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Optical setup: LP’s are neutral polarizing filters, BE1 and BE2 beam expanders, M a fixed mirror, MBS a moving beam splitter, MM a moving plane mirror, L1 a biconvex lens, H the fork–hologram, CCD1 and CCD2 two CCD cameras. The inset represents the spatial filtering for the white light: L2 is a camera lens and S a narrow slit (aperture < 1 mm). The two sources were obtained by using two distinct ∼ He-Ne lasers, in the monochromatic case, or a halogen lamp and two optical fibers in white light (not represented here).
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We experimentally and numerically tested the separability of two independent equally luminous monochromatic and white light sources at the diffraction limit, using optical vortices (OV). The diffraction pattern of one of the two sources crosses a fork hologram on its center generating the Laguerre-Gaussian (LG) transform of an Airy disk. The second...
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... than θ R . In this paper, we show that the Rayleigh limit may be better overcome by using for the two sources a combina- tion of integer and non–integer values of l . Sub–Rayleigh separability. — In this section we present the experimental and numerical results, achieved using OVs, about the sub–Rayleigh separation of two equally intense and uncorrelated monochromatic sources and also experimental results obtained in white light. The optical scheme of the experiment is shown in Fig. 1. Two 632 . 8 nm He–Ne lasers generate the two independent monochromatic sources, while white light sources were provided by a halogen lamp and two optical fibers. Airy disks were produced by equal pairs of pinholes with diameters of 35, 50, 400 and 500 μ m placed at the same distance from the fork–hologram H. During the experiment one beam was always coinciding with the optical center of the hologram, thus generating an OV with integer topological charge l = 1. The other beam spanned the hologram in different positions starting from the optical center. For non–central positions the second beam formed an OV carrying non–integer components of OAM. This phenomenon is typical of laterally displaced and an- gularly deflected beams, which Airy disk transforms are composed of an infinite set of azimuthal harmonics ex- pressed either in the form of Bonnet–Gaussian beams or with well–defined orbital and azimuthal values of L–G modes [21, 27]. However, the central dark regions are always superposed, because they have been generated by the same central optical singularity of H. The separation of the diffraction figures of the two sources was obtained by using a moving beam splitter (MBS). The two beams were kept parallel with a tolerance of 10 − 5 degrees (0.17 μ rad), with negligible effects on the OAM value due to beam tilting. In white light we corrected the chromatic dispersion due to the hologram by spatially filtering the first generated diffraction order with the slit S placed on the Fourier plane of the achromatic lens L1 (see inset in Fig. 1). The hologram H, 20 lines/mm, has an active area of 2 . 6 × 2 . 6 mm 2 with a 50 μ m–sized optical singularity. It is blazed at the first diffraction order and its efficiency is about 80% at the laser’s wavelength. An incoming Gaus- sian beam is projected by H in a superposition of L–G modes where the dominant modes have l = 0 and l = 1 for every value of p [12]. H was placed perpendicular to the optical axis at a distance d = 430 mm away from the two pinholes, giving a Fresnel number F ≃ 0 . 15, sufficient to satisfy the Fraunhofer diffraction prescriptions to obtain Airy diffraction patterns on the hologram [23]. This was verified by inserting in the optical path a moving mirror (MM) at 45 degrees and analyzing the spots with the CCD1 camera (see Fig. 2, bottom row). By measuring the ratio of the distances of the first two diffraction pattern maxima with respect to the center, we obtained a value of 1 . 59, close to 1 . 64 as provided by the theory. In [25, 26] was discussed the separability of two identical overlapping OVs with the same OAM value: the integer–valued L–G transforms of the two Airy profiles were numerically computed for the same integer l value and, following the Rayleigh separability criterion, the OVs of the two beams were rigidly superposed so that the maximum of one coincided with the dark center of the other. In this case, a sub–Rayleigh separation is achieved only when l = 1 at an angular distance θ the l =1 OV = becomes 0 . 64 θ R . larger, For OAM scaling values with l √ > l , and 1 the two size iden- of tical donought modes are separated at angular distances larger than θ R . For example, for l = 2, the angular separation would be θ l =2 = 1 . 03 θ R , already worse than the Rayleigh criterion (see lower inset of Fig. 5). The experimental results shown in Fig. 2 depict the sub–Rayleigh separability of two monochromatic OVs produced with our setup. Using the 400 μ m pinholes, the Rayleigh criterion limit was θ R = 1 . 93 mrad, corresponding to a linear separation δ R = 834 μ m on the hologram plane. The upper row of Fig. 2 shows the numerical simulations of L–G modes generated by an l = 1 fork– hologram, the central row shows our experimental results and the bottom row shows the corresponding Airy figures of the two equally intense sources. The first column of Fig. 2 represents two coincident sources, the second column represents two sources separated by 0 . 42 δ R and the third column shows the sources separated by 0 . 84 δ R . In Fig. 3 we plot the intensity of the central section of the combined profiles of the L–G patterns along the direction connecting the two sources. The profiles are normalized with respect to the peaks of the superposed sources. We can observe that, as the linear ...
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... than θ R . In this paper, we show that the Rayleigh limit may be better overcome by using for the two sources a combina- tion of integer and non–integer values of l . Sub–Rayleigh separability. — In this section we present the experimental and numerical results, achieved using OVs, about the sub–Rayleigh separation of two equally intense and uncorrelated monochromatic sources and also experimental results obtained in white light. The optical scheme of the experiment is shown in Fig. 1. Two 632 . 8 nm He–Ne lasers generate the two independent monochromatic sources, while white light sources were provided by a halogen lamp and two optical fibers. Airy disks were produced by equal pairs of pinholes with diameters of 35, 50, 400 and 500 μ m placed at the same distance from the fork–hologram H. During the experiment one beam was always coinciding with the optical center of the hologram, thus generating an OV with integer topological charge l = 1. The other beam spanned the hologram in different positions starting from the optical center. For non–central positions the second beam formed an OV carrying non–integer components of OAM. This phenomenon is typical of laterally displaced and an- gularly deflected beams, which Airy disk transforms are composed of an infinite set of azimuthal harmonics ex- pressed either in the form of Bonnet–Gaussian beams or with well–defined orbital and azimuthal values of L–G modes [21, 27]. However, the central dark regions are always superposed, because they have been generated by the same central optical singularity of H. The separation of the diffraction figures of the two sources was obtained by using a moving beam splitter (MBS). The two beams were kept parallel with a tolerance of 10 − 5 degrees (0.17 μ rad), with negligible effects on the OAM value due to beam tilting. In white light we corrected the chromatic dispersion due to the hologram by spatially filtering the first generated diffraction order with the slit S placed on the Fourier plane of the achromatic lens L1 (see inset in Fig. 1). The hologram H, 20 lines/mm, has an active area of 2 . 6 × 2 . 6 mm 2 with a 50 μ m–sized optical singularity. It is blazed at the first diffraction order and its efficiency is about 80% at the laser’s wavelength. An incoming Gaus- sian beam is projected by H in a superposition of L–G modes where the dominant modes have l = 0 and l = 1 for every value of p [12]. H was placed perpendicular to the optical axis at a distance d = 430 mm away from the two pinholes, giving a Fresnel number F ≃ 0 . 15, sufficient to satisfy the Fraunhofer diffraction prescriptions to obtain Airy diffraction patterns on the hologram [23]. This was verified by inserting in the optical path a moving mirror (MM) at 45 degrees and analyzing the spots with the CCD1 camera (see Fig. 2, bottom row). By measuring the ratio of the distances of the first two diffraction pattern maxima with respect to the center, we obtained a value of 1 . 59, close to 1 . 64 as provided by the theory. In [25, 26] was discussed the separability of two identical overlapping OVs with the same OAM value: the integer–valued L–G transforms of the two Airy profiles were numerically computed for the same integer l value and, following the Rayleigh separability criterion, the OVs of the two beams were rigidly superposed so that the maximum of one coincided with the dark center of the other. In this case, a sub–Rayleigh separation is achieved only when l = 1 at an angular distance θ the l =1 OV = becomes 0 . 64 θ R . larger, For OAM scaling values with l √ > l , and 1 the two size iden- of tical donought modes are separated at angular distances larger than θ R . For example, for l = 2, the angular separation would be θ l =2 = 1 . 03 θ R , already worse than the Rayleigh criterion (see lower inset of Fig. 5). The experimental results shown in Fig. 2 depict the sub–Rayleigh separability of two monochromatic OVs produced with our setup. Using the 400 μ m pinholes, the Rayleigh criterion limit was θ R = 1 . 93 mrad, corresponding to a linear separation δ R = 834 μ m on the hologram plane. The upper row of Fig. 2 shows the numerical simulations of L–G modes generated by an l = 1 fork– hologram, the central row shows our experimental results and the bottom row shows the corresponding Airy figures of the two equally intense sources. The first column of Fig. 2 represents two coincident sources, the second column represents two sources separated by 0 . 42 δ R and the third column shows the sources separated by 0 . 84 δ R . In Fig. 3 we plot the intensity of the central section of the combined profiles of the L–G patterns along the direction connecting the two sources. The profiles are normalized with respect to the peaks of the superposed sources. We can observe that, as the linear ...
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... Since the discovery of the orbital angular momentum (OAM) carried by optical vortices in 1992, [1,2] the modes have been profoundly investigated in various fields, such as microscopy and imaging, [3][4][5] quantum computing and information, [5][6][7][8] optical manipulation, [9][10][11][12][13] and astronomy. [14,15] Moreover, propelled by the increasing data within large information technology infrastructures, there has been growing interest in employing OAM as an innovative strategy to address challenges in wireless communications. ...
Although orbital angular momentum (OAM) is extensively explored and researched in various scientific domains, its practical application in wireless communications still faces numerous challenges. Notably, existing OAM beam generation technologies need to meet the diversified demands of modern wireless communication, such as miniaturization, cost‐effectiveness, and system integration. Driven by the immense potential of OAM in communication systems, in this work, an innovative method based on leaky cables capable of simultaneously generating multiple vortex beams, overcoming a series of implementation issues associated with multiplexing emitters, is introduced. A design prototype is fabricated and tested, and the measurement results align closely with the simulations, validating the multifunctionality and practicality of the method. Moreover, the proposed strategy can seamlessly extend to optical frequencies using the concept of leaky fibers. In this method, not only efficient spatial utilization and excellent isolation are realized but also high cost‐effectiveness is possessed. Compared to previous strategies, this technique may have an impact on simplifying the establishment of communication system platforms based on OAM multiplexing.
... We do not expect the performance of the APT and PMT detectors to differ in this light regime [32]. However, we do expect differences in the spatial resolution of our images, as the Rayleigh criterion [33] indicates that the 775 nm source and 8 mm pupil used at MCW will provide superior resolution to MU's 850 nm source and 7.5 mm pupil. This improved resolution does not appear to have a positive effect on SNR, as MU's data on average exhibited higher SNR. ...
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... Akin to the discrete frequencies of an OFC, the orbital angular momentum (OAM) of light offers another theoretically infinite dimension quantized by the spatial topological charges 3,4 . The signature helical wavefronts and phase singularities of OAM beams 5 create new quantum and classical states of light [6][7][8][9] for optical tweezing 10 , remote sensing 11 , communications 12 and resolution-enhanced imaging 13,14 . Although frequency and OAM are considered to be independent physical properties of light, mapping the OAM to the spectral lines of OFCs would harness the powerful frequency-domain metrology techniques to realize fast OAM tomography free from massive imaging elements 15 . ...
Synergistic control of the frequency and orbital angular momentum (OAM) of light offers new opportunities for the generation of spatio-temporal optical waveforms and optical metrology. However, their physical realizations are typically bulky and complex owing to challenges in creating, manipulating and detecting mutually coherent, high-dimensional OAM states. Here we achieve combined control over the frequency and the OAM of a comb structure on a photonic chip. Dissipative optical solitons are formed in a nonlinear ring microresonator and emitted owing to engraved angular gratings, with each comb line carrying a distinct OAM. The beam of such a vortex soliton microcomb manifests dynamically revolving, double-helical intensity profiles. The one-to-one correspondence between the OAM and frequencies features a high extinction ratio of over 18.5 dB, enabling precision spectroscopy of optical vortices. Our work provides an integrated solution for realizing coherent light sources that are multiplexed in the spatial and frequency domains, with the potential to establish a new approach to the generation of high-dimensional structured light.
... Regarding microscopy applications, OAM beams have been proposed as a tool for enhancing the edge detection in phase contrast microscopy [19][20][21], and for increasing the spatial resolution [22][23][24][25]. It has been proven that, at optical wavelengths, OAM beams enhance the image quality in phase-sensitive techniques, providing a uniform contrast at the interface between different elements, dislocations, or morphological height variations [18,26,27]. ...
Electromagnetic waves possessing orbital angular momentum (OAM) are powerful tools for applications in optical communications, quantum technologies, and optical tweezers. Recently, they have attracted growing interest since they can be harnessed to detect peculiar helical dichroic effects in chiral molecular media and in magnetic nanostructures. In this work, we perform single-shot per position ptychography on a nanostructured object at a seeded free-electron laser, using extreme ultraviolet OAM beams of different topological charge orders $\ell$ ℓ generated with spiral zone plates. By controlling $\ell$ ℓ , we demonstrate how the structural features of OAM beam profiles determine an improvement of about 30% in image resolution with respect to conventional Gaussian beam illumination. This result extends the capabilities of coherent diffraction imaging techniques, and paves the way for achieving time-resolved high-resolution (below 100 nm) microscopy on large area samples.
... Optical vortices, characterized by a spiral phase front represented by exp(−ilφ) and carrying the orbital angular momentum (OAM) of the lh per photon (where l denotes the topological charge number and φ denotes the azimuthal angle), have received widespread attention in the fields of optical trapping [1][2][3], optical communication [4,5], quantum entanglement [6,7], optical machining [8,9], and optical imaging [10,11]. Compared with vortex beams with conventional doughnut structures, optical vortex arrays (OVAs) are characterized by independent phase singularities and individual topological charges. ...
Optical vortex arrays are characterized by specific orbital angular momentums, and they have important applications in optical trapping and manipulation, optical communications, secure communications, and high-security information processing. Despite widespread research on optical vortex arrays, the 2 μm wavelength range remains underexplored. Pulsed lasers at 2 μm are vital in laser medicine, sensing, communications, and nonlinear optic applications. The need for 2 μm-pulsed structured optical vortices, combining the advantages of this wavelength range and optical vortex arrays, is evident. Therefore, using just three elements in the cavity, we demonstrate a compact self-Q-switched Tm:YALO3 vortex laser by utilizing the self-modulation effect of a laser crystal and a defect spot mirror. By tuning the position of the defect spot and the output coupler, the resonator delivers optical vortex arrays with phase singularities ranging from 1 to 4. The narrowest pulse widths of the TEM00 LG0,−1, two-, three-, and four-vortex arrays are 543, 1266, 1281, 2379, and 1615 ns, respectively. All the vortex arrays in our study have relatively high-power outputs, slope efficiencies, and single-pulse energies. This work paves the way for a 2 μm-pulsed structured light source that has potential applications in optical trapping and manipulation, free-space optical communications, and laser medicine.
... It has a higher degree of spatial freedom and can carry additional information [2]. This feature allows the vortex beam to have a wide range of applications in optical tweezer technology [3,4], quantum optics [5], super-resolution imaging [6], optical communication [7,8], and other fields. The 1.9 µm band has low dispersion and attenuation and can achieve longer distance optical communication transmission. ...
In this paper, the Laguerre–Gaussian (LG) mode superposition is obtained by using the technology of double-end off-axis pumping Tm:YLF crystal, and the LG mode superposition is achieved by combining the extra-cavity conversion method. The impact of changing the off-axis distance on the order of Hermite–Gaussian (HG) mode and the topological charge of LG mode is studied. The results show that when the off-axis distance of the pump source at both ends is tuned, when the off-axis distance is in the range of 260 μm~845 μm, the single-ended 0~10 order HG mode can be obtained. Subsequently, the mode converter is placed to obtain the LG mode beam, and the double-end simultaneously pumps the crystal to obtain the superimposed LG mode. The tuning off-axis quantity changes the topological charge number. When P = 0, l1=l2, the superimposed LG mode is a single-ring spot, and the vortex beam center’s dark hollow area increases with the topological charge number. When P = 0, l1=−l2, the superimposed LG mode is a petal-like spot. The number of petals differs from the topological charges of two opposite numbers. Finally, in the case of changing the topological charge number of the double-ended LG mode, the output of the vortex array structured beams of the tuning mode order 1.9 μm Tm:YLF is completed in the case of conversion and superposition.
... As a result, they promise an additional degree of freedom to meet the exponential growth in network capacity demand via mode division multiplexing in optical communications and wavelength division multiplexing. In addition, OAM-carrying beams have a wide range of applications across diverse disciplines, e.g. in optical micro-manipulation [5][6][7], optical tweezers [8][9][10], nano-scale microscopy [11,12], optical imaging [13], nonlinear optics [14,15], quantum optics [16], etc. Several methods, such as spiral-phase plates [17][18][19], computer-generated holograms [20,21], microresonator or subwavelength gratings [22,23] and helically twisted fiber [24], have been developed to generate OAM beams. ...
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... Note that a high-NA fiber has a large normalized waveguide frequency V number that supports higher-order vector 21 and HE 31 modes of high-NA fiber. Phase-matching curve of the TLPG for mode coupling between HE 11 and TE 01 (red dotted), HE 11 and HE 21 (cyan dotted) and HE 11 and TM 01 (yellow dotted). (b) Transmission spectra of the TLPG without and with an apodization (raised cosine). ...
In this paper we propose a novel design and theoretically analyse it for bi-directional orbital angular momentum (OAM) mode generation in high
numerical aperture (NA) optical fiber using combination of long period grating, short-period (Bragg) grating and a three port optical circulator. The proposed design consisting only standard fiber gratings rather than specially designed fibers, like ring-shaped fiber or other types of fiber, makings our model relatively simple. The full-vector true-mode analysis has been used to study the modal characteristics of the supported modes in the high-NA fiber. High-NA optical fiber can effectively relieve the degeneracy of the linearly polarised modes. A circularly polarised (CP) light is injected into a single mode fiber, the output end of which is axially spliced to a high NA fiber. An appropriately designed raised-cosine apodized tilted long period grating (TLPG) is used for broad bandwidth coupling of the fundamental HE11 mode to co-propagating HE21 mode. The employed TLPG converts the circularly polarised fundamental core mode (HE_x11 ± iHE_y11 ) to ±1-order OAM modes (HE_even 21 ± iHE_odd21 ). Both the CP mode and
the generated OAM pass through the circulator in the direction of port 1 to port 2. A second fiber is connected at the output of the port 2, and a tilted fiber Bragg grating (TFBG) is used to couple the forward propagating HE11 core mode with the counter-propagating HE21, EH11 and HE31 core modes. The TFBG reflected higher order (±1 and ±2) OAM modes transmit through the port 3. We have observed that the TFBG has a mode conversion efficiency of more than 95% for each mode conversion. The generated vortex beam’s topological charges have been varified using the coaxial interference method.
... Each photon of the vortex beam carries an orbital angular momentum (OAM) of lh, where l is the topological charge, θ is the azimuthal angle, andh is the reduced Planck constant [2]. Due to carrying discrete topological charges and their close relationship with OAM, the interest in vortex beams has been increasing and has yielded a significant return in many applications, including optical imaging [3,4], optical trapping [5][6][7], holography [8], optical coding [9], quantum information processing [10] and optical measurement [11]. It is worth noting that these modes provide a (theoretically) infinite and easily realized alphabet for encoding information and have been used extensively in both free-space and fiber-optical communications, in particular through the use of OAM multiplexing and modulation (encoding/decoding) [12][13][14][15]. ...
In communication links, the presence of atmospheric turbulence leads to crosstalk between the orbital angular momentum (OAM) states, thereby limiting the performance of information transmission. Thus, knowledge of the effect of turbulence on the spiral spectrum (also named the OAM spectrum) is of utmost importance in the field of optical communications. However, most of the existing studies are limited to weak turbulence calculation models. In this paper, based on the extended Huygens–Fresnel integral, the analytical expression is derived for the mutual coherence function of a Laguerre–Gaussian beam carrying the cross-phase and propagating through weak-to-strong anisotropic Kolmogorov atmospheric turbulence; subsequently, the analytical expression is used to study the behavior of the spiral spectrum. The discrepancies in the spiral spectrum between weak and strong turbulence are comparatively studied. The influences of the cross-phase and the anisotropy of turbulence on the spiral spectrum are investigated through numerical examples. Our results reveal that the cross-phase determines the distribution of the spiral spectrum. The spiral spectrum can be tuned to multiple OAM modes through the adaptation of the cross-phase coefficient. Moreover, increasing the cross-phase coefficient can reduce both the discrepancies of the spiral spectrum under two computational methods and the effects of the anisotropic factors of turbulence on the spiral spectrum.
... Orbital angular momentum (OAM) wave, also named as vortex beam, is a kind of electromagnetic wave with a doughnut intensity distribution and a helical wavefront expressed by a spatial phase factor i (where represents the number of OAM modes and represents transverse azimuthal angle) [1][2][3]. The OAM waves were originally studied in optical fields and have been widely used in many research areas, such as in optical tweezers [4], optical communications [5], imaging [6] and microscopy [7], etc. Recently, the OAM waves in microwave/millimetre-wave (MMV) frequencies have attract much attention since some optical characteristics are suitable in the microwave/MMV frequencies [8][9][10][11][12][13][14][15][16][17][18][19][20]. ...
... Remarkably, the topological charge is also associated to the quantized orbital angular momentum ℏ of a single photon [3]. OAM beams have been exploited for different applications, e.g. to finely control and manipulate nanoparticles [4], to overcome the diffraction limit in imaging methods [5], in astronomical and astrophysical observations [6,7], to realize high-contrast and broadband coronagraphy [8][9][10], to investigate photoelectric rules and transition states not accessible with ordinary light [11,12]. In particular, the telecommunications sector has benefited the most from the additional degree of freedom offered by the topological charge [13][14][15]. ...
... This enables direct comparison among the different LG beam states, regardless of the overall intensity level 0 in Eq. (4) for the different LG beams. Notice that this is similar to the normalization procedure adopted in Eq. (5). Results are shown in Fig. 6 and are summarized in Table 1. ...
In this work we experimentally demonstrate high sensitive strictly-local identification of azimuthal index of Laguerre–Gauss (LG) beams, with less than 160 photon counts. To this aim, detection of the azimuthal index of LG beams is performed with an innovative interferometer relying on a monolithic birefringent crystal, thus ensuring stability without the need of any feedback or thermal drift compensation. By first generating a reference interference pattern with a standard TEM00 mode, we then detect the value of the azimuthal index of a LG beam from the lateral shift of the pattern with respect to the reference one. An experimental setup has been realized to prove the effectiveness of the proposed scheme, which requires to access only a small portion (5%) of the entire wavefront. Moreover, being intrinsically endowed with extreme robustness and stability, we achieve effective high sensitive detection of the azimuthal index by collecting less than 160 photons only, while at the same time keeping the local features. Limitations and possible applications are also discussed.
