Abstract
In this chapter, we discuss some experiments in physics and chemistry (and related areas) which have become possible only because of the availability of highly coherent and intense laser beams.
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Notes
- 1.
By “polarization” we imply here the dipole moment induced by the electric field. This induced dipole moment is due to the relative displacement of the center of the negative charge from that of the nucleus.
- 2.
A piezoelectric material converts mechanical energy into electrical energy.
- 3.
The shift in frequency is usually measured in wavenumber units, which is defined later in this section. In Brillouin scattering, the shift is ≲ 0.1 cm–1. On the other hand, in Raman scattering, the shift is ≲ 104 cm–1.
- 4.
That the emitted photons of a particular frequency should appear in well-defined cones about the direction of the incident photons follows from the conservation of momentum. The direction of the emitted photon can be found by using the fact that a photon of frequency v has a momentum equal to \({{hv} \mathord{\left/ {\vphantom {{hv} c}} \right. \kern-\nulldelimiterspace} c}\)
- 5.
This is indeed the case for a laser beam where one usually has a Gaussian variation of intensity along the wave front.
- 6.
The use of lasers in photophysics and photochemistry has been discussed at a popular level by Letokhov (1977).
- 7.
1 ps = 10–12 s.
- 8.
The difference in path length between the two paths is extremely small; thus only a shift of a hundred-thousandth of a wavelength would be produced when the square is of side 3 m and is kept at a latitude of 40° on the surface of the earth.
- 9.
It is much beyond the scope of this book to go into the derivation of Eqs. (18.10) and (18.11). However, it may be worthwhile to mention that the probability distribution \(p\left( {n,\,t,\,T} \right)\) of registering n photo-electrons by an ideal detector in a time interval t to t + T is given by (see, e.g., Mandel (1959))
$$p\left( {n,t,T} \right) = \int_0^\infty {\frac{{\left( {\alpha w} \right)^n }}{{n!}}} {{e}}^{ - \alpha w} P\left( w \right){\textrm{d}}w$$where α is the quantum efficiency of the detector,
$$w {\,\, = \int_t^{t + T} {I\left( {t^{\prime}} \right){\textrm{d}}t^{\prime}} } $$is the integrated light intensity, and P(w) is the probability distribution corresponding to the variable w. Thus the photoelectron counting distribution given by the above equation depends on the particular form of the probability distribution P(w). Now, for a polarized thermal source, it can be shown that
$$\begin{aligned}&P\left( w \right) = \left( {{1 \mathord{\left/ {\vphantom {1 {\left\langle w \right\rangle }}} \right. \kern-\nulldelimiterspace} {\left\langle w \right\rangle }}} \right){{e}}^{ - {w \mathord{\left/ {\vphantom {w {\left\langle w \right\rangle }}} \right. \kern-\nulldelimiterspace} {\left\langle w \right\rangle }}},\quad \quad {\textrm{for}}\,T {<} {<} T_{\textrm{c}} \\&{}= \delta \left( {w - \left\langle w \right\rangle } \right),\quad \quad \quad \quad\quad\,\,\,\,{\textrm{for}}\,T {>} {>} T_{\textrm{c}}\end{aligned}$$where \(\left\langle w \right\rangle = T\left\langle I \right\rangle\) and angular brackets denote averaging. Further, for an ideal laser, the beam would not exhibit any intensity fluctuations and \(P\left( w \right) = \delta \left( {w - \left\langle w \right\rangle } \right)\). On substituting the above equations for P(w) in the equation for \(p\left( {n,\,t,\,T} \right)\), one gets Eqs. (18.10) and (18.11).
- 10.
The material in this section was kindly contributed by Dr. S.V. Lawande of Bhabha Atomic Research Centre, Mumbai.
- 11.
When an atom absorbs light, it jumps from one energy level to another, the difference in energy between the two levels being just equal to the energy of the incident photon. Since the energy levels are slightly different for two different isotopes, their absorption properties are also different. The isotope shift between hydrogen and deuterium is given as \({{\Delta v} \mathord{\left/ {\vphantom {{\Delta v} {v \approx 2.7 \times 10^{ - 4} }}} \right. \kern-\nulldelimiterspace} {v \approx 2.7 \times 10^{ - 4}}}\). For uranium, the isotope shift is given as \({{\Delta v} \mathord{\left/ {\vphantom {{\Delta v} {v \approx 0.6 \times 10^{ - 4} }}} \right. \kern-\nulldelimiterspace} {v \approx 0.6 \times 10^{ - 4} }}\).
- 12.
Reported in Physics Today 27(9), 17 (1974).
- 13.
Reported in Physics Today 27(9), 17 (1974).
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Thyagarajan, K., Ghatak, A. (2011). Lasers in Science. In: Lasers. Graduate Texts in Physics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-6442-7_18
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