1. Photonics 2015-20161 Carlo Altucci Consorzio Nazionale Interuniversitario di Struttura della Materia – CNISM Dipartimento di Scienze Fisiche, Università “Federico II”, Napoli, Italy UNIVERSITA’ DI NAPOLI “FEDERICO II” Ultrashort pulse characterisation

2. Photonics 2015-20162 1.Amplitude and Phase: FROG and FROG-like (Rick Trebino’s presentation) 2.Amplitude and Phase: SPIDER OUTLINE

3. Photonics 2015-20163 Spectrogram

4. 4 What do spectrograms look like? Notice that spectrograms are intuitive representations of the intensity and phase (frequency) of pulses. They were invented specifically for this purpose, but for cases when the waveform was known. In our case, we'll find it easy to generate one experimentally, and we'll retrieve the pulse from it.

5. Photonics 2015-20165 Why is the spectrogram a good idea?

6. Photonics 2015-20166 Frequency-Resolved Optical Gating (FROG) How do we measure a spectrogram of light? We use FROG!

7. Photonics 2015-20167 Polarization Gating (PG) Polarization-gated FROG (PG FROG) is the conceptually simplest FROG variant. Here, the gate pulse, polarized under 45° relative to the probe pulse, rotates the polarization of the latter when overlapping it in a  (3) medium (e.g. fused silica), and thus leads to transmission of the probe through a polarizer. As always with FROG, the transmitted probe signal is analyzed with a spectrometer. Advantages of PG FROG are easy alignment, the absence of ambiguities in the retrieval, and the generation of fairly intuitive FROG traces. A problem is that a polarizer with very high extinction ratio is required.

8. Photonics 2015-20168 PG details General  (3) response If |E 1 |=|E 2 | and k 1 =k 2 which is a field having  1 carrier and k 1 wave vector. It contains PG when E 2 and E 3 have orthogonal polarization. These fields co-propagating and combined together yield a beam which is polarized at 45° to E 1. Say E 1 is vertically polarized. Then the two vertical fields forms a transient grating with which creates an induced non-linear polarization perpendicular to E 1 but with  1 carrier.

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19. Photonics 2015-201619 Transient grating (TG)

20. Photonics 2015-201620 FROG geometries

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25. Photonics 2015-201625 Spectral Interferometry This is a class of interferometric methods, where interference in the frequency domain is exploited The intensity profile of the optical spectrum of a signal, such as an ultrashort pulse, can easily be measured using some kind of spectrometer. For the more difficult task of retrieving the spectral phase, methods of Fourier transform spectral interferometry provide various options. The basic principle of spectral interferometry is that two pulses are interferometrically combined, and the optical spectrum of that combination is recorded. An essential detail is that one of the pulses is subject to a time delay τ. If the electric fields of the two pulses are described with phasors E 1 (ω) and E 2 (ω), the additional time delay translates into a phase factor exp(−i ω τ) for one of the pulses. Apart from irrelevant prefactors, the combined field is thus See RP PhotonicsEncyclopedia

26. Photonics 2015-201626 the combined field is thus from which one can see that the optical spectrum is modulated. The oscillating term has a phase which shows that there is an oscillation determined by the time delay, the phase of which is also influenced by the difference of the spectral phases of the two pulses. Spectrum of two femtosecond pulses, where one pulse is nonlinearly chirped and delayed by 600 fs. The spectral modulation can be used to reconstruct the spectral phase of the chirped pulse. Spectrum of two femtosecond pulses, where one pulse is nonlinearly chirped and delayed by 600 fs. The spectral modulation can be used to reconstruct the spectral phase of the chirped pulse.

27. Photonics 2015-201627 It is possible to characterize an ultrashort pulse, if a reference pulse with a well-characterized spectral phase is available, the spectrum of which covers the full range of the spectrum of the pulse to be characterized. The time delay is chosen such that the period of spectral modulation can be well resolved with the given spectrometer, but is fast enough for an accurate phase determination. The phase of the recorded spectrum can be conveniently and precisely obtained with Fourier transform methods, applied to the spectral intensity curve. A high sensitivity can be achieved, as such a heterodyne method works well even if the signal pulse energy is much lower than that of the reference pulse. Also, no nonlinear crystal is required, thus avoiding possible bandwidth-limiting effects. Finally, an accurate intensity calibration of the spectrometer is not required, since only the fast modulation of the spectrum is of interest, not the slow variation of intensity. However, the need for a suitable reference pulse is clearly a disadvantage. Pulse characterization using another reference pulse

28. Photonics 2015-201628 Spectral shearing interferometry A convenient way of obtaining a reference pulse can be to send a copy of the signal pulse through a sinusoidally modulated phase modulator at a time close to the zero crossing of the phase. (For example, an electro-optic modulator may be inserted in one arm of a Mach–Zehnder interferometer.) The nearly linear temporal phase modulation then corresponds to some spectral shift of magnitude δω. The spectrum of the combined pulses then has a modulation phase where the approximate relation holds if δω is not too large. This shows that the spectral derivative of the phase of the signal pulse can be obtained, which is the frequency-dependent group delay. This method [I. Walmsley and other groups] works well for relatively long pulses. For very short pulses, where the group delay variation within a pulse duration is small, it is difficult to obtain a sufficiently large spectral shift in the modulator. A larger spectral shear can be achieved by using a nonlinear interaction.

29. Photonics 2015-201629 Spectral Phase Interferometry for Direct Electric-Field Reconstruction (SPIDER) Another method of spectral shearing interferometry, often applied for the complete characterization of ultrashort pulses, is called Spectral Phase Interferometry for Direct Electric-field Reconstruction (SPIDER) [I. Walmsley, C. Iaconis, L. Gallmann and others]. Here, the signal pulse is split into two identical copies with a significant temporal distance, so that there is no temporal overlap. A third pulse, derived from the same input pulse, is strongly temporally broadened by sending it through a highly dispersive optical element, such as a long block of glass or a pair of diffraction gratings. The long chirped pulse and the two copies of the signal pulse are then combined in a nonlinear crystal, where sum frequency generation occurs. The two signal pulses overlap with different temporal portions of the chirped pulse, which have different optical frequencies, so that there is also a spectral shear between the two upconverted pulses. Therefore, the optical spectrum of the sum frequency signal reveals the temporally resolved group delay. From the group delay, it is easy to retrieve the frequency-dependent spectral phase, so that complete pulse characterization is achieved.

30. Photonics 2015-201630 SPIDER SCHEME/PRINCIPLE The long chirped pulse and the two copies of the signal pulse are then combined in a nonlinear crystal, where sum frequency generation occurs. The two signal pulses overlap with different temporal portions of the chirped pulse, which have different optical frequencies, so that there is also a spectral shear between the two upconverted pulses. Therefore, the optical spectrum of the sum frequency signal reveals the temporally resolved group delay in a way which is analogous to that discussed above. From the group delay, it is easy to retrieve the frequency-dependent spectral phase, so that complete pulse characterization is achieved.

31. Photonics 2015-201631 SPIDER: SFG and DFG configurations

32. Photonics 2015-201632 Spider signal The fields in the frequency domain are: Then the signal of the interferogram is: In principle, with a knowledge of Ω and τ, it is possible to characterize the spectral phase. More precisely, what is recovered is the gradient of the spectral phase, and the spectral phase is revealed through concatenation or integration.

33. Photonics 2015-201633 SPIDER vs FROG In comparison with FROG, the SPIDER method has various advantages and disadvantages: SPIDER does not require a sophisticated iterative algorithm for retrieving the spectral phase. Its simple algorithm can be executed very rapidly on a PC, allowing for fast update rates which are limited only by the speed of the spectrometer, even for complicated pulse shapes. However, the FROG algorithm has the advantage of delivering additional consistency checks. SPIDER does not require a sophisticated iterative algorithm for retrieving the spectral phase. Its simple algorithm can be executed very rapidly on a PC, allowing for fast update rates which are limited only by the speed of the spectrometer, even for complicated pulse shapes. However, the FROG algorithm has the advantage of delivering additional consistency checks. Both methods can be applied also for very short pulses with durations below 10 fs. FROG then relies on the accurate calibration of the spectrometer in a wide wavelength range, whereas SPIDER requires only precise wavelength calibration, which is simpler to obtain. However, it may anyway be desirable to know the spectrum precisely. Both methods can be applied also for very short pulses with durations below 10 fs. FROG then relies on the accurate calibration of the spectrometer in a wide wavelength range, whereas SPIDER requires only precise wavelength calibration, which is simpler to obtain. However, it may anyway be desirable to know the spectrum precisely. For long pulses, FROG is more convenient, since SPIDER would require a spectrometer with very high resolution, and an optical element with a huge amount of chromatic dispersion. For long pulses, FROG is more convenient, since SPIDER would require a spectrometer with very high resolution, and an optical element with a huge amount of chromatic dispersion. Both methods have variants which allow for single-shot measurements. Both methods have variants which allow for single-shot measurements. A comprehensive comparison of SPIDER and FROG techniques is difficult, because there are many variants of both methods, which have specific advantages under certain circumstances.