Ultrafast optics, some introductory remarks and applications

Femtoseond lasers are the work horse in any ultrafast and nonlinear optics laboratory. Special properties of these femtosecond laser pulses are: extremely high peak power, femtoseond time-duration and ability to produce ultrashort pulses of new radiation via nonliear parametric/nonparametric generation processes.

In the picture below, cavity configuration of a simple femtosecond laser system based on Ti:Sapphire is shown. The positive GVD introduced by the crystal itself and by propagation in air is compensated by prism pairs. The mode-locking in these lasers is achieved by a mechanism known as the Kerr lensing.

Femtosecond pulses from a low repetition-rate laser such as a 1kHz Ti:Sapphire regen amplifier are easy to see in air. Just disturb the air a bit and because of the scattering from the dust particles, the pulses are seen as shown in the image below.

Following subimages describe a few details, which are enough to imagine the structure of femtosecond laser pulses.

Characteristics of femtosecond laser pulses can not be measured directly by fast photodetectors. Special techniques such as intensity autocorrelation or interferrometric autocorrelation are used for such purposes. A simple autocorrelator, based on a nonlinear crystal for second harmonic generation or a nonlinear photodiode is sufficient for characterizing pulses having time-duration >20 fs.

Typical interferrometric autocorrelation trace (IFAC) as measured by a nonlinear photodiode and another one, the intensity autocorrelation trace (SHGAC) due to SHG by a nonlinear crystal, are shown below for pulses having FWHM width of ~50 fs and centered at 800 nm.

To measure the above traces, a simple autocorrelator can be arranged as shown in the image below. Intensity autocorrelation is measured with a SHG crystal in combination with a normal photodiode, which has good sensitivity for the second harmonic. The energy and momentum conservation in the underlying second order process is also explained in the inset of the image.

For measuring interferrometric autocorrelation, the SHG crystal has to be replaced by a nonlinear photodiode only, which has good sensitivity at the second harmonic signal.

For complete pulse characterization, i.e., to know about the shape of the pulse, chirp in the pulse or spectral phase in general, advanced techniques such as FROG or SPIDER are used. It has been observed that pulses with pulse duration of ~20 fs or shorter differ from the usual Gaussian shape.

If the pulses are not transform limited, they are called chirped. The chirp can be either negative or positive, but in both cases, the time-domain shape is distorted. Whenever ultrashort pulses pass through any medium, due to dispersion, pulses get deformed owing to the pulse phase modulation. Primary effect that is of the highest concern most of the time is the pulse broadening in time due to group velocity dispersion (GVD) arising from second order dispersion. In the example image below, positive and negative chirping is explained. In a positively chirped pulse, red componenets travel ahead of the blue components and vice versa for the negatively chirped pulse.

Higher order dispersion effects distort the temporal shape also over and above broadening of the pulses. Due to the dispersion effects even in normal air, one needs to be very careful while handling of and performing experiments using ultrashort broad-band femtosecond laser pulses.

A pulse compressor based on either a diffraction grating or prism-pair/s can be easily developed to compensate or modify the dispersion, primarily, the GVD, and hence achieve nearly transform limited pulses. The compressor works simply on the principle that red components are made travel larger distance than the blue components or vice versa depending on the kind of chirp that needs to be compressed. In the process, one can think of ways to manipulate the spectral phase of the pulse to achieve pulse shaping, i.e., different shape of the laser pulse in time-domain.

Schematic of a grating based pulse shaper that can be used for GVD compensation also to achieve nearly transform limited pulses is shown in the image below. The image on the right is of an actual setup on in the lab.

Femtosecond time-resolved spectroscopy

The evolution of various physical phenomena in systems out of equilibrium can be studied using femtorsecond time-resolved pump-probe spectroscopy. The technique is quite general in nature and hence the choice of the excitation pulse to create the system under study out of equilibrium and also the probe pulse can be of any choice. For optical time-resolved spectroscopy, often femtorsecond pulses centered at wavelengths from UV to NIR are in use primarily because such sources and detection systems are readily available. Those experiments are arranged in a fashion as shown below in the schematic on the left and an actual setup in the lab on the right.

Generally, the pump-induced changes are extremely weak, many orders of magnitude smaller changes in the normal responses. Therefore, lock-in based balanced detections are used. Below, a few examples are given where optical pump-probe spectroscopy was used to study different types of condensed matter systems and even characterisitics of novel phases in them.

• Hot carriers dynamics in graphene and other allotropic forms.

Example references: Applied Physics Letters 95, 191911 (2009); Chemial Physics Letters 499, 152 (2010); Journal of Physical Chemistry C 125, 26583 (2021).

• Phonon bottleneck in quasiparticle dynamics in low energy gapped competing phases of condensed matter. FeAs-planes here have similar role to play as the copper oxide planes in the cuprates. Complex natue of the dynamics is indicated in the following data for an iron pnictide high-Tc superconductor where superconducting phase seems to build up from a high temperature spin density wave phase.

Example references: EPL 100, 57007 (2012); EPL 105, 47004 (2014); Solid State Communications 160, 8 (2013).

Nonlinear Optical Properties: Nonlinear refraction and absorption

Another most popular application of intense femtosecond laser pulses is investigate nonlinear optical processes and evalute materials for applications involving such processes. Sinble beam z-scan technique is widely used for such purposes. Open aperture and close aperture configurations in the technique help determine nonlinear refraction and absorption coefficients of homogeneous materials. Below is shown schematic of the experimental scheme and typical data from open and close aperture configurations.

Example references: Optics Express 21, 8483 (2013); Reviews in Plasmonics 2015, pp 131-167 (2016).

Nonlinear Microscopy and Imaging

Nonlinear light matter interaction and the response from the material can be used to investigate the properties of the materials and their structures microscopically. There are multiple ways in which this information can be used in applications. Below is shown an example of a multimodal nonlinear optical microscope which has been used by us for three-dimensial imaging by raster scanning the sample for second harmonic generation, third harmonic generation, four wave mixing, two-photon excited fluorescence and coherent anti-Stokes Raman scattering, all measured simultaneously.

Usually, CARS is done in a boxcars geometry using multiple beams. However, in our case, its just a single beam where, advantage from shaping of the pulse has been taken into account. The setup is initially aligned by working in the white light wide field imaging mode. The spectrum of the nonlinear signal for any of the modes, i.e., SHG, THG, FWM, CARS, etc. can also be recorded. All of these modes of the microscopy provide specific information about the sample and its structure. Hence, a multimodal microscope is a powerful tool in biology.

Example references: Optics Express 23, 13082 (2015); Optics Letters 39 5709-5712 (2014).

Terahertz (THz) Pulses for Spectroscopy

Another beautiful application of visible/NIR femtosecond laser pulses is in the generation and detection of electric field transients of far-infrared or terahertz (THz) radiation. There are multiple schemes which have become popular these days for the generation and detection of THz pulses.
THz time-domain spectroscopy has become one of the most powerful techniques in photonics, recently for nonivesive and nondestructive characterization of materials and structures.
The schematic shown below is a THz time-domain spectrometer based on photoconductive antennas. The femtosecond laser pulse in both the emitter and the detector excites the region between two electrodes. Whilte an external bias is used in the emitter to accelerate the photocarriers in the gap region, the THz electric field itself acts as bias to push the photocarriers generated by a femtosecond pulse in the detector.

Careful analysis of the THz pulses before and after interaction with the material/structure is very important. Since electric field or response proportional to it is measured experimentaly, one has access to both the change in the phase and amplitude of the pulses. This allows an umbiguous measurement of the real and imaginary parts of the dielectric function simultaneously without invoking the Kramers Kronig relations. This particular feature makes THz TDS different from other spectroscopic techniques.

Now, depending on the interests, one can perform simple steady state THz measurements or time-resolved study of a dynamical phenomenon created by a strong pump pulse and then the state of the system is probed by temporally delayed THz pulse.
The THz bandwidth depends on the schemes used for the generation and detection of the pulses. Most researchers like to use nonlinear crystals (such as ZnTe, LiNbO3 and so on) for THz pulse generation by optical rectifications and same for THz pulse detection by electro-optic sampling because ultrabroad THz bandwidth is allowed with them.

Example references: European Journal of Inorganic Chemistry 2010, 4363-4366 (2010); Journal of Chemical Physics 133, 014502-014506 (2010); Journal of Physical Chemistry C 114, 12446-12450 (2010).