The M2 parameter in space beam quality factor

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The M2 parameter in space---beam quality factor

• Chengao Wang

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Review of the fundamental Gaussian modes in laser
beams
Amplitude distribution at beam waist

Amplitude distribution at any position
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Review of the fundamental Gaussian modes in laser
beams

• Rayleigh Range

Propagation of the beam
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Review of the fundamental Gaussian modes in laser
beams

• In the far field,
• Divergence angle

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Review of the fundamental Gaussian modes in laser
beams

• Rewrite the propagation of the beam using the
  definition of the divergence angle

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The interpretation for beam quality

• How the beam diverges in the far-field and how it
  focuses in the near-field

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Uncertainty Relationship
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Uncertainty relationship in Gaussian beams
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Uncertainty relationship in Gaussian beams

• By Fourier transformation

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Uncertainty relationship in Gaussian beams
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Definition of the parameters in real laser beams

• spot size
• Divergence angle

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The definition of M

• M is named as times diffraction limit number,
  which characterize the beam quality for a real
  laser beam

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Propagation function for a real laser beam


For Gaussian beam

For real laser beams
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Introduction to the instrument
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Applications

• Quality control
• Process control
• Product or process development

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Thanks