Ultrashort Light Pulses: Picosecond Techniques and Applications
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The pulse formation is mostly determined by balancing between the net gain and losses. As a result, a pulse profile becomes shortened, and the pulse duration obtainable in this case is estimated by [ 4 ]. As will be discussed later, the laser pulse can be broadened by the dispersion. Under a proper condition, the shortening and broadening processes can be balanced. Thus, for a slow saturable absorber with the soliton effect, a short laser pulse is generated by the self-phase modulation SPM in combination with an appropriate amount of negative dispersion.
In this case, the pulse duration can be estimated by [ 4 ]. The laser pulse is formed when the loss decreases below the gain. The gain can be either unsaturated or saturated during the saturation absorption process. Under the unsaturated gain, the laser pulse gains energy quickly in the beginning of the saturation absorption process. When the gain is saturated during the saturable absorption, the decrease in the gain is slightly delayed and thus the net gain exists for the pulse formation. Laser pulse formation with saturable absorbers.
The gain is not saturated in a , but the gain is saturated in b during the saturation absorption process. Thus, a higher intensity in the pulse center experiences a higher transmittance and a lower intensity in the side is suppressed by the saturable absorption. When a fast saturable absorber is installed in an oscillator, the intensity of a transmitted laser pulse increases in a gain medium at a growing rate of. Here, I sat is the saturation intensity and g 0 is the unsaturated small signal gain.
Thus, the pulse profile is controlled by the intensity, and a higher gain at a higher intensity leads to the pulse shortening. The pulse duration is given by [ 5 ]. In reality, the fast saturable absorbing material operating in the femtosecond regime does not exist. Instead, there are materials having a strong nonlinear effect. These materials can possess the property of ultrafast loss modulation that is induced by the nonlinear effect.
The ultrashort pulse formation by these materials can be considered as the mode locking by the fast saturable absorber. In this section, self-phase modulation as a nonlinear effect which induces ultrafast change in reflection or transmission is discussed. The lower angular frequency in the rising part and the higher angular frequency in the falling part are induced.
When a light pulse passes through a medium, it experiences an intensity-dependent change in refractive index. This phenomenon is known as the Kerr effect. In order to derive how the Kerr effect is related with the instantaneous loss modulation, let us consider the refractive index depending on the laser intensity which is given by. Here, n 0 is the normal refractive index and n 2 is the nonlinear refractive index related with the Kerr effect.
After a nonlinear medium, the phase of the laser pulse is modified by. Thus, after a nonlinear medium, a laser pulse has lower frequency components in the rising edge and higher frequency components in the falling edge. When a Gaussian pulse having these induced frequency components is coherently added to the original one, the constructive interference occurs at the pulse center, but the destructive interference occurs at the edge.
The constructive and destructive interferences induce an instantaneous reflectance change in time. This leads to the pulse shortening effect in time.
Nonlinear coupled-cavity mode-locking technique introduced as the additive-pulse mode locking APM uses the instantaneous reflectance change induced by the self-phase modulation [ 6 ]. A similar phenomenon happens in the spatial domain as well. The phase variation induced by the nonlinear effect makes the wavefront quadratically curved in the radial direction. This means that, after the nonlinear medium with a positive nonlinear refractive index, the phase at a higher intensity becomes retarded to the phase at a lower intensity.
The focal length induced by the quadratic curvature is calculated as. This phenomenon is known as the self-focusing. Kerr-lens mode-locking KLM technique employs the self-focusing to induce an instantaneous intensity-dependent transmittance [ 7 ]. In the KLM technique, a higher intensity part can be separated by the self-focusing in combination with an aperture. A higher intensity part in time and space domain has a higher transmittance because of the self-focusing.
As a result, a higher intensity grows as a laser pulse circulates in a oscillator. The KLM technique forms an ultrashort pulse using this pulse shortening process. In the technique, a gain medium in the resonator also acts as a nonlinear medium that induces the self-focusing. Because of the refractive index of material depending on the wavelength, the phase of an ultrashort laser pulse after material experiences a distortion known as the dispersion. The dispersion is responsible for the broadening of a pulse duration and the distortion of the pulse profile in time.
In order to see the effect of dispersion, let us express the spectral phase depending on the angular frequency as the Taylor expansion,. Because the material has a refractive index depending on the frequency, Eqs. Here, v g is the group velocity and represents the pulse propagation in the material. The temporal broadening by the group delay dispersion is sometimes known as the chirping which originally means the frequency change in time.
Two kinds of temporal broadenings are possible depending on the sign of D 2. When the sign of D 2 is positive, a long red-like wavelength component travels faster than a blue-like one in the pulse. On the other hand, a short blue-like wavelength component travels faster than a red-like one with a negative sign of D 2. Refractive index depending on the wavelength induces the group delay dispersion GDD.
In the positive GDD, the long-wavelength electromagnetic field travels faster than the short-wavelength electromagnetic field in the medium.
Frequency chirping in the laser pulse. In the upper drawing, a short laser pulse experiences the positive chirping, thus the long-wavelength red component arrives faster than the short-wavelength blue component in the laser pulse. In the lower drawing, a short laser pulse experiences the negative chirping, thus the short-wavelength blue component arrives faster than the long-wavelength red component.
The pulse duration is broadened by the positive or negative chirping. Higher-order derivatives in the Taylor expansion affect the pulse profile in time as higher-order dispersions. Even-order dispersions are responsible for the symmetric distortion of a laser pulse in time and odd-order dispersions are responsible for the antisymmetric distortion in the laser pulse. The dispersion control and compensation are key techniques to have a transform-limited laser pulse with a given spectrum. Third-order dispersion TOD and fourth-order dispersion FOD should be considered to be compensated for the generation of transform-limited pulse.
The ultrashort laser pulse cannot be directly amplified in amplifiers because of damage issues in optical elements due to the nonlinear effect and the low-energy extraction efficiency. These hurdles were detoured by employing the chirped-pulse amplification CPA technique devised by Strickland and Mourou [ 8 ].
The key idea of the CPA technique is to temporarily stretch a laser pulse before amplification, to amplify the energy of the stretched pulse, and finally, after energy amplification, to compress the pulse duration to the original level. The control of pulse duration is usually performed by an optical setup which uses the GDD induced by the grating. The stretched pulse duration ranges from few hundreds of ps to nanosecond ns.
The output energy can be estimated from the Frantz-Nodvik equation. In this section, the basic principles for controlling the pulse duration and for amplifying the energy are explained. The control of pulse duration using the dispersion was first proposed by Treacy [ 10 ]. In the proposal, two gratings with a normal separation distance of b are placed in the parallel geometry to induce a negative GDD.
The total amount of GDD can be controlled by the separation distance. Parallel grating pulse stretching scheme. The parallel grating pulse stretcher introduces a negative GDD to the laser pulse. The first-order diffraction is only considered in this case. The diffraction angle is calculated by the grating equation as follows:. As shown in Eq. The positive GDD can be either introduced by installing a telescope in the parallel grating geometry, which was proposed by Martinez [ 11 ]. A telescope is an optical device that induces an angular dispersion. The GDD induced by an angular dispersion is given by.
GDD control by the grating pair with a telescope inside. The grating pair with the telescope can induce the positive and negative GDD depending on the total length between gratings. In many cases, a reflecting mirror can be put after the first lens to reduce the cost and space.
The positive GDD induced by two grating geometry having a telescope can be compensated for with the parallel grating pair. This is important because the pulse duration stretched by the positive or negative GDD can be recompressed by the negative or positive GDD. This is the principle for stretching and compressing an utrashort laser pulse in the CPA technique. The reason for this is that the material dispersion used in amplifier systems also produces a positive GDD. If a laser pulse has negative GDD by a stretcher, the pulse duration of a pulse is shortened as the pulse propagates in a medium having a positive GDD.
This might induce damage on optical elements that the pulse propagates. The other combination that uses a pulse stretcher introducing negative GDD and a pulse compressor introducing positive GDD is also possible. This combination is known as the down-chirped pulse amplification DCPA technique and also demonstrated with a grating stretcher and bulk material compressor. Although the DCPA technique works for the energy amplification of an ultrashort laser pulse, the pulse duration of the pulse is somewhat broadened because higher-order dispersions, such as TOD and FOD, induced by media in the laser system remain uncompensated.
As mentioned earlier, third-order dispersion TOD , and fourth-order dispersion FOD should be corrected or optimized to obtain a nearly transform-limited pulse duration through the pulse compressor. The misalignment in the parallelism of a grating induces an additional angular dispersion in the spatial domain. This is known as the spatial chirping. The spatial chirping can easily be examined by monitoring the intensity distribution of a focal spot.
If there is the spatial chirping in the laser beam profile, a focal spot is elongated along the chirping direction. Sometimes, the elongation by the spatial chirping is confused with astigmatism in the beam. However, the spatial chirping can be discriminated by the through-the-focus image because the elongation by the spatial chirping is not rotated by 90 degrees while the elongation by astigmatism can be rotated.
When a laser pulse passes through an amplification medium, the pulse obtains energy gain from the medium. The energy gain comes from a stored energy in the medium which is provided by an external power source.
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Absorption by the transition between electronic energy levels is used to store an external energy. Electrons at a lower energy level are excited to a higher energy level through the pumping process. When an electromagnetic wave photon with a specific wavelength defined by the atomic energy transition is radiated to an excited atom, the atom emits the same electromagnetic wave photon as the incoming one. This means that an incoming electromagnetic wave is amplified in intensity. This dynamics can be described by the rate equation. Diagram for energy levels, level transition rate, and the number of electrons at the energy level.
In the four-level system, the storage of external energy is accomplished by the absorption due to the electronic transition from level 0 to level 3, and the lasing or energy gain is obtained by the electronic transition from level 2 to level 1. The changing rate for the excited electron population increases by the electron population at level 0 and the pumping rate W p. In a short time, electrons at level 3 lose their energy and decay into level 2 with a transition probability W Electrons at level 3 also decay into level 1 and 0 with probabilities W 31 and W In fact, ultrashort pulse lasers were likely used during the crafting of the delicate touch-screen on your smartphone.
Ultrashort pulse lasers are already revolutionizing areas of chemistry, manufacturing, healthcare, and more. All thanks to many dedicated scientists who have put in long hours of hard work and intense research, so all of humanity can benefit from our increased understanding and mastery over the physical world around us.
Ethan J. Hulbert is a scientist and marketing professional from Los Angeles, CA. Find out more about Ethan's work at Hulbert Marketing.
New Technique Measures Ultrashort Laser Pulses At Focus -- ScienceDaily
Facebook 3. Twitter 1. LinkedIn 2. Pinterest 0. Written by Ethan J. Hulbert Ethan J. Kapteyn, , Monitoring molecular dynamics using coherent electrons from high harmonic generation, Proceedings of the National Academy of Sciences of the United States of America 36 : ; H. Niikura, N. Dudovich, D. Villeneuve, and P.
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When driven with a few-cycle light pulse, the emission can be confined to a single isolated attosecond pulse. The HHG process itself is the first example where attosecond dynamics are clearly responsible. HHG radiation is a quintessential application of the interaction of high intensity laser radiation with matter.
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This makes HHG sources particularly useful for femtosecond dynamics studies. Current areas of broad impact of HHG sources are mostly in materials and nanoscience. These include photoemission using high-harmonic light sources; 63 time- and angle- resolved photoemission TARPES ; 64 , 65 excited electron lifetime studies in the attosecond range; 66 transient reflectivity and absorption, including Magneto-Optic Kerr Effect MOKE 67 ultrafast demagnetization; 68 and laser-induced spin currents. Haight and P. Seidler, , High resolution atomic core level spectroscopy with laser harmonics, Applied Physics Letters Eich, A.
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