Heterodyne detection According to Phase-stabilized two-dimensional electronic spectroscopy the local oscillator, LO, used for heterodyned signal detection always arrives first at time $t_4$, which is -700fs. 

In 2D-spectoscopy short pulses are used, <100fs.
Unfortunately, I'm not familliar with hyterodyne detection on practise.
The intensity of current in detector is: $I=|E_{LO}+E_{S}|^2=E_{LO}^2+2E_{LO}E_{S}+E_{S}^2$, where $E_{LO}$, $E_{S}$-- are local oscillator field and signal, respectively.
When the signal arrives on detector, the LO would already pass.
Could someone explain how heterodyned signal detection is accomplished, when local oscillator arrives before signal (what type of detectors are used? what is the treatment of data looks like?) Where does optical heterodyning process occur in reality?
 A: The local oscillator field and the signal field "interact" at the detector. It may be easier to understand if the field intensity is written as follows:
$$
I=|E_{LO}+E_s|^2=E_{LO}^2+E_s^2+E_{LO}^*E_se^{i\omega T}+E_{LO}E_s^*e^{-i\omega T}
$$
What is happening here is that the LO and signal pulses are both being spectrally dispersed in the spectrometer and hitting what is probably a silicon CCD detector, since Fleming works in the visible mostly. These two pulses hit the detector very close to each other (in time), 700 fs, so the detector isn't fast enough to resolve them, (this is kind of like if you wave your hand in front of your face, it looks like a blur because your eye isn't resolving (taking single images) fast enough to tell that your hand is only in one place at a time). When the spectrally dispersed signal and LO pulses hit the CCD the frequencies interfere on the CCD, some interfere constructively and some destructively based on the phase of the LO and signal pulses. This results in a spectrum that has fringes on it, (sine wave type of pattern on top of the LO spectrum). These fringes have a frequency, $\omega$ which is dependent on the temporal separation of the LO and signal pulses, $T$.
Now, in the above expression for I we have the two "heterodyned" terms that are time dependent, $e^{i\omega T}$. These can be separated from the other terms that we don't care about via a process called fourier filtering.
I would recommend looking at a paper by T. Tahara that does a good job of explaining the process of heterodyning and some of the post-processing and reasons why people do it.
