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Propagation of short pulses Jörgen Larsson, Fysiska Instutionen Lunds Tekniska Högskola

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Propagation of short pulses Jörgen Larsson, Fysiska Instutionen Lunds Tekniska Högskola

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Distributed feedback laser

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Femtosecond X-Ray and Electron Source at the SLAC Linac 80 fs 8-10 keV 1x10 7 ph./pulse (2% bw.) 10 Hz Bending compress. <100 fsec ~1 Å Add 12-meter chicane compressor in linac at 1/3-point (9 GeV) Damping Ring 9 ps 0.4 ps 50 ps 1 GeV 20-50 GeV FFTB undulator femtosecond laser (synchronized) Short-pulse accelerator sources SPPS www-ssrl.slac.stanford.edu/jhhome.html

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Femtosecond fiber laser

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Splitters/Couplers

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Femtosecond fiber laser

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Wavelength Division Multiplexers

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Bragg grating

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Bandpass filter for fiber optics

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Manufacturing Bragg gratings

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Representation of short pulses Gaussian pulses Carrier EnvelopeAmplitude Frequency

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Representing ”chirp”

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Time-bandwidth product- Transform limited pulses If the pulse is chirped it is wider in the temporal domain Gaussian pulse

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Propagation of a range of frequencies After the pulse has propagated the distance x

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Propagation of a range of frequencies

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Group velocity dispersion

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Propagation of a range of frequencies

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GVD wavelength form Whiteboard

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Group velocity dispersion compensation All matererials show a positive GVD in the visible range – hence various set-ups have been deviced for GVD compensation

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GVD compensation using prisms

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Chirped mirrors

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Dispersion compensation using Bragg gratings

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Time-varying refractive indes Self-phase modulation FIG 2.18

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Time-varying refractive indes Self-phase modulation

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Passive modelocking Kerr lens

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Matrix representaiton of beam propagation

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Beam propagation in a linear cavity

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Stability analysis of Kerr-lens mode- locked laser Propagation matrix General stability criterion 2-mirror cavity Stability criterion

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Beampropagation in a folded cavity (out of plane – approx for in-plane)

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Beampropagation including Kerr- lens

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