Femtosecond spatial pulse shaping at the focal plane

Diffraction efficiency management by complex binary gratings

The diffraction efficiencies of a complex binary diffraction grating with a rectangular profile are controlled through the steps' phases, amplitudes, and duty cycle, based on analytical expressions. It is demonstrated that the zeroth-diffraction order can be canceled for any arbitrary value of the duty cycle, provided that a π-phase difference is imposed, along with a specific ratio of the steps' amplitudes. This feature is not feasible for separated amplitude-only and phase-only rectangular binary gratings in the context of one-dimensional gratings. In this framework, a key analytic relationship between the duty cycle and the steps' amplitude ratio is derived, allowing the design of such gratings with this desired feature across a wide range of conditions, not limited to a duty cycle of 0.5. Concerning the higher diffraction orders, it is proved that their intensities cancel or maximize for fixed duty cycle no matter the amplitude and phase values of the steps. The intensity of the m-th diffraction order possesses m maxima and m - 1 zeros on the full range of the duty cycle. All these features were corroborated experimentally. The broad insight of such a grating allows the design of gratings with diffraction efficiencies tailored for specific applications.

Modified biological spectrum and SNR of Laguerre-Gaussian pulsed beams with orbital angular momentum in turbulent tissue

We propose a modified biological spectrum that contains both short length-scale and long length-scale to study light propagation through turbulent biological tissue. Based on the two-scale modified biological spectrum, we derive an analytic expression of the two-frequency mutual coherence function of Laguerre-Gaussian pulsed beam and establish a model of the signal-to-noise ratio (SNR) of Laguerre-Gaussian pulsed beam carrying orbital angular momentum in turbulent biological tissue. The results show that the modified biological spectrum agrees well with experimental results. In addition, the structural length-scale of biological tissue has a significant influence on the bandwidths and SNR of orbital angular momentum states. This work provides theoretical preparation for more accurately medical diagnosis and optical imaging.

Multispectral Management of the Photon Orbital Angular Momentum

We report on a programmable liquid crystal spatial light modulator enabling independent orbital angular momentum state control on multiple spectral channels. This is done by using electrically controllable "topological pixels" that independently behave as geometric phase micro-optical elements relying on self-engineered liquid crystal defects. These results open interesting opportunities in optical manipulation, sensing, imaging, and communications, as well as information processing. In particular, spectral vortex modulation allows considering singular spatiotemporal shaping of ultrashort pulses which may find applications in many areas such as material processing, spectroscopy, or elementary particles acceleration.

Simulated propagation of ultrashort pulses modulated by low-Fresnel-number lenses using truncated series expansions

Numerical simulation of the paraxial propagation of pulses modulated by lenses is demonstrated using the Laguerre-Gaussian (LG) series expansion method. This technique allows for relatively swift evaluation of the structures of several individual monochromatic fields transformed by arbitrary amplitude and phase modulating pupil functions, which can be superimposed via the inverse Fourier transform to determine the structure of a modulated pulse. The transformation of ultrashort pulses by spherical, diffractive, and conical lenses is simulated using this method, which is particularly effective with the use of vector and matrix techniques available in many popular numerical software packages. A description of the convergence of the LG series to the results of the conventional integral techniques is presented for a conical lens under illumination by a continuous wave from which a simple but robust criterion for axial accuracy in problems of circular symmetry is suggested.