Lez.2 e 3 - Fisica At. Mol. Spec Carlo Altucci Consorzio Nazionale Interuniversitario di Struttura della Materia – CNISM Dipartimento di Scienze Fisiche, Università “Federico II”, Napoli, Italy UNIVERSITA’ DI NAPOLI “FEDERICO II” Ultrafast Lasers

Lez.2 e 3 - Fisica At. Mol. Spec Ultrafast lasers  Ultrafast lasers 1.Gain and cavity modes 2.Self-phase and Self-Amplitude modulations 3.Dispersion management 4.Amplifiers, chirped-pulse amplification (CPA)  Applications (short) 1.Pulse compression and manipulation 2.Coherent control: pulse shaping for optimization of chemical reactions and DNA-protein crosslinking OUTLINE

Lez.2 e 3 - Fisica At. Mol. Spec Ultrafast Laser Media  Broad gain spectrum required to generate sub-100-femtosecond pulses  Ti:sapphire offers ideal optical/thermal properties

Lez.2 e 3 - Fisica At. Mol. Spec  A more recent suitable laser medium: Yb:KGW  Usually emitting around 1030 nm  Based on Ytterbium-doped tungstates, direct laser diode nm, high emission and absorption cross-section, low quantum defect

Lez.2 e 3 - Fisica At. Mol. Spec Laser-Cavity Modes  Electromagnetic wave must satisfy boundary conditions  Simple picture: Mode with highest gain oscillates

Lez.2 e 3 - Fisica At. Mol. Spec What is the gain curve? It is essentially the fluorescence spectrum, given a pump source and cavity mirrors/filters, i.e. cavity spectral selectivity Wavelengths of light are extremely small compared to the length of a typical laser cavity, and in general, a complete roundtrip path through the cavity will be equivalent to several hundred thousand wavelengths of the light being amplified. Resonance is possible at each integral wavelength increment (for example 200,000, 200,001, 200,002, etc.), and because the corresponding wavelengths are very close, they fall within the gain bandwidth of the laser

Lez.2 e 3 - Fisica At. Mol. Spec Random vs. Modelocked Phases

Lez.2 e 3 - Fisica At. Mol. Spec Locked Modes  Average power same in all cases

Lez.2 e 3 - Fisica At. Mol. Spec Generation of Ultrashort Pulses: Modelocking Active Modelocking: Modulate intracavity transmission at mode separation Passive Modelocking: Insert nonlinear device whose transmission Increases with intensity (i.e. “saturable absorber”) It allowed shortening from ns to ps regime

Lez.2 e 3 - Fisica At. Mol. Spec Optical Kerr-effect The optical Kerr effect in the laser host crystal results in a fast change, proportional to the cycle-averaged laser intensity I(r,t), of the crystal refractive index being [cm 2 /W] the nonlinear refractive index Kerr-Lens Mode-Locking (KLM) results in a lensing effect, due to the radial intensity profile of the laser beam, which tends to more tightly focus the most intense part of the beam. A proper aperture placed at a suitable position in the cavity transmits a larger portion of the laser beam at instants of higher intensity, thus behaving as a fast saturable-absorber which reduces loss for higher intensities C. Altucci and D. Paparo “Elucidating the fundamental interactions of very small particles: Ultrafast sciences”, William Andrew Ed. (2008) This KLM effect, therefore, triggers and keeps the formation of an ultrashort radiation pulse in Ti:Sa and other solid-state lasers

Lez.2 e 3 - Fisica At. Mol. Spec SAM and SPM changes, upon each round trip of the laser pulse oscillating in the resonator cavity being measured in the retarded frame of reference where the pulse always peaks at  =0  being measured in the retarded frame of reference where the pulse always peaks at  =0 k SAM and k SPM denote the SAM and SPM coefficients respectively k SAM and k SPM denote the SAM and SPM coefficients respectively L is the Kerr medium length << confocal parameter k SAM and k SPM  and W -1, respectively, in Ti:Sa for instance. k SAM and k SPM  and W -1, respectively, in Ti:Sa for instance.

Lez.2 e 3 - Fisica At. Mol. Spec Typical intracavity powers in KLM regime  and W, in Ti:Sa for instance. Typical intracavity powers in KLM regime  and W, in Ti:Sa for instance. Due to SAM and SPM |  A/A|  10% which is too low to stop pulse broadening caused by dispersion into the medium. Due to SAM and SPM |  A/A|  10% which is too low to stop pulse broadening caused by dispersion into the medium. Need for negative GDD to compensate for dispersion Need for negative GDD to compensate for dispersion Dispersion corresponds to the change of the phase retardation of the optical system with respect to the frequency  (  ) Dispersion corresponds to the change of the phase retardation of the optical system with respect to the frequency  (  )

Lez.2 e 3 - Fisica At. Mol. Spec Dispersion  Femtosecond Laser Pulses  Dispersion inextricably linked to femtosecond laser pulses

Lez.2 e 3 - Fisica At. Mol. Spec Group Delay and Group Delay Dispersion (GDD) Group Delay, T g  ’(  0 ) represents the time it takes for the peak of the pulse to propagate through the dispersive medium  ’’(  0 ) is defined as the GDD and denoted by D (typically in fs 2 )  ’’’(  0 ) and  ’’’’(  0 ) and so on are the higher order dispersion terms D 3 and D 4 respectively … and so on. Above a critical value dispersion broadens the intracavity pulse. Thus, for instance, a GDD of  implies a pulse broadening of more than a factor of 2 and reveals how dramatic can dispersion-induced broadening be for ultrafast pulses which have a large frequency content

Lez.2 e 3 - Fisica At. Mol. Spec Chirp An ultrashort pulse which propagates through one of these media assumes a positive frequency sweep or, as it is usually termed, chirp For example, a sub-100-fs pulse tends to broaden while traversing even few mm of quartz or sapphire, and the shorter the pulse duration or the higher the pulse energy the more the pulse broadens, until self-phase-modulation due to optical Kerr effect can be triggered Counterpart in the time domain where the coefficient a [rad ·fs -2 ], is usually named the linear term chirp coefficient as it implies a frequency sweep which is linear in time, and the other coefficients, b [rad ·fs -3 ] and so on, are the higher order term chirp coefficients

To summarize: What are Chirp and Compression analytically? A chirped gaussian pulse in the freq domain: Then in the time domain: With characteristic width, instantaneous frequency, and chirp : In the frequency domain a compressor can be written b=0 is transform limited then a =   2 /16 a compressor can cancel the chirp to yield a transform limited pulse, but a transform limited pulse in yields a broadened, chirped pulse out for b>>a the shorter the pulse, the more it is broadened Lez.2 e 3 - Fisica At. Mol. Spec

Lez.2 e 3 - Fisica At. Mol. Spec Propagation of Ultrashort Pulses in Dispersive Media  Different colours have different propagation velocities (frequency chirp)  Most transparent materials have normal dispersion  Normal dispersion in the cavity is, in general, a problem and must be compensated

Lez.2 e 3 - Fisica At. Mol. Spec Adjustable Dispersion Compensation  Use prism pairs: anomalous dispersion can be varied by adjusting prism separation  Use grating pairs instead of prisms: much larger group delays can be achieved, but typically lossy  Chirped mirrors

Lez.2 e 3 - Fisica At. Mol. Spec Typical Values for Modelocked Ti:Sapphire Laser oscillators  Repetition rate: 20 MHz – 1 GHz  Pulse duration: 10 – 100 fs  Average power: 0.25 – 1.5 W  Pulse energy: 5 – 10 nJ  Peak power: 50 – 500 kW ns 10 – 100 fs  Most recent femtosecond oscillators: all-fiber based systems 1  m, compact, stable, high power, excellent beam quality, turn-key operation

Lez.2 e 3 - Fisica At. Mol. Spec Amplification of Ultrashort Laser Pulses  Amplification above MW power levels non-trivial due to nonlinear effects  Development of chirped-pulse amplification (CPA) Regenerative amplifier scheme (amplification of  10 5 – 10 6 )

Lez.2 e 3 - Fisica At. Mol. Spec Another CPA scheme: multipass ampl. Typical bow-tie configuration

Lez.2 e 3 - Fisica At. Mol. Spec Characteristics of Amplified Systems Repetition ratePeak PowerComments 200 kHz100 MWContinous-wave pumped 1 – 5 kHz10 GW – 1 TW >10 fs. Commercially available 1 – 10 Hz100 TW – 1 PW >30 fs, ~ 10 systems in world  All systems produce a near-diffraction-limited beam

Lez.2 e 3 - Fisica At. Mol. Spec Few-cycle pulses SPM acts as a new frequencies generator: the time-dependent nonlinear phase shift accumulated by the pulse propagating through the Kerr medium is, in fact: being the laser pulse intensity vs. the retarded time above defined, and the propagation length. Therefore, SPM broadens the pulse spectrum: the higher the laser intensity or the nonlinear medium refractive index or the longer the propagation length, the larger time-dependent phase shift and, hence, the pulse broadening I(  ) being the laser pulse intensity vs. the retarded time  above defined, and L the propagation length. Therefore, SPM broadens the pulse spectrum: the higher the laser intensity or the nonlinear medium refractive index or the longer the propagation length, the larger time-dependent phase shift and, hence, the pulse broadening.

Lez.2 e 3 - Fisica At. Mol. Spec Then SPM can be used to generate shorter pulses as it broadens the spectrum, properly compensating for GDD. Thus, the few-optical cycle regime (typically few fs pulses for NIR carrier wavelength) can be accessed either intracavity and extracavity. L. Xu et al. Appl. Phys. B (1997) Polimi collaboration

Lez.2 e 3 - Fisica At. Mol. Spec Intra- and extra-cavity few-cycle systems

Lez.2 e 3 - Fisica At. Mol. Spec Intense Laser-Matter Interactions: Nonlinear Optics (1-st mention)  The medium response to the applied laser electric field, E, is nonlinear Polarization of the medium P medium =  (1) E+  (2) E 2 +  (3) E Linear susceptibility Nonlinear susceptibility  2nd-order nonlinearity  (2) E 2 next slide  3rd-order nonlinearity  (3) E 3 intensity-dependent refractive index, two photon absorption, third harmonic generation

Lez.2 e 3 - Fisica At. Mol. Spec nd-Order Nonlinear Processes  2nd-Order Nonlinear Processes 22

Lez.2 e 3 - Fisica At. Mol. Spec Application: Pulse Compression Presently available ultrashort and ultraintense laser sources Ti:Sapphire 800 nm Doubled Nd-glass 527 nm  Fourier limited Goals: Temporal compression technique:  Hollow fiber technique  SPM in bulk much shorter pulses same energy

Lez.2 e 3 - Fisica At. Mol. Spec Application: Controlled Pulse Broadening  Self-phase modulation (SPM) for spectral broadening  Use of hollow fiber (propagation only of the fundamental mode) for homogeneous broadening and compression along the pulse wavefront

Lez.2 e 3 - Fisica At. Mol. Spec Block Diagram of the Compression System Laser y x Gas-filled hollow fibre y x Gas outGas in Time (fs) (nm) Spectrum I(t) Spectrum (nm) I(t) Time (fs) (nm) Spectrum I(t) Time (fs) Compressor Output pulse

Lez.2 e 3 - Fisica At. Mol. Spec Pulse-Propagation Equation (I) Dall’equazione di Maxwell/delle onde Considerato il campo La polarizzazione lineare è (campo elettrico polarizzatio linearmente -> polarizzazione lineare parallela -> risposta lineare scalare) La polarizzazione e la costante dielettrica non lineari sono

Lez.2 e 3 - Fisica At. Mol. Spec Pulse-Propagation Equation (II) Con il campo che assume la forma (nel dominio delle frequenze),  0 =2  n(  0 )/L Si arriva ad un’equazione per l’ampiezza d campo “longitudinale” nel dominio del tempo (vedi “Nonlinear Fiber Optics”, G.P. Agrawal, cap.2) In cui  contiene perdite e termini non lineari. Esplicitando  si arriva a:

33 Attenuation constant Pulse-Propagation Equation (III) A basic equation that governs propagation of optical pulses in nonlinear dispersive media (fibers etc. etc.), can be derived from the wave equation 1. For the pulse amplitude A, this equation reads (the so-called nonlinear Schrödinger equation): 1 Agrawal, Nonlinear Fiber Optics, 2nd edn, (Academic, San Diego, CA 1995) Self-phase modulation Self-steepening GVD:group-velocity dispersion Nonlinear parameter Lez.2 e 3 - Fisica At. Mol. Spec

34 Propagation regime Our parameters are:  Dispersion length:  Nonlinear length: Nonlinearity-dominant regime ≈ 10 3 m ≈ m Lez.2 e 3 - Fisica At. Mol. Spec

35 Measurement Optimization  Choice of a focusing lens  Beam direction-fiber alignement  Single-mode condition  Coupling optimization pulse energy maximization

36 Self-phase modulation  Frequency chirp  Broadening factor Multipeak structure in the pulse spectrum Lez.2 e 3 - Fisica At. Mol. Spec

37 Experimental Results and Numerical Simulations Argon Intensity (a.u) simulation experiment Pressure (mbar) FWHM of spectral intensity (nm)

Lez.2 e 3 - Fisica At. Mol. Spec Compressor design l I prism II prism  M Temporal profile (a.u) Initial laser pulse Compressed laser pulse  Compressor implementation: the shortest ever green amplified pulse (  < 40 fs)  Applications: fs laser ablation (nanoparticle production), photoinduced crosslink of DNA and proteins

Lez.2 e 3 - Fisica At. Mol. Spec Experimental setup

Lez.2 e 3 - Fisica At. Mol. Spec I Procino et al., Opt. Lett. 32, 1866 (2007)

Lez.2 e 3 - Fisica At. Mol. Spec Coherent Control: Chemical Reactions

Lez.2 e 3 - Fisica At. Mol. Spec Pulse Shaping

Lez.2 e 3 - Fisica At. Mol. Spec Femtosecond Pulse Shaper

Lez.2 e 3 - Fisica At. Mol. Spec Adaptive Femtosecond Quantum Control feedback

Lez.2 e 3 - Fisica At. Mol. Spec Coherent Control of Simple Reactions