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Abstract
With wavelength tunability, free-electron lasers (FELs) are well-suited for generating orbital angular momentum (OAM) beams in a wide photon energy range. We report here the first experimental demonstration of OAM beam generation using an oscillator FEL with the tens of picosecond pulse duration. Lasing around 458 nm, we have produced the four lowest orders of superposed Laguerre-Gaussian beams using a very long FEL resonator of 53.73 m. The produced beams have good beam quality, excellent stability, and substantial average power. We have also developed a pulsed operation mode for these beams with a highly reproducible temporal structure for a range of repetition rate of 1–30 Hz. This development can be extended to short wavelengths, for example to x-rays using a future x-ray FEL oscillator. The OAM operation of such a storage-ring FEL also paves the way for the generation of OAM gamma-ray beams via inverse Compton scattering.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The profound and unexpected properties of optical beams with orbital angular momentum (OAM) were first recognized in the early 1990s [1–3]. In the last two decades, OAM photon beams in the near-infrared and visible regimes have been generated using conventional lasers through various methods that incorporate spatial and phase filtering or manipulation [4–8]. Recent research has shown that the OAM photon beam is an excellent tool for non-contact optical manipulation of matter. A wide range of applications have been discovered [9–11], from biological cell handling in optical tweezers [12–14], to laser cooling, atom trapping and control of Bose-Einstein condensates [15–18], and to quantum information and quantum communication [19–22]. The OAM photon beam has also been shown to excite forbidden transitions in an atom [23–25], overcoming the transition selection rules associated with plane-wave photons. Many new research opportunities are expected with OAM beams at shorter wavelengths, from extreme ultraviolet (EUV) to gamma-ray. EUV and x-ray OAM beams can be used to improve the contrast of microscopy [26], enable new forms of spectroscopy [27–29], or alter material magnetic properties [30,31]. OAM gamma rays may open new possibilities in photo-nuclear physics research. Theoretically, they have been shown to modify photo-nuclear reaction rates [32], reveal novel spin effects [33,34], provide the means to separate resonances with different spins and parities [35], and enable new types of multipole analysis in photo-reactions [36–38]. OAM gamma rays may have been generated in extreme astrophysics environments [39–42]. The quantum vortex nature of an OAM photon’s wave function leads to “superkick” effects that may be observed both in the laboratory and astrophysics environment [43], addressing, among other things, the issue of the universe’s transparency to very high energy gamma rays.
The generation of OAM photon beams in the short wavelength region can be realized using accelerator-based light sources. For example, a relativistic electron beam traversing a helical undulator magnet produces higher-order harmonic radiation off-axis. This radiation was first recognized to exhibit an intrinsic spiral wavefront in a theoretical analysis [44,45], a finding confirmed later experimentally [46]. Recent advances have led to the generation of an OAM beam in several single-pass free-electron lasers (FELs) seeded using a laser in the fundamental Gaussian mode [47–49]. The laser interaction with the electron beam in an upstream undulator (a modulator) modulates the electron beam energy distribution and this energy modulation is turned into a charge density modulation. With a helical modulator, an electron beam with helical microbunching can be used to produce an OAM beam in a downstream undulator (a radiator) [47]. With a planar modulator, the electron beam with longitudinal microbunching can be used to produce an OAM beam via harmonic radiation in the downstream helical radiator, either via a straightforward second-harmonic generation [48], or using a high-gain harmonic generation scheme [50] to up-shift the radiation wavelength to the EUV [49].
While the transverse mode control in an FEL cavity has been proposed in previous simulation studies [51–53], in this work, we report the first experimental generation of superposed OAM laser beams using an oscillator FEL. The superposed OAM beams are generated as coherent suppositions of pure OAM beams with opposite helicities. They are self-healing [54] and more tolerant to distortions for use in quantum information [21,55]. They can be focused tightly [56] for applications such as particle trapping [57,58].
In this work, a self-seeded superposed OAM beam is amplified in multiple passes inside a laser resonator to reach saturation, unlike the previous OAM beam generation using seeded single-pass FELs [47–49]. An oscillator FEL is well suited for producing high intracavity power and high-repetition-rate coherent radiation in a wide wavelength range, with demonstrated operation from the far infrared to the vacuum UV [59–65]. The schematic layout of the Duke FEL is shown in Fig. 1. Powered by an electron storage ring, this FEL is comprised of a near-concentric, extremely long optical resonator of $53.73$ m and a magnetic system with multiple undulator magnets [66]. In a typical FEL configuration shown in Fig. 1, two middle helical undulators, OK-5B and OK-5C, are energized; these undulators, together with a buncher magnet B sandwiched between them form an optical klystron (OK) [67,68] to enhance the FEL gain. The Duke FEL is used as the drive to produce gamma rays via the Compton backscattering at the High Intensity Gamma-ray Source [69,70], which is the highest-flux Compton gamma-ray source in the world.
Fig. 1. Typical schematic layout of the storage ring FEL oscillator for the superposed OAM beam generation. The FEL is comprised of an optical klystron with two helical undulators OK-5B and OK-5C and a buncher magnet B in between, and a near-concentric optical resonator with mirrors M1 and M2. Downstream mirror M2 is covered with a special spatial mask with two non-reflective parts [see the bottom-right inset (a)]: an aluminum disk in the center and an aluminum annulus covering the exterior region of the mirror. The top-left inset (b) illustrates the coherent superposition of the ${\rm LG}_{0}^{1}$ and ${\rm LG}_{0}^{-1}$ modes, which have the same intensity profile but different wavefront structures.
2. Methods
When operating at its fundamental frequency, the FEL wavelength can be tuned by changing the electron beam energy ($E_e$) and the undulator magnetic field according to the formula: $\lambda _{\rm FEL} = {\lambda _u} \left (1 + {K^2}\right )/(2\gamma ^2)$. Here, $\gamma =E_e/m_ec^2$, $K = eB_0\lambda _u/(2\pi m_ec)$ is the undulator strength, with $m_e$ being the electron’s rest mass, $\lambda _u$ the undulator period, $B_0$ the rms magnetic field, and $c$ the speed of light. After repeated electron-photon beam interactions, the FEL beam builds up inside the cavity between two high-reflectivity mirrors. The typical FEL transverse mode is the lowest Gaussian mode, realized with good alignment of the electron beam orbit and optical axis. To generate OAM beams in the Laguerre-Gaussian ${\rm LG}_{p}^{l}$ modes (with radial order $p$ and OAM order $l$), the cylindrical symmetry of the cavity’s transverse boundary must be assured. We accomplish this by using a spatial mask inside the cavity.
This spatial mask is integrated with the downstream mirror M2 [see inset (a) of Fig. 1]. The mask consists of an aluminum central disk and an aluminum annulus. With a carefully chosen inner diameter ($D_{\rm annu}$), the annulus enforces the cylindrical symmetry of the exterior cavity boundary. The high-loss central disk (diameter $D_{\rm disk}$) is used to prevent the formation of the fundamental and other low-order modes. Multiple disks are fabricated with their dimensions estimated by comparing the loss of a particular mode with a set of possible FEL gain values. While the FEL cavity with a specific mask could still provide enough gain for a few modes to lase, only the mode with the highest gain after tuning up the FEL and the electron beam will be brought to lase due to mode competition during the FEL built-up process. For all experimental results with various orders of superposed OAM beams, a fixed $D_{\rm annu} =26$ mm is used, while $D_{\rm disk}$ is varied with the order of OAM modes to suppress undesirable lower order modes. Dimensions of the spatial mask, together with other key beam parameters are provided in Table 1. For results reported in this work, the typical experimental setup involves a single-bunch electron beam of $533$ MeV and FEL lasing at $\lambda _{\rm FEL}=458$ nm with circular polarization. Non-typical experimental settings will be noted explicitly. The measured electron bunch length varies from about $100$ ps to $210$ ps, depending on the storage ring FEL operating conditions. The FEL pulse length is about ten times less than the electron bunch length, on the order of tens of ps. Note that as the OAM mode order increases, the FEL power decreases rapidly.
Table 1. Summary of experimental parameters.
For an optical cavity with cylindrical symmetry, two pure OAM modes of the same frequency but opposite helicities, ${\rm LG}_{0}^{l}$ and ${\rm LG}_{0}^{-l}$ are degenerate—both have the same transverse intensity distribution, but different spiraling orientations of the wavefront. As a result, a coherently superposed beam ${\rm LG}_0^{|{l}|}$ is usually produced, with its electric field given by
Lasing in the superposed OAM mode is realized by maximizing gain via careful overlap of the electron beam and the optical mode and the use of an optical klystron configuration. If necessary a third undulator can be turned on to further enhance the gain. The transverse beam overlap is optimized not only by alignment, but also by increasing the electron vertical beam size by operating the storage ring near the transverse coupling resonance. The frequency of the storage ring rf system is tuned carefully to realize nearly perfect synchronization between the electron and FEL beams (i.e. zero FEL detuning). With careful tuning of the FEL, superposed OAM beams of several orders have been generated with excellent reproducibility.
3. Results
The extracted FEL beam from upstream mirror M1 is sent to a set of standard FEL diagnostics to measure the beam spectrum, power, etc., and to a new diagnostic to measure the beam profile. This FEL profile measurement system is comprised of a telescopic beam transport, a narrow bandpass filter, and a charge-coupled device (CCD) camera with 8-bit resolution [see Fig. 2(a)]. The optical telescope consists of two focusing lenses F1 and F2 with focal lengths $f_1 =50$ cm and $f_2=10$ cm, respectively.
Fig. 2. (a) Schematic layout for the FEL beam profile measurement system with a movable CCD and telescopic transport optics comprised of focusing lenses F1 and F2. Following F1 is a narrow bandpass filter BF. (b) Beam quality factor $M^2$ measurement of the ${\rm LG}_0^{|{2}|}$ beam. The inserted beam images show the transverse beam profiles at different longitudinal locations ($z$). $M_{x,y}^2$ is determined by fitting the measured square of the beam width, $w_{x,y}^2$, to a quadratic function of $z$. For this measurement, the electron single-bunch current $I_b\approx 25$ mA.
By moving the CCD camera along the beam direction, the beam profile can be recorded as a function of the longitudinal position ($z$). To effectively use the camera’s dynamic range and avoid saturation, the exposure time of the CCD is adjusted, and when needed, a neutral density filter is inserted before the camera. During the measurement, the FEL beam power may fluctuate slightly, which is typically corrected by fine-tuning the FEL optical axis or adjusting the FEL detuning. A series of beam images along the beam direction is shown in Fig. 2(b) for the ${\rm LG}_0^{|{2}|}$ beam. By using the projected beam distribution in the horizontal ($x$) and vertical ($y$) directions, the beam quality factor $M^2$ can be obtained using a quadratic curve fitting [74]. For this dataset, we find $M_{x}^2=3.2$ and $M_{y}^2=3.3$. These values are a factor of $1.07$ and $1.1$ above the theoretical value ($M^2=3$ for the ${\rm LG}_0^{|{2}|}$ mode), which represents one of the best results among multiple ${\rm LG}_0^{|{2}|}$ measurements. The discrepancy in $M^2$ may indicate the presence of a very small amount of other transverse modes in the beam, or some distortion in the optical image due to factors, such as diffraction, noise, etc.
Using the measured intensity profile at different longitudinal locations, an iterative phase retrieval technique [75] has been applied to ${\rm LG}_0^{|{1}|}$, ${\rm LG}_0^{|{2}|}$, ${\rm LG}_0^{|{3}|}$, and ${\rm LG}_0^{|{4}|}$ beams to obtain the wavefront of the electric field $E = Ae^{i\psi }$, with $|A|^2$ and $\psi$ the intensity and phase of the wavefront, respectively. Comparing the measured intensity and phase distributions with theoretical ones for these four beams (shown in Fig. 3), the measured results of the first three beams agree well with the theoretical ones. For the ${\rm LG}_0^{|{4}|}$ beam, the difference between the theoretical and the measured results is more pronounced, which is possibly due to a small FEL net gain for this large-size, higher-order mode due to substantial cavity losses. Using a modal analysis method [76], the transverse mode components of these beams can be determined. This result is shown in Fig. 3(a4)–(d4). This modal analysis reveals that for each of the four beams, the dominant modes are the two corresponding pure OAM modes with opposite helicity, with a slightly asymmetric distribution of other contributing modes with smaller amplitudes.
Fig. 3. (a0)–(d0) Intensity profiles of theoretical modes ${\rm LG}_0^{|{1}|}$, ${\rm LG}_0^{|{2}|}$, ${\rm LG}_0^{|{3}|}$, ${\rm LG}_0^{|{4}|}$, respectively. (a1)–(d1) Intensity profiles of the experimentally measured corresponding beams. (a2)–(d2) Phase distribution of corresponding ideal superposed OAM modes. (a3)–(d3) Phase distribution of the measured beams. (a4)–(d4) Relative intensity of various mode components ($I_{l,p}$) for the measured OAM beams, with at least $95$% of the total beam intensity in the lowest modes ${\rm LG}_{p}^{l}$, $p\leq 2$ and $|l|\leq 8$, i.e., $\sum _{l,p} I_{l,p}\ge 0.95$. For these measurements, the beam parameters vary, $E_{e}= 490$–$518$ MeV, $I_b=14$–$30$ mA, and $\lambda _{\rm FEL} = 454$–$457$ nm.
The storage ring FEL beam has a complex temporal structure with both macropulses and micropulses [77,78]. The micropulses are associated with the electron beam revolution ($2.79$ MHz in our case) and the macropulses are the result of two competing processes: FEL lasing and radiation damping of the electron beam. With zero FEL detuning, the FEL lasing in the fundamental Gaussian mode can produce a quasi-CW beam with reasonably stable micropulses without the apparent macropulse structure. However, the superposed OAM beams behave differently: they always remain in a pulsing mode even with zero detuning. For example, when free-running without external modulation, the temporal structure of an ${\rm LG}_0^{|{2}|}$ beam [Fig. 4(a)] is dominated by a pulsing frequency of $180$ Hz, the third harmonic of the line frequency of the ac power supply (see the top-right inset). This can be considered as a natural modulation frequency due to ac noise in the system. Besides substantial variations in the pulse shape and height, the arrival time of the well-formed macropulses varies by about $1$ ms (rms) after removing the time delay associated with $180$ Hz (see the top-left inset). For this free-running ${\rm LG}_0^{|{2}|}$ beam, the maximum extracted average power is about $14$ mW with a high beam current ($I_b\approx 50$ mA). This corresponds to a conservative estimate of the intracavity laser power of about $10$ W.
Fig. 4. (a) Measured temporal structure of the ${\rm LG}_0^{|{2}|}$ beam as the FEL is free-running without external modulation. Top-left inset: the first $12$ macropulses in a fixed time window with the time delay associated with $180$ Hz power line frequency removed; Top-right inset: the related power spectrum of the beam signal, the frequency for the highest peak is $180$ Hz. (b) Temporal structure of the ${\rm LG}_0^{|{2}|}$ beam with a $25$ Hz external modulation. Top-left inset: a plot of 12 macropulses in a fixed time window with the time delay associated with the modulation trigger removed; Top-right inset: the related power spectrum. For this measurement, the single-bunch current $I_b\approx 30$ mA.
The inherent chaotic macropulse structure of the FEL beam can lead to large fluctuations of intensity-based measurements of user experiments. To improve the reproducibility of the superposed OAM beam, we used an FEL gain modulator to deliberately modulate the longitudinal coupling between the electron beam and FEL beam. The FEL can be modulated with a wide range of frequencies ($f_{\rm mod}$), and in our measurements, $f_{\rm mod}$ was varied from $1$ to $67$ Hz. We find that the pulse energy of the ${\rm LG}_0^{|{2}|}$ beam remains relatively constant for $f_{\rm mod}$ between $1$ and $25$ Hz, and decreases at higher frequencies. On the other hand, the average FEL power increases linearly with $f_{\rm mod}$ up to about $25$ Hz and then tapers off at higher frequencies. A close examination of this operation at various modulation frequencies also shows this beam has the best reproducibility in terms of the energy per macropulse at $25$ Hz. The temporal structure of the ${\rm LG}_0^{|{2}|}$ beam at $25$ Hz is shown in Fig. 4(b), with very regularly displaced pulses in both the time and frequency domains (the top-right inset). The macropulses are highly reproducible as illustrated by using the first 12 pulses in the top-left insets of Fig. 4(b). Overall, the pulsed ${\rm LG}_0^{|{2}|}$ beam operation is optimum when modulated at about $25$ Hz to produce high average power and a consistent series of macropulses. It is worth noting that the pulse separation ($40$ ms) is somewhat smaller than the energy damping time of this electron beam (about $54$ ms). This shows that reproducible production of pulsed ${\rm LG}_0^{|{2}|}$ beams requires only modest damping.
4. Conclusions
In this work, we have reported the first experimental generation of superposed OAM beams using an oscillator FEL by incorporating a specially designed spatial mask inside the FEL cavity. Using masks of different dimensions, we have produced $\sim$458 nm superposed OAM beams in the four lowest orders, in the form of a coherent superposition of two LG modes of opposite helicities. These beams have been experimentally characterized to show an excellent mode quality factor, and consistent intensity and phase distributions compared with the theoretical ones. Based on the $M^2$ measurements we have confirmed that these beams are dominated by the expected LG modes, possibly with a smaller contribution from a few other low-order modes. The temporal structure of ${\rm LG}_0^{|{2}|}$ mode has been studied to show a natural pulsing due to ac power modulation. Modulated by an external drive, this superposed OAM beam produced using a $533$ MeV electron beam shows excellent reproducibility in terms of the pulse shape, pulse energy, and arrival time when the modulation frequency is less than $30$ Hz, with the best pulse energy consistency when modulated around $25$ Hz. With this beam, a reasonably high intracavity laser power, on the order of $10$ W, has been realized, and even higher power ($\sim$100 W) can be expected after further optimization of the optical mask and FEL mirrors. We are working to extend the superposed OAM generation to a range of wavelengths, from infrared to ultraviolet (UV) as allowed by the available FEL gain.
This work has demonstrated a novel method to generate superposed OAM beams of various orders inside an extremely long laser cavity using the oscillator FEL. The FEL technology opens the door for the generation and study of OAM beams with various features afforded by the FEL, including a wide spectral coverage, wavelength tunability, two-color lasing [79], polarization manipulation and control [70], etc. FEL operation showcased in this work can be extended to higher photon energies, e.g. using a future x-ray FEL oscillator [53,80]. Such operation in EUV can be explored using either an oscillator [81], or possibly, a regenerative amplifier [82,83]. Furthermore, using the superposed OAM FEL beam as the photon drive, a Compton light source can produce gamma-ray photons with OAM [84,85]. If a Compton gamma-ray beam with sufficient flux can be generated, it will pave the way for a new class of nuclear physics experiments that can exploit novel physics phenomena associated with photon’s OAM as a new degree of freedom in photo-nuclear reactions.
Funding
U.S. Department of Energy (DE-AC05-06OR23177, DE-FG02-97ER41033); Army Research Office (W911NF-23-1-0085).
Acknowledgments
We would like to thank the engineering and technical staff at DFELL/TUNL for their support. We also thank Patrick Wallace for proofreading the manuscript.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, et al., “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992). [CrossRef]
2. M. W. Beijersbergen, L. Allen, H. van der Veen, et al., “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96(1-3), 123–132 (1993). [CrossRef]
3. L. Allen, M. J. Padgett, and M. Babiker, “IV The orbital angular momentum of light,” in Prog. Opt., vol. 39 (Elsevier, 1999), pp. 291–372.
4. H. He, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical particle trapping with higher-order doughnut beams produced using high efficiency computer generated holograms,” J. Mod. Opt. 42(1), 217–223 (1995). [CrossRef]
5. M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, et al., “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112(5-6), 321–327 (1994). [CrossRef]
6. A. Ito, Y. Kozawa, and S. Sato, “Generation of hollow scalar and vector beams using a spot-defect mirror,” J. Opt. Soc. Am. A 27(9), 2072–2077 (2010). [CrossRef]
7. D. Naidoo, K. Aït-Ameur, M. Brunel, et al., “Intra-cavity generation of superpositions of Laguerre–Gaussian beams,” Appl. Phys. B 106(3), 683–690 (2012). [CrossRef]
8. D. Naidoo, F. S. Roux, A. Dudley, et al., “Controlled generation of higher-order poincaré sphere beams from a laser,” Nat. Photonics 10(5), 327–332 (2016). [CrossRef]
9. S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 2(4), 299–313 (2008). [CrossRef]
10. A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011). [CrossRef]
11. H. Rubinsztein-Dunlop, A. Forbes, M. V. Berry, et al., “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017). [CrossRef]
12. N. B. Simpson, L. Allen, and M. J. Padgett, “Optical tweezers and optical spanners with Laguerre–Gaussian modes,” J. Mod. Opt. 43(12), 2485–2491 (1996). [CrossRef]
13. D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003). [CrossRef]
14. R. Dasgupta, S. Ahlawat, R. S. Verma, et al., “Optical orientation and rotation of trapped red blood cells with Laguerre-Gaussian mode,” Opt. Express 19(8), 7680–7688 (2011). [CrossRef]
15. T. Kuga, Y. Torii, N. Shiokawa, et al., “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78(25), 4713–4716 (1997). [CrossRef]
16. J. Tabosa and D. Petrov, “Optical pumping of orbital angular momentum of light in cold cesium atoms,” Phys. Rev. Lett. 83(24), 4967–4970 (1999). [CrossRef]
17. M. Andersen, C. Ryu, P. Cladé, et al., “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97(17), 170406 (2006). [CrossRef]
18. K. C. Wright, L. S. Leslie, and N. P. Bigelow, “Optical control of the internal and external angular momentum of a Bose-Einstein condensate,” Phys. Rev. A 77(4), 041601 (2008). [CrossRef]
19. G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. 88(1), 013601 (2001). [CrossRef]
20. G. Gibson, J. Courtial, M. J. Padgett, et al., “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12(22), 5448–5456 (2004). [CrossRef]
21. E. Nagali, F. Sciarrino, F. De Martini, et al., “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103(1), 013601 (2009). [CrossRef]
22. G. Vallone, V. D’Ambrosio, A. Sponselli, et al., “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett. 113(6), 060503 (2014). [CrossRef]
23. C. T. Schmiegelow, J. Schulz, H. Kaufmann, et al., “Transfer of optical orbital angular momentum to a bound electron,” Nat. Commun. 7(1), 12998 (2016). [CrossRef]
24. A. Afanasev, C. E. Carlson, C. T. Schmiegelow, et al., “Experimental verification of position-dependent angular-momentum selection rules for absorption of twisted light by a bound electron,” New J. Phys. 20(2), 023032 (2018). [CrossRef]
25. A. Picón, J. Mompart, J. R. V. de Aldana, et al., “Photoionization with orbital angular momentum beams,” Opt. Express 18(4), 3660–3671 (2010). [CrossRef]
26. A. Sakdinawat and Y. Liu, “Soft-x-ray microscopy using spiral zone plates,” Opt. Lett. 32(18), 2635–2637 (2007). [CrossRef]
27. M. van Veenendaal and I. McNulty, “Prediction of strong dichroism induced by x rays carrying orbital momentum,” Phys. Rev. Lett. 98(15), 157401 (2007). [CrossRef]
28. J. R. Rouxel, B. Rösner, D. Karpov, et al., “Hard x-ray helical dichroism of disordered molecular media,” Nat. Photonics 16(8), 570–574 (2022). [CrossRef]
29. J.-L. Bégin, A. Jain, A. Parks, et al., “Nonlinear helical dichroism in chiral and achiral molecules,” Nat. Photonics 17(1), 82–88 (2023). [CrossRef]
30. J. Wätzel, Y. Pavlyukh, A. Schäffer, et al., “Optical vortex driven charge current loop and optomagnetism in fullerenes,” Carbon 99, 439–443 (2016). [CrossRef]
31. H. Fujita and M. Sato, “Ultrafast generation of skyrmionic defects with vortex beams: Printing laser profiles on magnets,” Phys. Rev. B 95(5), 054421 (2017). [CrossRef]
32. A. Afanasev, V. G. Serbo, and M. Solyanik, “Radiative capture of cold neutrons by protons and deuteron photodisintegration with twisted beams,” J. Phys. G: Nucl. Part. Phys. 45(5), 055102 (2018). [CrossRef]
33. A. Afanasev, C. E. Carlson, and M. Solyanik, “Circular dichroism of twisted photons in non-chiral atomic matter,” J. Opt. 19(10), 105401 (2017). [CrossRef]
34. I. P. Ivanov, N. Korchagin, A. Pimikov, et al., “Doing spin physics with unpolarized particles,” Phys. Rev. Lett. 124(19), 192001 (2020). [CrossRef]
35. I. P. Ivanov, N. Korchagin, A. Pimikov, et al., “Kinematic surprises in twisted-particle collisions,” Phys. Rev. D 101(1), 016007 (2020). [CrossRef]
36. A. Afanasev, C. E. Carlson, and M. Solyanik, “Atomic spectroscopy with twisted photons: Separation of M1- E2 mixed multipoles,” Phys. Rev. A 97(2), 023422 (2018). [CrossRef]
37. A. Afanasev and C. E. Carlson, “Delta baryon photoproduction with twisted photons,” Ann. Phys. 534(3), 2100228 (2022). [CrossRef]
38. Z.-W. Lu, L. Guo, Z.-Z. Li, et al., “Manipulation of giant multipole resonances via vortex γ photons,” arXiv, arXiv:2306.08377 (2023). [CrossRef]
39. Y. Taira and M. Katoh, “Generation of optical vortices by nonlinear inverse Thomson scattering at arbitrary angle interactions,” Astrophys. J. 860(1), 45 (2018). [CrossRef]
40. M. Katoh, M. Fujimoto, H. Kawaguchi, et al., “Angular momentum of twisted radiation from an electron in spiral motion,” Phys. Rev. Lett. 118(9), 094801 (2017). [CrossRef]
41. T. Maruyama, T. Hayakawa, and T. Kajino, “Compton Scattering of γ-Ray Vortex with Laguerre Gaussian Wave Function,” Sci. Rep. 9(1), 51 (2019). [CrossRef]
42. T. Maruyama, T. Hayakawa, and T. Kajino, “Compton Scattering of Hermite Gaussian Wave γ Ray,” Sci. Rep. 9(1), 7998 (2019). [CrossRef]
43. A. Afanasev, C. E. Carlson, and A. Mukherjee, “Recoil Momentum Effects in Quantum Processes Induced by Twisted Photons,” arXiv, arXiv:2007.05816 (2020). [CrossRef]
44. S. Sasaki and I. McNulty, “Proposal for generating brilliant x-ray beams carrying orbital angular momentum,” Phys. Rev. Lett. 100(12), 124801 (2008). [CrossRef]
45. A. Afanasev and A. Mikhailichenko, “On generation of photons carrying orbital angular momentum in the helical undulator,” arXiv, arXiv:1109.1603 (2011). [CrossRef]
46. J. Bahrdt, K. Holldack, P. Kuske, et al., “First observation of photons carrying orbital angular momentum in undulator radiation,” Phys. Rev. Lett. 111(3), 034801 (2013). [CrossRef]
47. E. Hemsing, A. Knyazik, M. Dunning, et al., “Coherent optical vortices from relativistic electron beams,” Nat. Phys. 9(9), 549–553 (2013). [CrossRef]
48. E. Hemsing, M. Dunning, C. Hast, et al., “First characterization of coherent optical vortices from harmonic undulator radiation,” Phys. Rev. Lett. 113(13), 134803 (2014). [CrossRef]
49. P. R. Ribič, B. Rösner, D. Gauthier, et al., “Extreme-ultraviolet vortices from a free-electron laser,” Phys. Rev. X 7(3), 031036 (2017). [CrossRef]
50. L.-H. Yu, M. Babzien, I. Ben-Zvi, et al., “High-gain harmonic-generation free-electron laser,” Science 289(5481), 932–934 (2000). [CrossRef]
51. B. Faatz, R. W. B. Best, D. Oepts, et al., “Control of the transverse mode distribution in free electron lasers,” Pure Appl. Opt. 2(3), 195–210 (1993). [CrossRef]
52. A. Pathak and S. Krishnagopal, “Resonator stability and higher-order modes in free-electron laser oscillators,” Phys. Rev. ST Accel. Beams 17(8), 080703 (2014). [CrossRef]
53. N. Huang and H. Deng, “Generating x-rays with orbital angular momentum in a free-electron laser oscillator,” Optica 8(7), 1020–1023 (2021). [CrossRef]
54. I. A. Litvin, L. Burger, and A. Forbes, “Angular self-reconstruction of petal-like beams,” Opt. Lett. 38(17), 3363 (2013). [CrossRef]
55. K. T. Kapale and J. P. Dowling, “Vortex phase qubit: generating arbitrary, counterrotating, coherent superpositions in Bose-Einstein condensates via optical angular momentum beams,” Phys. Rev. Lett. 95(17), 173601 (2005). [CrossRef]
56. P. Woźniak, P. Banzer, F. Bouchard, et al., “Tighter spots of light with superposed orbital-angular-momentum beams,” Phys. Rev. A 94(2), 021803 (2016). [CrossRef]
57. A. Dreismann, P. Cristofolini, R. Balili, et al., “Coupled counterrotating polariton condensates in optically defined annular potentials,” Proc. Natl. Acad. Sci. 111(24), 8770–8775 (2014). [CrossRef]
58. J. Webster, C. Rosales-Guzmán, and A. Forbes, “Radially dependent angular acceleration of twisted light,” Opt. Lett. 42(4), 675–678 (2017). [CrossRef]
59. M. Billardon, P. Elleaume, J. M. Ortega, et al., “First operation of a storage-ring free-electron laser,” Phys. Rev. Lett. 51(18), 1652–1655 (1983). [CrossRef]
60. N. A. Vinokurov, I. B. Drobyazko, G. N. Kulipanov, et al., “Lasing in visible and ultraviolet regions in an optical klystron installed on the VEPP-3 storage ring,” Rev. Sci. Instrum. 60(7), 1435–1438 (1989). [CrossRef]
61. F. Glotin, R. Chaput, D. Jaroszynski, et al., “Infrared subpicosecond laser pulses with a free-electron laser,” Phys. Rev. Lett. 71(16), 2587–2590 (1993). [CrossRef]
62. S. Takano, H. Hama, and G. Isoyama, “Lasing of a free electron laser in the visible on the UVSOR storage ring,” Nucl. Instrum. Methods Phys. Res., Sect. A 331(1-3), 20–26 (1993). [CrossRef]
63. G. R. Neil, C. Bohn, S. Benson, et al., “Sustained kilowatt lasing in a free-electron laser with same-cell energy recovery,” Phys. Rev. Lett. 84(4), 662–665 (2000). [CrossRef]
64. V. N. Litvinenko, S. H. Park, I. V. Pinayev, et al., “Operation of the OK-4/Duke storage ring FEL below 200 nm,” Nucl. Instrum. Methods Phys. Res., Sect. A 475(1-3), 195–204 (2001). [CrossRef]
65. O. A. Shevchenko, V. S. Arbuzov, N. A. Vinokurov, et al., “The Novosibirsk Free Electron Laser–unique source of terahertz and infrared coherent radiation,” Phys. Procedia 84, 13–18 (2016). [CrossRef]
66. Y. K. Wu, N. A. Vinokurov, S. Mikhailov, et al., “High-gain lasing and polarization switch with a distributed optical-klystron free-electron laser,” Phys. Rev. Lett. 96(22), 224801 (2006). [CrossRef]
67. N. A. Vinokurov and A. N. Skrinsky, “Budker Institute of Nuclear Physics,” Novosibirsk Report No. INP 77-59, 1977 (to be published).
68. V. N. Litvinenko, B. Burnham, S. H. Park, et al., “First UV/visible lasing with the OK-4/Duke storage ring FEL,” Nucl. Instrum. Methods Phys. Res., Sect. A 407(1-3), 8–15 (1998). [CrossRef]
69. H. R. Weller, M. W. Ahmed, H. Gao, et al., “Research opportunities at the upgraded HI?S facility,” Prog. Part. Nuclear Phys. 62(1), 257–303 (2009). [CrossRef]
70. J. Yan, J. M. Mueller, M. W. Ahmed, et al., “Precision control of gamma-ray polarization using a crossed helical undulator free-electron laser,” Nat. Photonics 13(9), 629–635 (2019). [CrossRef]
71. S. F. Pereira, M. B. Willemsen, M. P. van Exter, et al., “Pinning of daisy modes in optically pumped vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 73(16), 2239–2241 (1998). [CrossRef]
72. Y. F. Chen, Y. P. Lan, and S. C. Wang, “Generation of Laguerre–Gaussian modes in fiber-coupled laser diode end-pumped lasers,” Appl. Phys. B 72(2), 167–170 (2001). [CrossRef]
73. D. Lin, J. M. O. Daniel, and W. A. Clarkson, “Controlling the handedness of directly excited Laguerre–Gaussian modes in a solid-state laser,” Opt. Lett. 39(13), 3903–3906 (2014). [CrossRef]
74. A. E. Siegman, “New developments in laser resonators,” Proc. SPIE 1224, 2–14 (1990). [CrossRef]
75. P. Liu, J. Yan, H. Hao, et al., “Phase retrieval for short wavelength orbital angular momentum beams using knife-edge diffraction,” Opt. Commun. 474, 126077 (2020). [CrossRef]
76. P. Liu, J. Yan, W. Li, et al., “Transverse mode analysis for free-space laser beams using Bayesian analysis,” Appl. Opt. 60(12), 3344–3352 (2021). [CrossRef]
77. M. Billardon, “Storage ring free-electron laser and chaos,” Phys. Rev. Lett. 65(6), 713–716 (1990). [CrossRef]
78. M. Billardon, D. Garzella, and M. E. Couprie, “Saturation mechanism for a storage-ring free-electron laser,” Phys. Rev. Lett. 69(16), 2368–2371 (1992). [CrossRef]
79. Y. K. Wu, J. Yan, H. Hao, et al., “Widely tunable two-color free-electron laser on a storage ring,” Phys. Rev. Lett. 115(18), 184801 (2015). [CrossRef]
80. K.-J. Kim, Y. Shvyd’ko, and S. Reiche, “A proposal for an x-ray free-electron laser oscillator with an energy-recovery linac,” Phys. Rev. Lett. 100(24), 244802 (2008). [CrossRef]
81. G. Stupakov and M. S. Zolotorev, “FEL oscillator for EUV lithography,” Tech. rep., SLAC National Accelerator Lab., Menlo Park, CA (United States) (2014).
82. S. V. Benson, D. Douglas, P. Evtushenko, et al., “The JLAMP VUV/soft x-ray user facility at Jefferson Laboratory,” in Proceedings, 1st International Particle Accelerator Conference (IPAC 2010): Kyoto, Japan, 2010, (2010), p. 2302.
83. Y. Socol, G. Kulipanov, A. Matveenko, et al., “Compact 13.5-nm free-electron laser for extreme ultraviolet lithography,” Phys. Rev. ST Accel. Beams 14(4), 040702 (2011). [CrossRef]
84. U. D. Jentschura and V. G. Serbo, “Generation of high-energy photons with large orbital angular momentum by Compton backscattering,” Phys. Rev. Lett. 106(1), 013001 (2011). [CrossRef]
85. V. Petrillo, G. Dattoli, I. Drebot, et al., “Compton scattered x-gamma rays with orbital momentum,” Phys. Rev. Lett. 117(12), 123903 (2016). [CrossRef]
