# BLS

BLS | |
---|---|

관련코스 | 현대광학 |

소분류 | |

선행 키워드 | |

연관 키워드 |

Brillouin scattering is named after Leon Birllouin. Brillouin predicted inelastic scattering of light with thermal vibrations(phonons). Brillouin scattering is discovered by Leonid Mandelstam. Since BLS occurs in GHz scale, magnon also experiences Brillouin scattering with photon. BLS spectroscopy is similar to CARS in that both are light scattering spectroscopy, but Raman scattering occurs in THz scale.

#### Classical picture

In classical physics, Brillouin scattering can be explained using Doppler shift. It is suggested by Brillouin. The Doppler shift is relativistic effect. If the frequency and wave number of incidence and scattered wave is ω, ω' and k, k', then Doppler shifts can be written as

- [math] \bar{\omega}=\omega-\overset{\rightarrow}{q}\cdot\overset{\rightarrow}{v} [/math]

for incident wave,

- [math] \frac{\bar{E}}{\hbar}=\frac{E}{\hbar}-\overset{\rightarrow}{q}\cdot\overset{\rightarrow}{v} [/math]

for scattered wave,

- [math] \frac{\bar{E}'}{\hbar}=\frac{E'}{\hbar}-\overset{\rightarrow}{q}'\cdot\overset{\rightarrow}{v} [/math]

Since the frequency of the incident wave is not changed during the diffraction, [math]\bar{E}'[/math] is equal to [math]\bar{E}[/math], the frequency of scattered wave in original frame is:

- [math] \frac{E}{\hbar}'=\frac{E}{\hbar}+(\overset{\rightarrow}{q}'-\overset{\rightarrow}{q})\cdot{v} [/math]

By using Bragg condition:

- [math] \overset{\rightarrow}{q}'=\overset{\rightarrow}{q}+m\overset{\rightarrow}{k} [/math]

energy relation between incident and reflect wave is written as:

- [math] E'=E+m\hbar\omega_{\overset{\rightarrow}{k}s} [/math]

#### Quantum mechanical picture

In quantum mechanical picture, Brillouin scattering can be understood as an interaction between a electromagnetic wave and magnon or phonon. When the scattering is inelastic, photon loses and magnon(phonon) gains energy, or gains energy and magnon(phonon) loses energy. The former is Stokes (**k**_{s}=**k**_{1}+**q**, **ω**_{s}=**ω**_{s}+**ω**_{q}), and the latter is anti-Stokes(**k**_{s}=**k**_{1}-**q**, **ω**_{s}=**ω**_{s}-**ω**_{q}). In the scattering 10^{7} Hz<**ω**_{q}<10^{12} Hz.

#### BLS Measurement

For Brillouin light scattering spectroscopy, laser source and tandem Fabry-Perot interferometer are needed. Generally, the Fabry-Perot interferometer consists of two parallel mirrors. In the interferometer, single beam splits into two beams and they travel the different path each other before arriving the detector. Two beams make interference pattern. As a monochromatic beam goes into the sample, a fraction of light would interacts with magnon and induce elastic(Rayleigh scattering) or inelastic scattering(Brillouin scattering). Using FPI, the frequency and intensity of the scattered light is measured.