^{1,a)}, Y. K. Ho

^{1}, Ch. X. Tang

^{2}and W. Wang

^{3}

### Abstract

We analyze the axial electric field intensity distribution and the phase velocity distribution of high-order Hermite-Gaussian (HG) mode laser beams. Using a three-dimensional test particle simulation, the numerical results of electrons accelerated by Hermite-Gaussian , and mode laser beams are presented. It is established that electrons can be more favorably captured and accelerated in an odd high-order Hermite-Gaussian mode laser beam.

This work is supported partly by the National Natural Science Foundation of China under Contract Nos. 10475018 and 10335030.

I. INTRODUCTION

II. HIGH-ORDER HERMITE-GAUSSIAN MODE LASER BEAM EQUATIONS

III. LONGITUDINAL ELECTRIC FIELD DISTRIBUTION

IV. PHASE VELOCITY DISTRIBUTION

V. NUMERICAL RESULTS

VI. CONCLUSIONS AND DISCUSSIONS

### Key Topics

- Laser beams
- 38.0
- Electric fields
- 22.0
- Speed of light
- 5.0
- Continuous lasers
- 4.0
- Polynomials
- 4.0

## Figures

(Color online) Contour maps of the axial electric field amplitude of some low-order HG laser beams, with and . (a) Shows the mode in plane and (b) shows as a function of along the line . (c) and (d) show the mode, (e) and (f) the mode.

(Color online) Contour maps of the axial electric field amplitude of some low-order HG laser beams, with and . (a) Shows the mode in plane and (b) shows as a function of along the line . (c) and (d) show the mode, (e) and (f) the mode.

The minimum phase velocity distribution of the axial electric field . Values are distinguished by the level of shading, dark indicating small values, and bright indicating large. (a) Is for the laser beam of the mode with . The top inset of (a) shows as a function of along line (solid line) and along line , (dotted line). The right inset of (a) shows as a function of along line (solid line) and along line , (dotted line). (b) Shows the corresponding quantities for a laser beam with the mode.

The minimum phase velocity distribution of the axial electric field . Values are distinguished by the level of shading, dark indicating small values, and bright indicating large. (a) Is for the laser beam of the mode with . The top inset of (a) shows as a function of along line (solid line) and along line , (dotted line). The right inset of (a) shows as a function of along line (solid line) and along line , (dotted line). (b) Shows the corresponding quantities for a laser beam with the mode.

(Color online) The phase velocity along the trajectory and corresponding electric field amplitude distribution for different order mode laser beams with and . The solid lines, dotted lines, dashed lines, and dot-dashed lines are for , respectively. (a) The phase velocity of along the trajectory as a function of along the line . (b) The amplitude of as a function of along the line . (c) The phase velocity of parallel with the trajectory as a function of along line . (d) The amplitude as a function of along line .

(Color online) The phase velocity along the trajectory and corresponding electric field amplitude distribution for different order mode laser beams with and . The solid lines, dotted lines, dashed lines, and dot-dashed lines are for , respectively. (a) The phase velocity of along the trajectory as a function of along the line . (b) The amplitude of as a function of along the line . (c) The phase velocity of parallel with the trajectory as a function of along line . (d) The amplitude as a function of along line .

(Color online) The phase velocity parallel with the trajectory as a function of along line for different beam waist (solid line), (dashed line), and (dotted line). The dot-dashed line denotes the speed of light . (a) Shows the mode, and (b) shows the mode.

(Color online) The phase velocity parallel with the trajectory as a function of along line for different beam waist (solid line), (dashed line), and (dotted line). The dot-dashed line denotes the speed of light . (a) Shows the mode, and (b) shows the mode.

Dependence of the maximum net energy exchange on the incident angle . Triangles indicate the mode, circles are the mode, and squares are the , where , , and . The incoming momentum is (a) , (b) , and (c) .

Dependence of the maximum net energy exchange on the incident angle . Triangles indicate the mode, circles are the mode, and squares are the , where , , and . The incoming momentum is (a) , (b) , and (c) .

(Color online) Typical electron dynamics for the case that the electron gets an energy gain of in a mode laser beam with , , and . (a) The distribution of of a mode laser beam in the plane, where is the maximum longitudinal electric field amplitude in the whole time range. Values are distinguished by the level of shading, dark indicating small values and bright indicating large values. The dotted line shows the electron trajectory in the plane. (b) Electron energy as a function of . (c) The longitudinal (dotted line) and transverse (solid line) electric fields experienced by the electron as a function of . Other parameters are , , and .

(Color online) Typical electron dynamics for the case that the electron gets an energy gain of in a mode laser beam with , , and . (a) The distribution of of a mode laser beam in the plane, where is the maximum longitudinal electric field amplitude in the whole time range. Values are distinguished by the level of shading, dark indicating small values and bright indicating large values. The dotted line shows the electron trajectory in the plane. (b) Electron energy as a function of . (c) The longitudinal (dotted line) and transverse (solid line) electric fields experienced by the electron as a function of . Other parameters are , , and .

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