Continuously tunable orbital angular momentum generation using a polarization-maintaining fiber

Fast finite difference solver for optical microscopy in deep biological tissue

Optical scattering poses a significant challenge to high-resolution microscopy within deep tissue. To accurately predict the performance of various microscopy techniques in thick samples, we present a computational model that efficiently solves Maxwell's equation in highly scattering media. This toolkit simulates the deterioration of the laser beam point spread function (PSF) without making a paraxial approximation, enabling accurate modeling of high-numerical-aperture (NA) objective lenses commonly employed in experiments. Moreover, this framework is applicable to a broad range of scanning microscopy techniques including confocal microscopy, stimulated emission depletion (STED) microscopy, and ground-state depletion microscopy. Notably, the proposed method requires only readily obtainable macroscopic tissue parameters. As a practical demonstration, we investigate the performance of Laguerre-Gaussian (LG) versus Hermite-Gaussian (HG) depletion beams in STED microscopy.

All-fiber few-mode interference for complex azimuthal pattern generation

We report on an all-fiber setup capable of generating complex intensity patterns using interference of few guided modes. Comprised by a few-mode fiber (FMF) spliced to a multimodal interference (MMI) fiber device, the setup allows for obtaining different output patterns upon adjusting the phases and intensities of the modes propagating in the FMF. We analyze the output patterns obtained when exciting two family modes in the MMI device using different phase and intensity conditions for the FMF modal base. Using this simple experimental arrangement we are able to produce complex intensity patterns with radial and azimuthal symmetry. Moreover, our results suggest that this approach provides a means to generate beams with orbital angular momentum (OAM).

High-power cylindrical vector beam fiber laser based on an all-polarization-maintaining structure

We propose and demonstrate an all-polarization-maintaining (PM) high-power cylindrical vector beam (CVB) fiber laser based on the principle of mode superposition. The non-degenerated LPy 11a is generated from the oscillator with the maximum power of 11.9W, whose slope efficiency is 24.4%. Then the stable single TE₀₁ vector beam is achieved by the superposition of LPy 11a and LPx 11b in an all-PM architecture, its output power is 3.1W and mode purity of 91.2%. Due to the all-PM architecture, our configuration is free of adjusting polarization controller (PC) and reliable during long-term operation. This laser could be used as a high-power CVBs source for a wide range of applications towards scientific research and industrial field.

All-fiber passively Q-switched laser with flat-top beam emissions

Flat-top beams have plenty of applications in theoretical and applied research, but they are not eigenmodes of the wave equation. Here, we propose an effective strategy for generating flat-top beams in fibers, which originates from the incoherent superposition of orbital angular momentum (OAM) and fundamental (LP₀₁) modes. The designed all-fiber passively Q-switched laser can realize high-quality pulsed flat-top and OAM beam emissions. The normalized root mean square of the flat-top beam is around 4.7%, and the purity of the OAM mode is calculated to be higher than 98%. For the first time to the best of our knowledge, pulsed emission of a flat-top beam is achieved using an all-fiber laser. Moreover, its repetition rate and duration can be controlled by adjusting the pump.

Excitation of high order orbital angular momentum modes in ultra-short chiral long period fiber gratings

A class of ultra-short chiral long period fiber gratings (CLPFGs) are prepared by writing a spiral curve on the surface of a six-mode fiber. The CLPFGs are applied to excite ±2^nd- and ±3^rd-order orbital angular momentum (OAM) modes. The coupling efficiency of the CLPFG in these modes can be as high as 99%, when the length is only 0.5cm. The polarization characteristic of the excited higher-order OAM modes in CLPFGs was theoretically analyzed and experimentally investigated. Results show that the obtained ±2^nd- and ±3^rd-order OAM modes are polarization independent, as expected.

Experimental investigation of point-by-point off-axis Bragg gratings inscribed by a femtosecond laser in few-mode fibers

Off-axis Bragg gratings with varied horizontal and vertical distances off the center in a step-index two-mode fiber were fabricated by 800 nm infrared-femtosecond laser pulses through a point-by-point technique. In this article, we experimentally investigate these gratings via measuring the transmitted power and the reflected intensity profiles under different input polarization, with multiple characteristics reported for the first time to the best of our knowledge. To highlight, we find that the birefringence induced to the LP₀₁ reaches its maximum magnitude at an intermediate offset, followed by the fast and slow axes switching at a further slightly increased offset. We also show that the peak reflectivity of the LP₁₁ exhibits strong polarization dependence, with the much stronger peak reflectivity constantly corresponding to the polarization perpendicular to the damage-point-to-center line, whereas the peak reflectivity of the LP₀₁ has almost no polarization dependence. Moreover, we report that the reflected mode patterns of the cross-coupling of the LP₀₁ and LP₁₁ are linked to the direction of linear polarization, through which one can selectively excite an arbitrarily oriented LP₁₁ by merely altering the polarization.

Generation of stable orbital angular momentum beams with an all-polarization-maintaining fiber structure

In this paper, we propose a stable orbital angular momentum (OAM) mode fiber laser with an all-polarization-maintaining fiber (PMF) structure based on a combination of two linearly polarized modes. The mode intensity ratio between the two linearly polarized modes can be adjusted by adopting a double-pump structure. A pair of polarization-maintaining long-period fiber gratings (PM-LPFGs) are used as a mode converter. The number of topological charges of the OAM mode beam can be tuned between +1 and -1 by stretching the fiber. By adopting an all-PMF structure, we can build an OAM mode fiber laser without a polarization controller and that is resistant to environmental disturbances. The purity of the OAM mode was approximately 93.6%. This stable and compact OAM mode fiber laser can be used as a laser source in practical applications and scientific research.

All-fiber second-order orbital angular momentum generator based on a single-helix helical fiber grating

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.

Analysis of Bending-Induced Degradation of Orbital Angular Momentum Modes in Optical Fibers

In this work, bending-induced deterioration of orbital angular momentum (OAM) modes in ring core fiber (RCF), photonic crystal fiber (PCF), and vortex fiber (VF) was theoretically investigated: Bending losses, coupling losses, and intermodal crosstalk at the interface between straight and bent optical fibers were investigated from the modal analysis of those three types of OAM mode fibers. In addition, the degradation of a topological charge number of an OAM mode due to the bending-induced birefringence and horizontal mode asymmetry was also investigated. Our investigation revealed that, in all aspects, the PCF is most robust to bending among the three types of optical fibers, and the most serious bending-induced problem in the VF and the RCF is the degradation of the topological charge number. The allowed minimum bending radii of VF and RCF appeared to be ~15 and ~45 mm, respectively, for the specific structures considered in this work. We expect that the methodology and results of our quantitative analysis on bending-induced degradation of OAM modes will be of great use in the design of OAM mode fibers for practical use.

A Fiber-Coupled Stimulated Emission Depletion Microscope for Bend-Insensitive Through-Fiber Imaging

We present results for a new type of fiber-coupled stimulated emission depletion (STED) microscope which uses a single fiber to transport STED and excitation light, as well as collect the fluorescence signal. Our method utilizes two higher-order eigenmodes of polarization maintaining (PM) fiber to generate the doughnut-shaped STED beam. The modes are excited with separate beams that share no temporal coherence, yielding output that is independent of fiber bending. We measured the resolution using 45 nm fluorescent beads and found a median bead image size of 116 nm. This resolution does not change as function of fiber bending radius, demonstrating robust operation. We report, for the first time, STED images of fixed biological samples collected in the epi-direction through fiber. Our microscope design shows promise for future use in super-resolution micro-endoscopes and in vivo neural imaging in awake and freely-behaving animals.

On-Chip Guiding of Higher-Order Orbital Angular Momentum Modes

Higher-order orbital angular momentum (OAM) mode guiding in a waveguide which is suitable for on-chip integration has been investigated. Based on the relation between the Laguerre-Gaussian mode and the Hermite-Gaussian mode, it has been shown that two degenerate guided modes of π/2l-rotation symmetry can support the l-th order OAM mode. In order to mimic the rotational symmetry, we have proposed the waveguide structure of a cross-shaped core and designed a waveguide that can support OAM modes of ±1 and ±2 topological charges simultaneously at a wavelength of 1550 nm. Purity of the OAM modes guided in the designed waveguide has been assessed by numerically calculating their topological charges from the field distribution, which were close to the theoretical values. We also investigated the guiding of OAM modes of ±3 and ±4 topological charges in our proposed waveguide structure, which revealed the possibility of the separate guiding of those OAM modes with relatively lower purity.

A Review of Tunable Orbital Angular Momentum Modes in Fiber: Principle and Generation

Orbital angular momentum (OAM) beams, a new fundamental degree of freedom, have excited a great diversity of interest due to a variety of emerging applications. The scalability of OAM has always been a topic of discussion because it plays an important role in many applications, such as expanding to large capacity and adjusting the trapped particle rotation speed. Thus, the generation of arbitrary tunable OAM mode has been paid increasing attention. In this paper, the basic concepts of classical OAM modes are introduced firstly. Then, the tunable OAM modes are categorized into three types according to the orbital angular momentums and polarization states of mode carrying. In order to understand the OAM evolution of a mode intuitively, three kinds of Poincaré spheres (PSs) are introduced to represent the three kinds of tunable OAM modes. Numerous methods generating tunable OAM modes can be roughly divided into two types: spatial and fiber-based generation methods. The principles of fiber-based generation methods are interpreted by introducing two mode bases (linearly-polarized modes and vector modes) of the fiber. Finally, the strengths and weaknesses of each generation method are pointed out and the key challenges for tunable OAM modes are discussed.

Generation of LP11/LP21 modes with tunable mode lobe orientation controlled by polarization states

We propose and experimentally demonstrate a novel scheme to generate LP₁₁/LP₂₁ modes with tunable mode lobe orientation (MLO). Wherein, the MLOs have an excellent linear relationship with the linearly-polarized states of input fundamental modes. The proposed scheme is composed of a polarization controller (PC), a mode converter, a mode and polarization controller (PMC) which is twined with the few mode fiber (FMF) and a polarizer. Experimental results show that the deviations of MLOs between generated LP₁₁/LP₂₁ modes and simulated ones are less than 3.5 and 8 degrees over C band. Since polarization control up to nanosecond scale is available with GaAs or lithium based electro-optic modulator, the proposed scheme could enable nanosecond time scale MLO control, which would be immensely useful for optical trapping, fiber sensors and optical communications.

Two-Layer Erbium-Doped Air-Core Circular Photonic Crystal Fiber Amplifier for Orbital Angular Momentum Mode Division Multiplexing System

Orbital angular momentum (OAM) mode-division multiplexing (MDM) has recently been under intense investigations as a new way to increase the capacity of fiber communication. In this paper, a two-layer Erbium-doped fiber amplifier (EDFA) for an OAM multiplexing system is proposed. The amplifier is based on the circular photonic crystal fiber (C-PCF), which can maintain a stable transmission for 14 OAM modes by a large index difference between the fiber core and the cladding. Further, the two-layer doped region can balance the amplification performance of different modes. The relationship between the performance and the parameters of the amplifier is analyzed numerically to optimize the amplifier design. The optimized amplifier can amplify 18 modes (14 OAM modes) simultaneously over the C-band with a differential mode gain (DMG) lower than 0.1 dB while keeping the modal gain over 23 dB and noise figure below 4 dB. Finally, the fabrication tolerance and feasibility are discussed. The result shows a relatively large fabrication tolerance in the OAM EDFA parameters.

Twist-direction-dependent orbital angular momentum generator based on inflation-assisted helical photonic crystal fiber

A novel twist-direction-dependent high-order orbital angular momentum (OAM) generator based on an inflated helical photonic crystal fiber (IHPCF) was demonstrated by use of an inflation-assisted hydrogen-oxygen flame heating technique. Compared with the helical photonic crystal fiber, the IHPCF exhibits a perfect transmission dip without distinct splits, thus generating high-quality OAM_±6 modes. The helical phase of the generated OAM modes is dependent on the twist direction of the IHPCF and independent of the polarization state of the input light. In addition, the polarization state of the generated OAM modes is the same as that of the input light.

Continuously tunable orbital angular momentum generation controlled by input linear polarization

In this Letter, we theoretically and experimentally demonstrate a new method to generate tunable orbital angular momentum (OAM) by continuously changing the angle of linear polarization of the input light. We use the Fourier series of left- and right-hand projections to prove that the average OAM smoothly varied from l=-1 to l=1 with the angle of LP of input light changing from 0 to π, which is fulfilled by an electrical polarization controller.

Fabrication of optical vortex lattices based on holographic polymer-dispersed liquid crystal films

This Letter demonstrates optical vortex lattices based on holographic polymer-dispersed liquid crystal (HPDLC) films. The fabrication method uses a phase-only reflective spatial light modulator with numerically calculated phase profiles loaded on it to simplify multi-helical-wave interference. The beam profiles of the diffraction beams are simulated using the Fourier transform and compared with experimental results. The topological charges of the 1st-order diffraction beams reconstructed from the HPDLC films are examined using a Michelson interferometer.

Two-dimensional tunable orbital angular momentum generation using a vortex fiber

We demonstrate the two-dimensional tunable orbital angular momentum (OAM) generation in a ring-core (vortex) fiber. The LP₁₁ mode generated by an all fiber fused coupler is coupled into a vortex fiber. Because the vector modes of the LP₁₁ mode group in the vortex fiber are no longer degenerate, the mode status will change between linearly polarized modes (LPMs) and complex OAM modes periodically during propagation. The generated OAM can be tuned smoothly by filtering the mixed mode with different polarization directions or changing the wavelength at a certain polarization directions. The two-dimensional tuning of OAM from l=-1 to l=+1 is experimentally demonstrated in an all fiber OAM generator.

Single mode fiber based delivery of OAM light by 3D direct laser writing

We demonstrate orbital-angular momentum (OAM) light up to a topological charge of l=3 behind a single mode fiber. Femtosecond 3D direct laser writing is used to fabricate spiral phase plates of l=1,2 and 3, composed of 10 discrete steps, on the tip of single mode optical fibers. These structures efficiently convert out-coupled light from the fiber at 785 nm wavelength into optical vortex beams carrying an orbital-angular momentum of lℏper photon. Far field intensity patterns and interferograms of the OAM beams are recorded using a CCD camera. The results are in excellent agreement with numerical simulations obtained from the wave propagation method.

Tunable higher-order orbital angular momentum using polarization-maintaining fiber

For the first time, to the best of our knowledge, light with orbital angular momentum (OAM) of ±2ℏ per photon is produced using commercially available polarization-maintaining fiber with modal purity of 96%. Twist measurements demonstrate that the average orbital angular momentum can be continuously tuned between ±2ℏ. The authors consider beams of non-integer OAM, created using the presented method, as superpositions of integer OAM states.

All-fiber spatial rotation manipulation for radially asymmetric modes

We propose and experimentally demonstrate spatial rotation manipulation for radially asymmetric modes based on two kinds of polarization maintaining few-mode fibers (PM-FMFs). Theoretical finding shows that due to successful suppression of both polarization and spatial mode coupling, the spatial rotation of radially asymmetric modes has an excellent linear relationship with the twist angle of PM-FMF. Both elliptical core and panda type FMFs are fabricated, in order to realize manageable spatial rotation of LP₁₁ mode within ±360° range. Finally, we characterize individual PM-FMF based spatial orientation rotator and present comprehensive performance comparison between two PM-FMFs in terms of insertion loss, temperature sensitivity, linear polarization maintenance, and mode scalability.

Linearly polarized orbital angular momentum mode purity measurement in optical fibers

We presented a simple method for measuring the mode purity of linearly polarized orbital angular momentum (OAM) modes in optical fibers. The method is based on the analysis of OAM beam projections filtered by a polarizer. The amplitude spectrum and phase spectrum of a data ring derived from the beam pattern are obtained by Fourier transform. Then the coefficients of the mixed electric field expression can be determined and the mode purity can be obtained. The proposed method is validated and it is experimentally demonstrated in a two-mode fiber.

Simultaneous control of orbital angular momentum and beam profile in two-mode polarization-maintaining fiber

We report simultaneous control of the orbital angular momentum (OAM) and beam profile of vortex beams generated in two-mode polarization-maintaining optical fiber. Two higher-order eigenmodes of the fiber are combined to form optical vortices. Reduced coherence between the fiber modes decreases the mode purity. Varying the coherence of the fiber modes changes the average OAM while maintaining a constant annular intensity profile. Additionally, a donut mode has been shown to be insensitive to bends and twists in the fiber.