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Shortening a laser pulse at the focus of a lens

This study explores pulse lengthening and shortening phenomena at the focus of a lens through Fourier formulation. The axial temporal history and effects of Group Velocity Delay (GVD) and Self-Phase Modulation (SPM) are examined using numerical simulations to provide insights for experimental outlook. The potential for generating few-cycle pulses with a simpler setup is highlighted.

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Shortening a laser pulse at the focus of a lens

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  1. Shortening a laser pulse at the focus of a lens Yuelin LiAccelerator Systems DivisionArgonne National Laboratoryylli@aps.anl.gov

  2. Content • Introduction • Pulse lengthening at lens focus • Fourier formulation of the problem • Axial temporal history • Pulse shortening due to GVDE and SPM • Numerical simulation • Experiment outlook • Summary

  3. Content • Introduction • Pulse lengthening at lens focus • Fourier formulation of the problem • Axial temporal history • Pulse shortening due to GVD • Numerical simulation • Experiment outlook • Summary

  4. Pulse lengthening due to Group Velocity Delay Z. Bor, Opt. Lett. 15, 119 (1989)

  5. Content • Introduction • Pulse lengthening at lens focus • Fourier formulation of the problem • Axial temporal profile • Pulse shortening due to GVD, with SPM • Numerical simulation • Experiment outlook • Summary

  6. Formula of the problem: Fourier optics • Full wave optics (Fresnel diffraction) adapted from Kempe et al. (JOSA B 9, 1158 (1992)) • Group velocity dispersion and group velocity delay effect considered up to the second order

  7. On axis formula Field at focus, on axis U: field in frequency domain representation at the focus f : is the focal length r: ray location Kl, ka: wave vectors in the lens and air, n: refractive index in the lens. A(w): input filed (homogeneous) in the frequency domain. G , Lens transfer function d r f Inverse Fourier transform a=a(t)=F-1A(w) and g=g(r,t)=F-1G(r,w)

  8. Pulse with no SPM For a=a0exp(-2ln2t2/t2), no SPM, Relative delay between pulse slices due to Group Velocity DElay (GVDE) Chirping and broadening due to Group Velocity DIspersion (GVDI) GVDE and GVDI have both been studied. L=4kcT/t2.

  9. Pulse with SPM Assume smaller bandwidth and d2w/dn2=0, Max phase modulation, over lens of thickness d: Interference due to GVDE Delay due to GVDE Case not been studied. L=4kcT/t2.

  10. Pulse shortening at the focus Li and Crowell, Opt. Lett. 32, 92 (2007).

  11. Parameter tf/ti Max GVDE to pulse duration ratio rm=2p rm=3p Max phase modulation

  12. Numerical simulation Li and Crowell, Opt. Lett. 32, 92 (2007).

  13. Content • Introduction • Pulse lengthening at lens focus • Fourier formulation of the problem • Axial temporal history • Pulse shortening due to GVD • Numerical simulation • Experiment outlook • Summary

  14. C D AL SF ZSL PP ODL An envisaged experiment

  15. Summary • Pulse shortening demonstrated in simulation, up to 5 time shortening observed • Potential for few cycle pulse generation with simpler setup

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