Spatial and temporal pulse propagation for dispersive paraxial optical systems

Area of Science:

• Optics and Photonics
• Quantum Electronics

Background:

• Existing methods use 4x4 matrices for paraxial optical systems.
• Modeling complex spatial-temporal couplings and dispersion is challenging.

Purpose of the Study:

• Extend existing formalisms for pulse propagation.
• Incorporate non-separable spatial-temporal couplings and quadratic phase dispersion.
• Develop a simplified propagation formula for ultrashort Gaussian pulses.

Main Methods:

• Extended the 4x4 ray-pulse matrix formalism to 6x6 matrices.
• Derived an eikonal for a modified Huygens integral in the Fresnel approximation.
• Applied the formalism to paraxial optical systems with dispersion.

Main Results:

• Successfully incorporated non-separable spatial-temporal couplings in both transverse dimensions.
• Included temporal dispersive effects up to a quadratic phase.
• Presented a simple formula for ultrashort Gaussian pulse propagation.

Conclusions:

• The extended 6x6 matrix formalism accurately models complex dispersive paraxial optical systems.
• The derived eikonal and simplified formula offer practical tools for pulse propagation analysis.
• This work advances the understanding and simulation of ultrashort pulse behavior in optical systems.