Derong Li

Pulse broadening of the femtosecond pulses in a Gaussian beam passing an angular disperser

A general analytical formula has been found to describe the evolution of the pulse width of the femtosecond pulses in a Gaussian beam after passing an angular disperser without the assumption of well collimation. This formula is experimentally verified by measuring the pulse width with an autocorrelator based on two-photon absorption. It is found that the effect of the spectral lateral walk-off and group delay dispersion on the pulse-width evolution, and its dependence on the distance traveled, are substantially different when the beam has not been well collimated than from when it has been collimated. These differences result from the decaying nature of the angular dispersion of the Gaussian beam sent across a distance.

Analysis of the dispersion compensation of acousto-optic deflectors used for multiphoton imaging

The acousto-optic deflector (AOD) is highly preferred in laser scanning microscopy for its fast scanning ability and random-addressing capability. However, its application in two-photon microscopy is frustrated by the dispersion of the AOD, which results in beam distortion and pulse lengthening. We report the analysis of simultaneous compensation for the angular dispersion and temporal dispersion of the AOD by merely introducing a single dispersive element such as a prism or a grating. Besides serving as a scanner, the AOD is also a part of the compressor pair by integrating the dispersive nature of the AO interaction. This compensation principle is effective for both one-dimensional (1-D) AOD and two-dimensional (2-D) AOD scanning. Switching from a 1-D to a 2-D system requires proper optical alignment with the compensation element, but does not involve any new components. Analytical expressions are given to illustrate the working principle and to help with understanding the design of the system. Fluorescence images of beads and cells are shown to demonstrate the performance of two-photon microscopy when applying this compensated 2-D AOD as scanner.

Dispersion characteristics of acousto-optic deflector for scanning Gaussian laser beam of femtosecond pulses.

Pulse evolution after the acousto-optic deflector (AOD) and its dependence on AOD parameters is not clear, but is important to AOD applications in scanning microscopy. By considering the abnormal Bragg AOD as a combination of a dispersion media and a diffraction grating with Littrow structure, the dispersion characteristics of AOD when scanning Gaussian laser beam of femtosecond pulses were analyzed. Pulse width about AOD parameters was explored theoretically and verified with experiments. It is found that after exiting AOD, the pulse width of laser beam either merely decreases or first decreases and then increases before it finally goes steady with the propagation distance, depending on the interaction between the material dispersion and angular dispersion.

Analysis of fast axial scanning scheme using temporal focusing with acousto-optic deflectors

Multiphoton microscopy has gained broad application in biology and medicine in the recent decade by assessing biological structure and function with high spatial resolution. Recently it has achieved fast two-dimensional x–y imaging by using inertia-free scanning mechanisms. However, the axial scanning speed is severely limited by mechanical inertia. This paper proposes a fast axial scanning scheme using temporal focusing implemented with an inertia-free scanning device, such as an acousto-optic device (AOD), and presents an experimental demonstration of two-photon axial scanning over a 9 µm range using AODs operated from 80 to 120 MHz. A theoretical analysis provides the detailed characteristics of this method. The effects of both the ratio of collimating lens to objective lens focal lengths or magnification (M), and the degree of group delay dispersion (GDD) in the light source on the temporal focusing and axial scanning range are described by theory and experiments.

Beam spot size evolution of Gaussian femtosecond pulses after angular dispersion

Beam spot size evolution of spatially Gaussian femtosecond laser pulses after angular dispersion is analyzed and verified with experiments. A general analytical expression for beam spot size at arbitrary propagation distances is obtained, which indicates that beam spot size evolution after angular dispersion is determined by the direct interaction of spectral lateral walk-off by angular dispersion and the intrinsic divergence of the Gaussian beam. This work reveals insights into the propagation of Gaussian femtosecond laser pulses and beams after angular dispersion and may be important for the generation and application of femtosecond laser pulses.

Propagation dependence of chirp in Gaussian pulses and beams due to angular dispersion

The chirp acquired by a Gaussian ultrashort pulse due to angular dispersion, unlike that of plane waves, increases nonlinearly with propagation distance and eventually asymptotes to a constant. However, this interesting result has never been directly measured. In this Letter, we use two-dimensional spectral interferometry to measure the propagation dependence of the chirp for Gaussian ultrashort pulses and beams with angular dispersion. The measured chirp as a function of propagation distance agreed well with theory. This work verifies both an equation and a measurement technique that will be useful for predicting or determining the pulses chirp in ultrafast optics experiments that contain angular dispersion.

A generalized analysis of femtosecond laser pulse broadening after angular dispersion

We derive a general analytical expression for the width of a femtosecond laser pulse after passing through an angular dispersion device, valid for the plane wave, spherical wave, and Gaussian beam models. This expression is a simple function of two effects: spectral lateral walkoff and group delay dispersion. Plane waves and spherical waves experience no spectral lateral walkoff, as the beams are not explicitly limited in space. The group delay dispersion (GDD) of a Gaussian beam is similar to that of a plane wave at distances much less than the Rayleigh length, and similar to that of the spherical wave at distances far exceeding the Rayleigh length. The GDD of the spherical wave and Gaussian beam approach a constant value at large distances, which is entirely determined by the dispersion parameters of the optical component and the distance between disperser and source point or beam waist. The width of a plane wave pulse always increases in proportion to the propagation distance. The width of a spherical wave or Gaussian beam pulse widens rapidly at first, but soon levels off to nearly constant value.

Position of the prism in a dispersion-compensated acousto-optic deflector for multiphoton imaging

The performance of a dispersion-compensated acousto-optic deflector (AOD) for steering femtosecond laser pulses was examined with the prism located before or after the AOD, which is regarded as prism-AOD and AOD-prism, respectively. Comparisons are made over parameters including the spot spatial pattern, output pulse width, scanning linearity, the field of view, and the transmission rate. Fluorescence images of 170 nm diameter beads and cells were measured to provide an overall evaluation for these femtosecond laser beam scanning configurations. On the basis of these experiments, the prism-AOD configuration is concluded to be more advantageous for the purpose of simultaneous compensation for the spatial and temporal dispersion.

Evolution of the frequency chirp of Gaussian pulses and beams when passing through a pulse compressor

The evolution of the frequency chirp of a laser pulse inside a classical pulse compressor is very different for plane waves and Gaussian beams, although after propagating through the last (4th) dispersive element, the two models give the same results. In this paper, we have analyzed the evolution of the frequency chirp of Gaussian pulses and beams using a method which directly obtains the spectral phase acquired by the compressor. We found the spatiotemporal couplings in the phase to be the fundamental reason for the difference in the frequency chirp acquired by a Gaussian beam and a plane wave. When the Gaussian beam propagates, an additional frequency chirp will be introduced if any spatiotemporal couplings (i.e. angular dispersion, spatial chirp or pulse front tilt) are present. However, if there are no couplings present, the chirp of the Gaussian beam is the same as that of a plane wave. When the Gaussian beam is well collimated, the introduced frequency chirp predicted by the plane wave and Gaussian beam models are in closer agreement. This work improves our understanding of pulse compressors and should be helpful for optimizing dispersion compensation schemes in many applications of femtosecond laser pulses.