Nonlinear four-wave mixing with enhanced diversity and selectivity via spin and orbital angular momentum conservation

Light that can carry orbital angular momentum (OAM) has found a variety of applications in super-resolution microscopy, optical communications, and laser machining, bringing up the need for pure OAM light generation at on-demand power levels and wavelengths. Parametric four-wave mixing is a promising platform for such source generation, and while investigations of higher-order fiber modes have revealed enhanced phase-matching possibilities, the role of the angular momentum of light in this process has not yet been substantially considered. Here, with a specially designed ring-core fiber in which over 16 OAM modes can be stably guided, we demonstrate the first experiments, to our knowledge, investigating nonlinear four wave mixing between OAM modes in an optical fiber. The large modal space as well as spin and OAM conservation rules enable a high diversity of phase matching conditions while also providing high selectivity. We report parametric wavelength translations of over 438 nm and the ability to obtain kilowatt peak-power level ∼ nanosecond pulses of pure OAM beams at user defined colors. © 2020 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/1.5130715., s


I. INTRODUCTION
Light fields with helical phase fronts in the form of exp(±iLϕ) have been shown to carry orbital angular momentum (OAM). 1,2 This has attracted a lot of attention for potential applications in a wide range of fields such as nanoscale microscopy, 3,4 optical tweezers, 5 laser machining, 6 and communications in the classical 7 and quantum 8 regimes. In most, if not all, of these cases, there are needs for generating power-scalable pure OAM beams at ondemand wavelengths. The primary means of achieving this has been intracavity 9,10 or extracavity 11,12 mode conversion of a conventional laser or parametric oscillator source. Such techniques necessarily require mode converters that are, themselves, wavelengthdiverse and power scalable. Bulk χ (2) and χ (3) nonlinearities have also been exploited, 13,14 but the short interaction lengths have thus far prevented these techniques from being power scalable. A recent alternative approach is the generation of a supercontinuum 15 in an OAM fiber, but this yields new colors at only the same OAM mode order as that of the original pump. In addition, as with most supercontinuum sources, this approach yields low power-spectral densities and is most suitable primarily for ultrashort pulses.
Here, we report the first, to the best of our knowledge, demonstration of four-wave mixing (FWM) amongst fiber modes that stably carry OAM and hence demonstrate power-scalable wavelengthdiverse OAM generation. As a subset of higher order fiber modes (HOMs), OAM modes retain the inherent advantages of a multimode system-that of a dramatically enhanced degree of freedom for phase matching arising from the plethora of available modes. [16][17][18] The presence of angular momentum, as we will show, results in additional constraints that improve the selectivity of this multimode platform while also providing for more efficient interactions.

II. THE OAM-FWM PLATFORM
The parametric process of FWM enables new frequency generation when energy and momentum conservation conditions are simultaneously satisfied. For a conventional mono-mode FWM process, where all the interacting waves are in the same transverse spatial mode, the phase matching condition is governed by the second and fourth order dispersion terms. 19 As a general rule, when the pump beam is at a wavelength at which it experiences anomalous dispersion, broadband gain close to the pump wavelength is obtained-a process also referred to as modulation instability (MI). In contrast, narrow gain peaks that are substantially spectrally separated from the pump wavelength are obtained when the pump experiences normal dispersion. In the case of intermodal FWM, these simple dependencies on dispersion no longer hold, and the phase matching condition, ignoring the correction due to self-phase and cross-phase modulation, is given by 16 where Δβ is the total mismatch between propagation constants that must be minimized, the subscript "p," "q," "s," and "as" represent the two pumps, Stokes, and anti-Stokes waves, respectively, with corresponding mode order denoted by the superscripts "j" through "m." It is then trivial to show that phase matching is automatically satisfied when the four photons lie on a straight line of a n eff vs λ plot. Thus, more available spatial modes increase the degrees of freedom with which to obtain desired FWM interactions. In addition, FWM with spatial modes that stably (linearly) propagate in an optical fiber enables maximizing the lengths over which the nonlinear interaction remains coherent, yielding powerscalable parametric wavelength conversion. 20 All of the above is true for any multimode system, and we now describe the unique aspects of cases where these modes additionally carry angular momentum. The normalized transverse electric fields of OAM fiber modes are given by 21 where F(r) is the normalized radial field distribution and ϕ denotes the azimuthal angle. L is the topological charge, associated with ±L ̵ h OAM per photon, and σ ± denote the left and right circular polarizations, corresponding to ± ̵ h of spin angular momentum (SAM) per photon ( ̵ h is reduced Planck's constant). Hence, spin-orbital aligned (SOa) modes carry OAM and SAM of the same sign, while spinorbital antialigned (SOaa) modes have OAM and SAM of opposite signs.
The polarization dependence of χ (3) nonlinearities demands that SAM be independently conserved. 22 In addition, the strength of any FWM interaction is proportional to a field overlap integral, which, for OAM modes, is given by where the subscripts follow the same definitions as above and ΔL is the OAM mismatch between the four interacting waves. The overlap integrals of Eqs. (3) and (4) point to some interesting and beneficial differences. First, this integral is nonzero and hence FWM occurs only when OAM is conserved across the modes, that is, when ΔL = 0. This provides a higher degree of selectivity compared to conventional HOMs and reduces the possibility of parasitic FWM processes competing with a desired process. Second, as we will show below, OAM modes in fibers designed to stably propagate them differ primarily in phase and not amplitude, that is, their intensity profiles are similarly ring-shaped across mode order L. Thus, the overlap integral of Eq. (3) is maximized for OAM modes, making it more efficient than conventional HOM-FWM.
Here, we present three manifestations of FWM with modes that carry OAM, differing primarily in the superposition of OAM and SAM values for the pump mode: (a) degenerate OAM and SAM pump, which leads to traditional MI-like FWM close to the pump wavelength; (b) degenerate OAM but nondegenerate SAM values for the pump, leading to polarization diverse parametric generation; and (c) degenerate SAM but nondegenerate OAM values for the pump, leading to wideband, OAM diverse parametric generation.

III. EXPERIMENTAL SETUP
The experiment setup is shown in Fig. 1(a). The pump laser is a Yb-doped fiber amplifier seeded by a Nd:YAG microchip laser (Teem Photonics SNP-20F-100) that produces 0.6-ns pulses at a repetition rate of 19.5 kHz. The Yb-doped fiber amplifier comprises a 1.5-m-long polarization maintaining gain fiber (Nufern PLMA-YDF-25/250-VIII), yielding peak powers of up to 120 kWsubstantially more than that required in our experiments, in which the input powers were controlled by an attenuator comprising a half-wave plate (Thorlabs WPH05M-1064) and polarization beam splitter (Thorlabs CM1-PBS253).
A spatial light modulator (Hamamatsu LCOS-SLM ×10468-08) coded with a spiral phase plate is used to convert the Gaussian beam from our source into an OAM state with the desired topological charge in the far field. A quarter wave plate (Thorlabs WPQ05M-1064) that follows enables the desired OAM/SAM combinationseither the SOa or SOaa states or their superpositions-to be input into our test fiber.
The seed arm was built with a Ti:sapphire laser (Spectra-Physics, Model 3900S) tuned to 888.8 nm; the mode excitation setup is similar to that of the pump arm except that another half wave plate (Thorlabs WPH05M-1064) and quarter wave plate (Thorlabs WPQ05M-808) are used to compensate for the polarization scrambling from the dichroic mirror and the wavelength mismatch of the seed light with QWP2.
The fiber under test features an air core surrounded by a highindex ring that has been previously shown to facilitate stable guidance of OAM modes over km lengths. 23 Figure 1(b) shows the refractive index profile of this fiber. Simulations suggest that single-radial order OAM modes of |L| = 8, 9, 11, and 12 are stably guided at the pump wavelength of 1064 nm (the L = 10 mode is not stable due to an accidental degeneracy with other radial mode orders but is stable at other wavelengths, such as 1030 nm). The length of fiber used in experiments described in Secs. IV A-IV C is 1.5 m, which was cut back to 0.9 m for the experiments described in Sec. IV D. At the output of the air core fiber [see Fig. 1(a)], a camera (Thorlabs DCC1645C for 600-1100 nm and Allied Vision Technologies "Goldeye" for 1100-1500 nm), a free space large-area InGaAs 5-GHz detector (DET08C), an oscilloscope (Agilent 86100A), and an optical spectrum analyzer (OSA-Ando AQ6317) are used to characterize the mode image and purity, as well as its behavior in the temporal and frequency domains at all relevant wavelengths by employing bandpass filters (BPFs) to selectively interrogate different spectral components. A 200-μm core multimode fiber (Thorlabs FG200LEA) is used for coupling light from all the modes into the OSA. In addition, imaging the output with a tilted lens and circular polarization beam displacer (CPBD) in the beam path allows measuring the OAM and SAM of the output beams. This is because the polarization projection ratios reveal SAM, and the number and orientation of fringes when the output is projected in the far field off a tilted lens reveals the OAM order. 24 Figure 1(c) shows representative images of the beam at the output facet of the fiber for different input OAM and SAM orders at the pump wavelength of 1064 nm with ∼45%-50% coupling efficiency. We use spatial interferometry 25 to measure mode purity; Fig. 1(d) shows the relative powers of each parasitic mode, denoted by the difference of its topological charge in relation to the charge L of the desired beam. In all cases, the mode purity was >20 dB.

A. Degenerate OAM and SAM pump
When the input pump light is in a single OAM and SAM state, the system is effectively single-moded although the fiber is itself multimoded. Such monomode systems would follow the same rules as for traditional single mode systems described in Sec. II. Hence, anomalous dispersion at the pump wavelength would lead to MI, which is a manifestation of FWM leading to broadband emission close to the pump wavelength.
We confirm these expectations by individually pumping in the L = +9; σ + and L = +11; σ + modes of the fiber with peak powers of 8.3 kW and 6.5 kW, respectively. Both modes have anomalous dispersion (∼50 ps km −1 nm −1 and ∼72 ps km −1 nm −1 , respectively) at the pump wavelength of 1064 nm [ Fig. 2(a) shows the simulated dispersion vs λ for these two modes]. The corresponding spontaneous FWM spectra are shown in Fig. 2 Note that increasing pump mode order shifts the Stokes and anti-Stokes emission wavelengths toward the pump, and the bandwidth decreases as well. This is consistent with single mode FWM, where the peak emission wavelengths move closer to the pump, and emission bandwidths decrease, as the magnitude of anomalous dispersion at the pump wavelength increases. These spectral characteristics suggest that the entire emission in either of these experiments would have been in the same mode as the pump. Filtering out representative spectral components (1064 nm for pump and peak emission wavelengths, 1053 nm and 1076 nm for the anti-Stokes and Stokes with L = +9; σ + pump, respectively, 1055 nm and 1074 nm for the anti-Stokes and Stokes with L = +11; σ + pump) allows measurement of their mode content via the tilted lens technique mentioned in Sec. III. We find that all spectral features remain in the same OAM mode as that of the original pump mode, and polarization purity remains greater than 20 dB. Hence, these experiments confirm that FWM with single OAM states behave identically to single-mode FWM, with the added flexibility of tuning dispersion by mode order rather than waveguide design alone.

B. Degenerate OAM; nondegenerate SAM pump
Substantially distinct nonlinear behavior occurs simply by changing the pump mode from an OAM-SAM singlet state to a pump with the same OAM but with linear polarization. As the description of fiber OAM modes in Sec. II conveys, OAM fiber eigenmodes are either SOa or SOaa. Thus, a linear-x-polarization implies that the pump is now equipartitioned into two modes with different n eff (in our air core fibers, this difference is ∼10 −4 ). The dynamics of this intermodal process are better visualized with Fig. 3(a), which is a plot of the simulated n eff vs λ for the pump and a few neighboring OAM modes. The blue and orange curves represent the n eff distributions of the L = +11; σ + (SOa) and σ − (SOaa) modes, respectively-these are the pump modes used in our experiment. Also shown (in purple and dark green) are n effs of the L = +10; σ + and L = +12; σ − modes, respectively. The two pump modes, being spectrally degenerate, have an average n eff given by the midpoint between their respective n eff vs λ curves [apparent in the zoomedin inset of Fig. 3(a)]. These simulated curves enable prediction of the possible FWM pathways in the system. SAM conservation requires that, since the pump modes are split into σ + and σ − polarizations, the Stokes and anti-Stokes lines must also carry SAM of opposite signs, The two possible pathways given the above constraint are represented by straight dashed lines in the n eff vs λ curves of Fig. 3(a), recall, from Sec. II that intermodal processes represent straight lines in n eff vs λ when energy conservation of the four photons is assured. The red dashed line conserves OAM trivially, as in case A (degenerate SAM and OAM) but predicts Stokes (at 1082 nm) and anti-Stokes (1047 nm) emission in the σ − and σ + polarization state, respectively. Figure 3(b) shows experimentally measured spectra with 6.5 kW pump peak power-the excellent match with theoretical predictions is borne out not only by the spectral coincidence between the theory and experiment but also by the fact that modal content measurements at the Stokes and anti-Stokes wavelengths (using a CPBD and tilted lens) reveal exactly the same OAM and SAM content as predicted. Measured polarization extinction ratios for both modes were greater than 14 dB.
The second (green) dashed line in Fig. 3(a) predicts the alternative FWM pathway. Here, the polarization of the Stokes and anti-Stokes light flips compared to the first pathway as indicated in Fig. 3(c) but still yields SAM conservation according to Eq. (5). The participation of different mode orders also requires nontrivial OAM conservation, represented by the pathway, Given that intermodal n eff differences are an order of magnitude larger than the n eff differences between SOa and SOaa modes of the same |L|, the wavelength separation with respect to the pump at which FWM products appear is also larger, and the large slope difference between the phase matching and n eff curves predicts a much smaller bandwidth. The spectrum in Fig. 3 Fig. 3(b)]. This discrepancy may arise from the fact that simulations of n eff 's across modes may be less accurate than those for a single mode. To confirm that the observed pathway is the same as prediction, we also carried our SAM and OAM content measurements using the CPBD and titled lens technique described earlier. We find that the anti-Stokes emission is in the L = +12; σ − mode and the Stokes emission is in the L = +10; σ + mode, precisely as predicted by Eq. (6). Moreover, we measure polarization purity of each of these emissions to be greater than 16 dB, indicating a controlled and exclusive FWM process, as predicted by simulations.

Fig. 3(a) and experimental features in
Finally, we note that the strengths of emissions for the two distinct pathways are not similar. Using simulated field profiles and Eq. (3), we find that the overlap integral for the monomode pathway (red dashed line) is 8.76 × 10 −3 μm −2 and that for the other pathway (green dashed line) is 4.08 × 10 −3 μm −2 . The different overlap integrals and their relative magnitudes qualitatively match with the experiment, which indicates that the degenerate OAM pathway would be more efficient than the nondegenerate OAM pathway of Eq. (6).

C. Degenerate SAM; nondegenerate OAM pump
The last configuration we consider involves the pump modes sharing the same SAM state σ − , which, due to SAM conservation, implies, as in the first case A (pump with degenerate SAM and OAM), that all nonlinear products would also have the same polarization σ − . We consider an input pump comprising equal powers in the L = +8; σ − and L = +9; σ − modes, the phase matching relationships of which are depicted in Fig. 4(a) with solid curves representing, as before, n eff vs λ for each mode.
Multiple FWM pairs are expected since the pump modes now have vastly different n eff . As with the analysis of nondegenerate SAM pump (case B), the equivalent n eff for the pumps lies at the average of the n eff vs λ curves for the L = +8; σ − and L = +9; σ − modes at 1064 nm, resulting in three distinct phase matching pathways (shown by the dashed lines). The red dashed line intersects with the L = +9; σ − and L = +8; σ − n eff curves and creates a photon pair at 888.8 nm and 1326 nm; the green dashed line yields L = +11; σ − and L = +6; σ − photon pairs at 937.4 nm and 1231 nm, and finally, the orange dashed line gives rise to L = +10; σ − and L = +7; σ − photon pairs at 991.5 nm and 1149 nm, 11 (937.4 nm) ← 8 (1064 nm) + 9 (1064 nm) → 6 (1231 nm) , Performing the experiment required a setup slightly modified in comparison to the generic configuration shown in Fig. 1(a). Since we need to excite two distinct pump mode orders, the incoming pump light from the amplified Nd:YAG laser was split on to two distinct spatial patterns on SLM1, which were then recombined with a 3-dB coupler. Figure 4(b) shows the experimentally measured spectrum for this condition with 6.7 kW peak power in each pump mode. As the black dashed lines showing correspondence between the simulated crossing points in Fig. 4(a) and peaks of the spectral features  Fig. 4(b) indicate, an excellent match between theory and experiment is obtained. We also measure output images [ Fig. 4(c)]. The top row shows mode images at the output of the fiber after spectral isolation with appropriate spectral filters. The bottom row shows images after the output passes through a CPBD, hence selecting only the σ − polarization, and a tilted lens, which reveals the OAM content in the form of fringes whose number equals the |L| value of the mode as well as sign of OAM (top-down diagonal for +L and bottom-up diagonal for −L modes). We confirm that the experimentally deduced OAM and SAM content of each of these modes matches the predictions of Eqs. (7)-(9) and, along with the excellent spectral matches of the various FWM emissions, provides a high degree of confidence that the OAM-FWM platform indeed provides the multitude of degrees of freedom as predicted.
Note that, at the pump wavelength, the output mode image does not look as cylindrically symmetric as those at the Stokes and anti-Stokes lines. This apparent degradation is, in fact, expected since the pump comprises two modes L = +8; σ − and L = +9; σ − , respectively, and their coherent interference would indeed lead to the representative "heavy-side" circular image, as shown. A corresponding tilted lens image for the pump is not shown because this technique, which counts fringes, works well only when a single L value exists-instead, we independently confirmed pure mode excitation at the pump wavelength by doing similar measurements for each pump mode path at low power, when only linear transmission occurs.
We calculate the field overlap integral-Eq. (3)-of the three different pathways to compare with the experimentally observed strengths: Table I indicates a discrepancy between theoretically predicted efficiencies and experimentally observed spectral powers. The L = +10; σ − and L = +7; σ − pair, whose overlap integral is equal to 6.93 × 10 −3 , which should correspond to ∼14 dB higher efficiency than the L = +11; σ − and L = +6; σ − pair whose overlap integral is 6.78 × 10 −3 but, in fact, has the least power. This likely arises from the fact that either the L = +10; σ − mode at 991.5 nm or the L = +7; σ − at 1149 nm is linearly unstable. Previous characterizations of linear properties of OAM modes in our air core fiber have revealed that different OAM modes at specific, small wavelength ranges can suddenly become unstable because they correspond with wavelengths at which higher radial order parasitic modes are exactly phase matched. The use of OAM fibers typically entails designing the fiber to avoid such crossings in the wavelengths of interest. A linearly unstable mode would be unable to build up the nonlinear phase, thereby rendering any FWM process in which it participates inefficient. Additional tests on mode stability need to be performed to confirm this hypothesis for the origin of low efficiency for this case.
Finally, note the two other spectral features not predicted by the FWM pathways (dashed lines) of Fig. 4(a). We surmise that the broad band peak at 1120 nm is Raman scattering from the pump modes. This hypothesis is supported by the fact that it is 13 THz away from the pump wavelength, which corresponds to a Raman Stokes shift, and also because its measured SAM state is the same as the pump (σ − ), as expected for Raman scattering. 26 We were, however, unable to fully confirm this hypothesis by also measuring OAM content because the interferometric and tilted lens mode projection techniques we used to measure OAM content of other lines only work for single OAM states, and Raman, being a self-phase matched process, would be expected to have the same (mixed) mode content of the pump. The other feature is close to the pump peaking at 1051 nm and 1079 nm, respectively. We found that their mode content varied between L = +8; σ − and L = +9; σ − depending on the power ratio of the L = +8; σ − and L = +9; σ − content of the input pump. Hence, these are simply MI peaks arising from pump photons in each individual pump mode.

D. Power scaling
With various possible phase matching conditions on hand, the next question we want to address is whether we can build a powerscalable laser based on the OAM-FWM process, which demands that such processes be coherent and robust-a requirement potentially satisfied by OAM fiber modes, given their inherent linear stability with respect to modal as well as polarization perturbations. We test this with seeded FWM experiments so that parametric gain, power-scaling, etc., may be quantitatively assessed. The pump is a superposition of the L = +8; σ − and L = +9; σ − modes (as in case C) with a total peak power level of ∼10 kW entering the fiber sample at 1064 nm; the corresponding spectrum with pump alone is shown in Fig. 5(a). Since the spectra of Fig. 4(b) indicates that the FWM pathway yielding Stokes at 1326 nm in the L = +8; σ − mode and anti-Stokes at 888.8 nm in the L = +9; σ − mode is most efficient, we seed the anti-Stokes arm with 10 mW of power in the L = +9; σ − mode. The spectrum of the seed laser is shown in Fig. 5(b). The resultant spectrum with both pump and seed present is shown in Fig. 5(c). The seed light experienced 51 dB of intrapulse gain, calculated based on the on-off gain at the seed wavelength and repetition rate of the pump laser. This large gain is indicative of a robust, coherent FWM process. The insets of Figs. 5(b) and 5(c) also show the corresponding output mode images as well as beam projections through a tilted lens. Note that the amplified FWM products at both the Stokes and anti-Stokes lines appear to be of much higher mode purity than the input seed-this is consistent with the fact that the high selectivity of OAM-FWM processes ensures parametric amplification for only the phase-matched mode. Figure 5(d) shows the temporal profile of the measured pump pulse with (red line) and without (blue line) the seed. The center of the pump pulse has a maximum instantaneous depletion of ∼63%, and the overall pump depletion is 29%. This large pump depletion also accounts for the spectral suppression of parasitic nonlinear products shown in Fig. 5(c). The temporal profiles of the anti-Stokes and Stokes pulses are shown in Figs. 5(e) and 5(f), respectively, revealing an anti-Stokes pulse peak power of ∼2.8 kW and a Stokes pulse peak power of ∼1.85 kW. The ratio of these powers is identical to that of the inverse ratio of their respective wavelengths, indicating that photon number is conserved in this process, as expected of any robust FWM process. The resultant FWM products have pulse widths of 356 ps for the Stokes line and 390 ps for the anti-Stokes line-shorter than the 650 ps of the pump, consistent with the fact that nonlinear temporal shaping tends to reduce pulse widths. When optimizing the experimental parameters to obtain the above results, we found that the overall efficiency increased as fiber lengths were shortened. This is reminiscent of early FWM experiments with photonic crystal fibers (PCFs), 27 which found that fiber diameter fluctuations modulate the phase matching wavelength along the fiber length, leading to broadening of FWM lines and an attendant reduction in efficiency. Shorter lengths than the 0.9-m we used in our experiments would likely have resulted in even higher efficiency than the ∼63% peak depletion we measured, but we were unable to test this hypothesis due to limitations in available pump power. More importantly, just as FWM efficiencies improved with manufacturing improvements in PCFs, we expect that future manufacturing optimization of OAM fibers would improve efficiencies for OAM-FWM processes too. Finally, note that we used Q-Switched pump pulses for our experiments, which is why the overall efficiency was vastly different from the instantaneous peak efficiency. Optimal rectangular pump pulses would potentially yield overall efficiencies as high of the measured peak efficiency of 63%.

V. SUMMARY, CONCLUSIONS, AND OUTLOOK
We have demonstrated the first four-wave mixing experiments with fiber modes that can carry orbital angular momentum. OAM modes, being a subset of modes in a multimode fiber, retain several of the advantages that have been recently discussed in the emerging field of multimode nonlinear optics, namely, phase-matching diversity. In addition, they provide higher selectivity that enables avoiding undesired nonlinear pathways in favor of the desired processes. This has often been a problem in attempts at using multimode fibers for controllable nonlinear interactions because the modes of conventional fibers typically mix, hence reducing coherence of the APL Photon. 5, 010802 (2020); doi: 10.1063/1.5130715 5, 010802-7 ARTICLE scitation.org/journal/app nonlinear process. OAM fiber modes offer two major advantages in this regard: (1) they are the only known set of fiber modes, to date, that can transmit for km-lengths without mode mixing, hence providing for a very robust and stable platform in which to exploit the multimodality of such fibers; and (2) angular momentum conservation rules result in distinct, specific, and hence tailorable selection rules, enabling isolating and obtaining specific nonlinear products, at user-defined wavelengths and powers. The attributes illustrated in our experiments (wavelengthtranslation ranges exceeding 400 nm, peak powers exceeding kW, wavelength ranges unconstrained by material dispersion) suggest that OAM fiber modes are an attractive alternative to dispersiontailored single mode fibers (such as PCFs) for a variety of power-scalable nonlinear optics applications. In addition, given the immense current interest in free-space OAM beams, FWM with OAM fibers could also become the source generation and mode conversion methods of choice for applications where current options are constrained by the need for (often lossy) mode converters at nonstandard wavelengths.