Determining the phase-energy coupling coefficient in carrier-envelope phase measurements

Area of Science:

• Physics
• Optical Engineering
• Quantum Optics

Background:

• f-to-2f interferometers are crucial for measuring and stabilizing the carrier-envelope (CE) phase.
• White-light generation in sapphire plates is a common method for f-to-2f interferometry.
• Laser energy fluctuations are a known source of error in CE phase measurements.

Purpose of the Study:

• To quantify the effect of laser energy fluctuations on CE phase accuracy in f-to-2f interferometers.
• To determine the coupling coefficient between laser pulse energy and CE phase.
• To provide insights for improving CE phase stabilization techniques.

Main Methods:

• Utilized an in-loop f-to-2f interferometer to modulate pulse energy.
• Employed an out-loop interferometer to measure the resulting CE phase variation.
• Quantified the CE phase shift in response to controlled laser energy modulation.

Main Results:

• A direct relationship between laser energy fluctuation and CE phase shift was established.
• A 1% change in laser energy was found to induce a 160 mrad shift in the CE phase.
• The coupling coefficient between CE phase and laser energy was determined.

Conclusions:

• Laser energy stability is critical for accurate CE phase measurement and stabilization in f-to-2f interferometers.
• The quantified coupling effect provides a basis for developing more robust stabilization schemes.
• Understanding this energy-phase coupling is essential for advancing precision optical metrology.