What does gating problem mean
Characterization of ultrashort light pulses
Characterization of ultrashort light pulses By Tobias Caspers, supervised by Dr. Frank Noack, As part of the training seminar “Short Pulse Lasers and Applications” with Prof. Dr. Ingolf Hertel.
General: measurement of short events
0. Topic overview • Classification of the achievable parameters • “Simple” measuring devices • Correlation • Measurement of the pulse course: FROG and SPIDER
1. Classification of the achievable parameters • Pulse duration: 3fs • Bandwidth: a few hundred THz • Power: up to 1000 TW • Intensity: up to
2. "Simple" measuring devices • Energy: Pyroelectric Detector • Power: Photodetector • Intensity vs. Time: Photodiode • Intensity vs. Time: Streak Camera
2.1 Pyroelectric detector Basically: ion crystals with structure-related spontaneous polarization, e.g. tourmaline (aluminum borosilicate). Effect: When heated, a voltage builds up proportional to the rise in temperature. Compare piezo crystal! Use for energy measurement. • Typical data: • Energy measurement up to a few mJ possible. • Response time: a few ms • Electrical response: a few V / mJ
2.2 The photodetector Basically: Thermocouples consist of two metal contact points, one of which is kept constant at a reference temperature and the other is brought to the temperature to be measured. Caution: Only to measure the average power Some data:
2.3 The photodiode Basically: pn junctions operated in reverse direction reverse current proportional to the illuminance. Some data:
2.4 The streak camera Structure: temporal Resolution: Approx. 1 ps
Reconciliation Finding: There is the following problem: The measuring devices available to us have far too long response times. Solution?
Reconciliation Finding: There is the following problem: The measuring devices available to us have far too long response times. Solution: CORRELATION FUNCTIONS! Because: If known, it can be determined from (measurably!).
3. Something about correlation functions Definitions: Fourier transformation: Cross correlation function: Convolution: Autocorrelation function:
3. Some properties of correlation functions Correlation or convolution theorem: Let and Then: and Parseval's theorem:
3. Some examples of autocorrelation functions
3. Be careful! The autocorrelation is not objective Illustration!
Transition: Experimental Realization Statement: “normally” E-fields are superimposed additively according to the superposition principle, but we need multiplicative superimposition! Solution?
Transition: Experimental Realization Statement: “normally” E-fields are superimposed additively according to the superposition principle, but we need multiplicative superimposition! Solution: The prerequisite for the validity of the superposition principle is the linearity of the E-field • NON-LINEAR OPTICS! This means that higher order terms follow:
4. FROG & SPIDER • Prerequisite: non-linear optics • Objective • Preliminary stages: Cross correlation and autocorrelation • FROG • SPIDER
4.1 Non-linear optics Wave equation: linear case: non-linear case: with gives: ....
4.1 Non-linear optics Nonlinear case: With results in: .... SHG SFG DFG
4.1 Non-linear optics The terms are written out again: SHG: = Second Harmonic Generation SFG: = Sum Frequency Generation DFG: = Difference Frequency Generation Correspondingly, higher-order terms include: THG: = Third Harmonic Generation ....
4.1 Non-linear optics Other important third-order effects: SD: = Self Diffraction
4.1 Non-linear optics Further important third-order effects: PG: = Polarization Gating
4.1 Non-linear optics Summary: In non-linear media, different rays can influence each other and create new rays. The effects required here are: SHG: PG: SD: THG: 2nd order effects 3rd order effects
4.2 Objective ?: Measurement of the actual signal course !:
4.2 Objective How do you measure something like that? If E (t) is the waveform to be measured, the spectrogram is: See Fourier Trafo: where g (t-t) is the variable-delayed gate function and t is the delay. Without g (t-t), SpE (w, ) would simply be the spectrum.
4.3a preliminary stage: cross-correlation Apart from the square, it is comparable to a cross-correlation. The prerequisite, however, is that a correspondingly short gate function is available! (Reminder):
Reconciliation But what do you do when the signal to be measured is already the shortest that can be generated?
Reconciliation But what do you do when the signal to be measured is already the shortest that can be generated? You measure it with yourself! autocorrelation
4.3.b autocorrelation Crossing beams in an SHG crystal, varying the delay between them, and measuring the second-harmonic (SH) pulse energy vs. delay yields the intensity Autocorrelation: Input pulse aperture eliminates input pulses and also any SH created by the individual input beams. Mirror Beam-splitter SHG crystal Slow detector E (t) Mirrors E (t – t) Lens Delay The Intensity Autocorrelation:
4.3.b Autocorrelation in single shot mode It is often difficult to carry out a new measurement for each delay. • Is it possible to query different delays when measuring a pulse? Yes you can:
4.3.b Autocorrelation in single shot mode Again in detail: Time delay manifests itself on the local axis via:
4.3.b autocorrelation some examples
4.3.b autocorrelation some examples
4.3.b autocorrelation some properties • Symmetrical around • Maximum value at • Not unique! Loss of information • The autocorrelation provides information about the pulse duration: And for convolutions, the following applies: And thus: Caution! dependent on pulse shape.
Summary: We can measure: • Energy • Power • Spectrum • Pulse duration (with restrictions) Is that enough?
Summary: We can measure: • Energy • Power • Spectrum • Pulse duration (with restrictions) Is that enough? No! We have no information about the phase!
Cutscene: The Importance of the Phase The pulses shown here only differ in phase:
Cutscene: The Importance of the Phase The phase contains the time (or here: the location) information. Clear: frequency information from top left, phase information from top right. Frequency info from top right, phase info from top left.
4.4.a FROG Frequency Resolved Optical Gating Problem: The complete signal information cannot be obtained from the autocorrelation, since the one-dimensional phase restoration problem cannot be solved! Solution: The two-dimensional phase restoration problem can be solved (except for trivial ambiguities)! (Reason :) The fundamental theorem of algebra is valid in one, but not in two dimensions.
4.4.a FROG This 2-dimensional problem arises as follows: Simultaneous measurement of the spectrum and the delay. (Delay: as with one shot autocorrelation spectrum: perpendicular to this, the spectral distribution of the signal) This results in the so-called FROG trace: With gives:
4.4.a FROSome FROG traces Frequency Time Frequency Delay
4.4.a FROSome FROG traces, somewhat more complex Intensity Frequency Time Frequency Frequency Delay Delay
SHG FROG Measurements of a 4.5-fs Pulse! Baltuska, Pshenichnikov, and Weirsma, J. Quant. Electron., 35, 459 (1999).
Single-shot polarization gate FROG Kane and Trebino, Opt. Lett., 18, 823 (1993).
FROG geometries: Pros and Cons Second-harmonic generation most sensitive; most accurate Third- harmonic generation tightly focused beams useful for UV & transient-grating experiments Transient- grating simple, intuitive, best scheme for amplified pulses Polarization- gate Self- diffraction useful for UV
4.4.b SPIDER functional principle Chirped pulse t This pulse sums with the green part of the chirped pulse. This pulse sums with the blue part of the chirped pulse. t t t SFG The output pulse is split into two partial pulses: One experiences a frequency chirp, the other is delayed. Phase information results from the superposition!
4.4.b SPIDER spectral phase interferometry for direct electric-field reconstruction Structure: Participating filters: Temporal Phase Modulator Spectral Phase Modulator
4.4.b SPIDER The following results for the combined signal: If the response function of the spectrometer is assumed to be delta-shaped, the result is:
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