THE PHYSICS OF ULTRAFAST LASERS

Transcription

1 QUANTUM ELECTRONICS AP4 Assignment 2000 THE PHYSICS OF ULTRAFAST LASERS By Maire Nic Dhiarmada & Mark Walshe

2 Introduction Science and technology never cease to amaze! No sooner has some physical limit been reached that seems impossible to overcome, than someone somewhere comes up with an ingenious way to not only break this limit, but to surpass it admirably. Take the laser for instance. Nowadays, the newest lasers have a pulse duration of seconds and a peak pulse power of watts. These values are really incomprehensible! This generation of laser is called the Ultrafast or Femtosecond Laser. Back in 1960, the laser was a remarkable discovery and its importance and huge range of applications were recognized instantly. Physicists believed that the area of optics held no more surprises and they had mastered it completely. However, the discovery of the laser blew optics wide open again, as physicists did not expect nonlinear optic phenomena. It was a triumph of science. Naturally, the first (Ruby) laser was not a perfect design and was not very economical, so it needed to be improved upon. As the laser was introduced to more and more applications, better laser design and pulse power was required. And so, after its initial development, the laser s power and intensity increased at breakneck speed until it reached a fundamental limit. This limit was determined by the physical limitations of the system being used at the time. The first method employed to increase the intensity of the laser beam was Q-switching in 1962 [1]. By increasing the losses of the laser while pumping the laser continuously, pulses of high intensity (~10 6 W/cm 2 ) and short duration (~10-9 s) could be achieved when the losses were reduced periodically. Another technique that boosted laser intensity considerably was Mode Locking in This is a method of persuading a large number of amplified modes to oscillate together in phase, giving very fast pulse duration and high pulse intensities. When used in conjunction with Q-switching, the mode locked laser is capable of producing pulses with intensities in the region of 10 9 W/cm 2 and s duration. It was after this development that the evolution of lasers came to a standstill. It was not possible to increase the intensity of the laser pulse any further due to non-linear optic effects, which came into play above the gigawatt level. It was still possible, however, to reduce the pulse duration even further. Had the laser reached its optimum intensity level? It appeared so for 20 years until a technique known as Chirped Pulse Amplification came to the fore in This process could further increase the laser pulse intensity by stretching the pulse, amplifying it to avoid non-linear effects, before finally compressing it back to its original shape. Now, it was possible to generate laser pulses with much greater intensity than ever before. Lasers were breaching into the terawatt regime (10 12 W/cm 2 ). It was now appropriate to refer to them as ultrafast lasers since pulses were approaching femtosecond duration (10-15 s). Since then, the intensities involved have risen even further. These incredible lasers have opened up many previously inaccessible aspects of physics and they are used in some intriguing applications. In this report, we will discuss firstly the important physical ideas, which make it possible to construct Femtosecond Lasers. Key discoveries such as Chirped Pulse Amplification and Mode Locking will be explained in detail. The next thing to look at will be the applications of these lasers and the benefits that they can bring to technology. Finally, we will give a summary and conclusion on the report and mention the hopes and expectations for the future.

3 Mode Locking The generation of ultrashort light pulses is possible with the presence of mode locking, which can generate very narrow pulses. Mode locking essentially locks all the modes in a laser in phase with one another, resulting in short, intense pulses being emitted from the laser. These ultrashort pulses occur as a result of the constructive interference of the laser modes for a short duration of time, and the destructive interference of the modes at all other times. This is in direct contrast to the normal laser, which, due to the absence of mode locking, has independently oscillating modes, and thus a time-varying intensity. To generate an ultrashort pulse, many thousands of modes must be locked in phase. Dye lasers dominated advances in ultrashort lasers until the late 1980 s. The development of diode-pumped solid-state lasers changed all that, providing a more compact and reliable type of laser. Many new techniques of mode-locking had to be introduced with this new development, resulting from the fact that diode-pumped solid-state lasers have a gain cross section that is about 1000 times smaller than that of dye lasers. [Optics Letters, 16: , 1991 Femtosecond pulses from a continuously self-starting passively mode-locked Ti:sapphire laser U. Keller, G.W. Hooft, W.H. Knox, J.E. Cunningham]. The methods of achieving mode locking can be split into three main techniques: passive mode locking, active mode locking, and self-mode locking: Passive Mode Locking Passive mode locking is obtained by inserting a saturable absorber into the laser cavity, preferably close to one of the mirrors. A saturable absorber is a medium whose absorption coefficient decreases as the intensity of light passing through it increases; thus it transmits intense pulses with relatively little absorption and absorbs weak ones. When a saturable absorber is used to mode lock a laser, the laser is simultaneously Q-switched. A saturable dye can mimic the fast shutters used for active mode locking (explained later), providing the pulse has a sufficiently large irradiance to allow it to saturate the absorber each time it passes through. The recovery time must be shorter than the roundtrip time, otherwise multiple pulses could form. Initially, the laser medium emits spontaneous radiation, which gives rise to random temporal fluctuations of the energy density. Some of these fluctuations may be amplified by the laser medium and grow in irradiance to such an extent that the peak part of the fluctuation is transmitted by the saturable absorber with little attenuation. The low power parts of the fluctuation are more strongly attenuation and thus a high-power pulse can grow within the cavity. Adjusting the concentration of the dye within the cavity may cause an initial fluctuation to grow into a narrow pulse bouncing to and fro within the cavity, producing a periodic train of mode-locked pulses. Active Mode Locking This principle essentially involves placing a very fast shutter in the laser cavity. Mode locking takes place if the shutter opens only for a very short period of time, every time the light pulse makes a complete roundtrip in the cavity. This results in the constructive interference of the laser modes for a short duration of time, and destructive interference of the modes at all other times, causing the coupling of modes to occur, as previously described. It is, however, not necessary to

4 fully close the shutter. A sinusoidally modulated transmission with a modulation frequency equal to the intermode frequency separation =c /2L causes the attenuation of any radiation not arriving at the time of peak transmission. Two coupling mechanisms for lasers are: amplitude modulation and phase modulation. These produce additional electric field components called sidebands on each side of the mode closest to the centre of the laser gain profile. These sidebands have the same frequencies as the cavity modes on each side of the central mode. Energy is transferred from the central mode to these side modes at each pass through the modulator. Once the laser gain has been increased to include gain at these side mode frequencies, these side modes remain locked. These side modes will, in turn, transfer power to modes further out which will still be locked to the central mode. Self-Mode-Locking The self-mode-locked laser is based on the laser material, titanium-doped sapphire. Self-locking works on the principle that high energy pulses travelling through a material cause an increase of the index of refraction of the material at very high intensities. As a laser beam is most intense at it s centre, the light at the edges travel faster, causing a lens-like-effect, called the self-mode-lock or Kerr-mode-lock effect. According to U. Keller, G.W. Hooft, W.H. Knox, J.E. Cunningham [Optics Letters, 16: , 1991 Femtosecond pulses from a continuously self-starting passively mode-locked Ti:sapphire laser ] self starting mode locking is a serious problem, typically started by techniques such as banging or misaligning the laser, moving an end mirror or modulator This temporarily increases the noise of the laser, producing a sufficiently strong noise spike to initiate passive mode-locking. The output of a laser is directly affected by the relative phases, frequencies and amplitudes of the modes. This is apparent from the expression for the total electric field as a function of time : N-1 E(t) = Σ (E 0 ) n e i(ωn t + δn) n=0 where (E 0 ) n, ωn and δn are respectively the amplitude, angular frequency and phase of the nth mode. In lasers that are mode locked, we can presume that δn = δ. Therefore: N-1 E(t) = E 0 e Σ iδ e i ωn t n=0 The angular frequency ωn can be expressed as ωn = ω - ω, where ω is the angular frequency of the highest frequency mode and ω is the angular frequency separation between modes. Therefore: N-1 E(t) = E 0 e iδ Σ e i( ωn -n ω) n=0

5 N-1 - π i nc t/ L = E 0 e Σ i(ωt + δ) e n=0 where N is equal to the number of modes. or E (t) = E 0 e i(ωt + δ) (1 + e i φ + e 2i φ + + e - (N 1) i φ ) where φ = πct / L. As the term in brackets is a geometric progression: E (t) = E 0 e i(ωt + δ) sin(nφ / 2) sin (φ / 2) The irradiance is I = E (t) E* (t) or I (t) = E 0 2 sin 2 (Nφ / 2) sin 2 (φ / 2) This equation gives a lot of information about the mode-locked laser beam. It firstly shows that the shape of the mode-locked laser pulse is dependent on the number of modes, N. In the time interval t =2L /c (the period of the pulse train), the irradiance I is periodic ( φ = 2π). We see from the equation that the irradiance has a maximum value of N 2 2 E 0 for values of φ = 0 or 2pπ. The irradiance has minimum values of zero when φ = 2π /Ν, or t = (1 / N) (2L / c) p, where p is an integer not equal to zero, or a multiple of N. Thus t, the time duration of the maxima, (when p = 1) is given by (1 / N) (2L / c). This shows that the output of a mode-locked laser consists of a sequence of short pulses, separated in time by 2L /c, each of peak power equal to N times the average power. The ratio of the pulse spacing to the pulse width is approximately equal to the number of modes: (2L /c) = N (2L /c)(1/n) thus to obtain ultrashort pulses, it is essential to have a large number of modes. Chirped Pulse Amplification Although it was possible to achieve sub-picosecond pulses with dye and excimer laser systems, the intensities of their respective beam pulses were very low. The need at the time was for high intensity pulses, not just pulses of short duration. A process first devised in 1985, chirped pulse amplification, or CPA, broke the stalemate that had hindered the progress of laser intensity for 20 years. Scientists had been unable to increase laser pulse intensity above gigawatt level. At these intensities, non-linear quantum electrodynamics (nonlinear optics) is observed. The most

6 obvious effect is that the refractive index within the resonator cavity becomes intensity dependent and non-linear. This phenomenon is known as Self Focussing or the Kerr Effect. The refractive index is then given by: n = n 0 + n 2 I where I is the intensity, n 0 is the refractive index of the medium at low intensities, and n 2 is the non-linear refractive index [3]. For a laser beam travelling through the cavity, the beam will experience a greater refractive index at the central axis than at the edges. It follows that the outside edges of the beam will travel at a higher velocity than the centre of the beam. As a result, the beam will self focus, causing it to become distorted and having the capability to damage the laser if the focus occurs within the cavity. Other non-linear effects include Filamentation, which describes the breaking up of the laser beam into beamlets, and Self Phase Modulation, where the phase of the laser beam may become distorted, resulting in an increase or decrease of its frequency [7]. CPA can avoid all these unwanted effects and still reach unprecedented intensity levels. It is also possible to modify existing large laser sources to accommodate for CPA. Solid state amplifiers used in lasers were amplifying at energy densities close to their saturation value, E s, and so were reaching a limit in increasing the intensity of the pulses. The maximum possible intensity, I s, which can be amplified without saturation of the amplifier, is given by: I s = E s / T p where T p is the duration of the pulse [3]. When this saturation value is reached, the amplifier will not operate efficiently to give the highest pulse intensity. This can be avoided by using CPA and a solid state material, which has a high energy bandwidth. The basic process of CPA is relatively straightforward, but there is a great deal of underlying physics to accompany it. The initial pulse is received from the laser in femtosecond form. However, due to the nonlinear effects described previously, it is impossible to amplify the pulse to the desired level in its current state. The solution? Alter the characteristics of the pulse. By stretching the pulse in time, its intensity will be lowered and it will be possible to amplify it to a large intensity without any undesired effects. The pulse can be restored to its original composition by compressing it. The end result is a very high intensity, high bandwidth, ultrafast pulse. There are several methods of achieving the stretching and compression that is required for CPA. The first system designed for CPA comprised of a length of single mode optic fibre to stretch the pulse and a pair of diffraction gratings in parallel to recompress it. The fibre lengthens the pulse in time by slowing down higher frequencies in the blue region of the spectrum with respect to the lower frequencies in the red region with positive group velocity dispersion (GVD). Now the pulse is frequency coded and can be amplified safely without any undesired effects. For the final stage of the process, the pulse is directed to pass between the two parallel diffraction gratings. This has the opposite effect to the fibre since it slows down the red region with respect to the blue, thus recompressing the pulse by negative group dispersion. Although recompressed, the pulse will not be of perfect shape since the optical properties of the fibre stretcher and grating compressor are not matched correctly. This limits the stretching/compression ratio attainable by the system.

7 In the majority of cases, the highest intensity beam possible is desired from the laser, so the beam must be extremely coherent and diffraction limited. The best way to achieve this is to have the largest stretching/compression ratio available. Usually somewhere in the region of 10 3 to 10 5 is a good value [3]. Another necessity is to amplify large spectra of the pulse. It is good practice to match the stretcher and compressor characteristics in the system to allow the beam to be manipulated without being distorted. In fact, all dispersive elements within the laser must be matched [4]. A system that has been designed with this idea in mind comprises of a telescope stretcher and a grating compressor. The telescope with a magnification of 1 is placed between two anti-parallel diffraction gratings to stretch the pulse, while the pair of parallel gratings is again used to compress the pulse. This system is very well optically matched so as to achieve the stretching/compression needed to create ultrafast pulses. Pulses of less than 10 fs duration have been achieved with this setup. Figure 1: A schematic diagram showing the Chirped Pulse Amplification Process [6]. CPA also helped to revolutionise the energy storage media used in laser systems.ultra broadband amplifiers such as Titanium: Sapphire and Neodymium: Glass replaced dyes and excimers, which were not capable of amplifying the enormous spectra of the new generation of ultrafast pulses [2]. For linear amplification of the pulses, the bandwidth of the amplifier must be greater than that of the pulse, and the amplifier must not be saturated. The new high bandwith amplification media met this criteria well. Again the main points of CPA are:

8 Generate an ultrashort pulse Short Pulse Oscillator, Stretch the pulse by positive dispersion Stretcher, Amplify the pulse without damage to the laser Ultra Broadband Amplifier, Compress the pulse with negative dispersion Compressor, Applications The arrival of lasers capable of producing femtosecond pulses has created a lot of excitement in physics circles. These lasers can recreate conditions that were previously impossible to find on earth. With this in mind, ultrafast pulses can possibly recreate stellar conditions. These pulses can reach petawatt powers, gigagauss magnetic fields, terabar light pressures and electron accelerations of the order of m/s 2, values that can only be found at the core of a star or in the region approaching a black hole [4]. Further research and modeling in this area of astrophysics would greatly increase our knowledge and understanding of stars and our galaxy. It may also give more insight into Einstein s Theory of General Relativity. Femtosecond lasers are much more efficient and effective when used for industrial applications such as drilling, cutting, and welding [8]. The laser is usually focussed very carefully onto only the particular part of the workpiece that needs to be operated on. A huge amount of energy is delivered to this area to melt or boil material to remove it, depending on the process in question. Although previous lasers were competent in this regard, the pulse duration was not short enough to prevent heat diffusing into the surrounding area of the material. Any vaporised material may also be deposited on the work surface leading to rough edges. Also when a large burst of energy hits the material surface, it will create a shockwave that travels radially outwards from the point of impact. The combined effect of the heat and the shockwave usually damages the material. The damage can range from changes in the crystalline structure to cracks near the area being worked on. This is where the advantages of ultrashort lasers can be seen to good effect. The pulse is so short as to prevent heat energy dissipating out from the point of impact of the beam. This point is actually heated well above its boiling temperature creating a plasma, which acts to protect the surrounding material. The result is that no other part of the material has been acted on by the laser pulse and no clean up is required on the cut or hole made. The laser can be set up to remove tiny amounts of material, which makes it suited to cutting intricate shapes (micromachining) or working on very small or hazardous objects. Since these lasers can be so well controlled, they have been given a pivotal role in specific areas of medicine such as eye surgery. Operations to correct eye disorders such as myopia are now being corrected using a femtosecond laser. The laser takes the place of a surgical blade in removing a very thin slice from the cornea by creating a pattern of minute holes.

9 Figure 2: Picture (a) shows a hole cut by a conventional laser leaving cracks caused by thermal stress, while Picture (b) shows a very clean hole cut by a femtosecond laser with no damage to the surrounding material. Picture (c) shows a cut made in stainless steel with an infra-red laser leaving rough edges and Picture (d) shows a cut made in the same material with a femtosecond laser leaving a smooth clean cut [7]. At present, as the world s energy resources continue to dwindle, great efforts are being made to achieve efficient nuclear fusion. The use of ultrafast lasers is an integral part of this research. A technique known as inertial confinement fusion has been the most successful method so far in achieving fusion. It involves heating the surface a balloon filled with deuterium and tritium using high power lasers to create a very dense plasma [4]. The heating process must be uniform over the surface area of the balloon to ensure uniform compression of its contents by implosion. As the core reaches maximum compression, it is bombarded with an ultrafast pulse to ignite it and initiate nuclear fusion and thermonuclear burning. The process has not been perfected yet, but it is hoped that it will become efficient in the future. Another interesting aspect of femtosecond pulses is the ability to vary their wavelength from the visible to both the infra-red and the x-ray regions of the electromagnetic spectrum. This has led to ultrafast lasers being used to produce soft x-rays by high harmonic generation [5]. The strong electric field produced by the laser pulse can overcome the Coulomb force and pull an electron from an ionised atom, resulting in the electron gaining energy. If this free electron collides with the atom again, they will recombine and the electron s surplus energy will be emitted as a soft x-ray. Thus, as a coherent x-ray source, the femtosecond laser can be useful in microscopy and lithography. Other applications include electron-positron pair creation at very high intensities and the study of quantum electrodynamics; the quantum theory of charged particles and electromagnetism [4].

10 Figure 3: This shows how a femtosecond laser can be constructed on a benchtop! [7] Conclusion: The development of the femtosecond laser is, and will continue to be, of very great importance to science. Providing many breakthrough applications, in areas ranging from the medical field to the industrial field, to nuclear fusion, it has revolutionized the speed and accuracy with which many processes can be carried out. This of course, is a very commendable property, allowing unprecedented precision in such delicate processes as eye surgery. With the invention of the femtosecond laser, there is always the hope for the invention of lasers with even shorter pulse duration. There have been suggestions that pulses as short as an attosecond (one thousandth of a femtosecond) could be attained in the future. This, of course, would be of utmost importance, allowing the motions of electrons, protons and neutrons to be observed. Many benefits would stem from this discovery, including the observation of how drugs work at a chemical level. It has also be suggested that this discovery would make it possible to obtain coherent control of electrical currents in semiconductor devices and in femtosecond networks for digital optical communications. The future of ultrafast lasers certainly looks bright!

11 References Journals: 1. Terawatt Lasers, M.H.R. Hutchinson, Contemporary Physics, Vol. 30, No. 5, Ultrahigh-Intensity Lasers: Physics of the Extreme on a Tabletop, G.A. Mourou, Physics Today, Vol. 51, No. 1, Ultrashort Light Pulses: Life in the Fast Lane, H. Kapteyn, Physics World, Vol. 12, No. 1, Ultrashort Pulse Lasers: Big Payoffs in a Flash, J.M. Hopkins, Scientific American, Sept Femtosecond pulses from a continuously self-starting passively mode-locked Ti:sapphire laser U. Keller, G.W. Hooft, W.H. Knox, J.E. Cunningham. Optics Letters, 16: , 1991 Websites: 6. Figure 1 and 3 from here, Nov Figure 2 from here, Nov Books: 8. Ultrashort Laser Pulse Phenomena: Fundamentals, J-C Diels, Fundamentals of Photonics, B.E.A. Saleh, M.C. Teich, Lasers, Principles and Applications (1987) J. Wilson, J.F.B. Hawkes 11. Lasers, Theory and Practice (1995) J. Hawkes, I. Latimer