1
|
Barshak EV, Lapin BP, Vikulin DV, Yu Fedorov A, Alexeyev CN, Yavorsky MA. SWAP and Fredkin gates for OAM optical beams via the sandwich of anisotropic optical fibers. OPTICS EXPRESS 2023; 31:26865-26878. [PMID: 37710536 DOI: 10.1364/oe.497114] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/02/2023] [Accepted: 07/07/2023] [Indexed: 09/16/2023]
Abstract
We study the propagation of circularly-polarized optical vortices of higher order topological charges ℓ ≥ 2 in a sandwich of multihelical - anisotropic - multihelical fibers on the basis of the Jones formalism for modes with orbital angular momentum. We demonstrate that such a system can operate as the all - fiber two - bit SWAP as well as universal tree - bit controlled-SWAP (Fredkin) gates over states of optical vortices, in which the mode radial number carries the control bit, while circular polarization and topological charge are the controlled bits.
Collapse
|
2
|
Nguyen HT, Stepniewski G, Filipkowski A, Kasztelanic R, Pysz D, Le Van H, Stepien R, Klimczak M, Krolikowski W, Buczynski R. Transmission of an optical vortex beam in antiresonant fibers generated in an all-fiber system. OPTICS EXPRESS 2022; 30:45635-45647. [PMID: 36522966 DOI: 10.1364/oe.468461] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/21/2022] [Accepted: 10/31/2022] [Indexed: 06/17/2023]
Abstract
We report an experimental study on transmission of orbital angular momentum mode in antiresonant fibers generated with a dedicated all-fiber optical vortex phase mask. The vortex generator can convert Gaussian beam into vortex beams with topological charge l = 1. Generated vortex beam is directly butt-coupled into the antiresonant fiber and propagates over distance of 150 cm. The stability and sensitivity of the transmitted vortex beam on the external perturbations including bending, axial stress, and twisting is investigated. We demonstrate distortion-free vortex propagation for the axial stress force below 0.677 N, a bend radius greater than 10 cm.
Collapse
|
3
|
Hao Y, Guo C, Huang X, Xu J, Lu H, Zhao H, Wang P, Li H. Synthesizing the complex orbital-angular-momentum spectrum of hybrid modes existed in a few-mode fiber. OPTICS EXPRESS 2022; 30:26286-26296. [PMID: 36236823 DOI: 10.1364/oe.463608] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/11/2022] [Accepted: 06/21/2022] [Indexed: 06/16/2023]
Abstract
In this study, a simple and reliable method enabling to well synthesize the complex orbit-angular-momentum (OAM) spectrum of hybrid mode in a few-mode fiber is proposed and numerically demonstrated, which is realized by using the so-called inverse scattering method based on the genetic algorithm (GA), where the main Fourier components of a specially-selected ring in intensity distribution of the hybrid mode is used as the optimization objective. As a proof-of-concept example, power spectrum of a hybrid mode consisted of the first- and second-order OAM modes was successfully reconstructed with an accuracy higher than 0.99. This is the first time, to the best of our knowledge, that the complex OAM spectrum of a fiber hybrid mode consisted of more than two kinds of OAM modes is synthesized directly from the intensity distribution of the hybrid mode itself.
Collapse
|
4
|
Bernas M, Napiorkowski M, Zolnacz K, Statkiewicz-Barabach G, Kiczor A, Mergo P, Urbanczyk W. Fiber-based vortex beam source operating in a broadband or tunable mode. OPTICS EXPRESS 2022; 30:27715-27729. [PMID: 36236937 DOI: 10.1364/oe.463828] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2022] [Accepted: 06/13/2022] [Indexed: 06/16/2023]
Abstract
We demonstrate a fiber-based optical vortex beam source operating in broadband or tunable mode in the spectral range of 1100-1400 nm. The vector vortices of the total angular momenta equal to +2, 0, and -2 are obtained by converting the respective linearly polarized (LP11) modes of the two-mode birefringent PANDA fiber with stress-applying elements by gradually twisting its output section. At the input end, the PANDA fiber is powered by broadband supercontinuum or tunable Raman solitons generated in the LP11 polarization modes of a birefringent microstructured fiber with a specially designed dispersion profile and coupled to the respective LP11 modes of the PANDA fiber. Two pulse lasers operating in different regimes (1 ns/1064 nm and 190 fs/1037 nm) were used as the pump to generate supercontinuum or tunable solitons directly in the LP11 modes of the microstructured fiber purely excited with a special Wollaston prism-based method. The high modal and polarization purities of the beams after successive transformations were experimentally confirmed. We also proved the vortex nature of the output beams using shearing interferometry.
Collapse
|
5
|
Liu J, Zhang J, Liu J, Lin Z, Li Z, Lin Z, Zhang J, Huang C, Mo S, Shen L, Lin S, Chen Y, Gao R, Zhang L, Lan X, Cai X, Li Z, Yu S. 1-Pbps orbital angular momentum fibre-optic transmission. LIGHT: SCIENCE & APPLICATIONS 2022; 11:202. [PMID: 35790720 PMCID: PMC9256723 DOI: 10.1038/s41377-022-00889-3] [Citation(s) in RCA: 16] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/20/2022] [Revised: 06/08/2022] [Accepted: 06/10/2022] [Indexed: 05/25/2023]
Abstract
AbstractSpace-division multiplexing (SDM), as a main candidate for future ultra-high capacity fibre-optic communications, needs to address limitations to its scalability imposed by computation-intensive multi-input multi-output (MIMO) digital signal processing (DSP) required to eliminate the crosstalk caused by optical coupling between multiplexed spatial channels. By exploiting the unique propagation characteristics of orbital angular momentum (OAM) modes in ring core fibres (RCFs), a system that combines SDM and C + L band dense wavelength-division multiplexing (DWDM) in a 34 km 7-core RCF is demonstrated to transport a total of 24960 channels with a raw (net) capacity of 1.223 (1.02) Peta-bit s−1 (Pbps) and a spectral efficiency of 156.8 (130.7) bit s−1 Hz−1. Remarkably for such a high channel count, the system only uses fixed-size 4 × 4 MIMO DSP modules with no more than 25 time-domain taps. Such ultra-low MIMO complexity is enabled by the simultaneous weak coupling among fibre cores and amongst non-degenerate OAM mode groups within each core that have a fixed number of 4 modes. These results take the capacity of OAM-based fibre-optic communications links over the 1 Pbps milestone for the first time. They also simultaneously represent the lowest MIMO complexity and the 2nd smallest fibre cladding diameter amongst reported few-mode multicore-fibre (FM-MCF) SDM systems of >1 Pbps capacity. We believe these results represent a major step forward in SDM transmission, as they manifest the significant potentials for further up-scaling the capacity per optical fibre whilst keeping MIMO processing to an ultra-low complexity level and in a modularly expandable fashion.
Collapse
|
6
|
Dacha SK, Zhu W, Agrawal A, Ritter KJ, Murphy TE. Nonlinear rotation of spin-orbit coupled states in hollow ring-core fibers. OPTICS EXPRESS 2022; 30:18481-18495. [PMID: 36221648 DOI: 10.1364/oe.453944] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/18/2022] [Accepted: 04/23/2022] [Indexed: 06/16/2023]
Abstract
We experimentally demonstrate that when two spin-orbit coupled orbital angular momentum (OAM) modes of opposite topological charge co-propagate in the Kerr nonlinear regime in a hollow ring-core optical fiber, the vectorial mode superposition exhibits a unique power-dependent rotation effect. This effect is analogous to nonlinear polarization rotation in single-mode fibers, however, the added spatial dimension produces a visually observable rotation of the spatial pattern emerging from the fiber when imaged through a linear polarizer. A dielectric metasurface q-plate was designed and fabricated to excite the desired mode combination in a hollow ring-core fiber that supports stable propagation of OAM modes. The observed spatial patterns show strong agreement with numerical simulations of the vector coupled nonlinear Schrödinger equations. These results constitute the first measurements of what can be described as the spin-orbit coupled generalization of the nonlinear polarization rotation effect.
Collapse
|
7
|
Bernas M, Zolnacz K, Napiorkowski M, Statkiewicz-Barabach G, Urbanczyk W. Conversion of LP 11 modes to vortex modes in a gradually twisted highly birefringent optical fiber. OPTICS LETTERS 2021; 46:4446-4449. [PMID: 34525018 DOI: 10.1364/ol.433952] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/10/2021] [Accepted: 08/08/2021] [Indexed: 06/13/2023]
Abstract
We experimentally demonstrate the possibility of quasi-adiabatic conversion of LP11 modes to vortex modes in a twisted highly birefringent fiber with a gradually increasing twist rate. Based on the value of the effective indices, the LP11 modes are selectively converted to right- and left-handed circularly polarized vortex modes HE21 with a total angular momentum of ±2 and to quasi-TE01/TM01 modes with a total angular momentum of 0. Since the proposed conversion method has a purely topological origin, it is broadband in nature, in contrast to the methods based on resonant effects.
Collapse
|
8
|
Abstract
The orbital angular momentum (OAM) of light provides a new degree of freedom for carrying information. The stable propagation and generation of OAM modes are necessary for the fields of OAM-based optical communications and microscopies. In this review, we focus on discussing the novel fibers that are suitable for stable OAM mode transmission and conversion. The fundamental theory of fiber modes is introduced first. Then, recent progress on a multitude of fiber designs that can stably guide or generate OAM modes is reviewed. Currently, the mode crosstalk is regarded as the main issue that damages OAM mode stability. Therefore, the coupled-mode theory and coupled-power power theory are introduced to analyze OAM modes crosstalk. Finally, the challenges and prospects of the applications of OAM fibers are discussed.
Collapse
|
9
|
Generation of Vortex Optical Beams Based on Chiral Fiber-Optic Periodic Structures. SENSORS 2020; 20:s20185345. [PMID: 32961965 PMCID: PMC7571199 DOI: 10.3390/s20185345] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/22/2020] [Revised: 09/11/2020] [Accepted: 09/17/2020] [Indexed: 11/16/2022]
Abstract
In this paper, we consider the process of fiber vortex modes generation using chiral periodic structures that include both chiral optical fibers and chiral (vortex) fiber Bragg gratings (ChFBGs). A generalized theoretical model of the ChFBG is developed including an arbitrary function of apodization and chirping, which provides a way to calculate gratings that generate vortex modes with a given state for the required frequency band and reflection coefficient. In addition, a matrix method for describing the ChFBG is proposed, based on the mathematical apparatus of the coupled modes theory and scattering matrices. Simulation modeling of the fiber structures considered is carried out. Chiral optical fibers maintaining optical vortex propagation are also described. It is also proposed to use chiral fiber-optic periodic structures as sensors of physical fields (temperature, strain, etc.), which can be applied to address multi-sensor monitoring systems due to a unique address parameter—the orbital angular momentum of optical radiation.
Collapse
|
10
|
Mirjalili SM, Taleb H, Kabir MZ, Bianucci P. Design optimization of orbital angular momentum fibers using the gray wolf optimizer. APPLIED OPTICS 2020; 59:6181-6190. [PMID: 32672766 DOI: 10.1364/ao.391731] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/28/2020] [Accepted: 06/15/2020] [Indexed: 06/11/2023]
Abstract
Optical data communication based on the orbital angular momentum (OAM) of light is a recently proposed method to enhance the transmission capacity of optical fibers. This requires a new type of optical fiber, the main part of the optical communication system, to be designed. Typically, these fibers have a ring-shaped refractive index profile. We aim to find an optimized cross section refractive index profile for an OAM fiber in which the number of supported OAM modes (channels), mode purity, and the effective refractive index separation of OAM modes to other fibers modes are maximized. However, the complexity of the relationship between structural parameters and optical transmission properties of these fibers has resulted in the lack of a comprehensive analytical method to design them. In this paper, we investigate the process of designing OAM fibers and propose a framework to design such fibers by using artificial intelligence optimizers. It is worth mentioning here that this problem is intrinsically a multiobjective optimization problem, and the actual solution for such problems is not unique and leads to a set of optimum solutions. Therefore, at the end of the optimization process, a wide range of optimal designs will be obtained in which a trade-off is established in each of the solutions. We solve this problem with the multiobjective gray wolf optimizer (GWO) and compare the results with that of the single-objective GWO. The framework can easily find many optimal designs that support more than 20 OAM modes. The obtained results show that the proposed method is comprehensive and can optimize the structure of any OAM fibers. No human involvement, simplicity, and being straightforward are the main advantages of the proposed framework.
Collapse
|
11
|
Stafeev SS, Kozlova ES, Nalimov AG, Kotlyar VV. Tight focusing of a cylindrical vector beam by a hyperbolic secant gradient index lens. OPTICS LETTERS 2020; 45:1687-1690. [PMID: 32235974 DOI: 10.1364/ol.389803] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/05/2020] [Accepted: 02/28/2020] [Indexed: 06/11/2023]
Abstract
In this Letter, we investigate the tight focusing of a second-order cylindrical vector beam by a hyperbolic secant gradient index lens with a thickness of 10 µm, a radius of 9.43 µm, and a refractive index on the axis of 3.47 (silicon). It is shown that the lens forms the reverse energy flow near its shadow surface. Moreover, it was obtained that the spherical hole in the center of the shadow plane with a diameter of 0.3 µm allows us to localize the direct energy flow inside the lens material and with the reverse energy flow in an area of free space.
Collapse
|
12
|
Chen S, Li S, Fang L, Wang A, Wang J. OAM mode multiplexing in weakly guiding ring-core fiber with simplified MIMO-DSP. OPTICS EXPRESS 2019; 27:38049-38060. [PMID: 31878577 DOI: 10.1364/oe.27.038049] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/26/2019] [Accepted: 12/04/2019] [Indexed: 06/10/2023]
Abstract
We present a low-loss weakly guiding ring-core fiber for orbital angular momentum (OAM) mode group multiplexing (MGM) transmission. This special fiber design supports 50 radially fundamental modes divided into 13 mode groups with only 0.7% relative refractive index difference between the fiber ring core and cladding. Except the first two groups with 10-5 mode spacing, the other mode groups are separated with each other with effective refractive index difference (Δneff) larger than 10-4, indicating relatively low-level inter-group crosstalk. One can directly use different OAM mode groups for MGM communications without multiple-input multiple-output digital signal processing (MIMO-DSP) technique. Besides, one can employ different OAM modes among the same mode group to carry different data information assisted by small-scale MIMO technique. The target fiber exhibits small and flat dispersion within (14.3, 39.7) ps/nm/km which is comparable to that in the standard single-mode fiber (SMF), and extremely large mode area within (787.9, 841.2) µm2 over the whole C + L band. MIMO equalization complexities for modified small-scale MIMO-DSP assisted intra-group modes multiplexing combined with MIMO-free inter-group modes multiplexing method in both time and frequency domain are much simpler compared to traditional 50×50 MIMO equalization.
Collapse
|
13
|
Zhang X, Jiang Y, Xu Y, Chen R, Wang A, Ming H, Zhao W. Polarization-maintaining fiber composed of an elliptical ring core and two circular air holes. APPLIED OPTICS 2019; 58:8865-8870. [PMID: 31873665 DOI: 10.1364/ao.58.008865] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/02/2019] [Accepted: 10/19/2019] [Indexed: 06/10/2023]
Abstract
In this paper, a new polarization-maintaining fiber (PMF) composed of an elliptical ring core and two circular air holes is exploited. The PMF could support 10 guided modes with refractive index differences $\Delta {n_{{\rm eff}}}$Δneff of all the adjacent modes larger than ${{10}^{ - 4}}$10-4. Moreover, the optimum parameters of the PMF covering the entire $C + L$C+L band are obtained. Last, the chromatic dispersion $D$D of the designed elliptical ring core fiber, the confinement loss $\alpha $α, and the power fraction $\chi $χ of the two-air core are calculated. The calculation results show that $D$D, $\alpha $α, and $\chi $χ are compatible with traditional step-index fiber, and the designed elliptical ring core fiber is suitable for mode-division multiplexing and optical fiber sensors.
Collapse
|
14
|
Zhao H, Wang P, Yamakawa T, Li H. All-fiber second-order orbital angular momentum generator based on a single-helix helical fiber grating. OPTICS LETTERS 2019; 44:5370-5373. [PMID: 31675009 DOI: 10.1364/ol.44.005370] [Citation(s) in RCA: 26] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/19/2019] [Accepted: 10/07/2019] [Indexed: 06/10/2023]
Abstract
An all-fiber orbital angular momentum (OAM) generator enabling direct turning of the fundamental mode (${{\rm HE}_{11}}$HE11) to the second OAM modes (${ l} = {\pm 2}$l=±2) with an efficiency of $\sim90\% $∼90% has been proposed and experimentally demonstrated, which is realized based on utilization of a second-order helical fiber grating written in a few-mode fiber. This is the first time, to the best of our knowledge, that an all-fiber second-order OAM has been achieved with using only one component, i.e., the helical long-period fiber grating. The proposed method opens a new way to efficiently generate an all-fiber higher-order OAM using a conventional multimode fiber.
Collapse
|
15
|
Enhanced spin orbit interaction of light in highly confining optical fibers for mode division multiplexing. Nat Commun 2019; 10:4707. [PMID: 31624247 PMCID: PMC6797754 DOI: 10.1038/s41467-019-12401-4] [Citation(s) in RCA: 35] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/13/2019] [Accepted: 09/04/2019] [Indexed: 11/18/2022] Open
Abstract
Light carries both orbital angular momentum (OAM) and spin angular momentum (SAM), related to wavefront rotation and polarization, respectively. These are usually approximately independent quantities, but they become coupled by light’s spin-orbit interaction (SOI) in certain exotic geometries and at the nanoscale. Here we reveal a manifestation of strong SOI in fibers engineered at the micro-scale and supporting the only known example of propagating light modes with non-integer mean OAM. This enables propagation of a record number (24) of states in a single optical fiber with low cross-talk (purity > 93%), even as tens-of-meters long fibers are bent, twisted or otherwise handled, as fibers are practically deployed. In addition to enabling the investigation of novel SOI effects, these light states represent the first ensemble with which mode count can be potentially arbitrarily scaled to satisfy the exponentially growing demands of high-performance data centers and supercomputers, or telecommunications network nodes. Fiber designs that can that can keep up with increasing data demands are lacking. Here, the authors describe an interaction between the spin and orbital angular momenta of light which enables propagation of 24 states in a single optical fiber with low cross-talk, even in the presence of fiber perturbation.
Collapse
|
16
|
Cui Y, Ye J, Li Y, Dai P, Qu S. Vortex chirality-dependent filtering in helically twisted single-ring photonic crystal fibers. OPTICS EXPRESS 2019; 27:20816-20823. [PMID: 31510170 DOI: 10.1364/oe.27.020816] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/21/2019] [Accepted: 07/06/2019] [Indexed: 06/10/2023]
Abstract
Helically twisted microstructured optical fibers have a wide application prospect in the field of optical vortex communications. In this paper, a helically twisted single-ring photonic crystal fiber (HS-PCF) is proposed for orbital angular momentum (OAM) vortex modes selective filtering. And the theoretical framework of OAMs filtering is also constructed. Positive and negative OAM vortexes have different transmission losses in HS-PCF, and the loss difference between them increases significantly after the twist rate reaches a certain value. Such fibers can filter out OAMs with a certain sign of the topological charge (depending on the handedness of the thread), while dissipating oppositely charged OAMs. In addition to the general OAMs, i.e., zero-order radial vortex modes, the helically twisted fiber also performs a good selective filtering for the first-order radial vortex modes. Remarkably, the filtering bandwidth of HS-PCF is very broad, covering four communication bands from O- to C-band. This kind of fiber can be used as a broadband OAMs filter.
Collapse
|
17
|
Tu J, Liu Z, Gao S, Wang Z, Zhang J, Zhang B, Li J, Liu W, Tam H, Li Z, Yu C, Lu C. Ring-core fiber with negative curvature structure supporting orbital angular momentum modes. OPTICS EXPRESS 2019; 27:20358-20372. [PMID: 31510131 DOI: 10.1364/oe.27.020358] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/02/2019] [Accepted: 06/10/2019] [Indexed: 06/10/2023]
Abstract
Compared to glass walls with a positive curvature, those with a negative curvature have been proven to have stronger confinement of light. Therefore, we change the multi-layered air holes in a photonic crystal fiber into several negative curvature tubes. As a result, the confinement medium is shifted from a low-index cladding material into a special structure. The theoretical analysis shows that each vector eigenmode has a corresponding threshold value for the outer tube thickness. It means that we can confine the target modes and filter the unnecessary modes by shifting the outer tube thickness. After substantial investigation on this fiber, we obtain the appropriate values for each structural parameter and then fabricate this negative curvature ring-core fiber under the guidance of the simulation results. Firstly, we draw the central cane under vacuum condition, then stack the cane and six capillaries to form the preform, and finally draw the ring-core fiber by using vacuumization method. The fiber test experiment indicates that the fiber length should be at least 15 m∼20 m to form the donut facula, and the tested losses of OAM+1,1, OAM+2,1, OAM+3,1, and OAM+4,1 are 0.30 dB/m, 0.36 dB/m, 0.37 dB/m, and 0.42 dB/m, respectively.
Collapse
|
18
|
Prabhakar G, Gregg P, Rishoj L, Kristensen P, Ramachandran S. Octave-wide supercontinuum generation of light-carrying orbital angular momentum. OPTICS EXPRESS 2019; 27:11547-11556. [PMID: 31052998 DOI: 10.1364/oe.27.011547] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/11/2018] [Accepted: 03/04/2019] [Indexed: 06/09/2023]
Abstract
Nonlinear frequency generation of light-carrying orbital angular momentum (OAM), which facilitates realization of on-demand, frequency-diverse optical vortices, would have utility in fields such as super-resolution microscopy, space-division multiplexing and quantum hyper-entanglement. In bulk media, OAM beams primarily differ in spatial phase, so the nonlinear overlap integral for self-phase matched χ(3) processes remains the same across the 4-fold degenerate subspace of beams (formed by different combinations of spin and orbital angular momentum) carrying the same OAM magnitude. This indistinguishable nature of nonlinear coupling implies that supercontinuum generation, which substantially relies on self/cross-phase modulation, and Raman soliton shifting of ultrashort pulses typically results in multimode outputs that do not conserve OAM. Here, using specially designed optical fibers that support OAM modes whose group velocity can be tailored, we demonstrate Raman solitons in OAM modes as well as the first supercontinuum spanning more than an octave (630 nm to 1430 nm), with the entire spectrum in the same polarization as well as OAM state. This is fundamentally possible because spin-orbit interactions in suitably designed fibers lead to large effective index and group velocity splitting of modes, and this helps tailoring nonlinear mode selectivity such that all nonlinearly generated frequencies reside in modes with high spatial mode purity.
Collapse
|
19
|
Tandjè A, Yammine J, Dossou M, Bouwmans G, Baudelle K, Vianou A, Andresen ER, Bigot L. Ring-core photonic crystal fiber for propagation of OAM modes. OPTICS LETTERS 2019; 44:1611-1614. [PMID: 30933103 DOI: 10.1364/ol.44.001611] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/17/2018] [Accepted: 02/24/2019] [Indexed: 06/09/2023]
Abstract
We propose and fabricate a novel ring-core photonic crystal fiber made of a circular ring core surrounded by a cladding constituted of air holes organized in a first circular ring surrounded by hexagonal ones. The fiber efficiently supports four different groups of orbital angular momentum (OAM) modes. The effective indices of spin-orbit aligned and spin-orbit anti-aligned modes in the same OAM modes group are separated by at least 2.13×10-3 at 1550 nm. The realized fiber is expected to be a good platform for applications involving OAM modes.
Collapse
|
20
|
Endlessly mono-radial annular core photonic crystal fiber for the broadband transmission and supercontinuum generation of vortex beams. Sci Rep 2019; 9:2488. [PMID: 30792502 PMCID: PMC6385498 DOI: 10.1038/s41598-019-39527-1] [Citation(s) in RCA: 28] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/11/2018] [Accepted: 01/28/2019] [Indexed: 11/09/2022] Open
Abstract
We demonstrate a new guiding regime termed endlessly mono-radial, in the proposed annular core photonic crystal fiber (AC-PCF), whereby only modes of the fundamental radial order are supported by the fiber at all input wavelengths. This attribute is of high interest for applications that require the stable and broadband guiding of mono-radial (i.e. doughnut shaped) cylindrical vector beams and vortex beams carrying orbital angular momentum. We further show that one can significantly tailor the chromatic dispersion and optical nonlinearities of the waveguide through proper optimization of the photonic crystal microstructured cladding. The analytical investigation of the remarkable modal properties of the AC-PCF is validated by full-vector simulations. As an example, we performed simulations of the nonlinear fiber propagation of short femtosecond pulses at 835 nm center wavelength and kilowatt-level peak power, which indicate that the AC-PCF represents a promising avenue to investigate the supercontinuum generation of optical vortex light. The proposed fiber design has potential applications in space-division multiplexing, optical sensing and super-resolution microscopy.
Collapse
|
21
|
Sit A, Fickler R, Alsaiari F, Bouchard F, Larocque H, Gregg P, Yan L, Boyd RW, Ramachandran S, Karimi E. Quantum cryptography with structured photons through a vortex fiber. OPTICS LETTERS 2018; 43:4108-4111. [PMID: 30160728 DOI: 10.1364/ol.43.004108] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/13/2018] [Accepted: 07/26/2018] [Indexed: 06/08/2023]
Abstract
Optical fiber links and networks are integral components within and between cities' communication infrastructures. Implementing quantum cryptographic protocols on either existing or new fiber links will provide information-theoretical security to fiber data transmissions. However, there is a need for ways to increase the channel bandwidth. Using the transverse spatial degree of freedom is one way to transmit more information and increase tolerable error thresholds by extending the common qubit protocols to high-dimensional quantum key distribution (QKD) schemes. Here we use one type of vortex fiber where the transverse spatial modes serves as an additional channel to encode quantum information by structuring the spin and orbital angular momentum of light. In this proof-of-principle experiment, we show that two-dimensional structured photons can be used in such vortex fibers in addition to the common two-dimensional polarization encryption, thereby paving the path to QKD multiplexing schemes.
Collapse
|
22
|
Heng X, Gan J, Zhang Z, Li J, Li M, Zhao H, Qian Q, Xu S, Yang Z. All-fiber stable orbital angular momentum beam generation and propagation. OPTICS EXPRESS 2018; 26:17429-17436. [PMID: 30119554 DOI: 10.1364/oe.26.017429] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/09/2023]
Abstract
An all-fiber scheme for stable orbital angular momentum (OAM) beam generation and propagation is proposed and demonstrated. This scheme is based on a self-designed and manufactured graded-index few mode fiber (GI-FMF) and compatible mode selection coupler (MSC). The MSC, which consists of a conventional single mode fiber (SMF) and the GI-FMF, can effectively couple the fundamental mode in the SMF to the desired OAM mode in the GI-FMF based on phase matching condition. Meanwhile, the GI-FMF breaks the degeneracy between the desired eigenmodes and neighboring vector modes, thereby allowing the preservation and propagation of the selectively excited OAM modes. As a proof-of-principle, we have implemented an all-fiber device operating in stable OAM modes with |l| = 1. The experimental results show stable propagation of OAM beams with the mode purity of ∼95% and bandwidth of 100 nm. This all fiber device could be useful for further development of wide bandwidth OAM mode division multiplexed application.
Collapse
|
23
|
Temperature Insensitivity Polarization-Controlled Orbital Angular Momentum Mode Converter Based on an LPFG Induced in Four-Mode Fiber. SENSORS 2018; 18:s18061766. [PMID: 29857582 PMCID: PMC6022197 DOI: 10.3390/s18061766] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/11/2018] [Revised: 05/24/2018] [Accepted: 05/24/2018] [Indexed: 11/17/2022]
Abstract
We propose a novel method for generating ±1-order orbital angular momentum (OAM) in long-period fiber gratings (LPFGs) by adjusting a polarization controller (PC). An LPFG, inscribed in a four-mode fiber (4MF) using a CO₂ laser, was used to generate OAM±1 across a broad range of wavelengths from 1530 nm to 1630 nm. Additionally, the OAM vortex phase remained stable while the temperature increased from 23 °C to 50 °C. The LPFG, as a temperature sensor, and its temperature sensitivity was measured to be 38.6 ± 0.37 pm/°C at the resonant wavelength of 1625 nm. This design offers simple fabrication and several properties which are highly beneficial for all-fiber optical communications based on the OAM mode-division multiplexing technique.
Collapse
|
24
|
Li H, Zhang H, Zhang X, Zhang Z, Xi L, Tang X, Zhang W, Zhang X. Design tool for circular photonic crystal fibers supporting orbital angular momentum modes. APPLIED OPTICS 2018; 57:2474-2481. [PMID: 29714230 DOI: 10.1364/ao.57.002474] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2018] [Accepted: 02/28/2018] [Indexed: 06/08/2023]
Abstract
We propose a design tool for the family of circular photonic crystal fiber (C-PCF) supporting orbital angular momentum modes. The calibrated normalized parameters for the C-PCF family are presented. The information about the cutoff condition of modes, the number of modes supported in fibers, and the effective index difference between adjacent modes can be obtained by using the design tool. Also, the mode properties, such as confinement loss, effective mode area (Aeff), and spin-orbital coupling are analyzed using the design tool. At the end of paper, we also give some fiber design examples by using the design tool.
Collapse
|
25
|
Chen S, Wang J. Theoretical analyses on orbital angular momentum modes in conventional graded-index multimode fibre. Sci Rep 2017. [PMID: 28638058 PMCID: PMC5479839 DOI: 10.1038/s41598-017-04380-7] [Citation(s) in RCA: 43] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/05/2022] Open
Abstract
Orbital angular momentum (OAM) modes are another mode basis to represent spatial modes. There have been increasing interests in exploiting OAM modes in specialty fibres. In this paper, we present a comprehensive characterisation of OAM modes in conventional graded-index multimode fibre (MMF). 1) We synthesise the circularly polarized OAM modes by properly combining two fold degenerate cylindrical vector modes (eigenmodes) and analyse the total angular momentum, i.e. spin angular momentum and orbital angular momentum. 2) We divide all the OAM modes of the conventional graded-index MMF into 10 OAM mode groups with effective refractive index differences between different mode groups above 10−4 enabling low-level inter-group crosstalk. 3) We study the chromatic dispersion, differential group delay, effective mode area, and nonlinearity for each OAM mode group over a wide wavelength ranging from 1520 to 1630 nm covering the whole C band and L band. 4) We discuss the performance tolerance to fibre ellipticity and bending. 5) We further address the robustness of performance against fibre perturbations including the core size, index contrast and the imperfect index profile of the practically fabricated MMFs. The obtained results may provide theoretical basis for further space-division multiplexing applications employing OAM modes in conventional graded-index MMF.
Collapse
Affiliation(s)
- Shi Chen
- Wuhan National Laboratory for Optoelectronics, School of Optical and Electronic Information, Huazhong University of Science and Technology, Wuhan, 430074, Hubei, China.,Shenzhen Institute of Huazhong University of Science and Technology, Shenzhen, 518000, China
| | - Jian Wang
- Wuhan National Laboratory for Optoelectronics, School of Optical and Electronic Information, Huazhong University of Science and Technology, Wuhan, 430074, Hubei, China.
| |
Collapse
|
26
|
Abstract
In this work, we demonstrate the measurement of the Brillouin gain spectra of vector modes in a few-mode fiber for the first time using a simple heterodyne detection technique. A tunable long period fiber grating is used to selectively excite the vector modes supported by the few-mode fiber. Further, we demonstrate the non-destructive measurement of the absolute effective refractive indices (neff) of vector modes with ~10−4 accuracy based on the acquired Brillouin frequency shifts of the modes. The proposed technique represents a new tool for probing and controlling vector modes as well as modes carrying orbital angular momentum in optical fibers with potential applications in advanced optical communications and multi-parameter fiber-optic sensing.
Collapse
|
27
|
Vitullo DLP, Leary CC, Gregg P, Smith RA, Reddy DV, Ramachandran S, Raymer MG. Observation of Interaction of Spin and Intrinsic Orbital Angular Momentum of Light. PHYSICAL REVIEW LETTERS 2017; 118:083601. [PMID: 28282159 DOI: 10.1103/physrevlett.118.083601] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/21/2016] [Indexed: 06/06/2023]
Abstract
The interaction of spin and intrinsic orbital angular momentum of light is observed, as evidenced by length-dependent rotations of both spatial patterns and optical polarization in a cylindrically symmetric isotropic optical fiber. Such rotations occur in a straight few-mode fiber when superpositions of two modes with parallel and antiparallel orientation of spin and intrinsic orbital angular momentum (IOAM=2ℏ) are excited, resulting from a degeneracy splitting of the propagation constants of the modes.
Collapse
Affiliation(s)
- Dashiell L P Vitullo
- Department of Physics and Oregon Center for Optical, Molecular, and Quantum Science, University of Oregon, Eugene, Oregon 97403, USA
| | - Cody C Leary
- Department of Physics, College of Wooster, Wooster, Ohio 44691, USA
| | - Patrick Gregg
- Department of Electrical and Computer Engineering, Boston University, Boston, Massachusetts 02215, USA
| | - Roger A Smith
- Department of Physics and Oregon Center for Optical, Molecular, and Quantum Science, University of Oregon, Eugene, Oregon 97403, USA
| | - Dileep V Reddy
- Department of Physics and Oregon Center for Optical, Molecular, and Quantum Science, University of Oregon, Eugene, Oregon 97403, USA
| | - Siddharth Ramachandran
- Department of Electrical and Computer Engineering, Boston University, Boston, Massachusetts 02215, USA
| | - Michael G Raymer
- Department of Physics and Oregon Center for Optical, Molecular, and Quantum Science, University of Oregon, Eugene, Oregon 97403, USA
| |
Collapse
|
28
|
Novel Equalization Techniques for Space Division Multiplexing Based on Stokes Space Update Rule. PHOTONICS 2017. [DOI: 10.3390/photonics4010012] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
|
29
|
Gregg P, Kristensen P, Ramachandran S. 13.4km OAM state propagation by recirculating fiber loop. OPTICS EXPRESS 2016; 24:18938-47. [PMID: 27557175 DOI: 10.1364/oe.24.018938] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
Enabled by an enhanced effective index separation (Δneff = 1.7 × 10-4) and low transmission loss (0.8dB/km), OAM states are propagated over 13.4km in an air core fiber using a recirculating fiber loop. We observe that intermodal crosstalk decreases rapidly with increasing effective index separation, Δneff, and an order of magnitude lower crosstalk may be achieved just by doubling Δneff. We find that, in agreement with coupled power theory, our fiber has mode coupling properties analogous to elliptical core PM fibers, which yield ~10 × or more lower crosstalk than for conventional LP fiber mode orders with the same Δneff. This confirms that, for OAM modes, birefringent perturbations rather than shape perturbations matter most. In the process of performing the loop experiment, we demonstrate that OAM states in these fibers can be preserved with low loss (≤ 0.2dB) and low crosstalk (-15dB) while splicing distinct segments of the air-core fiber. For well-designed fibers, we demonstrate that OAM modes can travel distances relevant for large-scale data centers.
Collapse
|
30
|
Li H, Ren G, Lian Y, Zhu B, Tang M, Zhao Y, Jian S. Broadband orbital angular momentum transmission using a hollow-core photonic bandgap fiber. OPTICS LETTERS 2016; 41:3591-3594. [PMID: 27472626 DOI: 10.1364/ol.41.003591] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We present the viability of exploiting a current hollow-core photonic bandgap fiber (HC-PBGF) to support orbital angular momentum (OAM) states. The photonic bandgap intrinsically provides a large refractive index spacing for guiding light, leading to OAM transmission with low crosstalk. From numerical simulations, a broad OAM±1 mode transmission window with satisfied effective index separations between vector modes (>10-4) and low confinement loss (<3 dB/km) covering 240 nm bandwidth is observed. The OAM purity (defined as normalized power weight for OAM mode) is found to be affected by the modal effective area. Simulation results also show HC-PBGF based OAM transmission is immune to fabrication inaccuracies near the hollow core. This work illustrates that HC-PBGF is a competitive candidate for high-capacity communication harnessing OAM multiplexing.
Collapse
|
31
|
Ye J, Li Y, Han Y, Deng D, Guo Z, Gao J, Sun Q, Liu Y, Qu S. Excitation and separation of vortex modes in twisted air-core fiber. OPTICS EXPRESS 2016; 24:8310-8316. [PMID: 27137269 DOI: 10.1364/oe.24.008310] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
An air-core fiber imposed by torsion is investigated in this paper. We refer to this kind of fiber as twisted air-core fiber (TAF). It has been demonstrated that the eigenstates of the TAF consist of guided optical vortex waves with different propagation constants of a different effective index. With the increase of the twist rate, TAF could separate the OAM modes which are near degenerate or degenerate in the air-core fiber. The separation of OAM modes in TAF is conductive to ultralong distance propagation with low crosstalk. TAF could be considered as an ideal candidate fiber for OAM based optical communication. Moreover, we investigated the twisted air-core photonic crystal fiber (TAPCF) which can improve the relative energy distribution of the OAM modes. Compared with TAF, more energy is located in the ring shaped core, which is conductive to ultralong distance propagation. TAF and TAPCF are of potential interest for increasing channel capacity in optical telecommunications, and the result is also of interest to the photonic crystal community.
Collapse
|
32
|
Xu Y, Ren M, Lu Y, Lu P, Lu P, Bao X, Wang L, Messaddeq Y, LaRochelle S. Multi-parameter sensor based on stimulated Brillouin scattering in inverse-parabolic graded-index fiber. OPTICS LETTERS 2016; 41:1138-1141. [PMID: 26977653 DOI: 10.1364/ol.41.001138] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
We propose a unique multi-parameter optical fiber sensor based on intramodal stimulated Brillouin scattering of higher-order acoustic modes in inverse-parabolic graded-index fiber (IPGIF) without a mode converter. Both optical modes and acoustic modes guided in the IPGIF are characterized and demonstrated theoretically and experimentally. Simulation analysis shows that the multi-peak feature in the Brillouin gain spectrum of the IPGIF is attributed to the couplings between the guided optical mode and the higher-order acoustic modes. Thanks to the distinct acoustic properties of the peaks induced by the sharp refractive index profile of the IPGIF, the different temperature and strain dependences of the first three Brillouin peaks enable the discrimination of the temperature and strain at an accuracy of 0.85°C and 17.4 με.
Collapse
|
33
|
Zhang Z, Gan J, Heng X, Wu Y, Li Q, Qian Q, Chen D, Yang Z. Optical fiber design with orbital angular momentum light purity higher than 99.9. OPTICS EXPRESS 2015; 23:29331-29341. [PMID: 26698417 DOI: 10.1364/oe.23.029331] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
The purity of the synthesized orbital-angular-momentum (OAM) light in the fiber is inversely proportional to channel crosstalk level in the OAM optical fiber communication system. Here the relationship between the fiber structure and the purity is firstly demonstrated in theory. The graded-index optical fiber is proposed and designed for the OAM light propagation with the purity higher than 99.9%. 16 fiber modes (10 OAM modes) have been supported by a specific designed graded-index optical fiber with dispersion less than 35 ps/(km∙nm). Such fiber design has suppressed the intrinsic crosstalk to be lower than -30 dB, and can be potentially used for the long distance OAM optical communication system.
Collapse
|
34
|
Li S, Wang J. Supermode fiber for orbital angular momentum (OAM) transmission. OPTICS EXPRESS 2015; 23:18736-18745. [PMID: 26191933 DOI: 10.1364/oe.23.018736] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We present a multi-orbital-angular-momentum (OAM) multi-core supermode fiber (MOMCSF) to transmit OAM modes. The MOMCSF consists of equally-spaced and circularly-arranged multiple cores, in which the core pitch is small enough to support strong coupling OAM supermodes. The characteristics of OAM modes in MOMCSFs with different core pitches and core numbers are analyzed. The performances of mode coupling and nonlinearity are optimized by designing multiple degrees of freedom of the supermode fiber. The obtained results show that the designed MOMCSF can transmit multiple OAM modes with favorable performance of low mode coupling, low nonlinearity, and low modal dependent loss.
Collapse
|
35
|
Yu J, Zhou C, Lu Y, Wu J, Zhu L, Jia W. Square lattices of quasi-perfect optical vortices generated by two-dimensional encoding continuous-phase gratings. OPTICS LETTERS 2015; 40:2513-2516. [PMID: 26030545 DOI: 10.1364/ol.40.002513] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We propose a type of two-dimensional (2D) encoding continuous-phase gratings capable of simultaneously generating a square lattice of multiple quasi-perfect vortices. As an example, a symmetrical and an asymmetrical 5×5 lattice of quasi-perfect vortices are experimentally demonstrated. It is shown that multiple quasi-perfect vortices with different topological charges are generated at different diffraction orders. The ring-width of these vortices is nearly constant, while there is a shift in the average ring-diameter when the carried charges are large enough, or when the ring-diameter is small. Additional axicon phase has been embedded into these 2D encoding gratings for the compensation of such shift in the average ring-diameter, and experimental results show that the shift can be greatly minimized after this compensation.
Collapse
|
36
|
Brunet C, Ung B, Wang L, Messaddeq Y, LaRochelle S, Rusch LA. Design of a family of ring-core fibers for OAM transmission studies. OPTICS EXPRESS 2015; 23:10553-10563. [PMID: 25969095 DOI: 10.1364/oe.23.010553] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We propose a family of ring-core fibers, designed for the transmission of OAM modes, that can be fabricated by drawing five different fibers from a single preform. This novel technique allows us to experimentally sweep design parameters and speed up the fiber design optimization process. Such a family of fibers could be used to examine system performance, but also facilitate understanding of parameter impact in the transition from design to fabrication. We present design parameters characterizing our fiber, and enumerate criteria to be satisfied. We determine targeted fiber dimensions and explain our strategy for examining a design family rather than a single fiber design. We simulate modal properties of the designed fibers, and compare the results with measurements performed on fabricated fibers.
Collapse
|
37
|
Ramachandran S, Gregg P, Kristensen P, Golowich SE. On the scalability of ring fiber designs for OAM multiplexing. OPTICS EXPRESS 2015; 23:3721-3730. [PMID: 25836225 DOI: 10.1364/oe.23.003721] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
The promise of the infinite-dimensionality of orbital angular momentum (OAM) and its application to free-space and fiber communications has attracted immense attention in recent years. In order to facilitate OAM-guidance, novel fibers have been proposed and developed, including a class of so-called ring-fibers. In these fibers, the wave-guiding region is a high-index annulus instead of a conventional circular core, which for reasons related to polarization-dependent differential phase shifts for light at waveguide boundaries, leads to enhanced stability for OAM modes. We review the theory and implementation of this nascent class of waveguides, and discuss the opportunities and limitations they present for OAM scalability.
Collapse
|