A state-of-the-art Titanium Sapphire laser system

Assignment and Laboratory exercise in Laserphysics VT-2005

Introduction

This assignment and demonstration will focus on the so called "kilohertz" laser system. This system is part of the Lund Laser Center and is used for ultrafast physics research. The kHz laser produces femtosecond laser pulses with a duration of about 35 fs (1fs =10-15 s) and an energy of 1.6 mJ at a central wavelength of 800 nm (infra red).

The kHz system comprises four parts. An oscillator that produces 15 fs pulses in the IR, a stretcher that streches the pulses to 180 ps, an amplifier stage that increases the pulses energy up 1.6 mJ and a compressor that compresses the pulses to 35 fs.

Introduction to femtosecond lasers

Pulsed lasers are powerful tools in many research areas and in the industry.Since the very first days of the laser, there has been a quest to achieve shorter and shorter laser pulses. Light pulses shorter than 100 fs were observed for the first time in 1981; pulses of 6 fs were obtained by a group at Bell Laboratories in 1987.

These ultra short pulses are of great interest for many applications.

- In the temporal domain: fs light pulses are equivalent to a super-stroboscope and enable us to look at ultrafast phenomena. For instance, one can observe the first steps of chemical reactions.

- In nonlinear optics: the energy is released during the very short duration of the pulses. Very high peak powers (up to Petawatts) can be reached using short pulses.

The generation of ultrashort pulses implies the amplification of a broad frequency spectrum. The time-frequency uncertainty relation gives with a almost equal to 1 (depending on the temporal profile chosen). From that relation we can see that to a small t corresponds to a large frequency spectra . This important relation will have many consequences on the choice of the different parts used to build the laser. (The amplification media should amplify a broad frequency spectrum, the mirrors must be broadband, etc.)

Titanium sapphire has an energy level diagram, which is typical for solid laser materials (four level lasers). The unique property of this material is a broad absorption band, which can be pumped by fixed-frequency lasers and a wide lower laser level. The bandwidth over which laser can be obtained is wide enough to allow for 3 fs long pulses. The absorption band has its peak at around 500 nm and the emission spectrum is peaked around 800 nm. Since the absorption and emission bands are well separated, losses due to reabsorption of the laser radiation are minimized.

Two conditions determine the frequency components available to build up a wide frequency spectrum. The first is the (approximately) resonance condition for a standing wave: n=L or expressed in frequency =nc/2L where L is the length of the cavity. The second one is the spectral bandwidth of the laser. The laser bandwidth is mainly limited by the gain profile of the amplifying medium.

Passive Kerr lens mode locking(Svelto 344- 345)

In a cavity consisting only of a gain medium, end mirror and output coupling mirror, all modes are oscillating in random phase. By introducing additional components in the cavity, it is possible to phase-lock these modes to each other. Depending on the method by which the phases are locked one refers to either active or passive mode-locking. When the phase difference between the modes is constant, the modes are oscillating in phase and interfere constructively. If we add the E-fields from the standing modes, the sum as function of time will be a short pulse propagating back and forth in the cavity.

At low intensities, the refractive index (for a given wavelength) is constant. At high intensities, the refractive index vary by n=n1+n2I. Due to the fact that the laser has a spatial intensity variation, the refractive index will be larger in the center of the beam, where the intensity is the highest. This makes the crystal behave like a lens (referred to as a Kerr lens). A Kerr lens can be used to create losses for CW radiation, whereas the losses for high intensity pulses obtained by mode-locking are minimal. Thus, a Kerr lens can be used for passive mode-locking. It is common that Kerr lensing in the amplifying medium is used. The amplifying medium is used both to obtain gain and to obtain mode-locking.

Dispersion compensation (Svelto 347-355)

Due to dispersion, different frequency components propagate with different velocities in all materials. In solids, glass, crystals etc., the effect can be significant. In nearly all materials, shorter wavelengths propagate slower than longer wavelengths. This phenomenon is known as positive group velocity dispersion (GVD). The consequence is that a short pulse consisting of many wavelengths is stretched in time. In order to compensate this effect, negative group velocity dispersion is needed. Negative GVD means that short wavelengths propagate more rapidly than longer wavelengths. This can be obtained with the prism arrangement shown below.

Amplification of the laser light

As mentioned previously, the oscillator of the kHz laser system delivers laser light pulses of 15 fs with an energy of 2 nJ. This power is not enough for the applications we are aiming at. The laser pulses are then amplified to 2 mJ, using the Chirped Pulse Amplification technique (1989).

The figure below resumes the main steps of the amplification.

Pulse stretching

If we directly amplify the short pulses from the oscillator, we will reach very high peak intensities. The high intensities would damage the amplifier medium. In order to decrease the peak intensities we induce a varying phase (a chirp) on the different spectral components of the pulse, leading to a stretching of the pulse duration. In the kHz system a grating stretcher is used. The different frequencies will not have the same optical path length, and the pulses get as long as 180 ps.

Amplification stage

The stretched pulses (180 ps) are sent into the first amplification stage. This is performed by using Pockel’s cells and polarizers.

The first amplification step is done by a regenerative amplifier cavity, with two concave mirors. The selected pulses do a few round trips before they are coupled out. The Ti:Sapphire crystal in the regenerative cavity is pumped by a frequency doubled Nd-YLF laser. The beam is then sent to two other amplification stages. In these amplifiers the pulses pass the gain medium twice (two pass amplifier).

The amplification of a laser pulse, through an amplifier medium – assumed to have a 4-level energy scheme – is given by:

,

where are the input, output fluence (energy/beam area) of the amplified pulse, and the saturation fluence. is the unsaturated gain, and is connected to the upper level population (N0) through

.

If the energy per unit area absorbed by the amplifying medium is given by p, the pump wavelength is λp, and the amplified pulse has a wavelength of λa, then the fluence available for amplification is

so that

To describe a regenerative or multipass amplifier, the above equation has to be solved for the consecutive passes through the crystal. In that case, T - the transmission of the crystal - should also represent other losses (e.g. mirror reflection) in the cavity through a roundtrip. The unsaturated gain coefficient g0 decreases after each pass, with the decrease of the upper level population. We neglect any loss of the upper population through spontaneous decay mechanisms, so in the nth round we have

.

Compression

After the amplification we still have long pulses. In order to achieve high power we have to recompress the pulses. To achieve that, we use a grating compressor. As in the stretcher, the different optical frequency components will not have the same path in the cavity. The compressor compensates for the chirp of the pulses and recompresses the pulses in time. We then get high intensity peaks.

Measurement techniques

To be able to control the pulses we need to measure and characterize our fs pulses. The only methods available on that timescale (fs) are optical. The fastest electronic detector can only detect on a ps timescale. We have to use the pulse itself to measure it.

Preparatory exercises

1) Calculate the average and the peak power at the output of the kHz oscillator (2nJ, 15 fs at a repetition rate of 89MHz).

2) After the grating stretcher, each pulse have a duration of 180 ps. Calculate the average and peak power of these pulses (take into account that there is a 50% loss in the grating stretcher).

3) Calculate the peak intensity in W/cm2 at the output of the amplifier (1.7mJ, 35fs) if the beam is focused on a target with a spot size of 1mm diameter.

4) It is often difficult to have an idea of a femtosecond. To be aware of how short it is, calculate the distance covered by the light in 1 fs. The cavity of the regenerative amplifier is approximately 3.6 m long. Calculate the time needed for the seed pulse for a round trip. To achieve optimum amplification, we have approximately 20 passes. What limit that presents for the repetition rate of the amplified pulse train? (The real, 1 kHz repetition rate is imposed by the repetition rate of the pump laser.)

5) Assume a Gaussian shaped pulse in the time domain of 15 fs with a central wavelength λ0 of 800nm. Determine the corresponding spectrum:

- in the angular frequency domain ω0, Δω.

- in the wavelength domain λ0, Δλ.

If by spectral narrowing the bandwidth is reduced to half, how will the pulse duration change?

Assignment

1) Mode locking

The optical length of the oscillator cavity is 1,7 m. Calculate the mode spacing in the frequency domain.

The bandwidth of a Ti:Sapphire crystal is 100 THz centered on ν0=375 THz , which enables generation of 3 fs pulses. The spatial extension of a fs pulse is ~10 μm. In this exercise, it is desired to have a longer pulse to be able to visualize the pulse in the cavity. We reduce the bandwidth to 10 GHz. The broadening mechanism is assumed to be mainly inhomogeneous, which implies a Gaussian line shape. The intensities of the modes in the cavity are proportional to the gain. Plot the electric field amplitude of the modes as a function of mode frequency.

The cavity modes are standing waves. Plot the superposition of the cavity modes for random phases of the modes at t=0 in function of the cavity length. The Matlab command: phi=2π*rand(1,N) is useful. Make a time evolution of the superposed standing waves (choose an appropriate timescale).

Under mode locked operation the phase difference between consecutive modes is constant. Plot the electric field in the cavity at time t=0 and make a time evolution.

Calculate the temporal length of the pulse out of spatial extension. The time frequency dependence of a Gaussian pulse is:

Does the calculated temporal length fulfill the time frequency dependence?

2) Dispersion

Titanium Sapphire is a broadband amplifier medium. We can assume that in the frequency domain we get is a Gaussian spectrum:

The oscillator of the kHz lab delivers pulses whose spectra is centered on λ0=800 nm and a width of Δλ=70nm. With Matlab or any other program, retrieve the shape of the pulse in the time domain for a phase φ(ω)=0 (no phase difference between the different spectral components).

Warning: when computing a Fourier transform with Matlab the Fourier transformed vector should be equally spaced with omega.

When a pulse with a broadband frequency goes through a material of a length L whose refractive index n(ω) changes with ω the phase can be written as . That can be written under a Taylor expansion form:

Each coefficient is a constant that can be obtained for a given material.

Modify the former program to add a phase to the spectrum. Retrieve the pulse in the time domain for several α1(ω), and α2(ω). Can you identify the changes induced by these chirp rates? Plot these results on a graph.

Hint: typical order of magnitude for α1(ω) is 10-15 s, α2(ω) is 10-28s2

A typical dispersive media is a SF57 glass plate whose chirp rate is α2=2,25.10-25 s2/m. Compute the passage of a pulse (λ0=800, Δλ=70nm) through 1mm of this material. Plot the incoming and outgoing pulses on a graph and estimate their duration.

3) Amplification

Using the following numerical values to calculate the output energy of the amplified pulse after each pass, until the amplification reaches saturation, and the pulse energy starts to decrease. Plot the pulse energy as a function of the number of passes. Vary the pump energy and observe how the build-up changes.

sat = 1 J/cm2

Ep = 7 mJ or 14 mJ, 95% of what is being absorbed by the medium

d = 0.08 cm diameter of both beams

Ein = 0.2 mJ for the first pass

T = 0.9

λp = 532 nm and λa = 800 nm