1. INTRODUCTION

Optical vortex beams (OVBs) are spatially structured beams with a helical phase front. Such beams are characterized by a topological charge (order), also called orbital angular momentum (OAM) beams. Vortex beams have a phase singularity at the center with a doughnut-shaped spatial intensity. Due to their polarization and amplitude symmetry, OVBs attract a lot of attention and have been investigated in many areas, such as high-resolution measurement ^[1], particle trapping ^[2], material processing ^[3], remote sensing ^[4], microscopy ^[5], and quantum information technology ^[6]. OAM recently has been used in applications in multidimensional multiplexing technologies in optical communications, such as wavelength-division multiplexing (WDM), mode-division multiplexing (MDM) ^[7], and all-optical processes ^[8]. A traditional method is used to convert a Gaussian beam to a vortex beam using phase elements, such as a q-plate ^[9], or computer-generated holograms created by a programmed spatial light modulator (SLM) ^[10]. Such phase elements are typically designed for a specific laser wavelength and this inherently constrains the wavelength versatility of the vortex laser sources. Optical vortex modes could be directly generated from a laser cavity by certain methods, such as the use of an annular pump beam for the laser medium ^[11] and using an SLM as a cavity reflector ^[12]. Different kinds of vortex lasers based on fiber mode conversion devices have been proposed, such as few-mode fiber Bragg gratings (FBGs) ^{[1315" target="_self" style="display: inline;">–15]}. Recently, nonlinear frequency conversion based on optical parametric oscillation ^[16], optical parametric amplification ^[17], or stimulated Raman scattering ^[18,19] is proven to be a valid approach to generate optical vortices in the new waveband. Single-pass optical parametric generation of a Yb-fiber laser was demonstrated to generate optical vortices in the mid-infrared region ^[20]. However, most of them have two disadvantages: high cost and low integration.

Multiwavelength switchable fiber lasers have the advantages of wavelength flexibility and high coherence. They have been considered excellent sources for optical WDM and sensing systems. Many methods have been proposed to obtain multiwavelength fiber lasers, such as using a Lyot–Sagnac filter ^[21], a Mach–Zehnder interferometer (MZI) ^[22], and a superimposed chirped fiber Bragg grating (CFBG) ^[23]. Zhan et al. reported a triple-wavelength switchable lasing laser with equal wavelength spacing of 2.6 nm by using cascaded long-period fiber grating (LPG) ^[24]. Luo et al. reported a wavelength-switchable femtosecond pulse fiber laser using a gold-nanorod saturable absorber (SA) ^[25].

However, to the best of our knowledge, there have been few reports about a multiwavelength switchable fiber laser with vortex beams. In our prior work, a single-mode fiber (SMF) and few-mode fiber (FMF) coupler was first proposed to overcome the constraint of broadband mode conversion ^[26,27], which is a promising method to produce efficient femtosecond OVBs. By using a similar fiber mode coupler, cylindrical vector beams with a switchable dual-wavelength pulsed laser were also presented ^[28]. Multiwavelength vortex beams with identical OAM properties are desirable for multiplexing, exchanging, and routing to further improve the capacity of the optical fiber transmission.

In this paper, we demonstrate a method to experimentally generate multiwavelength switchable and continuously tunable OVBs in an all-fiber laser. A polarization-dependent microknot resonator (MKR), acting for comb filtering and polarization switching, is inserted in the cavity to adjust the wavelength region of net gain. Multiwavelength switchable OVBs with topological charges of OAM±1 can be obtained, and each wavelength channel preserves identical OAM properties.

2. EXPERIMENTAL SETUP

The schematic setup to generate multiple-wavelength OVBs in an all-fiber configuration is shown in Fig. 1. The gain medium of a 40 cm erbium-doped fiber (EDF, LIEKKI ER80-8/125) with group velocity dispersion of −20ps2/km and peak absorption of 80 dB/m at 1530 nm is pumped by a 980 nm semiconductor laser with the maximum power of 605 mW. A broadband high birefringence Sagnac loop mirror (HiBi-SLM filter) is made of a 50:50 coupler, a section of 15 cm polarization-maintaining fiber (PMF), and two polarization controllers (PCs) (PC1 and PC2) ^[25]. An optical circulator assures unidirectional operation. The outer ring cavity consists of the MKR (with a red ring structure in the picture), PC3, and an SMF and FMF coupler (coupling ratio 90:10), which is used to convert LP01 mode to high-order LP11 mode ^[26,27]. The output spectrum is analyzed by an optical spectrum analyzer (OSA, YOKOGAWA, AQ6370C) and the output beam profiles are recorded using a CCD camera (InGaAs camera, Model C10633-23 from Hamamatsu Photonics).

Fig. 1. Experimental setup used to excite OVB pulse. WDM, wavelength division multiplexing coupler; EDF, erbium-doped fiber; PC, polarization controller; OSA, optical spectrum analyzer; CCD, charge-coupled infrared camera; PMF, polarization-maintaining fiber.

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2.3 A. MKR Characteristics

The fiber is tapered by using a flame brushing method to a microfiber of the diameter (approximately 3 μm). Similar to wrapping a rope, the microfiber is manually tied into a knot and then slowly tightened ^[29]. The diameter of the loop could be further decreased by pulling the fiber ends symmetrically using the stages. The ring diameter of the knot used in the experiment is approximately 660 μm. The microscopy image of the fabricated MKR and the overlapping area are shown in Figs. 2(a) and 2(b). The MKR can be encapsulated for a stable condition. Resonant light is coupled from the fiber and circulating in the MKR.

Fig. 2. Microscopy image of (a) the fabricated MKR and (b) the overlapping region.

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As shown in Fig. 3(a), the red and the blue lines present the transmission spectra with different incident states of polarization (SOP). The off-resonance loss of the MKR is less than 2.5 dB, and the transmission loss for different SOP is wavelength-dependent. The wavelength resonances of the transmission spectrum keep unchanged and overlapped with different SOP, but their transmission losses are dependent on the incident SOP. The transmissivity difference is large when the wavelengths are near the transmission resonance.

Fig. 3. Spectral response of MKR: (a) Transmission spectrum with different incident states of polarization (SOP); (b) transmission spectra from 1553 nm to 1557 nm; and (c) polarization-dependent loss of the MKR.

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The typical transmission spectra of the MKR with periodic wavelength response covering the whole C-band are shown in Fig. 3(b). The peak-to-notch contrast ratio of the fabricated MKR is around 11 dB, indicating that the MKR is well fabricated, and it also could be further improved by decreasing the surface roughness and changing the diameter of the microfiber. The free spectral range (FSR) is inversely proportional to the perimeter of MKR. Here, the measured FSR is 0.813 nm, which is consistent with the calculated result, FSR=λ2/nπD ^[30]. The polarization dependent loss (PDL) of the MKR has been measured using a tunable laser and a polarization analyzer. Due to the lack of circular symmetry, the coupling in the overlapping regions of the MKR is highly polarization-dependent. Figure 3(c) shows the PDL of the MKR from 1530 nm to 1570 nm, which is the maximum transmission difference (up to 7 dB) near the resonant wavelengths under all polarization states. The transmission spectra exhibit unequal variations with different incident SOP.

2.4 B. Generating OAM Based on Fused SMF–FMF Couplers

To obtain OVBs, a fused SMF–FMF fiber coupler, which acts as a mode converter, has been investigated ^[26]. When propagation constant β1 of LP01 mode in SMF equals the propagation constant β2 of LP11 mode in FMF, LP01 mode in SMF can be phase-matched and converted to LP11 mode in FMF according to the coupled-mode theory ^[31]. LP11 mode is actually the superposition of vector modes, TE0,1, TM0,1 and HE2,1even (HE2,1odd). And OAM optical vortex can be obtained by combining different vector modes HE2,1even(HE2,1odd) and TE0,1 (TM0,1) when l=1, or combining HEl+1,meven (HEl+1,modd) and EHl−1,meven (EHl−1,modd) when l>1 with a π/2 phase shift, where l refers to the azimuthal index and m refers to the radial index ^[32]. Then a π/2 phase shift between two vector modes is an indispensable part of generating OAM OVBs. A polarization controller (PC4) is used to achieve a π/2 phase shift between vector modes.

The commercial simulation software (Rsoft) is used to solve the modes propagating in the SMF–FMF couplers. The simulation results are shown in Fig. 4. SMF and FMF core diameters are set to 5.60 μm and 10.90 μm, respectively. The corresponding mode effective indices are 1.444. The coupling region length is set to 2300 μm, and the core distance between the two fibers is set to 5 μm. The conversion efficiency is the ratio of LP01 mode in SMF coupled to LP11 mode in FMF as a function of the wavelengths, as shown in Fig. 4(a). The coupling efficiency is more than 95% from 1507 nm to 1595 nm. Figure 4(b) shows the power exchange in the coupling region when LP01 mode from the SMF converts to LP11 mode in the FMF at the wavelength of 1520, 1550, and 1580 nm, respectively.

Fig. 4. Simulation results: (a) Coupling efficiency as a function of the wavelengths; and (b) power exchange in the coupling region when LP01 mode in SMF converts to LP11 mode in FMF.

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Before the fusing process of the SMF–FMF fiber coupler, SMF (core/cladding diameter = 8/125 μm) is pre-tapered to the cladding diameter of around 85 μm, while the core/cladding diameter of FMF fiber is 20/125 μm. Then the pre-tapered SMF and FMF are twisted, stretched, and fused together using an oxyhydrogen flame so that their fiber core diameters are near to the phase-matching condition. Optimum taper diameters are determined after experimental fine tuning of pre-tapered SMF diameters ^[26]. The powers from the output SMF port and FMF port are carefully monitored. The coupling ratio (CR) is expressed by the ratio between the out power in FMF (P2) and the total output power of SMF (P1) and FMF (P2): CR=P2/(P1+P2). When the desired coupling ratio is achieved, the automated fusing and pulling process is stopped. The change of the power coupling is observed during the fiber pulling and fusing process, and a different splitting ratio can be obtained by controlling the pulling length.

Fiber OAM±1 modes can be obtained by combining vector modes HE2,1even (HE2,1odd) and TE0,1 (TM0,1) with a π/2 phase shift ^[32]. By rotating the PC4 on the output of FMF and adjusting the pressure appropriately, a π/2 phase shift between vector modes can be achieved. The mode selective coupler with a broad bandwidth is further verified by inputting a femtosecond pulse with a spectrum bandwidth of 32 nm (centered at 1550 nm) and its pulse duration is around 150 fs. Femtosecond optical vortex beams are obtained from the FMF output port of the mode selective coupler, as shown in Fig. 5. The output high-order mode patterns and the corresponding interference patterns of OAM±1, OAM±2 modes are clearly seen, respectively, which indicate that the mode selective coupler can work as an efficient mode converter within a large bandwidth.

Fig. 5. Output near-field intensity distribution from a mode selective coupler by inputting a femtosecond pulse. (a), (e) Intensity profiles of the LP11 and LP21 modes; (b), (f) donut-shaped OAM mode patterns when pressing the output FMF; (c) and (d), and (g) and (h) corresponding clockwise and anticlockwise spiral interferograms of OAM±1 and OAM±2, respectively.

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3. RESULTS AND DISCUSSION

The mechanism of wavelength-switchable fiber laser is easy to explain. The MKR comb filter exhibits a polarization-dependent transmission loss for different wavelengths, which leads to unequal cavity losses at the lasing wavelength channels. Due to the existence of mode competition in erbium-doped fiber, a small change of cavity loss can lead to the different lasing wavelengths. By adjusting the state of polarization of the PCs to change the transmission loss of the MKR cavity, it leads to unequal cavity losses at the lasing wavelength channels. The wavelength-switching operation can be obtained for different wavelengths. To extend the tuning range, a broadband HiBi-SLM filter is used. It is known that its reflective spectrum is a periodic sinusoidal curve, and the reflective bandwidth is inversely proportional to the PMF length. In fact, only the gain at the wavelengths near the center of the reflective profile of the HiBi–SLM filter can offset the cavity loss to generate the lasing. The PMF length is about 15 cm and its reflective bandwidth is about 30 nm. Moreover, the effective gain region can be tuned along with the reflective profile ^[33], which is first tuned by adjusting the PC1 and PC2 to the desired lasing band. Then the SOP of the MKR is adjusted to switch the lasing wavelengths continuously by using PC3.

Multiwavelength switchable lasing based on the MKR is demonstrated experimentally, as shown in Fig. 6. By adjusting the PCs appropriately, adjacent single- and dual-wavelength outputs are successively tuned out in the lasing channels. The signal-to-noise ratio (SNR) of each channel keeps as higher than 40 dB, which is mainly attributed to the high contrast of the comb spectrum of the MKR (Fig. 3). Moreover, the measured 3 dB linewidth of each channel reaches approximately 0.018 nm, limited by the measurement of OSA precision. Single-longitudinal-mode oscillation can be realized based on a fiber Fabry–Perot interferometer and the MKR in the state of single-wavelength lasing ^[34]. The wavelength interval is 0.813 nm, which is in agreement with the FSR of the MKR. As shown in Fig. 6(a), the single wavelength can be tuned from 1546.95 nm to 1562.29 nm, and continuous 19 wavelengths in total are generated. Then multiwavelength operation is achieved based on these wavelengths. The output spectra of more multiwavelength lasing are observed. As shown in Figs. 6(b)–6(d), stable adjacent dual-, triple- and quadruple-wavelength channels can also be tuned continuously through controlling the polarization state of light inside the HiBi-SLM filter, the MKR, and the fiber ring cavity.

Fig. 6. Output spectra of successively tunable (a) single-, (b) dual-, (c) triple-, and (d) quadruple-wavelength lasing operations.

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The proposed multiwavelength switchable fiber laser exhibits some advantages. First, multiwavelength channels can be flexibly tuned with different number combinations of lasing channels, which cover versatile single-, dual-, triple-, and quadruple-wavelength lasing. Second, it is a compact and simple configuration of a polarization-dependent MKR and a HiBi-SLM filter, which offers comb filtering and polarization switching.

We also investigate the generation stability of multiwavelength lasing channels. The output triple-wavelength spectra are repeatedly scanned every minute, as shown in Fig. 7(a). The output power can be increased by reducing the whole cavity loss or increasing the power of pump or even double pump configuration. Here, the output power of the vortex beams is about 2 mW. The fluctuation of output power is less than 2.5 dBm, and central wavelengths of different channels remain within 0.03 nm in 10 min, which show the stability of the output laser, as shown in Fig. 7(b).

Fig. 7. Stability of triple-wavelength output spectrum. (a) Repeat scans of triple-wavelength output spectrum every minute. (b) Power fluctuation (black) and central wavelength (blue) of each channel in the triple-wavelength output every minute.

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We further exploit the polarization characteristics of multiwavelength switchable outputs through a fused SMF–FMF coupler inserted in the cavity. The mode patterns from the FMF output of the broadband mode coupler are observed when the fiber laser is running at the state of switchable wavelengths. The fused SMF–FMF coupler has been verified effectively when acting as a mode selective converter. A polarizer is added before the CCD camera; by rotating the polarization direction, linearly polarized vortex beams are observed.

We show in Fig. 8 that four columns present the experimental near-field intensity patterns of the LP11 mode and the corresponding OAM±1 of a single wavelength (1559.09 nm), dual wavelengths (1559.09 nm and 1559.90 nm), triple wavelengths (1559.09, 1559.90, and 1560.71 nm), and quadruple wavelengths (1559.09, 1559.90, 1560.71, and 1561.52 nm), respectively. Figures 8(a) and 8(b) are the experimental near-field patterns of LP11 mode and the donut-shaped mode pattern when adjusting the PC4 on the FMF output. Figures 8(c) and 8(d) are the corresponding clockwise and anticlockwise spiral interferograms. Figure 8(e) is the output spectrum of the single-wavelength lasing operation. Other columns present the experimental results of dual-, triple- and quadruple-wavelength lasing operations. The purities of the modes are estimated to be more than 95% using the tight bend approach ^[35].

Fig. 8. Near-field distribution of LP11 intensities, OAM patterns, spiral interferograms, and the out spectra of wavelength-switchable laser. Four columns present (a)–(e) single-, (f)–(j) dual-, (k)–(o) triple-, and (p)–(t) quadruple-wavelength lasing operations. First row, LP11 intensity profiles; second row, donut-shaped mode patterns of vortex beams; third and fourth rows, corresponding clockwise and anticlockwise spiral interferograms; and fifth row, the output spectra.

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The clockwise and counterclockwise spiral interference patterns indicate the vortex beams with OAM−1 and OAM+1. LP11 and OAM mode intensities are preserved identically between the multiwavelength channels and keep the same polarization properties, which are due to the polarization switching of the MKR and HiBi–SLM filter. The near-field LP11 mode intensity patterns, the vortex patterns, and their corresponding spiral interferograms of adjacent single, dual, triple, and quad wavelengths are clearly observed without any distortion. It is concluded that each wavelength channel carries identical properties of OAM+1 or OAM−1.

We successfully obtain multiwavelength vortex beams with identical OAM properties, which are desirable for multiplexing, exchanging, and routing to further improve the capacity of optical fiber transmission. The multiwavelength switchable lasing shows a potential application in mode-division multiplexing, OAM modes switching, and routing.

4. CONCLUSION

In conclusion, we experimentally demonstrate a method to generate multiple-wavelength switchable OVBs in an all-fiber laser based on a polarization-dependent MKR. The tuning wavelengths range from 1546 nm to 1562 nm, and single-, dual-, triple-, and quadruple-wavelength channels can be switched. The wavelength interval is 0.813 nm, which is in agreement with the FSR of the MKR. Variable wavelength intervals can be acquired by just changing the diameter of the MKR. We use a fused SMF–FMF mode coupler to successfully obtain broadband mode conversion and achieve multiwavelength switchable OVBs. It also verifies that each wavelength channel preserves identical OAM properties through their clear spiral interferograms. The proposed wavelength-switchable and widely tunable OAM fiber laser may be useful in various fields, such as mode-division multiplexing, optical fiber communication, and material processing.

5 Acknowledgment

Acknowledgment. X. Zeng acknowledges the support of the Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning and Science and Technology Commission of Shanghai Municipality. F. Pang was supported by the Shuguang Program of Shanghai Education Development Foundation and Shanghai Municipal Education Commission.