Chapter 16: Design of Femtosecond Pulse Sequences to Control Reactions
Power Spectrum Of One- and Two- Photon Processes
The notion of Multiple Pathway Interference can be understood by considering the expression for the second order amplitude:
where 
and the summation is performed over all possible intermediate states of the unperturbed atom. If we assume that all the intermediate states are far from resonance, their contribution will add coherently only for a very short duration, and we obtain:
Rewriting the second factor in eq. (2) in the frequency domain we obtain:
where 
is the Fourier transform of 
and 
and 
are the spectral amplitude and the spectral phase, respectively. Eq. (5) indicates that two-photon transitions occur for all pairs of photons with frequencies
and 
,
with 
and and
lying within the spectrum of the exciting pulse. The two photon transition probability can therefore be controlled by tailoring the spectral phase within a single pulse. The program below assumes that
and
where 
and
are user input. The program plots
and 
determines the 2-photon absorption spectrum, given energy level separation 
.
The notion of Multiple Pathway Interference can be understood by considering the expression for the second order amplitude:
and the summation is performed over all possible intermediate states of the unperturbed atom. If we assume that all the intermediate states are far from resonance, their contribution will add coherently only for a very short duration, and we obtain:
is the Fourier transform of and and
are the spectral amplitude and the spectral phase, respectively. Eq. (5) indicates that two-photon transitions occur for all pairs of photons with frequencies
and ,
with and and
lying within the spectrum of the exciting pulse. The two photon transition probability can therefore be controlled by tailoring the spectral phase within a single pulse. The program below assumes that
and
where and
are user input. The program plots
and
determines the 2-photon absorption spectrum, given energy level separation .