Spectral interferometry

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Spectral Interferometry

Spectral interferometry (SI) or frequency-domain interferometry is a linear technique used to measure [optical pulses], with the condition that a reference pulse that was previously characterized is available. This technique provides information about the intensity and phase of the pulses. SI was first proposed by Claude Froehly and coworkers in the 1970s.

A known (reference) and an unknown pulse arrive at a spectrometer, with a time delay $\tau$ between them, in order to create spectral fringes. A spectrum is produced by the sum of these two pulses and by measuring said fringes, one can retrieve the unknown pulse. If $E_{un}(\omega )$ and $E_{ref}(\omega )$ are the electric fields of the reference and unknown pulse respectively, the time delay can be expressed as a phase factor $e^{-i\omega \tau }$ for the unknown pulses. Then, the combined field is:

$E_{SI}=E_{ref}(\omega )+E_{un}(\omega )e^{-i\omega \tau }$

The average spacing between fringes is inversely proportional to the time delay $\tau$. Thus, the SI signal is given by:

$S_{SI}=S_{ref}(\omega )+S_{un}(\omega )+2{\sqrt {S_{ref}(\omega )}}{\sqrt {S_{un}(\omega )}}cos[\phi _{SI}]$

where $\phi _{SI}=\phi _{un}(\omega )-\phi _{ref}(\omega )+\omega T$ is the oscillation phase. Furthermore, the spectral fringes width can provide information on the spectral phase difference between the two pulses $\Delta \phi =\phi _{un}(\omega )-\phi _{ref}(\omega )$; narrowly spaced fringes indicate rapid phase changes with frequency.

Comparison with the Time Domain

Compared to time-domain interferometry, SI presents some interesting advantages. Firstly, by using a CCD detector or a simple camera, the whole interferogram can be recorded simultaneously. Furthermore, the interferogram is not nullified by small fluctuations of the optical path, but reduction in the fringe contrast should be expected in cases of exposure time being bigger than the fluctuation time scale. However, SI produces phase measurements through its cosine only, meaning that results arise for phase differences in multiples of $2\pi$ which can lead to solutions that degrade the signal-to-noise ratio.

There have been efforts to measure pulse intensity and phase in both the time and the frequency domain by combining the autocorrelation and the spectrum. This technique is called Temporal Information Via Intensity (TIVI), it involves an iterative algorithm to find an intensity consistent with the autocorrelation, followed by another iterative algorithm to find the temporal and spectral phases consistent with the intensity and spectrum but the results are inconclusive.

Uses

Spectral Interferometry has gain momentum in recent years. It is frequently used for measuring the linear response of materials, such as the thickness and refractive index of normal dispersive materials, the amplitude and phase of the electric field in semiconductor nanostructures and the group delay on laser mirrors.

In the realm of femtosecond spectroscopy, SI is the technique on which SPIDER is based, thus it is used for four-wave mixing experiments and various phase-resolved pump-probe experiments.

Experimental Difficulties

This technique is not commonly used since it relies on a number of factors in order to obtain strong fringes during experimental processes. Some of them include:

• Precision in mode-matching
• Phase stability
• Perfectly collinear beams

Spectral Shearing Interferometry

In cases of relatively long pulses, one can opt for Spectral Shearing Interferometry. For this method, the reference pulse is obtained by sending its mirror image through a sinusoidal phase modulation. Hence, a spectral shift of magnitude $\delta \omega$ can be correlated to the produce linear temporal phase modulation and the spectrum of the combined pulses then has a modulation phase of:

$\phi (\omega )=\phi _{ref}(\omega +\delta \omega )+\omega \tau ={\frac {\partial \phi _{ref}}{\partial \omega }}\delta \omega +\omega \tau$

where the approximate relation is appropriate for small enough $\delta \omega$. Thus, the spectral derivative of the phase of the signal pulse which corresponds to the frequency-dependent group delay can be obtained.

Spectral Phase Interferometry for Direct Electric-field Reconstruction

SPIDER set-up

[Spectral Phase Interferometry for Direct Electric-field Reconstruction] (SPIDER) is a nonlinear self-referencing technique based on spectral shearing interferometry. For this method, the reference pulse should produce a mirror image of itself with a spectral shift, in order to provide the spectral intensity and phase of the probe pulse via a direct [Fast Fourier Transform] (FFT) filtering routine. However, unlike SI, in order to produce the probe pulse phase, it requires phase integration extracted from the interferogram.

Self-Referenced Spectral Interferometry

Self-Referenced Spectral Interferometry (SRSI) is a technique where the reference pulse is self created from the unknown pulse being. The self referencing is possible due to pulse shaping optimization and non-linear temporal filtering. It provides all the benefits associated with SI (high sensitivity, precision and resolution, dynamic and large temporal range) but, unlike the SPIDER technique, neither shear nor harmonic generation are necessary in order to be implemented.

For SRSI, the generation of a weak mirror image of the unknown pulse is required. That image is perpendicularly polarized and delayed with respect to the input pulse. Then, in order to filter the reference pulse in the time domain, the main portion of the pulse is used for cross-polarized wave generation (XPW) in a nonlinear crystal. The interference between the reference pulse and the mirror image is recorded and analyzed via Fourier transform spectral interferometry (FTSI). Known applications of the SRSI technique include the characterization of pulses below 15 fs.

Frequency-Resolved Optical Gating

Frequency Resolved Optical Gating (FROG) is a technique that determines the intensity and phase of a pulse by measuring the spectrum of a particular temporal component of said pulse. This results in an intensity trace, related to the spectrogram of the pulse $S_{E}(\omega ,\tau )$, versus frequency and delay:

$S_{E}(\omega ,\tau )=\left\vert \int \limits _{-\infty }^{\infty }E(t)g(t-\tau )e^{-i\omega }dt\right\vert ^{2}$

where $g(t-\tau )$ is a variable-delay gate pulse. FROG is commonly combined with Second Harmonic Generation (SHG) processes.

Other Linear Techniques

There is a variety of linear techniques that are based on the main principles of spectral interferometry. Some of them are listed below.

Dual-Quadrature Spectral Interferometry

Acquiring the two quadratures of the interference signal resolves the issue generated by the phase differences being expressed in multiples of $2\pi$. The acquisition should happen simultaneously via polarization multiplexing, with the reference beam under circular polarization.

Fourier-Transform Spectral Interferometry

It is a technique created for direct determination of $\Delta \phi$, mainly used for femtosecond pump-probe experiments in materials with long dephasing times. It is based on the inverse Fourier transform of the signal: $F.T._{SI}^{-1}(t)=E_{ref}^{\ast }(-t)\otimes E_{ref}(t)+E_{un}^{\ast }(-t)\otimes E_{un}(t)+f(t-\tau )+f(-t-\tau )^{\ast }$

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Ultrafast dynamics in matter (UdynI) group

UdynI group

Ultrafast dynamics in matter group
Group photo in June 2021
Formation	2009
Founder	Caterina Vozzi
Founded at	Milan, Italy
Type	Research group
Legal status	Active
Headquarters	IFN-CNR,   Politecnico di Milano
Location	Milan, Italy
Fields	Attosecond Science,   Ultrafast dynamics
Membership	Salvatore Stagira Michele Devetta Eugenio Cinquanta Davide Faccialà Anna Gabriella Ciriolo Gabriele Crippa Lorenzo Gatto Bogdan Constanin Ispas Stavroula Vovla Andrea Annunziata
Official language	English,   Italian
Leader	Caterina Vozzi
Website	udyni.eu

The Ultrafast dynamics in matter (UdynI) group is a joint research group between the Istituto di Fotonica e Nanotecnologie of the Italian National Research Council (CNR-IFN) and the Physics Department of Politecnico di Milano. Their research is focused on attosecond science and ultrafast spectroscopy. The group is lead by Caterina Vozzi.

Research Activity

Ultrafast THz Spectroscopy

Ultrafast THz Spectroscopy is a state-of-the-art techniques that encompass the study of light-matter interaction with an unprecedented temporal and spatial resolution. Ultrafast means times in the femtosecond and attosecond scale. It revolves around the generation of isolated attosecond light pulses and their phase matching.

Attosecond Science

In Attosecond Science, these aforementioned pulses excite and probe matter on the temporal scales typical of electron dynamics. The sample is excited by two signals, one from the pump exciting carriers in the valence band and one from the probe exciting carriers in core orbitals, with a delay in respect to the first one. The signal is then measured with a spectrometer which produces either absorption or reflectivity spectra.

High Harmonic Generation (HHG) spectroscopy

Pulse generation is based on High-order Harmonic Generation (HHG). HHG is a strongly non-linear optical process which involves the emission of coherent radiation, co-linear to the pump, with a characteristic comb-like spectrum of odd harmonics of the fundamental laser field.

Publications

2020

G. Folpini et al. “Ultrafast charge carrier dynamics in quantum confined 2D perovskite” JOURNAL OF CHEMICAL PHYSICS 152, (2020)

O. Plekan et al. “Experimental and Theoretical Photoemission Study of Indole and Its Derivatives in the Gas Phase” JOURNAL OF PHYSICAL CHEMISTRY A 124, 4115-4127 (2020)

A. G. Ciriolo et al. “High-order harmonic generation in a microfluidic glass device” Journal of Physics: Photonics 2, 024005 (2020)

A. G. Ciriolo et al. “Femtosecond Laser-Micromachining of Glass Micro-Chip for High Order Harmonic Generation in Gases” MICROMACHINES 11, 165 (2020)

T. J. Asel et al. “Influence of Surface Chemistry on Water Absorption in Functionalized Germanane” CHEMISTRY OF MATERIALS 32, 1537-1544 (2020)

M. Mudrich et al. “Ultrafast relaxation of photoexcited superfluid He nanodroplets” NATURE COMMUNICATIONS 11, 112 (2020)

2019

E. Cinquanta et al. “Ultrafast THz Probe of Photoinduced Polarons in Lead-Halide Perovskites” PHYSICAL REVIEW LETTERS 122, 166601 (2019)

2008

A. G. Ciriolo et al. “Generation of ultrashort pulses by four wave mixing in a gas-filled hollow core fiber” J. Opt. 20, 125503 (2018)

J. Mauritsson et al. “Emerging attosecond technologies” J. Opt. 20, 110201 (2018)

M. Negro et al. “Fast stabilization of a high-energy ultrafast OPA with adaptive lenses” Sci Rep 8, 14317 (2018)

S. Bietti et al. “Ga metal nanoparticle-GaAs quantum molecule complexes for terahertz generation” Nanotechnology 29, 365602 (2018)

V. Cardin et al. “Self-channelled high harmonic generation of water window soft x-rays” J. Phys. B-At. Mol. Opt. Phys. 51, 174004 (2018)

D. Facciala et al. “High-order harmonic generation spectroscopy by recolliding electron caustics” J. Phys. B-At. Mol. Opt. Phys. 51, 134002 (2018)

2017

S. L. Cousin et al. “Attosecond Streaking in the Water Window: A New Regime of Attosecond Pulse Characterization” Phys. Rev. X 7, 041030 (2017)

K. Kovacs et al. “Attosecond lighthouse above 100eV from high-harmonic generation of mid-infrared pulses” J. Opt. 19, 104003 (2017)

M. Di Fraia et al. “Impulsive laser-induced alignment of OCS molecules at FERMI” Phys. Chem. Chem. Phys. 19, 19733-19739 (2017)

M. Shcherbinin et al. “Interatomic Coulombic decay in helium nanodroplets” Phys. Rev. A 96, 013407 (2017)

O. Tchulov et al. “Laser induced strong-field ionization gas jet tomography” Sci Rep 7, 6905 (2017)

S. Kuhn et al. “The ELI-ALPS facility: the next generation of attosecond sources” J. Phys. B-At. Mol. Opt. Phys. 50, 132002 (2017)

C. Callegari et al. “Application of Matched-Filter Concepts to Unbiased Selection of Data in Pump-Probe Experiments with Free Electron Lasers” Appl. Sci.-Basel 7, 621 (2017)

C. Vozzi et al. “Tracking the dynamics of electron expulsion” Science 356, 1126 (2017)

A. G. Ciriolo et al. “Optical Parametric Amplification Techniques for the Generation of High-Energy Few-Optical-Cycles IR Pulses for Strong Field Applications” Appl. Sci.-Basel 7, 265 (2017)

M. Ilchen et al. “Circular Dichroism in Multiphoton Ionization of Resonantly Excited He+ Ions” Phys. Rev. Lett. 118, 013002 (2017)

T. Takanashi et al. “Time-Resolved Measurement of Interatomic Coulombic Decay Induced by Two-Photon Double Excitation of Ne-2” Phys. Rev. Lett. 118, 033202 (2017)

2016

D. Iablonskyi et al. “Slow Interatomic Coulombic Decay of Multiply Excited Neon Clusters” Phys. Rev. Lett. 117, 276806 (2016)

D. Facciala et al. “Probe of Multielectron Dynamics in Xenon by Caustics in High-Order Harmonic Generation” Phys. Rev. Lett. 117, 093902 (2016)

F. Calegari et al. “Advances in attosecond science” J. Phys. B-At. Mol. Opt. Phys. 49, 062001 (2016)

K. C. Prince et al. “Coherent control with a short-wavelength free-electron laser” Nat. Photonics 10, 176+ (2016)

C. Vozzi et al. “2015 International Year of Light and beyond” J. Opt. 18, 010201 (2016)

B. D. Bruner et al. “Multidimensional high harmonic spectroscopy of polyatomic molecules: detecting sub-cycle laser-driven hole dynamics upon ionization in strong mid-IR laser fields” Faraday Discuss. 194, 369-405 (2016)

2015

A. Dubrouil et al. “Two-photon resonant excitation of interatomic coulombic decay in neon dimers” J. Phys. B-At. Mol. Opt. Phys. 48, 204005 (2015)

E. Cinquanta et al. “Optical response and ultrafast carrier dynamics of the silicene-silver interface” Phys. Rev. B 92, 165427 (2015)

M. Reduzzi et al. “Advances in high-order harmonic generation sources for time-resolved investigations” J. Electron Spectrosc. Relat. Phenom. 204, 257-268 (2015)

J. Moses et al. “Special issue on optical parametric processes” J. Opt. 17, 090201 (2015)

2014

M. Negro et al. “Non-collinear high-order harmonic generation by three interfering laser beams” Opt. Express 22, 29778-29786 (2014)

H. Soifer et al. “Studying the universality of field induced tunnel ionization times via high-order harmonic spectroscopy” J. Phys. B-At. Mol. Opt. Phys. 47, 204029 (2014)

L. Poletto et al. “Spectrometer for X-ray emission experiments at FERMI free-electron-laser” Rev. Sci. Instrum. 85, 103112 (2014)

P. O'Keeffe et al. “Experimental investigation of the interatomic Coulombic decay in NeAr dimers” Phys. Rev. A 90, 042508 (2014)

L. Poletto et al. “Double-configuration grating monochromator for extreme-ultraviolet ultrafast pulses” Appl. Optics 53, 5879-5888 (2014)

M. Negro et al. “CO2 exploding cluster dynamics probed by XUV fluorescence” New J. Phys. 16, 073004 (2014)

M. Negro et al. “High-order harmonic spectroscopy for molecular imaging of polyatomic molecules” Faraday Discuss. 171, 133-143 (2014)

O. Vendrell et al. “Chemical reaction dynamics I and electron dynamics in molecules: general discussion” Faraday Discuss. 171, 145-168 (2014)

2013

D. Shafir et al. “Trajectory-Resolved Coulomb Focusing in Tunnel Ionization of Atoms with Intense, Elliptically Polarized Laser Pulses” Phys. Rev. Lett. 111, 023005 (2013)

F. Frassetto et al. “Active-grating monochromator for the spectral selection of ultrashort pulses” Opt. Express 21, 12996-13004 (2013)

D. Fazzi et al. “Ultrafast spectroscopy of linear carbon chains: the case of dinaphthylpolyynes” Phys. Chem. Chem. Phys. 15, 9384-9391 (2013)

M. Nisoli et al. “Current frontiers of ultrafast and high field optics: Attosecond science” Riv. Nuovo Cimento 36, 105-172 (2013)

2012

B. Mahieu et al. “Full tunability of laser femtosecond high-order harmonics in the ultraviolet spectral range” Appl. Phys. B-Lasers Opt. 108, 43-49 (2012)

F. Calegari et al. “Temporal gating methods for the generation of isolated attosecond pulses” J. Phys. B-At. Mol. Opt. Phys. 45, 074002 (2012)

S. Bonora et al. “Optimization of low-order harmonic generation by exploitation of a resistive deformable mirror” Appl. Phys. B-Lasers Opt. 106, 905-909 (2012)

C. Vozzi et al. “Strong-field phenomena driven by mid-infrared ultrafast sources” J. Mod. Opt. 59, 1283-1302 (2012)

V. Tosa et al. “Isolated Attosecond Pulse Generation by Two-Mid-IR Laser Fields” IEEE J. Sel. Top. Quantum Electron. 18, 239-247 (2012)

2011

M. Negro et al. “Gating of high-order harmonics generated by incommensurate two-color mid-IR laser pulses” Laser Phys. Lett. 8, 875-879 (2011)

C. Vozzi et al. “Generalized molecular orbital tomography” Nat. Phys. 7, 822-826 (2011)

F. Calegari et al. “Quantum path control in harmonic generation by temporal shaping of few-optical-cycle pulses in ionizing media” Phys. Rev. A 84, 041802 (2011)

I. S. Lopez et al. “Local nanotailoring of polymeric photophysics by Au nanoparticles implantation” Cryst. Res. Technol. 46, 833-835 (2011)

C. Vozzi et al. “Phase-matching effects in the generation of high-energy photons by mid-infrared few-cycle laser pulses” New J. Phys. 13, 073003 (2011)

G. Cerullo et al. “Few-optical-cycle light pulses with passive carrier-envelope phase stabilization” Laser Photon. Rev. 5, 323-351 (2011)

S. Coraggia et al. “Carbon coatings for extreme-ultraviolet high-order laser harmonics” Nucl. Instrum. Methods Phys. Res. Sect. A-Accel. Spectrom. Dect. Assoc. Equip. 635, S43-S46 (2011)

N. D. Ouart et al. “Analysis of the simultaneous measurements of iron K- and L-shell radiation from ultrashort laser produced plasmas” J. Phys. B-At. Mol. Opt. Phys. 44, 065602 (2011)

2010

C. Vozzi et al. “High harmonic generation spectroscopy of hydrocarbons” Appl. Phys. Lett. 97, 241103 (2010)

F. Ferrari et al. “High-energy isolated attosecond pulses generated by above-saturation few-cycle fields” Nat. Photonics 4, 875-879 (2010)

C. Altucci et al. “Interplay between group-delay-dispersion-induced polarization gating and ionization to generate isolated attosecond pulses from multicycle lasers” Opt. Lett. 35, 2798-2800 (2010)

C. Vozzi et al. “High Order Harmonics Driven by a Self-Phase-Stabilized IR Parametric Source” Laser Phys. 20, 1019-1027 (2010)

M. Negro et al. “Polarization pulse shaping induced by impulsive molecular alignment in optical filamentation and application to high-order harmonic generation” Opt. Lett. 35, 1350-1352 (2010)

T. Virgili et al. “Role of intramolecular dynamics on intermolecular coupling in cyanine dye” Phys. Rev. B 81, 125317 (2010)

C. Vozzi et al. “High-order harmonics generated by 1.5 mu m parametric source” J. Mod. Opt. 57, 1008-1013 (2010)

F. Calegari et al. “Filamentation-assisted time-resolved Raman spectroscopy in molecular gases” J. Mod. Opt. 57, 967-976 (2010)