Space-time duality and the theory of temporal imaging

1994/01/01 by B.H. Kolner, Brian H. Kolner · 25 citations
Physics and Astronomy · Engineering · #Photorefractive and Nonlinear Optics #Advanced Optical Imaging Technologies #Photonic and Optical Devices

paper · doi:10.1109/3.301659

Abstract

There exists a beautiful duality between the equations that describe the paraxial diffraction of beams confined in space and the dispersion of narrow-band pulses in dielectrics. We will see that this duality leads naturally to the conclusion that a quadratic phase modulation in time is the analog of a thin lens in space. Therefore, by a suitable combination of dispersion and quadratic phase modulation (now a "time lens"), we can synthesize the time-domain analog of an imaging system. Such a temporal-imaging system can magnify time waveforms in the same manner as conventional spatial-imaging systems magnify scenes. We analyze this space-time duality and derive expressions for the focal length and f-number of a time lens. In addition, the principles of temporal imaging are developed and we derive time-domain analogs for the imaging condition, magnification ratio, and impulse response of a temporal-imaging system.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Cited by

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• Multi-wavelength arbitrary waveform generation through spectro-temporal\n unitary transformations
• Ultra-fast optical time-domain transformation techniques
• Temporal Paraxial Optics under Adiabatic Modulations
• Quantum time reflection and refraction of ultracold atoms
• Dynamically Preparing Robust Bell States in Su-Schrieffer-Heeger Systems
• Demonstration of a photonic time-frequency Fourier transform and temporal double slit using atomic quantum memory
• Nonresonant background suppression for coherent anti-Stokes Raman scattering microscopy using a multi-wavelength time-lens source. [europepmc]
• Panoramic-reconstruction temporal imaging for seamless measurements of slowly-evolved femtosecond pulse dynamics. [europepmc]
• On-chip temporal focusing of elastic waves in a phononic crystal waveguide. [europepmc]
• Multi-color background-free coherent anti-Stokes Raman scattering microscopy using a time-lens source. [europepmc]
• Single-shot real-time femtosecond imaging of temporal focusing. [europepmc]
• Field-programmable silicon temporal cloak. [europepmc]
• Raman Techniques: Fundamentals and Frontiers. [europepmc]
• Nonlinearity- and dispersion- less integrated optical time magnifier based on a high-Q SiN microring resonator. [europepmc]
• Broadband frequency translation through time refraction in an epsilon-near-zero material. [europepmc]
• Fibers-based temporal super-resolved imaging. [europepmc]
• Full recovery of ultrafast waveforms lost under noise. [europepmc]
• Rotation Active Sensors Based on Ultrafast Fibre Lasers. [europepmc]
• Single-Photon Level Dispersive Fourier Transform: Ultrasensitive Characterization of Noise-Driven Nonlinear Dynamics. [europepmc]
• Bright and dark Talbot pulse trains on a chip. [europepmc]
• Experimental realization of temporal refraction and reflection in elastic beams. [europepmc]

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