The right tool for a given measurement: An overview The pulse train The pulse of a train The single amplified pulse The methods Correlations Femtonitpicker -- Picasso Spider Cross-correlation Frog

The right tool for a given measurement An overview THE PULSE TRAIN TOOLS: Simple analog oscilloscope and frequency doubling crystal. Electronic Spectrum analyzer Spectrometer What to look for? Both fundamental and second harmonic: a straight line. No sideband and higher harmonics Continuous spectrum, central wavelength MANY OPPORTUNITIES TO CHEAT WITH ANY METHOD The more sophisticated the instrument, the easier it is for the manufacturer to cheat. There is no point in taking an autocorrelation, frog of spider if the above conditions are not satisfied.

The right tool for a given measurement An overview THE PULSE TRAIN Both fundamental and second harmonic: a straight line. Electronic Spectrum analyzer

The right tool for a given measurement An overview THE PULSE TRAIN What we should not see: Modulation of the train on a ms scale Q-switched-mode-locked train (Shows as a sideband on spectrum analyzer on a 100 KHz scale)

The right tool for a given measurement An overview THE PULSE OF A TRAIN Do you want to tune the laser to get the shortest pulse? TOOLS: Scanning autocorrelator, Intensity, interferometric, spatially encoded Spider Tuning a laser oscillator Tuning a high power system Single pulse characterization at high repetiton rate: SPIDER

The right tool for a given measurement An overview THE SINGLE AMPLIFIED PULSE Short pulse Stretched pulse Complex pulse shapc Single shot autocorrelations Cross-correlations (intensity and interferometric) Frog (high dynamic range) Femtonitpicker (Picasso) Spider Spider 1 KHz WOULD NOT WORK WITH FROG Basic difference between FROG and SPIDER: FROG: 2D frames Spider Frog SPIDER: 2 x 1D frames FASTER: pulse reconstruction at 1 kHz

The right tool for a given measurement An overview THE SINGLE AMPLIFIED PULSE Ultra- Short pulse Complex pulse shapc Single shot autocorrelations Cross-correlation Femtonitpicker (Picasso) Tadpole SEA- SPIDER 1 KHz WOULD NOT WORK WITH FROG Not so fast as spider: 2D frames Frog (high dynamic range) Spider

The choice of the optimum metrology method for a given problem Playing with analogies…. More serious stuff: what is a pulse what is a pulse train? The right tool for a given measurement: An overview The pulse train The pulse of a train The single amplified pulse The methods Correlations Femtonitpicker -- Picasso Spider Frog Measurement of Carrier to Envelope Offset (CEO) by “correlation” – next lecture Measurement of Carrier to Envelope Phase (CEP)

t I Correlations ref I s t Phase information: parallel polarization and replace the polarizing beam splitter by a non-polarizing beam splitter.

Interferometric Intensity Autocorrelation

Interferometric correlation

What do these autocorrelation tell us? Intensity autocorrelations: Continuous signal with100% mod. Cw + noise pulse

What do these autocorrelation tell us? Interferometric autocorrelations Linearly chirped pulse Bandwidth limited pulse

What do these autocorrelation tell us? How to measure a linear chirp.

Single shot interferometric autocorrelation

The choice of the optimum metrology method for a given problem Playing with analogies…. More serious stuff: what is a pulse what is a pulse train? The right tool for a given measurement: An overview The pulse train The pulse of a train The single amplified pulse The methods Correlations Femtonitpicker -- Picasso Spider Frog Measurement of Carrier to Envelope Offset (CEO) by “correlation” – next lecture Measurement of Carrier to Envelope Phase (CEP)

b) Apply a transformation to the object, so that it can be observed How to make a cross correlation when there is no shorter pulse available? b) Apply a transformation to the object, so that it can be observed The transformed object is visible “Linear Transformation” Object (a flea) Applying a transformation to the object, so that it can be observed: this is --- to a certain extent – what one does when labelling molecules, Viruses with organic dyes. It is never known for certain that the properties of the object to be observed are not affected by the labeling.

How to make a cross correlation when there is not shorter pulse available? Ideal for the range 100 fs to 1 ps. Reference pulse The prism transforms the transverse coordinate into a delay Applying a transformation to the object, so that it can be observed---

How to make a cross correlation when there is not shorter pulse available? Reconstruction by iterative deconvolution Ideal for the range 100 fs to 1 ps. Example

How to make a cross correlation when there is no shorter pulse available? Advantages: Fast convergence (small number of iterations) Disadvantage: Small dynamic range, unless the pulse deformation is adjustable Uncertainty principle (should apply to all methods). The larger the temporal contrast between original and “transformed” pulse: References The better the amplitude reconstruction Femtonitpicker: Chi Yan and J.-C. Diels, J. of the Opt.~Soc.~Am.~B, 8:1259-1263 (1991) The smaller the interference contrast Reduced phase accuracy Picaso J.~W.~Nicholson and W.~Rudolph, J. of the Opt.~Soc.~Am.~B, 19:330-339 (2002)

Femtonitpicker and Picasso Reconstruction Pulse 1 short

Interferometric correlation Case of autocorrelation: the last term is the IFT of the second harmonic spectrum

MOSAIC : a treatment derived from the interferometric autocorrelation MOSAIC Trace Delay x 2 FFT FFT-1 Frequency Frequency Delay 1) M. Sheik-Bahae, Opt. Lett. 22, (1997) 2) T. Hirayama and M. Sheik-Bahae, Opt. Lett. 27, (2002)

Less information leads to … more info? By eliminating the middle term, we get more sensitivity to chirp Unchirped Chirped -200 -100 100 200 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 Delay (fs) Interferometric Auto Correlation MOdified Spectrum Auto Interferometric Correlation

*D. A. Bender and M. Sheik-Bahae, Opt. Lett. 32, 2822 (2007). 15 1 pt. by pt. line search R-MOSAIC 10 5 Signal (a. u.) 0.5 Phase (rad) -5 -10 -15 -1 -1 -0.5 0.5 0.5 1 1 13 Frequency (Hz) x 10 x 10 *D. A. Bender and M. Sheik-Bahae, Opt. Lett. 32, 2822 (2007).

The choice of the optimum metrology method for a given problem Playing with analogies…. More serious stuff: what is a pulse what is a pulse train? The right tool for a given measurement: An overview The pulse train The pulse of a train The single amplified pulse The methods Correlations Femtonitpicker -- Picasso Spider Cross-correlation Frog

Spectral Phase Interferometry for Direct Electric-field Reconstruction SPIDER Spectral Phase Interferometry for Direct Electric-field Reconstruction Basic principle: Pulse to be measured shifted in frequency and delayed, and made to interfere with the original pulse in a spectrometer. Measure: where Inverse Fourier transform: 2 one-dimentional measurements: Fourier transform The spectrum The sheared spectrum Extract

Spectral Phase Interferometry for Direct Electric-field Reconstruction SPIDER Spectral Phase Interferometry for Direct Electric-field Reconstruction Basic technique: Chirp generator Sum frequency pulse sequencer t Spectro- meter The two pulses are “spectrally sheared” by the product with the chirped pulse

SPIDER t Ideal for high (kHz) repetition rate Chirp generator Sum frequency pulse sequencer t Spectro- meter Advantage: 2 x 1D therefore fast (kHz) reconstruction Disadvantages: 1. Raw data not informative 2. Shear and delay not independent Spatially encoded arrangement for SPIDER SEA-SPIDER 2D data but ideal for ultrashort pulses

SEA-SPIDER Ideal for few cycle pulses Spectrum and shear along x, delay along y. Reference: Webb site of Ian Walmsley, thesis of Adam S. Wyatt (2007)

SEA-SPIDER The experimental setup

The FROG Frequency Resolved Optical Gating It is a time gated spectrum, measuring a two D function: References: Advantage: the raw data give a nice representation Disadvantage: considerable iterations FROG Trebino, Kluwer, 2002 Adam S. Wyat PhD Thesis University of Oxford (2007)

Spectrograms for Linearly Chirped Pulses Negatively chirped Unchirped Positively chirped Frequency Time Frequency Delay Like a musical score, the spectrogram visually displays the frequency vs. time (and the intensity, too).

The uncertainty principle applies – as in any other method Algorithms exist to retrieve E(t) from its spectrogram. The spectrogram essentially uniquely determines the waveform intensity, I(t), and phase, (t). There are a few ambiguities, but they’re “trivial.” The gate need not be—and should not be—much shorter than E(t). Suppose we use a delta-function gate pulse: = The Intensity. No phase information!

The choice of the optimum metrology method for a given problem Playing with analogies…. More serious stuff: what is a pulse what is a pulse train? The right tool for a given measurement: An overview The pulse train The pulse of a train The single amplified pulse The methods Correlations Femtonitpicker -- Picasso Spider Frog