Light Amplification by Stimulated Emission of Radiation
Photophysics of molecules
The deactivation of molecules in their excited states involves many possible photophysical paths, such as internal conversion, intersystem crossing, and fluorescence quenching by colloisions and other physical means. Photochemical pathways are also important. These include electron transfer, isomerization and photolysis. These aspects of molecular deexcitation are discussed here in the context of molecular systems that can be used to prepare excited states for stimulated emission.
Laser fundamentals: The Einstein relation and simulated emission
The concept of a laser starts with the understanding that stimulated emission of radiation can lead to amplification of input light. If a collection of molecules is in the excited state the incoming radiation could lead to a chain reaction in which one photon gives rise to output photons. Then those two photons could give rise to 4, and 4 to 8 etc. as each input photon stimulates the emission by one of the molecules in the excited state. The question is how can we prepare a system in which most of the molecules are in the excited state. We can understand this type of process by examination of the Einstein model for absorption and emission of radiation. The Einstein coefficient of absorption is equal to that of stimulated emission, which means that if we drive the system to steady state in a very intense radiation field, we can obtain at most one half of the molecules in the excited state (and one half in the ground state). Such a population distribution is not sufficient for lasing. Any input light could induce stimulated emission (and produce one extra photon), but with equal probability it could result in absorption (and consume one photon). We conclude that in order to make a laser we need a three level system at a minimum.
Laser fundamentals: The Einstein relation and spontaneous emission
Spontaneous emission competes with stimulated emission and deactivates the excited state, thus decreasing the magnitude of the laser effect. The Einstein relation also provides a relationship between the magnitude of simulated and spontaneous emission:
The spontaneous emission rate increases as the cube of the frequency. This tells us that the tendency of spontaneous emission to interfere with lasing is significantly greater at higher frequency. In general, it is much harder to build a laser in the ultraviolet region than in the visible region.
Laser fundamentals: Three and four level systems
To make a laser we need to create a population inversion. This is done by pumping a system with at least three levels such that one level is a bottlenec state that traps the energy. We excite from the ground state to the second excited state and then there is rapid transfer to the first excited state where the excitation energy builds up. When there is a greater populatino in the excited state than in the ground state we can speak of a population in inversion. That is the minimum condition for a laser. A four level system has these properties, but in addition there is a level above the ground state that is usually meta-stable and rapidly dissociates or deactivates to form the ground state. Thus, the lasing can occur between the long-lived excited state and the meta-stable state, which have high population and nearly zero population, respectively.
Practical considerations for construction of a laser
In order to make a suable light source from a collection of molecules that have a population inversion we need to construct a laser cavity and put a tuning element in the beam path so that we can realize the potential of a narrow bandwidth, directional and polarized light source. A laser cavity is defined by two mirrors, a high reflectivity mirror and an output coupler, which has much loaser reflectivity. The light is confined within a cavity of length L between the mirrors.
The common lasers such as Ar ion, Kr ion, Nd:YAG, Nd:YLF and so on are all fixed wave length lasers. Many problems in chemistry require tunability. Dye lasers were used initially to obtain a tuning region. One can excite a dye with a fixed wave length laser and then select a narrow bandwidth region from the gain curve of the laser dye using a birefringent filter. However, laser dyes are difficult to maintain. Dye lasers have been replaced by solid state lasers based on Ti:sapphire. The gain region of Ti:sapphire is from 700 - 1000 nm. To make this material useful for a broad range of chemical problems, one can use non-linear optical effects to alter the frequency. The video discusses the general idea of non-linear optics in terms of frequency doubling, sum frequency and difference frequency generation. Frequency doubling to generate 350 - 500 nm light. One can also tripling and quadruping to generate 235 - 335 nm and 175 - 250 nm light. These regions are idealized since it is not possible to use the entire gain curve, but one can get covereage in the UV and visible regoins using the effects of doubling, tripling and quadrupling. Sum frequency generation can be used to convert a photon of a given energy into two photons that sum up to that energy. This is easiest to discuss in terms of the wave number. For example, a 800 nm pulse in a Ti:sapphire laser has a wave number of 12,500 cm-1. Two two pulses whose energies are 12,500 cm-1 can be summed to yield a 25,000 cm-1 pulse.
