Femtosecond pulse shaping

In optics, Femtosecond pulse shaping refers to various techniques to modify the temporal profile of an ultrashort pulse from a laser. Pulse shaping can be used to shorten/elongate the duration of optical pulse, or to generate more complex pulses.

Introduction

Generation of sequences of ultrashort optical pulses is key in realizing ultra high speed optical networks, Optical Code Division Multiple Access (OCDMA) systems, chemical and biological reaction triggering and monitoring etc. Based on the requirement, pulse shapers may be designed to stretch, compress or produce a train of pulses from a single input pulse. The ability to produce trains of pulses with femtosecond/picosecond separation implies transmission of optical information at very high speeds.

Techniques

A pulse shaper may be visualized as a modulator. The input pulse is multiplied with a modulating function to get a desired output pulse. The modulating function in pulse shapers may be in time domain or a frequency domain (obtained by Fourier Transform of time profile of pulse). This gives rise to two well known femtosecond pulse shaping techniques:

a) Direct space-to-time pulse shaping (DST-PS)
b) Fourier transform pulse shaping (FT-PS)

Direct space-to-time pulse shaping

In DST-PS, the output sequence of pulses is directly proportional to the modulating function of the system. Let us assume that occurrence of an optical pulse as 1 and absence of pulse as 0. Then, information can be transmitted by presence or absence of optical pulses which will correspond to a specific sequence of 1s and 0s.In DST-PS, for any required output temporal sequence of pulses, the modulating function is exactly the same. If the modulating function of the system is defined by binaries 1101, then the output sequence of optical pulses is again 1101 (1s mean pulse is present and 0s mean pulse is absent).

Fourier transform pulse shaping

In contrast to DST-PS, the FT-PS uses a modulating function which is a Fourier Transform of the required sequence. This implies that for a specific temporal sequence of pulses, the modulating function is its Fourier Transform and acts in frequency domain. The reason for using this technique is because in optics a lens performs a Fourier Transform of the input light. A typical FT-PS will consist of a input laser, a lens which will perform Fourier Transform (conversion of time data to frequency data), a modulating function (which may be a phase or intensity modulation), a second lens which will perform another Fourier Transform (converting frequency data back to time data).In FT-PS, for a specific output pulse sequence, the modulating function is simply its Fourier Transform.

Details of FT-PS

An ultrashort pulse with a well-defined electrical field $E(t)$ can be modified with an appropriate filter acting in the frequency domain. Mathematically, the pulse is Fourier transformed, filtered, and back-transformed to yield a new pulse::$E\text{'}(t)\; =\; mathcal\{F\}^\{-1\}\{mathcal\{F\}\{E(t)\}(omega)f(omega)\}(t).$It is possible to design an optical setup with an arbitrary filter function $f(omega)$ which can be complex-valued, as long as $|f(omega)|le1$. Figure 1 shows how a bandwidth-limited pulse could be transformed into a chirped pulse (with a filter only acting on the phase) or into a more complex pulse (with the filter acting on both phase and amplitude).

Optical design

Basic principles

Typically, a pulse shaper is based on the design of a pulse stretcher, but in a 4"f" configuration such that the stretcher actually neither stretches nor compresses incoming pulses. This is shown in Figure 2. A diffraction grating directs different frequency (wavelength) components into different directions and each frequency component is focused at a particular spot in the focal plane. A second grating and a mirror are used to recombine the different frequency components. The two lenses have a focal length "f", and the distance from the center of the first grating to the center of the second grating is $4f$.

In the focal plane, undesired frequency components can easily be blocked, which would correspond to a real-valued filter function without any effect on the phase.

To make the filter act on the phase of the frequency components, a slab of transparent material with a varying thickness could be used to introduce an extra frequency-dependent delay, as shown in Figure 3. Although one might think that an extra delay is introduced for longer wavelengths (shown in red), the actual effect is that the pulse as a whole will have a shorter travel distance, mainly because the light has a shorter travel distance to the rightmost grating. This is in agreement with the fact that a Fourier filter $f(omega)=exp(iomega\; au)$ ('linear phase shift') is equivalent to a time-shift $au$.

For a more interesting effect on the pulse shape, a quadratic or higher-order phase shift is needed, as shown in Figures 4 and 5.

Active filters

The examples above are with static filters. With liquid crystal technology, it is possible to create a filter that can have an arbitrary computer-controlled phase and amplitude spectrum. Multiphoton Intrapulse Interference Phase Scan (MIIPS) is a technique based on the computer-controlled phase scan of Spatial light modulator. Through the phase scan to an ultrashort pulse, MIIPS can not only characterize but also manipulate the ultrashort pulse to get the needed pulse shape at target spot (such as Transform-Limited pulse for optimized peak power, and other specific pulse shapes). This technique features with full calibration and control of the ultrashort pulse, with no moving parts, and simple optical setup.

ingle versus double-pass design

In the configuration shown above, the light hits each of the two gratings twice. In many applications, the back-reflecting mirror on the right is omitted, which makes the design simpler. The main disadvantage of such a single-pass design is that the different frequency components do not overlap in space, as can be seen in Figures 4 and 5. However, for many applications, it is only necessary to separate different frequencies in time by only a few picoseconds, which corresponds to just a few tenths of a millimeter of transversal displacement, which is only a minor concern.

Related Techniques

* MIIPS Multiphoton Intrapulse Interference Phase Scan, a method to characterize and manipulate the ultrashort pulse.