Shaping the light beam is always essential for laser technology and its applications. Among the shaping technologies, shaping the laser in its Fourier domain is a widely used and effective method, such as a pulse shaper, or a 4f system with a phase mask or an iris in between. Orbital angular momentum (OAM) modes spectrum, the Fourier transform of the light field in azimuth, provides a perspective for shaping the light. Here, we propose and experimentally demonstrate a shaping strategy for the azimuthal field by modulating the complex amplitude of the OAM mode spectrum. The scheme utilizes multi-plane light conversion technology and consists only of a spatial light modulator and a mirror. Multiple functions, including beam rotating, beam splitting/combining in azimuth, and OAM mode filtering, are demonstrated. Our work provides a compact and programmable solution for modulating the OAM mode spectrum and shaping beams in azimuth.
KEYWORDS: Interferograms, Angular momentum, Cameras, Signal intensity, Receivers, Interferometry, Superposition, Signal detection, Holography, Signal processing
Orbital angular momentum (OAM) spectrum diagnosis is a fundamental building block for diverse OAM-based systems. Among others, the simple on-axis interferometric measurement can retrieve the amplitude and phase information of complex OAM spectra in a few shots. Yet, its single-shot retrieval remains elusive, due to the signal–signal beat interference inherent in the measurement. Here, we introduce the concept of Kramers–Kronig (KK) receiver in coherent communications to the OAM domain, enabling rigorous, single-shot OAM spectrum measurement. We explain in detail the working principle and the requirement of the KK method and then apply the technique to precisely measure various characteristic OAM states. In addition, we discuss the effects of the carrier-to-signal power ratio and the number of sampling points essential for rigorous retrieval and evaluate the performance on a large set of random OAM spectra and high-dimensional spaces. Single-shot KK interferometry shows enormous potential for characterizing complex OAM states in real time.
Abruptly autofocusing beams (AAFBs) exhibit unique focusing properties that, such beams keep a low intensity profile during propagation, and their intensity can be increased by several orders of magnitude when reaching the focus. Most of previous studies concerned about the trajectory and focusing properties of AAFBs. Here, we propose and demonstrate an alternative method for constructing multi-focus abruptly autofocusing beams (MFAAFBs). This is accomplished by designing the AAFBs of each focus and superimposing the corresponding wavefronts in spatial domain. By modulating the complex amplitude of the light field, we can manipulate the beams to propagate along varied pre-designed trajectories and focus on multiple focal points. Additionally, we show that the number of generated foci, and other characteristics of each focal point (such as position in 3D space, peak intensity, size of the focal spot, and the subsequent oscillation) are tunable. We also discuss several possible experimental means to generate MFAAFBs, among which a diffractive optical element (DOE) with discrete amplitude and phase modulations is practical and effective, verified by our simulation results. This method is expected to further expand the application of AAFBs and the field of photonic integration.
Optical vortex beams carrying orbital angular momentum are being widely investigated for boosting the information capacity of communication systems by virtue of their unbounded state space for spatial mode division multiplexing or high-dimensional encoding. Vortex mode sorters are a critical component in such systems and a spiral transformation scheme working in the paraxial regime for vortex mode sorting has been proposed very recently to achieve high modal resolution with unity efficiency. Here we modify the spiral transformation scheme by developing a phase corrector in the nonparaxial regime, which is confirmed to have a more accurate phase-correcting function in implementing the spiral transformation and eventually lead to a better mode separation, especially in the case of a compact vortex mode sorter. Based on the above principle, a home-made compact vortex mode sorter is demonstrated by integrating the two phase elements implementing the spiral transformation onto the opposite sides of a thin quartz plate as flat diffractive optical elements, which achieves high-resolution and high-efficiency vortex mode sorting as expected. The modified optical spiral transformation and the compact design of vortex mode sorter based on this scheme therefore provide a much better tool for the effective mode separation, which can enable new applications in both classical and quantum information systems based on vortex modes.
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