are measured when (a, b, c) a LP11 MSC with the CR of 17%, (d, e, f) a LP02 MSC with the CR of 21%, (g, h, i) a LP21 MSC with the CR of 15% are inserted in the resonant cavity, respectively.

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Mode-locking condition can also be achieved when a LP02 (LP21) MSC with the CR of 21% (15%) is inserted in the resonant cavity as a power splitter. The spectral characteristics and the mode-locked pulse trains of LP02 and LP21 are described in Figs. 7(d)-7(e) and Figs. 7(g)-7(h), respectively. The 3dB-spectrum bandwidth is measured to be 15.5 (18) nm for LP02 (LP21) mode. All of the output spectra have steep spectral edges, which indicate that the mode-locked pulses are dissipative solitons. The structured spectra are caused by the interference between the degenerated HOMs [26]. It can be seen that the fundamental repetition frequencies of LP11, LP02 and LP21 mode output pulse are about 26 MHz, which are consistent with the cavity length of 7.9 m.

As shown in Figs. 7(f) and 7(i), the max output power of 65 (16) mW mode-locked LP02 (LP21) mode can be obtained when the pump power is 468 (455) mW and the calculated slope efficiency is 18% (6.1%). The difference of pump threshold for HOMs mode-locking is attributed to the different insert loss of the MSCs. Though the pulse durations are not measured at 1 μm at the moment, further dispersion optimization of fiber cavity is expected to produce femtosecond-scale HOMs. Meanwhile, further power scaling of HOMs can be expected by using double-cladding YDF and in-band pump approach, such as utilizing 1020 nm source instead of 980 nm pump [38].

5. Conclusion

In conclusion, we demonstrate efficient generation of HOMs output both from CW and mode-locked Yb-doped fiber lasers by using the MSCs for the first time. The fabrication of MSCs is presented and the pre-tapering diameters of the SMF are optimized to achieve complete mode conversion in the first-half coupling period. The MSCs are inserted both into CW and mode-locked fiber laser cavities to pursue efficient generation of HOMs. The slope efficiency of the CW laser cavity increases with the CR and also depends on the insert loss. Highest slope efficiency of 57% is obtained by inserting LP11 MSC with output CR of 89% in a CW laser. The output cylindrical vector beams and orbital angular momentum beams are produced from the MSCs. Benefitting from broadband characteristic of the MSCs, efficient HOMs (LP11, LP02 and LP21) mode-locked pulses are experimentally generated at 1 μm. The highest slope efficiency of 31% is achieved for pulsed LP11 mode generation. The concept-of-proof implementation of the MSCs demonstrates high efficiency of HOMs generation, especially for all-fiber mode-locked lasers, which hold promising applications in laser material processing.

Funding

National Natural Science Foundation of China (NSFC) (91750108, 61635006); Science and Technology Commission of Shanghai Municipality (16520720900); Shanghai Municipal Education Commission (16SG35).

Acknowledgments

Zeng Xianglong acknowledges the Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning and Pang Fufei acknowledges “Shuguang Program” supported by Shanghai Education Development Foundation.

Disclosures

The authors declare that there are no conflicts of interest related to this article.

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34. B. Sun, A. Wang, L. Xu, C. Gu, Z. Lin, H. Ming, and Q. Zhan, “Low-threshold single-wavelength all-fiber laser generating cylindrical vector beams using a few-mode fiber Bragg grating,” Opt. Lett. 37(4), 464–466 (2012). [CrossRef]   [PubMed]  

35. K. Toyoda, K. Miyamoto, N. Aoki, R. Morita, and T. Omatsu, “Using optical vortex to control the chirality of twisted metal nanostructures,” Nano Lett. 12(7), 3645–3649 (2012). [CrossRef]   [PubMed]  

36. S. Araki, K. Ando, K. Miyamoto, and T. Omatsu, “Ultra-widely tunable mid-infrared (6-18 μm) optical vortex source,” Appl. Opt. 57(4), 620–624 (2018). [CrossRef]   [PubMed]  

37. D. McGloin, N. B. Simpson, and M. J. Padgett, “Transfer of orbital angular momentum from a stressed fiber-optic waveguide to a light beam,” Appl. Opt. 37(3), 469–472 (1998). [CrossRef]   [PubMed]  

38. L. Huang, J. Xu, J. Ye, X. Liu, H. Zhang, X. Wang, and P. Zhou, “Power scaling of linearly polarized random fiber laser,” IEEE J. Sel. Top. Quant. 24(3), 1–8 (2018).

References

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    [Crossref] [PubMed]
  2. L. G. Wright, Z. M. Ziegler, P. M. Lushnikov, Z. Zhu, M. A. Eftekhar, D. N. Christodoulides, and F. W. Wise, “Multimode Nonlinear Fiber Optics: Massively Parallel Numerical Solver, Tutorial, and Outlook,” IEEE J. Sel. Top. Quant. 24(3), 1–16 (2018).
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  6. L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86(23), 5251–5254 (2001).
    [Crossref] [PubMed]
  7. K. Toyoda, F. Takahashi, S. Takizawa, Y. Tokizane, K. Miyamoto, R. Morita, and T. Omatsu, “Transfer of light helicity to nanostructures,” Phys. Rev. Lett. 110(14), 143603 (2013).
    [Crossref] [PubMed]
  8. A. Nicolas, L. Veissier, L. Giner, E. Giacobino, D. Maxein, and J. Laurat, “A quantum memory for orbital angular momentum photonic qubits,” Nat. Photonics 8(3), 234–238 (2014).
    [Crossref]
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  10. G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3(5), 305–310 (2007).
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    [Crossref] [PubMed]
  13. V. Sizyuk, A. Hassanein, and T. Sizyuk, “Hollow laser self-confined plasma for extreme ultraviolet lithography and other applications,” Laser Part. Beams 25(1), 143–154 (2007).
    [Crossref]
  14. J. Hamazaki, R. Morita, K. Chujo, Y. Kobayashi, S. Tanda, and T. Omatsu, “Optical-vortex laser ablation,” Opt. Express 18(3), 2144–2151 (2010).
    [Crossref] [PubMed]
  15. R. Zhou, J. W. Haus, P. E. Powers, and Q. Zhan, “Vectorial fiber laser using intracavity axial birefringence,” Opt. Express 18(10), 10839–10847 (2010).
    [Crossref] [PubMed]
  16. B. Piccirillo, V. D’Ambrosio, S. Slussarenko, L. Marrucci, and E. Santamato, “Photon spin-to-orbital angular momentum conversion via an electrically tunable q-plate,” Appl. Phys. Lett. 97(24), 241104 (2010).
    [Crossref]
  17. D. Lin, K. Xia, J. Li, R. Li, K. Ueda, G. Li, and X. Li, “Efficient, high-power, and radially polarized fiber laser,” Opt. Lett. 35(13), 2290–2292 (2010).
    [Crossref] [PubMed]
  18. L. Li, Z. Ren, X. Chen, M. Qi, X. Zheng, J. Bai, and Z. Sun, “Passively mode-locked radially polarized Nd-doped yttrium aluminum garnet laser based on graphene-based saturable absorber,” Appl. Phys. Express 6(8), 082701 (2013).
    [Crossref]
  19. Y. Zhou, J. Lin, X. Zhang, L. Xu, C. Gu, B. Sun, A. Wang, and Q. Zhan, “Self-starting passively mode-locked all fiber laser based on carbon nanotubes with radially polarized emission,” Photon. Res. 4(6), 327–330 (2016).
    [Crossref]
  20. Y. Zhou, A. Wang, C. Gu, B. Sun, L. Xu, F. Li, D. Chung, and Q. Zhan, “Actively mode-locked all fiber laser with cylindrical vector beam output,” Opt. Lett. 41(3), 548–550 (2016).
    [Crossref] [PubMed]
  21. T. Liu, S. P. Chen, and J. Hou, “Selective transverse mode operation of an all-fiber laser with a mode-selective fiber bragg grating pair,” Opt. Lett. 41(24), 5692–5695 (2016).
    [Crossref] [PubMed]
  22. L. Li, M. Wang, T. Liu, J. Leng, P. Zhou, and J. Chen, “High-power, cladding-pumped all-fiber laser with selective transverse mode generation property,” Appl. Opt. 56(17), 4967–4970 (2017).
    [Crossref] [PubMed]
  23. T. Liu, S. Chen, X. Qi, and J. Hou, “High-power transverse-mode-switchable all-fiber picosecond MOPA,” Opt. Express 24(24), 27821–27827 (2016).
    [Crossref] [PubMed]
  24. X. Yang, Z. H. Xu, S. P. Chen, and Z. F. Jiang, “High power LP11 mode supercontinuum generation from an all-fiber MOPA,” Opt. Express 26(11), 13740–13745 (2018).
    [Crossref] [PubMed]
  25. T. Wang, F. Wang, F. Shi, F. Pang, S. Huang, T. Wang, and X. Zeng, “Generation of femtosecond optical vortex beams in all-fiber mode-locked fiber laser using mode selective coupler,” J. Lightwave Technol. 35(11), 2161–2166 (2017).
    [Crossref]
  26. F. Wang, F. Shi, T. Wang, F. Pang, T. Wang, and X. Zeng, “Method of generating femtosecond cylindrical vector beams using broadband mode converter,” IEEE Photonics Technol. Lett. 29(9), 747–750 (2017).
    [Crossref]
  27. D. Mao, Z. He, H. Lu, M. Li, W. Zhang, X. Cui, B. Jiang, and J. Zhao, “All-fiber radially/azimuthally polarized lasers based on mode coupling of tapered fibers,” Opt. Lett. 43(7), 1590–1593 (2018).
    [Crossref] [PubMed]
  28. J. Zheng, A. Yang, T. Wang, X. Zeng, N. Cao, M. Liu, and T. Wang, “Wavelength-switchable vortex beams based on a polarization-dependent microknot resonator,” Photon. Res. 6(5), 396–402 (2018).
    [Crossref]
  29. X. Liu, J. Lagsgaard, and D. Turchinovich, “Monolithic highly stable Yb-doped femtosecond fiber lasers for applications in practical biophotonics,” IEEE. J. Sel. Top. Quant. 18(4), 1439–1450 (2012).
    [Crossref]
  30. M. Koyama, T. Hirose, M. Okida, K. Miyamoto, and T. Omatsu, “Power scaling of a picosecond vortex laser based on a stressed Yb-doped fiber amplifier,” Opt. Express 19(2), 994–999 (2011).
    [Crossref] [PubMed]
  31. N. Riesen, J. D. Love, and J. W. Arkwright, “Few-core spatial-mode multiplexers/demultiplexers based on evanescent coupling,” IEEE Photonics Technol. Lett. 25(14), 1324–1327 (2013).
    [Crossref]
  32. N. Riesen and J. D. Love, “Weakly-guiding mode-selective fiber couplers,” IEEE J. Sel. Top. Quant. 48(7), 941–945 (2012).
    [Crossref]
  33. A. W. Snyder, “Coupled-mode theory for optical fibers,” J. Opt. Soc. Am. A 62(11), 1267–1277 (1972).
    [Crossref]
  34. B. Sun, A. Wang, L. Xu, C. Gu, Z. Lin, H. Ming, and Q. Zhan, “Low-threshold single-wavelength all-fiber laser generating cylindrical vector beams using a few-mode fiber Bragg grating,” Opt. Lett. 37(4), 464–466 (2012).
    [Crossref] [PubMed]
  35. K. Toyoda, K. Miyamoto, N. Aoki, R. Morita, and T. Omatsu, “Using optical vortex to control the chirality of twisted metal nanostructures,” Nano Lett. 12(7), 3645–3649 (2012).
    [Crossref] [PubMed]
  36. S. Araki, K. Ando, K. Miyamoto, and T. Omatsu, “Ultra-widely tunable mid-infrared (6-18 μm) optical vortex source,” Appl. Opt. 57(4), 620–624 (2018).
    [Crossref] [PubMed]
  37. D. McGloin, N. B. Simpson, and M. J. Padgett, “Transfer of orbital angular momentum from a stressed fiber-optic waveguide to a light beam,” Appl. Opt. 37(3), 469–472 (1998).
    [Crossref] [PubMed]
  38. L. Huang, J. Xu, J. Ye, X. Liu, H. Zhang, X. Wang, and P. Zhou, “Power scaling of linearly polarized random fiber laser,” IEEE J. Sel. Top. Quant. 24(3), 1–8 (2018).

2018 (6)

2017 (6)

2016 (4)

2014 (1)

A. Nicolas, L. Veissier, L. Giner, E. Giacobino, D. Maxein, and J. Laurat, “A quantum memory for orbital angular momentum photonic qubits,” Nat. Photonics 8(3), 234–238 (2014).
[Crossref]

2013 (4)

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

K. Toyoda, F. Takahashi, S. Takizawa, Y. Tokizane, K. Miyamoto, R. Morita, and T. Omatsu, “Transfer of light helicity to nanostructures,” Phys. Rev. Lett. 110(14), 143603 (2013).
[Crossref] [PubMed]

L. Li, Z. Ren, X. Chen, M. Qi, X. Zheng, J. Bai, and Z. Sun, “Passively mode-locked radially polarized Nd-doped yttrium aluminum garnet laser based on graphene-based saturable absorber,” Appl. Phys. Express 6(8), 082701 (2013).
[Crossref]

N. Riesen, J. D. Love, and J. W. Arkwright, “Few-core spatial-mode multiplexers/demultiplexers based on evanescent coupling,” IEEE Photonics Technol. Lett. 25(14), 1324–1327 (2013).
[Crossref]

2012 (4)

N. Riesen and J. D. Love, “Weakly-guiding mode-selective fiber couplers,” IEEE J. Sel. Top. Quant. 48(7), 941–945 (2012).
[Crossref]

B. Sun, A. Wang, L. Xu, C. Gu, Z. Lin, H. Ming, and Q. Zhan, “Low-threshold single-wavelength all-fiber laser generating cylindrical vector beams using a few-mode fiber Bragg grating,” Opt. Lett. 37(4), 464–466 (2012).
[Crossref] [PubMed]

K. Toyoda, K. Miyamoto, N. Aoki, R. Morita, and T. Omatsu, “Using optical vortex to control the chirality of twisted metal nanostructures,” Nano Lett. 12(7), 3645–3649 (2012).
[Crossref] [PubMed]

X. Liu, J. Lagsgaard, and D. Turchinovich, “Monolithic highly stable Yb-doped femtosecond fiber lasers for applications in practical biophotonics,” IEEE. J. Sel. Top. Quant. 18(4), 1439–1450 (2012).
[Crossref]

2011 (2)

2010 (4)

2008 (1)

N. P. Robins, C. Figl, M. Jeppesen, G. R. Dennis, and J. D. Close, “A pumped atom laser,” Nat. Phys. 4(9), 731–736 (2008).
[Crossref]

2007 (2)

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3(5), 305–310 (2007).
[Crossref]

V. Sizyuk, A. Hassanein, and T. Sizyuk, “Hollow laser self-confined plasma for extreme ultraviolet lithography and other applications,” Laser Part. Beams 25(1), 143–154 (2007).
[Crossref]

2001 (1)

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86(23), 5251–5254 (2001).
[Crossref] [PubMed]

1999 (1)

L. Allen, M. J. Padgett, and M. Babiker, “IV The orbital angular momentum of light,” Prog. Opt. 39, 291–372 (1999).
[Crossref]

1998 (1)

1972 (1)

A. W. Snyder, “Coupled-mode theory for optical fibers,” J. Opt. Soc. Am. A 62(11), 1267–1277 (1972).
[Crossref]

Allen, L.

L. Allen, M. J. Padgett, and M. Babiker, “IV The orbital angular momentum of light,” Prog. Opt. 39, 291–372 (1999).
[Crossref]

Ando, K.

Aoki, N.

K. Toyoda, K. Miyamoto, N. Aoki, R. Morita, and T. Omatsu, “Using optical vortex to control the chirality of twisted metal nanostructures,” Nano Lett. 12(7), 3645–3649 (2012).
[Crossref] [PubMed]

Araki, S.

Arkwright, J. W.

N. Riesen, J. D. Love, and J. W. Arkwright, “Few-core spatial-mode multiplexers/demultiplexers based on evanescent coupling,” IEEE Photonics Technol. Lett. 25(14), 1324–1327 (2013).
[Crossref]

Babiker, M.

L. Allen, M. J. Padgett, and M. Babiker, “IV The orbital angular momentum of light,” Prog. Opt. 39, 291–372 (1999).
[Crossref]

Bai, J.

L. Li, Z. Ren, X. Chen, M. Qi, X. Zheng, J. Bai, and Z. Sun, “Passively mode-locked radially polarized Nd-doped yttrium aluminum garnet laser based on graphene-based saturable absorber,” Appl. Phys. Express 6(8), 082701 (2013).
[Crossref]

Bai, L.

Beversluis, M. R.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86(23), 5251–5254 (2001).
[Crossref] [PubMed]

Bozinovic, N.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

Brown, T. G.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86(23), 5251–5254 (2001).
[Crossref] [PubMed]

Cao, N.

Chen, J.

Chen, S.

Chen, S. P.

Chen, X.

L. Li, Z. Ren, X. Chen, M. Qi, X. Zheng, J. Bai, and Z. Sun, “Passively mode-locked radially polarized Nd-doped yttrium aluminum garnet laser based on graphene-based saturable absorber,” Appl. Phys. Express 6(8), 082701 (2013).
[Crossref]

Christodoulides, D. N.

L. G. Wright, Z. M. Ziegler, P. M. Lushnikov, Z. Zhu, M. A. Eftekhar, D. N. Christodoulides, and F. W. Wise, “Multimode Nonlinear Fiber Optics: Massively Parallel Numerical Solver, Tutorial, and Outlook,” IEEE J. Sel. Top. Quant. 24(3), 1–16 (2018).
[Crossref]

L. G. Wright, D. N. Christodoulides, and F. W. Wise, “Spatiotemporal mode-locking in multimode fiber lasers,” Science 358(6359), 94–97 (2017).
[Crossref] [PubMed]

Chujo, K.

Chung, D.

Close, J. D.

N. P. Robins, C. Figl, M. Jeppesen, G. R. Dennis, and J. D. Close, “A pumped atom laser,” Nat. Phys. 4(9), 731–736 (2008).
[Crossref]

Cui, X.

D’Ambrosio, V.

B. Piccirillo, V. D’Ambrosio, S. Slussarenko, L. Marrucci, and E. Santamato, “Photon spin-to-orbital angular momentum conversion via an electrically tunable q-plate,” Appl. Phys. Lett. 97(24), 241104 (2010).
[Crossref]

Dennis, G. R.

N. P. Robins, C. Figl, M. Jeppesen, G. R. Dennis, and J. D. Close, “A pumped atom laser,” Nat. Phys. 4(9), 731–736 (2008).
[Crossref]

Eftekhar, M. A.

L. G. Wright, Z. M. Ziegler, P. M. Lushnikov, Z. Zhu, M. A. Eftekhar, D. N. Christodoulides, and F. W. Wise, “Multimode Nonlinear Fiber Optics: Massively Parallel Numerical Solver, Tutorial, and Outlook,” IEEE J. Sel. Top. Quant. 24(3), 1–16 (2018).
[Crossref]

Figl, C.

N. P. Robins, C. Figl, M. Jeppesen, G. R. Dennis, and J. D. Close, “A pumped atom laser,” Nat. Phys. 4(9), 731–736 (2008).
[Crossref]

Giacobino, E.

A. Nicolas, L. Veissier, L. Giner, E. Giacobino, D. Maxein, and J. Laurat, “A quantum memory for orbital angular momentum photonic qubits,” Nat. Photonics 8(3), 234–238 (2014).
[Crossref]

Giner, L.

A. Nicolas, L. Veissier, L. Giner, E. Giacobino, D. Maxein, and J. Laurat, “A quantum memory for orbital angular momentum photonic qubits,” Nat. Photonics 8(3), 234–238 (2014).
[Crossref]

Gu, C.

Hamazaki, J.

Han, J.

Hassanein, A.

V. Sizyuk, A. Hassanein, and T. Sizyuk, “Hollow laser self-confined plasma for extreme ultraviolet lithography and other applications,” Laser Part. Beams 25(1), 143–154 (2007).
[Crossref]

Haus, J. W.

He, Z.

Hirose, T.

Hou, J.

Huang, H.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

Huang, L.

L. Huang, J. Xu, J. Ye, X. Liu, H. Zhang, X. Wang, and P. Zhou, “Power scaling of linearly polarized random fiber laser,” IEEE J. Sel. Top. Quant. 24(3), 1–8 (2018).

Huang, S.

Jeppesen, M.

N. P. Robins, C. Figl, M. Jeppesen, G. R. Dennis, and J. D. Close, “A pumped atom laser,” Nat. Phys. 4(9), 731–736 (2008).
[Crossref]

Jiang, B.

Jiang, Z. F.

Kobayashi, Y.

Koyama, M.

Kristensen, P.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

Lægsgaard, J.

Lagsgaard, J.

X. Liu, J. Lagsgaard, and D. Turchinovich, “Monolithic highly stable Yb-doped femtosecond fiber lasers for applications in practical biophotonics,” IEEE. J. Sel. Top. Quant. 18(4), 1439–1450 (2012).
[Crossref]

Laurat, J.

A. Nicolas, L. Veissier, L. Giner, E. Giacobino, D. Maxein, and J. Laurat, “A quantum memory for orbital angular momentum photonic qubits,” Nat. Photonics 8(3), 234–238 (2014).
[Crossref]

Leng, J.

Li, F.

Li, G.

Li, J.

Li, L.

L. Li, M. Wang, T. Liu, J. Leng, P. Zhou, and J. Chen, “High-power, cladding-pumped all-fiber laser with selective transverse mode generation property,” Appl. Opt. 56(17), 4967–4970 (2017).
[Crossref] [PubMed]

L. Li, Z. Ren, X. Chen, M. Qi, X. Zheng, J. Bai, and Z. Sun, “Passively mode-locked radially polarized Nd-doped yttrium aluminum garnet laser based on graphene-based saturable absorber,” Appl. Phys. Express 6(8), 082701 (2013).
[Crossref]

Li, M.

Li, R.

Li, X.

Lin, D.

Lin, J.

Lin, Z.

Liu, M.

Liu, T.

Liu, X.

L. Huang, J. Xu, J. Ye, X. Liu, H. Zhang, X. Wang, and P. Zhou, “Power scaling of linearly polarized random fiber laser,” IEEE J. Sel. Top. Quant. 24(3), 1–8 (2018).

X. Liu, J. Lagsgaard, and D. Turchinovich, “Monolithic highly stable Yb-doped femtosecond fiber lasers for applications in practical biophotonics,” IEEE. J. Sel. Top. Quant. 18(4), 1439–1450 (2012).
[Crossref]

Love, J. D.

N. Riesen, J. D. Love, and J. W. Arkwright, “Few-core spatial-mode multiplexers/demultiplexers based on evanescent coupling,” IEEE Photonics Technol. Lett. 25(14), 1324–1327 (2013).
[Crossref]

N. Riesen and J. D. Love, “Weakly-guiding mode-selective fiber couplers,” IEEE J. Sel. Top. Quant. 48(7), 941–945 (2012).
[Crossref]

Lu, H.

Lushnikov, P. M.

L. G. Wright, Z. M. Ziegler, P. M. Lushnikov, Z. Zhu, M. A. Eftekhar, D. N. Christodoulides, and F. W. Wise, “Multimode Nonlinear Fiber Optics: Massively Parallel Numerical Solver, Tutorial, and Outlook,” IEEE J. Sel. Top. Quant. 24(3), 1–16 (2018).
[Crossref]

Mao, D.

Marrucci, L.

B. Piccirillo, V. D’Ambrosio, S. Slussarenko, L. Marrucci, and E. Santamato, “Photon spin-to-orbital angular momentum conversion via an electrically tunable q-plate,” Appl. Phys. Lett. 97(24), 241104 (2010).
[Crossref]

Maxein, D.

A. Nicolas, L. Veissier, L. Giner, E. Giacobino, D. Maxein, and J. Laurat, “A quantum memory for orbital angular momentum photonic qubits,” Nat. Photonics 8(3), 234–238 (2014).
[Crossref]

McGloin, D.

Milione, G.

Ming, H.

Miyamoto, K.

S. Araki, K. Ando, K. Miyamoto, and T. Omatsu, “Ultra-widely tunable mid-infrared (6-18 μm) optical vortex source,” Appl. Opt. 57(4), 620–624 (2018).
[Crossref] [PubMed]

K. Toyoda, F. Takahashi, S. Takizawa, Y. Tokizane, K. Miyamoto, R. Morita, and T. Omatsu, “Transfer of light helicity to nanostructures,” Phys. Rev. Lett. 110(14), 143603 (2013).
[Crossref] [PubMed]

K. Toyoda, K. Miyamoto, N. Aoki, R. Morita, and T. Omatsu, “Using optical vortex to control the chirality of twisted metal nanostructures,” Nano Lett. 12(7), 3645–3649 (2012).
[Crossref] [PubMed]

M. Koyama, T. Hirose, M. Okida, K. Miyamoto, and T. Omatsu, “Power scaling of a picosecond vortex laser based on a stressed Yb-doped fiber amplifier,” Opt. Express 19(2), 994–999 (2011).
[Crossref] [PubMed]

Molina-Terriza, G.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3(5), 305–310 (2007).
[Crossref]

Morita, R.

K. Toyoda, F. Takahashi, S. Takizawa, Y. Tokizane, K. Miyamoto, R. Morita, and T. Omatsu, “Transfer of light helicity to nanostructures,” Phys. Rev. Lett. 110(14), 143603 (2013).
[Crossref] [PubMed]

K. Toyoda, K. Miyamoto, N. Aoki, R. Morita, and T. Omatsu, “Using optical vortex to control the chirality of twisted metal nanostructures,” Nano Lett. 12(7), 3645–3649 (2012).
[Crossref] [PubMed]

J. Hamazaki, R. Morita, K. Chujo, Y. Kobayashi, S. Tanda, and T. Omatsu, “Optical-vortex laser ablation,” Opt. Express 18(3), 2144–2151 (2010).
[Crossref] [PubMed]

Nicolas, A.

A. Nicolas, L. Veissier, L. Giner, E. Giacobino, D. Maxein, and J. Laurat, “A quantum memory for orbital angular momentum photonic qubits,” Nat. Photonics 8(3), 234–238 (2014).
[Crossref]

Novotny, L.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86(23), 5251–5254 (2001).
[Crossref] [PubMed]

Okida, M.

Omatsu, T.

Padgett, M. J.

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
[Crossref]

L. Allen, M. J. Padgett, and M. Babiker, “IV The orbital angular momentum of light,” Prog. Opt. 39, 291–372 (1999).
[Crossref]

D. McGloin, N. B. Simpson, and M. J. Padgett, “Transfer of orbital angular momentum from a stressed fiber-optic waveguide to a light beam,” Appl. Opt. 37(3), 469–472 (1998).
[Crossref] [PubMed]

Pang, F.

F. Wang, F. Shi, T. Wang, F. Pang, T. Wang, and X. Zeng, “Method of generating femtosecond cylindrical vector beams using broadband mode converter,” IEEE Photonics Technol. Lett. 29(9), 747–750 (2017).
[Crossref]

T. Wang, F. Wang, F. Shi, F. Pang, S. Huang, T. Wang, and X. Zeng, “Generation of femtosecond optical vortex beams in all-fiber mode-locked fiber laser using mode selective coupler,” J. Lightwave Technol. 35(11), 2161–2166 (2017).
[Crossref]

Piccirillo, B.

B. Piccirillo, V. D’Ambrosio, S. Slussarenko, L. Marrucci, and E. Santamato, “Photon spin-to-orbital angular momentum conversion via an electrically tunable q-plate,” Appl. Phys. Lett. 97(24), 241104 (2010).
[Crossref]

Powers, P. E.

Qi, M.

L. Li, Z. Ren, X. Chen, M. Qi, X. Zheng, J. Bai, and Z. Sun, “Passively mode-locked radially polarized Nd-doped yttrium aluminum garnet laser based on graphene-based saturable absorber,” Appl. Phys. Express 6(8), 082701 (2013).
[Crossref]

Qi, X.

Ramachandran, S.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

Ren, Y.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

Ren, Z.

L. Li, Z. Ren, X. Chen, M. Qi, X. Zheng, J. Bai, and Z. Sun, “Passively mode-locked radially polarized Nd-doped yttrium aluminum garnet laser based on graphene-based saturable absorber,” Appl. Phys. Express 6(8), 082701 (2013).
[Crossref]

Riesen, N.

N. Riesen, J. D. Love, and J. W. Arkwright, “Few-core spatial-mode multiplexers/demultiplexers based on evanescent coupling,” IEEE Photonics Technol. Lett. 25(14), 1324–1327 (2013).
[Crossref]

N. Riesen and J. D. Love, “Weakly-guiding mode-selective fiber couplers,” IEEE J. Sel. Top. Quant. 48(7), 941–945 (2012).
[Crossref]

Robins, N. P.

N. P. Robins, C. Figl, M. Jeppesen, G. R. Dennis, and J. D. Close, “A pumped atom laser,” Nat. Phys. 4(9), 731–736 (2008).
[Crossref]

Santamato, E.

B. Piccirillo, V. D’Ambrosio, S. Slussarenko, L. Marrucci, and E. Santamato, “Photon spin-to-orbital angular momentum conversion via an electrically tunable q-plate,” Appl. Phys. Lett. 97(24), 241104 (2010).
[Crossref]

Shi, F.

T. Wang, F. Wang, F. Shi, F. Pang, S. Huang, T. Wang, and X. Zeng, “Generation of femtosecond optical vortex beams in all-fiber mode-locked fiber laser using mode selective coupler,” J. Lightwave Technol. 35(11), 2161–2166 (2017).
[Crossref]

F. Wang, F. Shi, T. Wang, F. Pang, T. Wang, and X. Zeng, “Method of generating femtosecond cylindrical vector beams using broadband mode converter,” IEEE Photonics Technol. Lett. 29(9), 747–750 (2017).
[Crossref]

Simpson, N. B.

Sizyuk, T.

V. Sizyuk, A. Hassanein, and T. Sizyuk, “Hollow laser self-confined plasma for extreme ultraviolet lithography and other applications,” Laser Part. Beams 25(1), 143–154 (2007).
[Crossref]

Sizyuk, V.

V. Sizyuk, A. Hassanein, and T. Sizyuk, “Hollow laser self-confined plasma for extreme ultraviolet lithography and other applications,” Laser Part. Beams 25(1), 143–154 (2007).
[Crossref]

Slussarenko, S.

B. Piccirillo, V. D’Ambrosio, S. Slussarenko, L. Marrucci, and E. Santamato, “Photon spin-to-orbital angular momentum conversion via an electrically tunable q-plate,” Appl. Phys. Lett. 97(24), 241104 (2010).
[Crossref]

Snyder, A. W.

A. W. Snyder, “Coupled-mode theory for optical fibers,” J. Opt. Soc. Am. A 62(11), 1267–1277 (1972).
[Crossref]

Sun, B.

Sun, Z.

L. Li, Z. Ren, X. Chen, M. Qi, X. Zheng, J. Bai, and Z. Sun, “Passively mode-locked radially polarized Nd-doped yttrium aluminum garnet laser based on graphene-based saturable absorber,” Appl. Phys. Express 6(8), 082701 (2013).
[Crossref]

Takahashi, F.

K. Toyoda, F. Takahashi, S. Takizawa, Y. Tokizane, K. Miyamoto, R. Morita, and T. Omatsu, “Transfer of light helicity to nanostructures,” Phys. Rev. Lett. 110(14), 143603 (2013).
[Crossref] [PubMed]

Takizawa, S.

K. Toyoda, F. Takahashi, S. Takizawa, Y. Tokizane, K. Miyamoto, R. Morita, and T. Omatsu, “Transfer of light helicity to nanostructures,” Phys. Rev. Lett. 110(14), 143603 (2013).
[Crossref] [PubMed]

Tanda, S.

Tokizane, Y.

K. Toyoda, F. Takahashi, S. Takizawa, Y. Tokizane, K. Miyamoto, R. Morita, and T. Omatsu, “Transfer of light helicity to nanostructures,” Phys. Rev. Lett. 110(14), 143603 (2013).
[Crossref] [PubMed]

Torner, L.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3(5), 305–310 (2007).
[Crossref]

Torres, J. P.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3(5), 305–310 (2007).
[Crossref]

Toyoda, K.

K. Toyoda, F. Takahashi, S. Takizawa, Y. Tokizane, K. Miyamoto, R. Morita, and T. Omatsu, “Transfer of light helicity to nanostructures,” Phys. Rev. Lett. 110(14), 143603 (2013).
[Crossref] [PubMed]

K. Toyoda, K. Miyamoto, N. Aoki, R. Morita, and T. Omatsu, “Using optical vortex to control the chirality of twisted metal nanostructures,” Nano Lett. 12(7), 3645–3649 (2012).
[Crossref] [PubMed]

Tur, M.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

Turchinovich, D.

X. Liu, J. Lagsgaard, and D. Turchinovich, “Monolithic highly stable Yb-doped femtosecond fiber lasers for applications in practical biophotonics,” IEEE. J. Sel. Top. Quant. 18(4), 1439–1450 (2012).
[Crossref]

Ueda, K.

Veissier, L.

A. Nicolas, L. Veissier, L. Giner, E. Giacobino, D. Maxein, and J. Laurat, “A quantum memory for orbital angular momentum photonic qubits,” Nat. Photonics 8(3), 234–238 (2014).
[Crossref]

Wang, A.

Wang, F.

F. Wang, F. Shi, T. Wang, F. Pang, T. Wang, and X. Zeng, “Method of generating femtosecond cylindrical vector beams using broadband mode converter,” IEEE Photonics Technol. Lett. 29(9), 747–750 (2017).
[Crossref]

T. Wang, F. Wang, F. Shi, F. Pang, S. Huang, T. Wang, and X. Zeng, “Generation of femtosecond optical vortex beams in all-fiber mode-locked fiber laser using mode selective coupler,” J. Lightwave Technol. 35(11), 2161–2166 (2017).
[Crossref]

Wang, M.

Wang, T.

J. Zheng, A. Yang, T. Wang, X. Zeng, N. Cao, M. Liu, and T. Wang, “Wavelength-switchable vortex beams based on a polarization-dependent microknot resonator,” Photon. Res. 6(5), 396–402 (2018).
[Crossref]

J. Zheng, A. Yang, T. Wang, X. Zeng, N. Cao, M. Liu, and T. Wang, “Wavelength-switchable vortex beams based on a polarization-dependent microknot resonator,” Photon. Res. 6(5), 396–402 (2018).
[Crossref]

F. Wang, F. Shi, T. Wang, F. Pang, T. Wang, and X. Zeng, “Method of generating femtosecond cylindrical vector beams using broadband mode converter,” IEEE Photonics Technol. Lett. 29(9), 747–750 (2017).
[Crossref]

F. Wang, F. Shi, T. Wang, F. Pang, T. Wang, and X. Zeng, “Method of generating femtosecond cylindrical vector beams using broadband mode converter,” IEEE Photonics Technol. Lett. 29(9), 747–750 (2017).
[Crossref]

T. Wang, F. Wang, F. Shi, F. Pang, S. Huang, T. Wang, and X. Zeng, “Generation of femtosecond optical vortex beams in all-fiber mode-locked fiber laser using mode selective coupler,” J. Lightwave Technol. 35(11), 2161–2166 (2017).
[Crossref]

T. Wang, F. Wang, F. Shi, F. Pang, S. Huang, T. Wang, and X. Zeng, “Generation of femtosecond optical vortex beams in all-fiber mode-locked fiber laser using mode selective coupler,” J. Lightwave Technol. 35(11), 2161–2166 (2017).
[Crossref]

G. Milione, T. Wang, J. Han, and L. Bai, “Remotely sensing an object’s rotational orientation using the orbital angular momentum of light,” Chin. Opt. Lett. 15(3), 030012 (2017).
[Crossref]

Wang, X.

L. Huang, J. Xu, J. Ye, X. Liu, H. Zhang, X. Wang, and P. Zhou, “Power scaling of linearly polarized random fiber laser,” IEEE J. Sel. Top. Quant. 24(3), 1–8 (2018).

Willner, A. E.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

Wise, F. W.

L. G. Wright, Z. M. Ziegler, P. M. Lushnikov, Z. Zhu, M. A. Eftekhar, D. N. Christodoulides, and F. W. Wise, “Multimode Nonlinear Fiber Optics: Massively Parallel Numerical Solver, Tutorial, and Outlook,” IEEE J. Sel. Top. Quant. 24(3), 1–16 (2018).
[Crossref]

L. G. Wright, D. N. Christodoulides, and F. W. Wise, “Spatiotemporal mode-locking in multimode fiber lasers,” Science 358(6359), 94–97 (2017).
[Crossref] [PubMed]

Wright, L. G.

L. G. Wright, Z. M. Ziegler, P. M. Lushnikov, Z. Zhu, M. A. Eftekhar, D. N. Christodoulides, and F. W. Wise, “Multimode Nonlinear Fiber Optics: Massively Parallel Numerical Solver, Tutorial, and Outlook,” IEEE J. Sel. Top. Quant. 24(3), 1–16 (2018).
[Crossref]

L. G. Wright, D. N. Christodoulides, and F. W. Wise, “Spatiotemporal mode-locking in multimode fiber lasers,” Science 358(6359), 94–97 (2017).
[Crossref] [PubMed]

Xia, K.

Xu, J.

L. Huang, J. Xu, J. Ye, X. Liu, H. Zhang, X. Wang, and P. Zhou, “Power scaling of linearly polarized random fiber laser,” IEEE J. Sel. Top. Quant. 24(3), 1–8 (2018).

Xu, L.

Xu, Z. H.

Yang, A.

Yang, X.

Yao, A. M.

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
[Crossref]

Ye, J.

L. Huang, J. Xu, J. Ye, X. Liu, H. Zhang, X. Wang, and P. Zhou, “Power scaling of linearly polarized random fiber laser,” IEEE J. Sel. Top. Quant. 24(3), 1–8 (2018).

Youngworth, K. S.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86(23), 5251–5254 (2001).
[Crossref] [PubMed]

Yue, Y.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

Zeng, X.

Zhan, Q.

Zhang, H.

L. Huang, J. Xu, J. Ye, X. Liu, H. Zhang, X. Wang, and P. Zhou, “Power scaling of linearly polarized random fiber laser,” IEEE J. Sel. Top. Quant. 24(3), 1–8 (2018).

Zhang, W.

Zhang, X.

Zhao, J.

Zheng, J.

Zheng, X.

L. Li, Z. Ren, X. Chen, M. Qi, X. Zheng, J. Bai, and Z. Sun, “Passively mode-locked radially polarized Nd-doped yttrium aluminum garnet laser based on graphene-based saturable absorber,” Appl. Phys. Express 6(8), 082701 (2013).
[Crossref]

Zhou, P.

L. Huang, J. Xu, J. Ye, X. Liu, H. Zhang, X. Wang, and P. Zhou, “Power scaling of linearly polarized random fiber laser,” IEEE J. Sel. Top. Quant. 24(3), 1–8 (2018).

L. Li, M. Wang, T. Liu, J. Leng, P. Zhou, and J. Chen, “High-power, cladding-pumped all-fiber laser with selective transverse mode generation property,” Appl. Opt. 56(17), 4967–4970 (2017).
[Crossref] [PubMed]

Zhou, R.

Zhou, Y.

Zhu, Z.

L. G. Wright, Z. M. Ziegler, P. M. Lushnikov, Z. Zhu, M. A. Eftekhar, D. N. Christodoulides, and F. W. Wise, “Multimode Nonlinear Fiber Optics: Massively Parallel Numerical Solver, Tutorial, and Outlook,” IEEE J. Sel. Top. Quant. 24(3), 1–16 (2018).
[Crossref]

Ziegler, Z. M.

L. G. Wright, Z. M. Ziegler, P. M. Lushnikov, Z. Zhu, M. A. Eftekhar, D. N. Christodoulides, and F. W. Wise, “Multimode Nonlinear Fiber Optics: Massively Parallel Numerical Solver, Tutorial, and Outlook,” IEEE J. Sel. Top. Quant. 24(3), 1–16 (2018).
[Crossref]

Adv. Opt. Photonics (1)

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
[Crossref]

Appl. Opt. (3)

Appl. Phys. Express (1)

L. Li, Z. Ren, X. Chen, M. Qi, X. Zheng, J. Bai, and Z. Sun, “Passively mode-locked radially polarized Nd-doped yttrium aluminum garnet laser based on graphene-based saturable absorber,” Appl. Phys. Express 6(8), 082701 (2013).
[Crossref]

Appl. Phys. Lett. (1)

B. Piccirillo, V. D’Ambrosio, S. Slussarenko, L. Marrucci, and E. Santamato, “Photon spin-to-orbital angular momentum conversion via an electrically tunable q-plate,” Appl. Phys. Lett. 97(24), 241104 (2010).
[Crossref]

Chin. Opt. Lett. (1)

IEEE J. Sel. Top. Quant. (3)

L. G. Wright, Z. M. Ziegler, P. M. Lushnikov, Z. Zhu, M. A. Eftekhar, D. N. Christodoulides, and F. W. Wise, “Multimode Nonlinear Fiber Optics: Massively Parallel Numerical Solver, Tutorial, and Outlook,” IEEE J. Sel. Top. Quant. 24(3), 1–16 (2018).
[Crossref]

L. Huang, J. Xu, J. Ye, X. Liu, H. Zhang, X. Wang, and P. Zhou, “Power scaling of linearly polarized random fiber laser,” IEEE J. Sel. Top. Quant. 24(3), 1–8 (2018).

N. Riesen and J. D. Love, “Weakly-guiding mode-selective fiber couplers,” IEEE J. Sel. Top. Quant. 48(7), 941–945 (2012).
[Crossref]

IEEE Photonics Technol. Lett. (2)

N. Riesen, J. D. Love, and J. W. Arkwright, “Few-core spatial-mode multiplexers/demultiplexers based on evanescent coupling,” IEEE Photonics Technol. Lett. 25(14), 1324–1327 (2013).
[Crossref]

F. Wang, F. Shi, T. Wang, F. Pang, T. Wang, and X. Zeng, “Method of generating femtosecond cylindrical vector beams using broadband mode converter,” IEEE Photonics Technol. Lett. 29(9), 747–750 (2017).
[Crossref]

IEEE. J. Sel. Top. Quant. (1)

X. Liu, J. Lagsgaard, and D. Turchinovich, “Monolithic highly stable Yb-doped femtosecond fiber lasers for applications in practical biophotonics,” IEEE. J. Sel. Top. Quant. 18(4), 1439–1450 (2012).
[Crossref]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. A (1)

A. W. Snyder, “Coupled-mode theory for optical fibers,” J. Opt. Soc. Am. A 62(11), 1267–1277 (1972).
[Crossref]

J. Opt. Soc. Am. B (1)

Laser Part. Beams (1)

V. Sizyuk, A. Hassanein, and T. Sizyuk, “Hollow laser self-confined plasma for extreme ultraviolet lithography and other applications,” Laser Part. Beams 25(1), 143–154 (2007).
[Crossref]

Nano Lett. (1)

K. Toyoda, K. Miyamoto, N. Aoki, R. Morita, and T. Omatsu, “Using optical vortex to control the chirality of twisted metal nanostructures,” Nano Lett. 12(7), 3645–3649 (2012).
[Crossref] [PubMed]

Nat. Photonics (1)

A. Nicolas, L. Veissier, L. Giner, E. Giacobino, D. Maxein, and J. Laurat, “A quantum memory for orbital angular momentum photonic qubits,” Nat. Photonics 8(3), 234–238 (2014).
[Crossref]

Nat. Phys. (2)

N. P. Robins, C. Figl, M. Jeppesen, G. R. Dennis, and J. D. Close, “A pumped atom laser,” Nat. Phys. 4(9), 731–736 (2008).
[Crossref]

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3(5), 305–310 (2007).
[Crossref]

Opt. Express (5)

Opt. Lett. (5)

Photon. Res. (2)

Phys. Rev. Lett. (2)

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86(23), 5251–5254 (2001).
[Crossref] [PubMed]

K. Toyoda, F. Takahashi, S. Takizawa, Y. Tokizane, K. Miyamoto, R. Morita, and T. Omatsu, “Transfer of light helicity to nanostructures,” Phys. Rev. Lett. 110(14), 143603 (2013).
[Crossref] [PubMed]

Prog. Opt. (1)

L. Allen, M. J. Padgett, and M. Babiker, “IV The orbital angular momentum of light,” Prog. Opt. 39, 291–372 (1999).
[Crossref]

Science (2)

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

L. G. Wright, D. N. Christodoulides, and F. W. Wise, “Spatiotemporal mode-locking in multimode fiber lasers,” Science 358(6359), 94–97 (2017).
[Crossref] [PubMed]

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Figures (7)

Fig. 1
Fig. 1 (a) Schematic of the MSC. The LP01 mode at 1.0 μm is lunched into the SMF input port (blue) and one of HOMs is excited at the FMF output port (red). The microscopic images of the coupling region are inserted. (b) Mode conversion evolution of LP01 to LP11, LP21, LP02 and LP31 modes in the simulation and the experimental intensity profiles of corresponding high-order modes.
Fig. 2
Fig. 2 Coupling efficiency (CE) and insert loss (IL) of (a) LP11 and (c) LP02 MSCs as a function of the diameter of the pre-tapered SMF. The corresponding transmission spectra of (b) LP11 and (d) LP02 MSCs at the wavelength of 1.0 μm.
Fig. 3
Fig. 3 (a) Experimental setup of a continuous-wave HOMs laser. (b) Output spectra for different CRs (17%, 33%, 55%, 70% and 89%). (c) Output power (green point) and the corresponding SBR (blue point) of LP11 MSCs inside a CW laser cavity for different CR. (d) Spectrum from a LP11 MSC with the CR of 89% after attenuation. FBG: Fiber Bragg grating; WDM: Wavelength Division Multiplexing coupler; PC: Polarization Controller; YDF: ytterbium-doped Fiber; CCD: Charge Coupled Device, infrared camera.
Fig. 4
Fig. 4 HOMs (LP11, LP02 and LP21) output power and slope efficiency (SE) versus the pump power for different CRs of the MSCs. Insert figures are near-field intensity distribution of HOMs.
Fig. 5
Fig. 5 Near-field distribution of (a) CVBs and (b) OAMs output from the CW laser. The first column of (a): the vector modes with donut-shape intensity profiles. The second, third, fourth and fifth columns are the near-field distributions of each vector modes with a polarizer placed in front of the CCD. (b): Near-field distribution of LP modes, donut-shape OAM patterns and spiral interferograms of OAM+1, OAM-1, OAM+2 and OAM-2.
Fig. 6
Fig. 6 Experimental setup of mode-locked HOM laser. PD-ISO: Polarization dependent Isolator; OSC: Oscilloscope; OSA: Optical Spectrum Analyzer.
Fig. 7
Fig. 7 Characteristics of HOMs output from Yb-doped MLFL. The output spectra, mode-locked pulse trains and output power versus pump power are measured when (a, b, c) a LP11 MSC with the CR of 17%, (d, e, f) a LP02 MSC with the CR of 21%, (g, h, i) a LP21 MSC with the CR of 15% are inserted in the resonant cavity, respectively.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

|A(z) | 2 =1k sin 2 (Dz)
|B(z) | 2 =k sin 2 (Dz)
z= z c = (2n1)π 2c k
k [1+ ( β A β B ) 2 4 c 2 ] 1

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