4.2 Nonlinear Phenomena
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Fig. 4.2 Sum-frequency generation: a Schematic illustration b Energy band diagram
4.2.2 Sum- and Difference-Frequency Generation
4.2.2.1 Sum-Frequency Generation
Sum-frequency generation (SFG) is similar to second-harmonic generation, the only
difference is that in place of a single input frequency, now there are two input frequencies ω 1 and ω 2 . Figure 4.2 schematically illustrates the process of sum-frequency
generation with the help of a block diagram and an energy band diagram. It can
be seen that two input frequencies are fed into the nonlinear system of significant
second-order susceptibility and a mixture of three frequencies is obtained on the
output side. The three components of the output are the two original frequencies ω 1
and ω 2 , and a third-frequency ω 3 which is the sum of the two input frequencies, i.e.,
ω 3 = ω 1 + ω 2 . Due to this reason, the process is also called three-wave mixing [188,
189]. The energy band diagram in Fig. 4.2b shows the mechanism behind the sumfrequency generation. Absorption of a photon of frequency ω 1 excites the atom from
the ground state to energy level 1, which, if followed by absorption of a photon of frequency ω 2 , further excites the atom to energy level 2. The excited atom returns to the
ground state releasing a photon of the sum-frequency ω 3 = ω 1 + ω 2 , which is greater
than either of the two input frequencies. It is important to understand here that the
second-harmonic generation can be considered as a special case of sum-frequency
generation, where the two input frequencies are equal. Sum-frequency generation is
a useful technique of obtaining a tunable high-frequency laser, if one of the inputs is
a fixed low-frequency laser whereas the other one is fed by a tunable low-frequency
laser.
4.2.2.2 Difference-Frequency Generation
Difference-frequency generation (DFG), as the name suggests, is the reverse of sumfrequency generation. In DFG, the input comprises a high frequency and a low
frequency, and the output contains the two input frequencies and a third frequency
which is the difference of the two input frequencies. In this way, DFG is a three-wave
mixing process too. Figure 4.3 schematically illustrates the mechanism of differencefrequency generation in the usual fashion. Some part of the two input waves of
frequencies ω 1 and ω 2 yield a difference-frequency (ω 3 = ω 1 − ω 2 ) wave in the
87
Fig. 4.2 Sum-frequency generation: a Schematic illustration b Energy band diagram
4.2.2 Sum- and Difference-Frequency Generation
4.2.2.1 Sum-Frequency Generation
Sum-frequency generation (SFG) is similar to second-harmonic generation, the only
difference is that in place of a single input frequency, now there are two input frequencies ω 1 and ω 2 . Figure 4.2 schematically illustrates the process of sum-frequency
generation with the help of a block diagram and an energy band diagram. It can
be seen that two input frequencies are fed into the nonlinear system of significant
second-order susceptibility and a mixture of three frequencies is obtained on the
output side. The three components of the output are the two original frequencies ω 1
and ω 2 , and a third-frequency ω 3 which is the sum of the two input frequencies, i.e.,
ω 3 = ω 1 + ω 2 . Due to this reason, the process is also called three-wave mixing [188,
189]. The energy band diagram in Fig. 4.2b shows the mechanism behind the sumfrequency generation. Absorption of a photon of frequency ω 1 excites the atom from
the ground state to energy level 1, which, if followed by absorption of a photon of frequency ω 2 , further excites the atom to energy level 2. The excited atom returns to the
ground state releasing a photon of the sum-frequency ω 3 = ω 1 + ω 2 , which is greater
than either of the two input frequencies. It is important to understand here that the
second-harmonic generation can be considered as a special case of sum-frequency
generation, where the two input frequencies are equal. Sum-frequency generation is
a useful technique of obtaining a tunable high-frequency laser, if one of the inputs is
a fixed low-frequency laser whereas the other one is fed by a tunable low-frequency
laser.
4.2.2.2 Difference-Frequency Generation
Difference-frequency generation (DFG), as the name suggests, is the reverse of sumfrequency generation. In DFG, the input comprises a high frequency and a low
frequency, and the output contains the two input frequencies and a third frequency
which is the difference of the two input frequencies. In this way, DFG is a three-wave
mixing process too. Figure 4.3 schematically illustrates the mechanism of differencefrequency generation in the usual fashion. Some part of the two input waves of
frequencies ω 1 and ω 2 yield a difference-frequency (ω 3 = ω 1 − ω 2 ) wave in the