## Frequency Conversion by a Third Order Nonlinear Optical Process

The third-order term %(3) also leads to new optical frequency generation by mixing of three waves of frequencies v1; v2, and v3. The two examples presented here, which are of importance for bioimaging are third-harmonic generation, abbreviated as THG, and coherent anti-Stokes Raman scattering, abbreviated as CARS.

The third harmonic generation is the third-order nonlinear optical analogue of second-harmonic generation. This process is schematically represented in Figure 5.8.

In this process, the incident photons are of frequency v (wavelength 1). In a %(3) medium, three incident photons combine together to generate a new photon of frequency 3v (wavelength 1/3). Thus, an incident fundamental light of wavelength at 1064 nm (from an Nd:YAG laser) will produce a third-harmonic beam at ~355nm in the UV. Again, like in the case of second-harmonic generation, it is a coherent process and does not involve absorption of three photons of frequency v. The frequency conversion occurs through virtual states, as shown by the right-hand-side energy diagram of Figure 5.8.

Coherent anti-Stokes Raman scattering is also a %(3) process, but unlike third-harmonic generation, it is a resonant process. In other words, it involves a real level of the molecule (Figure 5.9). In this process, two input light beams of frequencies v1 and v2 generate a new output beam at frequency (2v1 - v2), provided that the %(3) medium consists of molecules with a vibrational frequency vR observed in Raman spectra such that v1 - v2 = vR. In other words,

Figure 5.8. Third harmonic generation (abbreviated as THG) in a c(3) medium. The THG process (left); energy level description (right).

hv | ||

hv |
' 3hv | |

hv |

Figure 5.8. Third harmonic generation (abbreviated as THG) in a c(3) medium. The THG process (left); energy level description (right).

Input beam

New output beam

Input beam

New output beam v1

Figure 5.9. Coherent anti-Stokes Raman scattering, abbreviated as CARS. The CARS process (left); energy level description (right).

Figure 5.9. Coherent anti-Stokes Raman scattering, abbreviated as CARS. The CARS process (left); energy level description (right).

this frequency mixing process is a resonant process involving a vibration of the molecule at frequency vR = v1 - v2. Thus, by monitoring the new output CARS signal at frequency vAS = 2v1 -v2 as a function of v1 -v2 where v1 or v2 is fixed and v2 or v1 is varied, one can obtain the Raman spectra of the molecule.

Unlike the second-order nonlinear optical processes, which can take place only in a noncentrosymmetrically oriented medium, the third-order processes can take place in any medium, random or ordered. Hence, they can be observed in liquids, amorphous solid media, or crystalline media. But because it is a higher-order process, third-harmonic generation is a less efficient process than second-harmonic generation, for a medium where both can occur. In other words, it will take a more intense optical pulse (higher electric field E (v) to generate third-harmonic) than what will be required for second-harmonic generation.

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