Implementation of the spatial and the temporal cross-ambiguity function for waveguide fields and optical pulses

Area of Science:

• Optics and Photonics
• Waveguide Theory
• Optical Metrology

Background:

• Space-time duality is a fundamental concept in physics.
• The cross-ambiguity function is a powerful tool for signal analysis.
• Optical techniques are crucial for high-resolution measurements.

Purpose of the Study:

• To propose experimental setups for optical implementation of the cross-ambiguity function.
• To explore its applications in both spatial and temporal domains.
• To leverage space-time duality for novel optical measurements.

Main Methods:

• Utilizing space-time duality principles.
• Designing one- and two-dimensional experimental configurations.
• Relating spatial cross-ambiguity to waveguide coupling efficiency.
• Connecting temporal cross-ambiguity to spectrogram and frequency-resolved optical gating (FROG) techniques.

Main Results:

• Demonstration of optical implementation of the cross-ambiguity function.
• Establishment of a link between spatial cross-ambiguity and optical waveguide coupling.
• Establishment of a link between temporal cross-ambiguity and optical pulse characterization methods.
• Validation of the proposed experimental setups in one and two dimensions.

Conclusions:

• The proposed optical methods provide a unified framework for analyzing signals in both space and time.
• The cross-ambiguity function has practical applications in integrated optics and ultrafast optics.
• Space-time duality offers a promising avenue for advanced optical measurement techniques.