Mode analysis with a spatial light modulator as a correlation filter

Statistics of modal condensation in nonlinear multimode fibers

Optical pulses traveling through multimode optical fibers encounter the influence of both linear disturbances and nonlinearity, resulting in a complex and chaotic redistribution of power among different modes. In our research, we explore the phenomenon where multimode fibers reach stable states marked by the concentration of energy into both single and multiple sub-systems. We introduce a weighted Bose-Einstein law, demonstrating its suitability in describing thermalized modal power distributions in the nonlinear regime, as well as steady-state distributions in the linear regime. We apply the law to experimental results and numerical simulations. Our findings reveal that, at power levels situated between the linear and soliton regimes, energy concentration occurs locally within higher-order modal groups before transitioning to global concentration in the fundamental mode within the soliton regime. This research broadens the application of thermodynamic principles to multimode fibers, uncovering previously unexplored optical states that exhibit characteristics akin to optical glass.

Polarization-resolved mode evolution in TMI-limited Yb-doped fiber amplifiers using a novel high-speed Stokes polarimeter

In this work we have developed a high-speed Stokes polarimeter method based on simultaneous 4-channel imaging with a high-speed camera. Thus, current speed limitations of imaging polarimeters for wavelengths around 1 µm can be overcome, allowing a sub-ms polarization-resolved characterization of transverse mode instability (TMI). Additionally, the Stokes parameters of each individual mode are calculated by a simultaneous 4-beam mode reconstruction algorithm during post-processing and can be analyzed with unprecedented temporal resolution. We demonstrate the measurement capabilities of this polarimeter setup by characterizing TMI of a large-mode-area Yb-doped polarization maintaining (PM) fiber amplifier with 30 kHz video frame rate. Upon thorough characterization, we have found for the first time that at the onset of TMI in a PM fiber, the modal polarization states begin to oscillate on circular and elliptical trajectories at the same frequencies as the modal energy transfer occurs. The ability to measure the modal polarization states with sub-ms temporal resolution is key to developing a fundamental understanding and subsequently possible mitigation strategies of TMI in PM-fiber lasers.

Measuring small displacements of an optical point source with digital holography

The image of an optical point source is blurred due to light diffraction so that estimating small displacements of the point source with direct imaging demands elaborate processing on the observation data of a camera. Using quantum parameter estimation, we show that for the imaging systems with a real point spread function, any measurement basis constituted by a complete set of real-valued spatial-mode functions is optimal for estimating the displacement. For small displacements, we can concentrate the information about the value of displacement to the measurement of a few spatial modes, which can be selected in terms of the Fisher information distribution. We use digital holography with a phase-only spatial light modulator to implement two simple estimation strategies that are mainly based on the projection measurement of two spatial modes and the readout of a single pixel of a camera.

Complex structured beam direct generation by coherent superposition of a complete set of degenerate eigenmodes

Structured beams have played an important role in many fields due to their rich spatial characteristics. The microchip cavity with a large Fresnel number can directly generate structured beams with complex spatial intensity distribution, which provides convenience for further exploring the formation mechanism of structured beams and realizing low-cost applications. In this article, theoretical and experimental studies are carried out on complex structured beams directly generated by the microchip cavity. It is demonstrated that the complex beams generated by the microchip cavity can be expressed by the coherent superposition of whole transverse eigenmodes within the same order, thus forming the eigenmode spectrum. The mode component analysis of complex propagation-invariant structured beams can be realized by the degenerate eigenmode spectral analysis described in this article.

Contribution to the Improvement of the Correlation Filter Method for Modal Analysis with a Spatial Light Modulator

Modal decomposition of light is essential to study its propagation properties in waveguides and photonic devices. Modal analysis can be carried out by implementing a computer-generated hologram acting as a match filter in a spatial light modulator. In this work, a series of aspects to be taken into account in order to get the most out of this method are presented, aiming to provide useful operational procedures. First of all, a method for filter size adjustment based on the standard fiber LP-mode symmetry is presented. The influence of the mode normalization in the complex amplitude encoding-inherent noise is then investigated. Finally, a robust method to measure the phase difference between modes is proposed. These procedures are tested by wavefront reconstruction in a conventional few-mode fiber.

Complete modal decomposition of a few-mode fiber based on ptychography technology

An exact modal decomposition method plays an important role in revealing the modal characteristics of a few-mode fiber, and it is widely used in various applications ranging from imaging to telecommunications. Here, ptychography technology is successfully used to achieve modal decomposition of a few-mode fiber. In our method, the complex amplitude information of the test fiber can be recovered by ptychography, and then the amplitude weight of each eigenmode and the relative phase between different eigenmodes can be easily calculated by modal orthogonal projection operations. In addition, we also propose a simple and effective method to realize coordinate alignment. Numerical simulations and optical experiments validate the reliability and feasibility of the approach.

Simulating multilevel diffractive optical elements on a spatial light modulator

Multilevel diffractive optical elements (DOEs) offer a solution to approximate complex diffractive phase profiles in a stepwise manner. However, while much attention has focused on efficiency, the impact on modal content in the context of structured light has, to our best knowledge, remained unexplored. Here, we outline a simple theory that accounts for efficiency and modal purity in arbitrary structured light produced by multilevel DOEs. We make use of a phase-only spatial light modulator as a "testbed" to experimentally implement various multileveled diffractive profiles, including orbital angular momentum beams, Bessel beams, and Airy beams, outlining the subsequent efficiency and purity both theoretically and experimentally, confirming that a low number of multilevel steps can produce modes of high fidelity. Our work will be useful to those wishing to digitally evaluate modal effects from DOEs prior to physical fabrication.

Spatial tomography of light resolved in time, spectrum, and polarisation

Measuring polarisation, spectrum, temporal dynamics, and spatial complex amplitude of optical beams is essential to studying phenomena in laser dynamics, telecommunications and nonlinear optics. Current characterisation techniques apply in limited contexts. Non-interferometric methods struggle to distinguish spatial phase, while phase-sensitive approaches necessitate either an auxiliary reference source or a self-reference, neither of which is universally available. Deciphering complex wavefronts of multiple co-propagating incoherent fields remains particularly challenging. We harness principles of spatial state tomography to circumvent these limitations and measure a complete description of an unknown beam as a set of spectrally, temporally, and polarisation resolved spatial state density matrices. Each density matrix slice resolves the spatial complex amplitude of multiple mutually incoherent fields, which over several slices reveals the spectral or temporal evolution of these fields even when fields spectrally or temporally overlap. We demonstrate these features by characterising the spatiotemporal and spatiospectral output of a vertical-cavity surface-emitting laser.

The work harnesses principles of spatial state tomography to fully characterise an optical beam in space, time, spectrum, and polarisation. Analysis of the output of a vertical-cavity surface-emitting laser illustrates the technique’s capabilities.

Modal decomposition of an incoherent combined laser beam based on the combination of residual networks and a stochastic parallel gradient descent algorithm

With the increase of the superimposed eigenmodes number, the traditional numerical modal decomposition (MD) technique will inevitably suffer from ambiguity and local minima problems and thus is typically unsuitable for conducting modal decomposition of an incoherent combined laser beam. In this paper, we propose a novel, to the best of our knowledge, MD algorithm, named ResNet-SPGD, which combines the advantages of residual networks (ResNet) and stochastic parallel gradient descent (SPGD) algorithm. Via setting the modal mode coefficients obtained from the CNN model as the initial value of the SPGD algorithm, such algorithm shows an attractive solution to mitigate the problem of modal ambiguity. The proposed algorithm is preliminarily applied to the modal decomposition of an incoherent combined laser beam, and the feasibility is demonstrated via numerical simulations. Complete MD is performed with high accuracy, and the only cost is the sacrifice of some real-time capacity.

Statistical mechanics of beam self-cleaning in GRIN multimode optical fibers

Since its first demonstration in graded-index multimode fibers, spatial beam self-cleaning has attracted a growing research interest. It allows for the propagation of beams with a bell-shaped spatial profile, thus enabling the use of multimode fibers for several applications, from biomedical imaging to high-power beam delivery. So far, beam self-cleaning has been experimentally studied under several different experimental conditions. Whereas it has been theoretically described as the irreversible energy transfer from high-order modes towards the fundamental mode, in analogy with a beam condensation mechanism. Here, we provide a comprehensive theoretical description of beam self-cleaning, by means of a semi-classical statistical mechanics model of wave thermalization. This approach is confirmed by an extensive experimental characterization, based on a holographic mode decomposition technique, employing laser pulses with temporal durations ranging from femtoseconds up to nanoseconds. An excellent agreement between theory and experiments is found, which demonstrates that beam self-cleaning can be fully described in terms of the basic conservation laws of statistical mechanics.

Mode-resolved analysis of pump and Stokes beams in LD-pumped GRIN fiber Raman lasers

All-fiber Raman lasers have demonstrated their potential for efficient conversion of highly multimode pump beams into high-quality Stokes beams. However, the modal content of these beams has not yet been investigated. In this work, based on a mode decomposition technique, we are able to reveal the details of intermodal interactions in the different operation regimes of continuous wave multimode graded-index fiber Raman lasers. We observed that, above the laser threshold, the residual pump beam is strongly depleted in its transverse modes with principal quantum number below 10. However, the generated Stokes signal beam mainly consists of the fundamental mode, but higher-order modes are also present, albeit with exponentially decreasing population.

Fast fiber mode decomposition with a lensless fiber-point-diffraction interferometer

Recently, the growing interest in few-mode fibers in telecommunications and high-power lasers has stimulated the demand for fiber mode decomposition (MD). Here we present a fast fiber MD method with a lensless fiber-point-diffraction interferometer. The complex amplitude at the fiber end is achieved by the polarization phase-shifting technique and the lensless imaging technique. Then, the eigenmode coefficients are determined by the mode orthogonal operations of the complex amplitude. In the experiment, the SMF-28e fiber containing 10 linear polarized modes at the wavelength of 632.8 nm is studied for MD. The decomposition of the 50 * 50 pixels interferograms takes only 0.0168 s. The similarity of the intensity patterns of the testing light is larger than 97% before and after the MD. This new, to the best of our knowledge, method can achieve fast and accurate 10-mode MD without using any imaging systems.

Transverse mode analysis for free-space laser beams using Bayesian analysis

Reliable and rapid assessment of the transverse mode quality of a free-space laser beam has a wide range of applications in laser development, research, and utilization. It has become even more important with recent advances in developing orbital angular momentum photon beams across a broad spectral region. In this work, a general modal analysis method for a free-space multimode laser beam has been developed based on Bayesian analysis. After transforming mode decomposition into a linear system problem, a Gaussian probabilistic model is used to find a closed-form solution. The method is found to be robust with the presence of Gaussian noise. Prior knowledge about the mode content can be incorporated into the method to improve the solution for situations when coherent disturbances or contamination are present in the laser beam. This method can be used to analyze the mode content for laser beams in different bases, such as Hermite-Gaussian (HG) modes and Laguerre-Gaussian (LG) modes. Three applications of this method are presented: a detailed modal analysis of the beam image from the incoherent intensity addition of HG modes and two examples of mode decomposition using the complex wavefront from the coherent superposition of HG and LG modes. The feasibility of this method is demonstrated using various simulation results. Based on digital images of a laser beam recorded without complex wavelength-limiting optics, in principle, this method can be used in a wide wavelength range from infrared to ultraviolet, and possibly x ray.

Modal analysis of structured light with spatial light modulators: a practical tutorial

A quantitative analysis of optical fields is essential, particularly when the light is structured in some desired manner, or when there is perhaps an undesired structure that must be corrected for. A ubiquitous procedure in the optical community is that of optical mode projections-a modal analysis of light-for the unveiling of amplitude and phase information of a light field. When correctly performed, all the salient features of the field can be deduced with high fidelity, including its orbital angular momentum, vectorial properties, wavefront, and Poynting vector. Here, we present a practical tutorial on how to perform an efficient and effective optical modal decomposition, with emphasis on holographic approaches using spatial light modulators, highlighting the care required at each step of the process.

High dynamic range spatial mode decomposition

An accurate readout of low-power optical higher-order spatial modes is of increasing importance to the precision metrology community. Mode sensors are used to prevent mode mismatches from degrading quantum and thermal noise mitigation strategies. Direct mode analysis sensors (MODAN) are a promising technology for real-time monitoring of arbitrary higher-order modes. We demonstrate MODAN with photo-diode readout to mitigate the typically low dynamic range of CCDs. We look for asymmetries in the response of our sensor to break degeneracies in the relative alignment of the MODAN and photo-diode and consequently improve the dynamic range of the mode sensor. We provide a tolerance analysis and show methodology that can be applied for sensors beyond first order spatial modes.

Maximum coupling efficiency to an optical resonator based on the Laguerre-Gauss decomposition of a beam

We present a new numerical method to calculate the optimum lens transformation to implement on a monochromatic laser beam path, in order to maximize its coupling to the fundamental Gaussian mode of a resonator or to a single-mode optical fiber whose mode can be described as Gaussian to a good approximation. This method relies on a useful mathematical relation on Laguerre-Gauss modes of different waists and reduces in the end to numerically maximizing a polynomial that is a function of the state of the beam in a finite interval, thus being numerically very efficient. We show with a simple example that this method is particularly efficient against other common methods used in the laboratory when it comes to laser beams composed of a coherent superposition of higher-order Laguerre-Gauss modes, as it is the case for instance for beams traversing optical elements suffering from spherical aberration.

Fast modal analysis for Hermite-Gaussian beams via deep learning

The eigenmodes of Hermite-Gaussian (HG) beams emitting from solid-state lasers make up a complete and orthonormal basis, and they have gained increasing interest in recent years. Here, we demonstrate a deep learning-based mode decomposition (MD) scheme of HG beams for the first time, to the best of our knowledge. We utilize large amounts of simulated samples to train a convolutional neural network (CNN) and then use this trained CNN to perform MD. The results of simulated testing samples have shown that our scheme can achieve an averaged prediction error of 0.013 when six eigenmodes are involved. The scheme takes only about 23 ms to perform MD for one beam pattern, indicating promising real-time MD ability. When larger numbers of eigenmodes are involved, the method can also succeed with slightly larger prediction error. The robustness of the scheme is also investigated by adding noise to the input beam patterns, and the prediction error is smaller than 0.037 for heavily noisy patterns. This method offers a fast, economic, and robust way to acquire both the mode amplitude and phase information through a single-shot intensity image of HG beams, which will be beneficial to the beam shaping, beam quality evaluation, studies of resonator perturbations, and adaptive optics for resonators of solid-state lasers.

Beyond the display: phase-only liquid crystal on Silicon devices and their applications in photonics [Invited]

Existing for almost four decades, liquid crystal on Silicon (LCOS) technology is rapidly growing into photonic applications. We review the basics of the technology, from the wafer to the driving solutions, the progress over the last decade and the future outlook. Furthermore we review the most exciting industrial and scientific applications of the LCOS technology.

Adaptive phase correction of dynamic multimode beam based on modal decomposition

We propose and demonstrate a method for the adaptive phase correction of dynamic multimode fiber beams. The phase of incident beam is reconstructed in real-time based on the complete modal information, which obtained by using the modal decomposition of correlation filter method. For the proof of principle, both of the modal decomposition and the phase correction are implemented using the same computer-generated hologram, which was encoded into a phase-only spatial light modulator. We demonstrate the phase correction of dynamic multimode beam at a rate of 5 Hz and achieve a 1.73-fold improvement on the average power-in-the-bucket. The experimental results indicate the feasibility of the real-time phase correction for the large mode area fiber laser by adaptive optics.

Spatial mode detection by frequency upconversion

The efficient creation and detection of spatial modes of light has become topical of late, driven by the need to increase photon bit-rates in classical and quantum communications. Such mode creation/detection is traditionally achieved with tools based on linear optics. Here we put forward a new spatial mode detection technique based on the nonlinear optical process of sum-frequency generation. We outline the concept theoretically and demonstrate it experimentally with intense laser beams carrying orbital angular momentum and Hermite-Gaussian modes. Finally, we show that the method can be used to transfer an image from the infrared band to the visible, which implies the efficient conversion of many spatial modes.

Interferometry-based modal analysis with finite aperture effects

We analyze the effects of aperture finiteness on interferograms recorded to unveil the modal content of optical beams in arbitrary bases using generalized interferometry. We develop a scheme for modal reconstruction from interferometric measurements that accounts for the ensuing clipping effects. Clipping-cognizant reconstruction is shown to yield significant performance gains over traditional schemes that overlook such effects that do arise in practice.

Stability of Ince-Gaussian beams in elliptical core few-mode fibers

A comparative stability analysis of Ince-Gaussian and Hermite-Gaussian modes in elliptical core few-mode fibers is provided to inform the design of spatial division multiplexing systems. The correlation method is used to construct crosstalk matrices that characterize the spatial modes of the fiber. Up to six low-order modes are shown to exhibit about -20  dB crosstalk. The crosstalk performance of each mode set is found to be similar. However, a direct comparison between modes of equal Gouy phase shift, a parameter that ensures identical beam quality, and phase at the detector, demonstrates better relative power transmission for Ince-Gaussian beams. This result is consistent with the natural modes supported by a 100 m elliptical core fiber for which a mode ellipticity of ϵ=2 was found to be optimal. The relative power difference is expected to be magnified over longer fiber lengths in favor of Ince-Gaussian modes.

Photonic lantern kW-class fiber amplifier

Pump-limited kW-class operation in a multimode fiber amplifier using adaptive mode control and a photonic lantern front end was achieved. An array of three single-mode fiber inputs was used to adaptively inject the appropriate superposition of input modes in a three-mode gain fiber to achieve the desired mode at the output. Mode fluctuations at high power were compensated by adjusting the relative phase, amplitude, and polarization of the single-mode fiber inputs. The outlook for further power scaling and adaptive-optic compensation is described.

Femtosecond-Laser-Based 3D Printing for Tissue Engineering and Cell Biology Applications

Fabrication of 3D cell scaffolds has gained tremendous attention in recent years because of its applications in tissue engineering and cell biology applications. The success of tissue engineering or cell interactions mainly depends on the fabrication of well-defined microstructures, which ought to be biocompatible for cell proliferation. Femtosecond-laser-based 3D printing is one of the solution candidates that can be used to manufacture 3D tissue scaffolds through computer-aided design (CAD) which can be efficiently engineered to mimic the microenvironment of tissues. UV-based lithography has also been used for constructing the cellular scaffolds but the toxicity of UV light to the cells has prevented its application to the direct patterning of the cells in the scaffold. Although the mask-based lithography has provided a high resolution, it has only enabled 2D patterning not arbitrary 3D printing with design flexibility. Femtosecond-laser-based 3D printing is trending in the area of tissue engineering and cell biology applications due to the formation of well-defined micro- and submicrometer structures via visible and near-infrared (NIR) femtosecond laser pulses, followed by the fabrication of cell scaffold microstructures with a high precision. Laser direct writing and multiphoton polymerization are being used for fabricating the cell scaffolds, The implication of spatial light modulators in the interference lithography to generate the digital hologram will be the future prospective of mask-based lithography. Polyethylene glycol diacrylate (PEG-DA), ormocomp, pentaerythritol tetraacrylate (PETTA) have been fabricated through TPP to generate the cell scaffolds, whereas SU-8 was used to fabricate the microrobots for targeted drug delivery. Well-designed and precisely fabricated 3D cell scaffolds manufactured by femtosecond-laser-based 3D printing can be potentially used for studying cell migration, matrix invasion and nuclear stiffness to determine stage of cancer and will open broader horizons in the future in tissue engineering and biology applications.

Fast modal decomposition for optical fibers using digital holography

Eigenmode decomposition of the light field at the output end of optical fibers can provide fundamental insights into the nature of electromagnetic-wave propagation through the fibers. Here we present a fast and complete modal decomposition technique for step-index optical fibers. The proposed technique employs digital holography to measure the light field at the output end of the multimode optical fiber, and utilizes the modal orthonormal property of the basis modes to calculate the modal coefficients of each mode. Optical experiments were carried out to demonstrate the proposed decomposition technique, showing that this approach is fast, accurate and cost-effective.

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.

Controlling light's helicity at the source: orbital angular momentum states from lasers

Optical modes that carry orbital angular momentum (OAM) are routinely produced external to the laser cavity and have found a variety of applications, thus increasing the demand for integrated solutions for their production. Yet such modes are notoriously difficult to produce from lasers due to the strict symmetry requirements for their creation, together with the need to break the degeneracy in helicity. Here, we review the progress made since 1992 in producing such twisted light modes directly at the source, from gas to solid-state lasers, bulk to integrated on-chip solutions, through to generic devices for on-demand OAM in both scalar and vector forms.This article is part of the themed issue 'Optical orbital angular momentum'.

Integration of helicity-control and pulse-modulation for vortex laser based on a black phosphorus plate

Using a home-made black phosphorus plate (BPP) as handedness controller and Q-switch modulator synchronously, a ~1.6 µm pulsed vortex laser with well-determined handedness is demonstrated in this letter. Stable vortex pulses of LG_{0, + 1}, LG_0,-1, LG_{0, + 2} and LG_0,-2 modes were respectively achieved from compact resonant cavities in this experiment. Such pulsed vortex laser should have promising applications in various fields based on its simple structure, controllable handedness, and carried orbital angular momentum.

Advanced Spatial-Division Multiplexed Measurement Systems Propositions-From Telecommunication to Sensing Applications: A Review

The concepts of spatial-division multiplexing (SDM) technology were first proposed in the telecommunications industry as an indispensable solution to reduce the cost-per-bit of optical fiber transmission. Recently, such spatial channels and modes have been applied in optical sensing applications where the returned echo is analyzed for the collection of essential environmental information. The key advantages of implementing SDM techniques in optical measurement systems include the multi-parameter discriminative capability and accuracy improvement. In this paper, to help readers without a telecommunication background better understand how the SDM-based sensing systems can be incorporated, the crucial components of SDM techniques, such as laser beam shaping, mode generation and conversion, multimode or multicore elements using special fibers and multiplexers are introduced, along with the recent developments in SDM amplifiers, opto-electronic sources and detection units of sensing systems. The examples of SDM-based sensing systems not only include Brillouin optical time-domain reflectometry or Brillouin optical time-domain analysis (BOTDR/BOTDA) using few-mode fibers (FMF) and the multicore fiber (MCF) based integrated fiber Bragg grating (FBG) sensors, but also involve the widely used components with their whole information used in the full multimode constructions, such as the whispering gallery modes for fiber profiling and chemical species measurements, the screw/twisted modes for examining water quality, as well as the optical beam shaping to improve cantilever deflection measurements. Besides, the various applications of SDM sensors, the cost efficiency issue, as well as how these complex mode multiplexing techniques might improve the standard fiber-optic sensor approaches using single-mode fibers (SMF) and photonic crystal fibers (PCF) have also been summarized. Finally, we conclude with a prospective outlook for the opportunities and challenges of SDM technologies in optical sensing industry.

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

We demonstrate the generation of orbital angular momentum (OAM) in a two-mode polarization-maintaining (PM) optical fiber. We combine two linearly polarized modes of PM fiber to generate linearly polarized optical vortex beams with OAM. The average OAM can be finely varied by changing the phase between modes. We have quantitatively measured the resulting OAM to vary between ±1ℏ per photon while varying the relative phase between the LP_11e- and LP_11o-like fiber modes. The modal purity is 97%.

Mode crosstalk matrix measurement of a 1 km elliptical core few-mode optical fiber

The spatial modes of a 1 km elliptical core few-mode optical fiber (6 spatial modes) are analyzed by using liquid crystal on silicon spatial light modulators to measure the fiber's mode crosstalk matrix in Hermite-Gaussian, Laguerre-Gaussian, and linearly polarized spatial mode bases. It is shown that the fiber's spatial modes can be described by Hermite-Gaussian modes, which can propagate 1 km over the optical fiber with <-20  dB (1%) average mode crosstalk even when the fiber has multiple 1 cm diameter bends. The use of elliptical core few-mode optical fibers for space division multiplexing in data centers is discussed.

Photonic lantern adaptive spatial mode control in LMA fiber amplifiers

We demonstrate adaptive-spatial mode control (ASMC) in few-moded double-clad large mode area (LMA) fiber amplifiers by using an all-fiber-based photonic lantern. Three single-mode fiber inputs are used to adaptively inject the appropriate superposition of input modes in a multimode gain fiber to achieve the desired mode at the output. By actively adjusting the relative phase of the single-mode inputs, near-unity coherent combination resulting in a single fundamental mode at the output is achieved.

Ultrafast two-color all-optical transverse mode conversion in a graded-index fiber

We report on experimental conversion of picosecond probe pulses from the fundamental mode (LP01) to the next higher-order mode (LP11) by optically induced transient long-period gratings in a graded-index fiber using subpicosecond control pulses. In contrast to former experiments, the temporally synchronized control (1030 nm) and probe pulses (1250 nm) were easily distinguishable by their wavelengths, allowing for the first direct observation of such an ultrafast transverse mode conversion. Despite a nonperfect pulse duration ratio between control and probe pulses as well as an unavoidable excitation of unwanted higher-order modes, a clear energy conversion of 18% between the LP01-mode and the LP11-mode was observed at 2.3 times lower control pulse energies compared to previous experiments.

Real-time mode decomposition for few-mode fiber based on numerical method

Today a specific attention has been paid to look into the modal characteristics of the high-power laser beam. And the instantaneous monitoring and analyzing on modal content via the mode decomposition technique will provide a novel route. We implement the first-ever experimental investigation on the real-time mode decomposition technique for few-mode laser beam based on stochastic parallel gradient descent algorithm. It will reduce the cost and the complexity of the mode decomposition system. We have succeeded to decompose the mode spectra as well as calculating the beam quality factor at about 9 Hz monitoring rate, while the high agreement between the measured and reconstructed intensity profiles in each frame indicating the high accuracy and stability during the process. By employing a fiber-squeezing-based polarization controller, the modal content under test can be time-varying automatically.

On the scalability of ring fiber designs for OAM multiplexing

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.

Spatiotemporal dynamics of multimode optical solitons

As optical fiber communications and fiber lasers approach fundamental limits there is considerable interest in multimode fibers. In nonlinear science, they represent an exciting environment for complex nonlinear waves. As in single-mode fiber, solitons may be particularly important. Multimode solitons consist of synchronized, non-dispersive pulses in multiple spatial modes, which interact via the Kerr nonlinearity of the fiber. They are expected to exhibit novel spatiotemporal characteristics, dynamics and, like single-mode solitons, may provide a convenient intuitive tool for understanding more complex nonlinear phenomena in multimode fibers. Here we explore experimentally and numerically basic properties and spatiotemporal behaviors of these solitons: their formation, fission, and Raman dynamics.

TEM00 mode content measurements on a passive leakage channel fiber

Mode content measurements with a scanning ring cavity were performed in order to determine the TEM00 mode content of the output beam profile of a resonantly enhanced leakage channel fiber. The measurements were performed at 1.0 and 1.5 μm. In addition, the influence of different bending diameters as well as launching conditions has been investigated. Furthermore, a numerical simulation was used to determine the maximum theoretical TEM00 overlap, if only the fundamental fiber mode is guided. The simulation was also used to analyze how the TEM00 overlap for the case of any additional higher order fiber mode can be determined consistently.

Experimental realization of femtosecond transverse mode conversion using optically induced transient long-period gratings

We present the experimental realization of transverse mode conversion in an optical fiber via an optically induced long-period grating. The transient gratings are generated by femtosecond laser pulses, exploiting the Kerr effect to translate intensity patterns emerging from multimode interference into a spatial refractive index modulation. Since these modulations exist only while the pump beam is present, they can be used for optical switching of transverse modes. As only a localized part of the grating was written at a time and the probe beam was co-propagating with the pump beam the required pulse energies could be reduced to 120 nJ which is about a factor of 600 lower than in previous quasi-continuous-wave experiments. Accompanying numerical simulations allow a better understanding of the involved effects and show excellent agreement to the experimental results.

Measurement of effective refractive index differences in multimode optical fibers based on modal decomposition

We demonstrate the nondestructive measurement of the effective refractive index difference of two arbitrary modes within a multimode optical fiber by utilizing a tunable fiber grating. We use a mechanical grating of variable period to couple the respective modes and measure the mode content at the fiber output based on the correlation filter technique. From the dependence of the coupling efficiency on the grating period, the effective index difference of the modes can be extracted with high accuracy.

Sub-second mode measurement of fibers using C2 imaging

We implement cross-correlated imaging in the frequency domain (fC(2)) in order to reconstruct different modes propagating in a multi-mode optical fiber, and measure their relative powers. Our system can complete measurements in under a second (950 ms), with a maximum signal to noise ratio of 25 dB. The system is capable of group-delay temporal resolution as high as 720 fs, and this number can be tailored for a variety of modal discrimination levels by choice of apodization functions and effective bandwidths of the tunable source we use. Measurements are made on a double-clad test fiber to demonstrate simultaneous reconstruction of six guided modes. Finally, the system is used to optimize alignment into the fiber under test and achieve mono-mode purity > 95%, underscoring the utility of fC(2) imaging for near-real-time modal content analysis.

A new optical surface measurement method with iterative sparsity-constrained threshold phase retrieval algorithm

Due to its low complexity and acceptable accuracy, phase retrieval technique has been proposed as an alternative to solve the classic optical surface measurement task. However, to capture the overall wave field, phase retrieval based optical surface measurement (PROSM) system has to moderate the CCD position during the multiple-sampling procedure. The mechanical modules of CCD movement may bring about unexpectable deviation to the final results. To overcome this drawback, we propose a new PROSM method based on spatial light modulator (SLM). The mechanical CCD movement can be replaced by an electrical moderation of SLM patterns; thus the deviation can be significantly suppressed in the new PROSM method. In addition, to further improve the performance, we propose a new iterative threshold phase retrieval algorithm with sparsity-constraint to effectively reconstruct the phase of wave field. Experimental results show that the new method provides a more simple and robust solution for the optical surface measurement than the traditional techniques and achieves higher accuracy.

Measurement of higher-order mode propagation losses in effectively single mode fibers

We present a direct and nondestructive measurement of the propagation loss of higher-order modes (HOMs) in effectively single-mode fibers. Lossy HOMs are excited by applying local stress at various points alongside a straight single mode fiber. The change of the HOM power as a function of the propagation distance is recorded at the fiber end by performing a modal decomposition with a correlation filter. The results for the HOM propagation loss are compared to simulations yielding very good agreement.

Holographic spatial coherence analysis of a laser

We show that the second-order coherent-mode representation of a stationary quasi-monochromatic scalar light beam can be experimentally characterized by dual-mode holographic interference using an arbitrary basis. Analysis of the laser beam emitted from a stable spherical mirror cavity, using a mismatched Hermite-Gaussian basis, recovered the profiles and powers of a set of cavity modes with the expected spot size, including a hybrid of frequency degenerate modes. Observed near- and far-field irradiance transverse profiles and associated M2 parameter measures confirmed the results.

Generating and measuring nondiffracting vector Bessel beams

Nondiffracting vector Bessel beams are of considerable interest due to their nondiffracting nature and unique high-numerical-aperture focusing properties. Here we demonstrate their creation by a simple procedure requiring only a spatial light modulator and an azimuthally varying birefringent plate, known as a q-plate. We extend our control of both the geometric and dynamic phases to perform a polarization and modal decomposition on the vector field. We study both single-charged Bessel beams as well as superpositions and find good agreement with theory. Since we are able to encode nondiffracting modes with circular polarizations possessing different orbital angular momenta, we suggest these modes will be of interest in optical trapping, microscopy, and optical communication.

Spatial properties of coaxial superposition of two coherent Gaussian beams

In this paper, we explore theoretically and experimentally the laser beam shaping ability resulting from the coaxial superposition of two coherent Gaussian beams (GBs). This technique is classified under interferometric laser beam shaping techniques contrasting with the usual ones based on diffraction. The experimental setup does not involve the use of some two-wave interferometer but uses a spatial light modulator for the generation of the necessary interference term. This allows one to avoid the thermal drift occurring in interferometers and gives a total flexibility of the key parameter setting the beam transformation. In particular, we demonstrate the reshaping of a GB into a bottle beam or top-hat beam in the focal plane of a focusing lens.

Reconstruction of laser beam wavefronts based on mode analysis

We present the reconstruction of a laser beam wavefront from its mode spectrum and investigate in detail the impact of distinct aberrations on the mode composition. The measurement principle is presented on a Gaussian beam that is intentionally distorted by displaying defined aberrations on a spatial light modulator. The comparison of reconstructed and programmed wavefront aberrations yields excellent agreement, proving the high measurement fidelity.

Modal characterization of fiber-to-fiber coupling processes

We present a detailed experimental investigation of a fiber-to-fiber coupling process by characterizing the mode content at the output of the system. In our experiment a single-mode fiber is transversally scanned with respect to a multimode fiber, revealing position-dependent higher-order mode excitation. The outlined measurement system can be used for automated optimization of fundamental mode content and beam quality. Additionally, our approach characterizes the modal transmission properties of the multimode waveguide in its present state and is hence of high relevance for the conception of transport fibers and fiber laser systems.

Diffractive optical elements for mode-division multiplexing of temporal signals with the aid of Laguerre-Gaussian modes

Optical aspects of space-division multiplexing with orthogonal modes of coherent light were considered in theory and experiments with the coherent optical correlator. We resorted to the mathematical tool of generating functions and technologies of diffractive optical elements to implement complex spatial filters matched to rotationally symmetrical transverse modes. Successful multiplexing and demultiplexing in free-space transmission of low-frequency temporally modulated signals through different spatial modes was demonstrated. Experimental results show low cross talk between different mode channels and feasibility of further applications in multimode fiber optical communication data links.

Exciting higher-order radial Laguerre-Gaussian modes in a diode-pumped solid-state laser resonator

In this paper we experimentally demonstrate the intracavity generation of selected Laguerre-Gaussian modes of variable radial order, from 0 to 5. Our technique requires only an amplitude mask made up of absorbing rings to be placed inside the cavity, with the ring radii selected to coincide with the zeros of the desired Laguerre-Gaussian mode. We demonstrate high mode purity and a mode volume proportional to the order of the mode. Our results suggest a possible route to high brightness diode-pumped solid-state laser sources.

Mode resolved bend loss in few-mode optical fibers

We present a novel approach to directly measure the bend loss of individual modes in few-mode fibers based on the correlation filter technique. This technique benefits from a computer-generated hologram performing a modal decomposition, yielding the optical power of all propagating modes in the bent fiber. Results are compared with rigorous loss simulations and with common loss formulas for step-index fibers revealing high measurement fidelity. To the best of our knowledge, we demonstrate for the first time an experimental loss discrimination between index-degenerated modes.