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Ultrafast Optics Laboratory exercise in Advanced Optics and Lasers VT 2015 Computer exercises about modelocking How to create 100 fs light pulses How to measure short laser pulses 1 Introduction The shortest event created my man is a compressed laser pulse from a modelocked laser. The shortest visible laser pulse that has been created lasted for 4 fs (when this is written in June 2003). During 4 fs, light travel 1200 nm. These short laser pulses have a wavelength of about 800 nm. This corresponds to a period time of 2.7 fs. (Light pulses in the ultraviolet spectral range with a sub-femtosecond pulse duration (<100 as) has been created by a process known as high-order harmonic generation). During the lab, we will not work with pulses that are quite that short. We will be working with pulses that last for about 100 fs. The fastest available electronic detector has a temporal resolution of about 300 fs. Not even this detector would be suitable for measuring the duration of the pulses we create during this lab. We will instead use the shortest event available (The laser pulse itself) and measure its duration using autocorrelation. Modelocking is a relatively abstract concept. We will during the lab attempt to visualize modelocking through a few computer exercises. The material in the lab manual is intended to give an overview of the material needed to benefit from the lab. It may be a good idea to read chapter 15.4D in Saleh&Teich about modelocking. 2 Modelocking and short pulses In order for pulses to be short, many frequency components must be available. (Heisenberg’s uncertainty principle) But how is the pulse duration effected by the relative phase of these frequency components? Longitudinal modes Two conditions determine the frequency components available to build up a wide frequency spectrum. The first is the resonance condition for a standing wave: n=L or expressed in frequency =nc/2L The second one is the spectral bandwidth of the laser. The laser bandwidth is mainly limited by the gain profile of the amplifying medium. In a cavity consisting only of a gain medium, end mirror and output coupler, 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 modelocking. 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. 3 Active modelocking (Saleh&Teich 615-620) In active modelocking, an external rf-field is applied to an acousto-optic modulator in the cavity. The rf-frequency is chosen so that the sidebands that are generated match the frequency separation between adjacent lasermodes (rf: =2c/). This gives a preference for the modes to oscillate in phase. Passive modelocking (Saleh&Teich 615-620) When considering passive modelocking, it is easier to think in the temporal domain. The idea behind passive modelocking is to introduce a medium in the cavity, which has high losses for low intensities and low losses for high intensities. An example of such an element is a saturable absorber. For short pulses structures the losses are low. When the medium is pumped the population in the ground state is lowered which makes the absorption decrease and thereby the losses. If the laser pulse duration is short, relaxation to the ground state does not occur while the pulse lasts. If on the other hand the laser operates at low intensities providing CW radiation the population in the upper state has time to relax and we have a constant high population in the ground state and high absorption. This is the way a saturable absorber gives preference to short pulses, which are obtained when the cavity modes are oscillating in phase. Passive Kerrlens modelocking (Saleh&Teich 619) 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 appear 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 modelocking are minimal. Thus, a Kerr lens can be used for passive modelocking. It is common that the Kerr lensing in the amplifying medium is used. The amplifying medium is used both to obtain gain and to obtain modelocking. 4 Titanium sapphire crystal Aperture Low intensities large losses Laser beam x n=n1+n2I I High intensity small losses The beams spatial profile creates the "Kerr lens" Dispersion compensation (Saleh&Teich 184-186) Due to dispersion, different frequency components propagate with different velocities in any material. In solids, like different types of glass, crystals etc. the effect can be substantial. In nearly all materials, shorter wavelengths propagate slower than longer wavelengths. This phenomenon is known as positive group velocity dispersion (GVD). The consequence of this is that a short pulse consisting of many wavelengths is prolonged in time. In order to compensate for this something with negative group velocity dispersion is needed. Negative GVD means that short wavelengths propagate a shorter optical path. This can be obtained with the prism arrangement shown below. Prism pair with negativ group velocity dispersion Short wavelengths are deflected more P2 P1 Longer wavelengths travel a longer optical path 5 laser in Titanium sapphire Titanium sapphire has an energy level diagram, which is typical for solid laser materials (four level laser). The unique properties of this material are 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 at around 800 nm. Since the absorption and emission bands are well separated, there are minimal losses due to reabsorption of the laser radiation. 2 Relaxation 3 Pump Lasing 500 nm 800 nm 4 Relaxation 1 6 Equipment The Ti:Al2O3 laser (The titanium sapphire laser) Note; The set-up will vary from one year to the other. Please read it as an orientation without paying too much attention to detail. The titanium sapphire laser is built from 7 components (+an additional lens to focus the pump radiation). See the figure below. OC CM1 CM2 P2 L pump from Nd-laser C M P1 P1,P2 prisms CM1, CM2 curved mirror, krökt spegel (these are transparent for the pump radiation) M mirror, spegel C crystal, kristall OC output coupler utkopplingsspegel L lens for the pump laser The components include two plane end mirrors, two prisms to give a negative GVD, two spherical mirrors surrounding the amplifying medium. The titanium sapphire crystal works as gain medium as well as a Kerr lens. When the laser is optimized for CW operation (not modelocked) the two curved mirrors are placed symmetrically around the titanium sapphire crystal. They are placed such that the focus from the crystal is imaged a few meters behind the end mirrors. (The curved mirrors are slightly more than one focal length away from the center of the crystal.) This is for the same reason that curved mirrors often are used in lasers, the g1*g2 product should be less than 1 in order for the laser to be stable! (More on this in Saleh&Teich chapter 10.2) When the laser is optimized for modelocked operation, one of the curved mirrors is moved forward. The spatial profile of the laser inside the crystal is no longer optimally matched to the pump volume defined by the green light from the pump laser. The movement of the curved mirror is compensated for, by the Kerr lens, as soon as the laser is modelocked. The laser is optimized for short modelocked pulses. Expressed in terms of the stability diagram, the laser is closer to an unstable region when the laser is not modelocked. In addition the laser spatial 7 profile in the gain medium has a better overlap with the pumped volume in modelocked operation compared to CW operation. The laser in the lab has been set up in this way, but when the titanium sapphire crystal is pumped, lasing will start where the gain is highest (a small number of modes at the peak of the gain medium). The laser emits CW radiation, but since a number of modes are present and interference may occur, the intensity will vary slightly with a random temporal structure. (Compare to what you observe in the computer exercises.) By introducing a phase perturbation in the system, many of the modes may randomly get the same phase. When this occurs, an intensity spike is obtained. (Compare to the computer exercises.) When this happens, the titanium sapphire crystal will start to work as a Kerr lens. For lower intensity radiation in between the spikes, the losses will be large. In the temporal domain, we observe that the randomly generated pulse will start take over as its losses are lower. In the frequency domain this means that we have obtained a number of laser modes which are oscillating in phase. The autocorrelator The autocorrelator consists of two laser beams with k-vectors Ka and Kbwhich cross at a small angle in a frequency doubling crystal. The geometry can be chosen such that the two generating and the generated beam with double frequency fulfill either of the phase-matching conditions. (Ka+Ka=Ka2) or (Kb+Kb=Kb2). To express this differently, both of them give rise to frequency doubled radiation. It is however also to obtain phasematching by the condition Ka+Kb=Kab2This frequency doubled radiation propagates in a direction, which is defined by the vector sum Ka+KbThis means that the generated beam propagates in between the two generating beams. For a pulsed laser, this third beam can be generated only if the generated beams are temporally overlapped in the crystal. A sketch of an autocorrelator is shown below. 8 PMT M mirrors BS beam splitter KDP Frequency doubling crystal PMT Photo multiplier tube M1 KDP 20 Hz 1mm M2 M4 BS M3 Manually adjustable The autocorrelator The beam is split up into two equally strong pulses, which are delayed by propagating different paths in the two arms of the autocorrelator. Then they are spatially overlapped in the crystal. By moving one of the mirrors in the autocorrelator they can also be temporally overlapped. By moving the scanning mirror around the point where a temporal overlap is obtained, it is possible to determine the temporal structure by measuring the intensity as function of the mirror position. The only thing one needs to know to calibrate the autocorrelator is the speed of light in air. Mathematically we can express the signal as S() = (t-)*I(t) , where I(t) is the pulse shape and is the delay between the pulses. The integral above is known as the autocorrelation function. This has been a mathematical tool long before the duration of laser pulses was measured with autocorrelators. The spectrometer The laser beam is incident on a slit. Diffraction yields a divergent beam, which illuminates the grating. The 1st order is imaged onto the output plane of the spectrometer. The output plane hits a 1-dimensional readout camera which is connected to an oscilloscope. 9 The power meter The power meter has a build-in thermo-resistor. This is mounted in a connection similar to a Wheatstone’s bridge. The thermo-resistor gives a measure of the temperature and thereby the absorbed average power. The photo diode The diode is made from a semi-conductor material. Free carriers are created by the optical field. These are accelerated through the potential difference generated by a 9V battery. The current generated by the carriers is measured over a 50 ohm resistor. The oscilloscope A digital oscilloscope Tektronix (TDS 724) will be used. It has an analog bandwidth of 500 MHz and a digital sampling rate of 1 Gsample/s. Four signals are connected. The signal from the photodiode monitoring the pulse train (CH2). The signal controlling the wave generator which determine the position of tone of the mirrors in the autocorrelator (EXT1) and the signal from the detector in the autocorrelator (CH1). The fourth signal is the signal from the spectrometer (EXT2). 10 Practical laboratory exercises Computer exercise The program MODES.exe visualizes a number of standing modes in a cavity. How are the frequencies related to each other? At the bottom you can see the absolute value of the sum of E-field Describe what you see! Modify the settings! Describe what happens! Describe what you see in terms of the concept of modelocking. The program modlas.exe is designed around two windows. The first show the frequency composition and the second the temporal structure. Using the menus, you can set the laser bandwidth, the cavity length, the frequency width of a single laser mode and the phase relationship between the modes. Hint: If you click inside a window, you can read the time (frequency) and intensity for this time (frequency). Set a short cavity length of about 0.1 m. How is the pulse shape influenced by the number of modes? (For a given cavity length this is coupled to the spectral width). How does the number of modes influence the pulse duration? How does the cavity length influence the distance between pulses? How does the spectral shape influence the temporal structure? What happens when phases are set to random? Can “pulse-like” structures occur? How is this connected to the start-up of the titanium sapphire laser? What happens with well-defined phases but random amplitudes? Which are more important, controlling phases or amplitudes? What happens with equal amplitudes and a chirped pulse? What is chirp? What importance can it have to the mode-locking process? 11 Laboratory work using the laser Use safety goggles for 800 nm! Do not touch the green beam! Do not insert objects into the beam (In particular the green beam)! Stand up in the laboratory! Remove watches, rings and other shiny objects! When the pump laser is turned on, the titanium sapphire laser will start to emit laser radiation. Make sure that the laser beam is blocked (i.e. by a power meter)! The instructor will show you how to modelock the laser. What happens to the output power as the laser is modelocked? Why? The curved mirror CM2 focus the spontaneous emission from the crystal. Measure the distance from the focus to the end mirror. (The supervisor will tell you the distance from the crystal to the end mirror). You can now compare this which is near the stability limit to your FRED simulation. The supervisor will move CM2 to a new position about 1 mm more away from the crystal. Measure the output power. Are we in a more stable or unstable regime for the CW radiation? Is it possible to modelock the laser? Explain! The supervisor will move CM2 back and modelock the laser. Observe the temporal structure of the laser radiation using a photodiode and the oscilloscope. (Modelocked and not modelocked.) What happens to the temporal structure when the laser is modelocked? How does this compare to the results from the computer exercises? What information can we obtain from the temporal structure? Observe the spectrum using the spectrometer. What happens to the spectral width as the laser is modelocked? Measure the spectral width! How short pulses are it (in principle) possible to get from the laser? 12 When looking for a signal with the autocorrelator, how carefully must the arm lengths be adjusted? Compare the autocorrelator to the sketch in the manual. Identify the different components. Scan the adjustable arm until you observe a signal that depends on both beams. Start the wave generator and study the signal using the oscilloscope. How can we calibrate the time scale? What is the width of the autocorrelation function? What is our pulse duration? (Assume a Gaussian shape). Compare the pulse duration to what you calculated from the spectral shape. Is the pulse Fourier limited? How is it possible to obtain even shorter pulses? What is the peak power? 13 Preparation problems Solve these problems before the lab 1. The shortest pulse was 3.4 fs in duration. Assuming a Gaussian pulse shape, how wide was the pulse in the frequency plane? 2. With help from the figure showing the autocorrelator, determine how much the temporal delay between the pulses is changed as the mirror M2 is moved 30 m. 3. 4. Fourier transform the gaussian E=E0exp(-(t/T)2+it) (or find it in a table). What is the FWHM in the temporal and frequency domain respectively? The product of these full widths at half maximum is referred to as the “time-bandwidth product”. What is it for a Gaussian? In the laboratory we observe the intensity (not the e-field). How does the result compare to the value given by Saleh&Teich pages 938-939? Do you want to modify your result from problem 1? The shape of the autocorrelation signal S(t I t d may make you associate with a convolution (faltning in Swedish) integral. We want to measure the pulse duration and pulse shape. We can do that by measuring the autocorrelation signal. Autocorrelation means that the pulse is convoluted with itself. What is the relation between the FWHM of the autocorrelation signal to that of the pulse? Assume a Gaussian pulse shape. Hint: F(g*h)= F(g)F(h), F denote the Fourier transform, * denotes an operation called convolution. (If you don’t know what a convolution is – skip this problem) 14 5. 6. A modelocked titanium sapphire laser emits a beam with 300 mW average power at 800 nm. The wavelength width is 25 nm. (FWHM in intensity). The optical path length between the end mirrors is 1.8 m. What is the peak power in the pulses? Make suitable assumptions! How many modes are locked in the laser in problem 5? Additional reading Saleh & Teich: Fundamentals of photonics 2nd edition Modelocking (15.4D), pages 615-620 Group Velocity & Group Velocity Dispersion, pages 184-186 Measurement of Intensity Autocorrelation, pages 1002-1003 15