Optical Cooling Using the Dipole Force pp 71-113 | Cite as

# The transfer matrix model

## Abstract

Chapter 2, and in particular Sect. 2.4, developed the necessary tools to describe the interaction of an atom with the electromagnetic field, as parametrised by the atoms characteristic polarisability. In one dimension, one can succinctly describe the fields interacting with a linear scatterer through what is called the transfer matrix approach [1]. Restricting ourselves to one spatial dimension is not an overly restrictive approximation, despite the quote at the beginning of this chapter; the formalism that is discussed in this chapter allows us to describe a wealth of physical situations. The purpose of this chapter is to extend this model significantly, enabling it to account for moving as well as static scatterers; this is done in Sect. 4.1 and the model that results is solved generally in Sect. 4.2. The extended model discussed here takes into account the first-order Doppler shift but not relativistic effects, and it is therefore correct only up to first order in the velocity of the scatterer.

## Keywords

Transfer Matrix Input Field Noise Mode Momentum Diffusion Optical Bloch Equation## References

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