Hello Sumit (and other readers) --

In general, attosecond pulses are generated using high harmonic generation. For those unfamiliar, this process can generally be described by the "three step model": 

1) Ionization: An intense oscillating electric field (i.e. your driving laser) ionizes an electron from an atom (commonly a noble gas) and accelerates it away into free space.

2) Acceleration: When the electric field changes direction, the electron turns around and accelerates back towards the parent ion, gaining a substantial amount of kinetic energy in the process.

3) Recombination: If the electron recombines with the parent ion, the excess amount of kinetic energy is released as a single high-energy photon (usually in the VUV to soft x-ray region, depending on the laser). This burst possesses attosecond time signatures.

This process occurs every half-cycle of your driving laser, meaning a linearly-polarized, multi-cycle pulse will generate an attosecond pulse train, with the spectrum of this output showing discrete, odd-order high harmonics of the incident laser pulse energy (which makes sense if you think about the Fourier transform of a train of closely-separated ultrashort pulses).

Experimentally, it may be more useful to use isolated attosecond pulses. To generate only one attosecond pulse instead of a train of closely-separated pulses, one of several different types of optical gating can be used. In general, this can be done by modifying any of the steps in the "three step model" above:

1) Ionization: Under ionization gating, a single field maximum of the driving laser pulse is responsible for ionizing a substantial portion of the atoms in the interaction region. While these electrons can be accelerated and recombined to generate an attosecond pulse, there are either a) no more electrons for the following driving laser cycles to ionize because the target has been depleted or b) no longer appropriate phase matching conditions because of the plasma created by the pulse. This effectively results in the production of a single attosecond pulse. 

2) Acceleration: Under amplitude gating, the strongest field maximum of the driving laser pulse accelerates the photoionized electrons the hardest, leading to the generation of the highest-energy photons out of all the laser cycles. By filtering out the spectral components below the cutoff generated by the next strongest field maximum, it is ensured that the remaining spectrum all originated from the same attosecond burst. This effectively results in the production of a single attosecond pulse.

3) Recombination: Under polarization gating, the ellipticity of the laser field is caused to vary with time such that a single linearly-polarized field maximum is surrounded on both sides by field maxima with increasing ellipticity. Because these elliptically-polarized fields lead their associated electrons on trajectories away from the parents ions, only the electrons accelerated by the single linearly-polarized field maximum will experience recombination and yield high-energy photons. This effectively results in the production of a single attosecond pulse.

Some of these methods can be combined, allowing one to reap the benefits of each kind of gating. As an example, double optical gating and its variants combine polarization gating and two-color gating (an ionization-type gating) to relax the restrictions on the driving laser.

There are also wavefront-based gating methods (attosecond lighthouse and noncollinear optical gating) where, instead of generating only a single attosecond pulse, an attosecond pulse train is produced in which each pulse is angularly-resolvable from the other.

Of course, each gating has its advantages and disadvantages (driving laser requirements on pulse duration or carrier-envelope phase stability; achievable spectrum; need for finding the right filters; etc.), but this should already be enough introductory material to help someone not familiar with the field.

Best,

~Eric (Institute for the Frontier of Attosecond Science and Technology, UCF)

Hello Sumit (and other readers) --

In general, attosecond pulses are generated using high harmonic generation. For those unfamiliar, this process can generally be described by the "three step model": 

1) Ionization: An intense oscillating electric field (i.e. your driving laser) ionizes an electron from an atom (commonly a noble gas) and accelerates it away into free space.

2) Acceleration: When the electric field changes direction, the electron turns around and accelerates back towards the parent ion, gaining a substantial amount of kinetic energy in the process.

3) Recombination: If the electron recombines with the parent ion, the excess amount of kinetic energy is released as a single high-energy photon (usually in the VUV to soft x-ray region, depending on the laser). This burst possesses attosecond time signatures.

This process occurs every half-cycle of your driving laser, meaning a linearly-polarized, multi-cycle pulse will generate an attosecond pulse train, with the spectrum of this output showing discrete, odd-order high harmonics of the incident laser pulse energy (which makes sense if you think about the Fourier transform of a train of closely-separated ultrashort pulses).

Experimentally, it may be more useful to use isolated attosecond pulses. To generate only one attosecond pulse instead of a train of closely-separated pulses, one of several different types of optical gating can be used. In general, this can be done by modifying any of the steps in the "three step model" above:

1) Ionization: Under ionization gating, a single field maximum of the driving laser pulse is responsible for ionizing a substantial portion of the atoms in the interaction region. While these electrons can be accelerated and recombined to generate an attosecond pulse, there are either a) no more electrons for the following driving laser cycles to ionize because the target has been depleted or b) no longer appropriate phase matching conditions because of the plasma created by the pulse. This effectively results in the production of a single attosecond pulse. 

2) Acceleration: Under amplitude gating, the strongest field maximum of the driving laser pulse accelerates the photoionized electrons the hardest, leading to the generation of the highest-energy photons out of all the laser cycles. By filtering out the spectral components below the cutoff generated by the next strongest field maximum, it is ensured that the remaining spectrum all originated from the same attosecond burst. This effectively results in the production of a single attosecond pulse.

3) Recombination: Under polarization gating, the ellipticity of the laser field is caused to vary with time such that a single linearly-polarized field maximum is surrounded on both sides by field maxima with increasing ellipticity. Because these elliptically-polarized fields lead their associated electrons on trajectories away from the parents ions, only the electrons accelerated by the single linearly-polarized field maximum will experience recombination and yield high-energy photons. This effectively results in the production of a single attosecond pulse.

Some of these methods can be combined, allowing one to reap the benefits of each kind of gating. As an example, double optical gating and its variants combine polarization gating and two-color gating (an ionization-type gating) to relax the restrictions on the driving laser.

There are also wavefront-based gating methods (attosecond lighthouse and noncollinear optical gating) where, instead of generating only a single attosecond pulse, an attosecond pulse train is produced in which each pulse is angularly-resolvable from the other.

Of course, each gating has its advantages and disadvantages (driving laser requirements on pulse duration or carrier-envelope phase stability; achievable spectrum; need for finding the right filters; etc.), but this should already be enough introductory material to help someone not familiar with the field.

Best,

~Eric (Institute for the Frontier of Attosecond Science and Technology, UCF)

thank you very much sir. what about the femtosecond laser pulse by Ti sapphire laser...what are the differences in both...

The technology used (Ti:Sa, Yb) will mostly affect the duration of the generating pulse.

Consequently it will influence your attosecond generation from attosecond pulse train (long pulse) down to single attosecond pulse (few cycle generating pulse).

Changing the wavelength of the generating pulse to longer wavelength is in principle better for isolated attosecond pulse generation.

@ Eric Cunningham ...sir can you give me the some information about experimental set-up.

Hello Sumit (and others) --

I think now I understand your question a little bit better.

Prof. Delagnes's answer is a good one: people use several different kinds of lasers for producing the femtosecond pulse durations needed to drive high harmonic generation. This is actually its own field of research: in addition to Ti:sapphire-based systems, many researchers have achieved truly remarkable results relevant to attoscience with laser architectures based on optical parametric chirped-pulse amplification (OPCPA) or chirped-pulse amplification (CPA) in fibers and other solid-state gain media. Of course, each type of laser has its advantages (e.g. repetition rate, pulse energy, wavelength) that may make it more suitable for certain applications over others.

Speaking specifically of Ti:sapphire lasers (since you asked), most current setups used for generating isolated attosecond pulses involve a femtosecond oscillator, a pulse stretcher, the amplifier itself (which may consist of regenerative or multi-pass configurations, or both), and a pulse compressor. Because of gain-narrowing due to amplification of the pulse energy from the ~nJ to the ~mJ level, the pulse duration is usually limited to >25 fs, which is too long for generating isolated attosecond pulses with most common gating methods. (Because it relates to my own research, I will mention that an exception to this rule of thumb is double optical gating (along with its variants), which allows isolated attosecond pulse generation with pulses directly from the amplifier and compressor. This method can also work without facing the challenges of carrier-envelope phase (CEP) stabilization, which is required for most few-cycle gating methods like amplitude gating and ionization gating.)

Because of the long pulse durations after the compressor, most typical setups use a hollow-core fiber or filamentation tube to generate an ultrabroadband spectrum (e.g. several hundred nm) through self-phase modulation (SPM). This spectrum can be compressed using ultrabroadband chirped mirrors down to pulse durations as short as

According to one cycle phenomena, the wavelength attributing to atto second pulse lies in VUV or  Xray spectral region while that of fs pulse may be in be in NIR. IS NOT IT?

@ Eric Cunningham Dear Prof. Eric Cunningham, I would like to ask the same question. How do you think, what happen with the train of attosecond pulses in case of two-color pump scheme of HHG?