## 4 Multiple-Beam Interferometer for _Cep Drift_ Measurement  
The influence of the _CEP_ on the outcome of experiments increases dramatically with decreasing the duration of the pulses driving the interaction below a few optical cycles [82]. The generation of high harmonics [83, 84, 85] and attosecond pulses [86, 87, 88], as well as frequency comb-based metrology techniques [89] demand precise detection and subsequent low-jitter stabilization of _CEP_[90]. Nowadays, _CEP_ stabilization is well-established for Ti:sapphire lasers by the means of \(f\)-to-\(2f\) and \(0\)-to-\(f\) interferometry [91, 92]. Recent developments suppressed the CEP noise of the few cycle pulses in the visible- near infrared spectral range to a previously unexpected level of a few tens of mrad [93, 94]. Unfortunately, a wide range of lasers cannot satisfy the necessary conditions for such nonlinear interferometries [92]_i.e._, octave-spanning spectrum or enough power for frequency doubling. It is possible to overcome the condition of broad spectrum by the generation of white light continuum of the laser pulse to be measured, but it requires a complex experimental setup with multiple nonlinear conversions [95]. Similarly to the dispersion coefficients, the _relative CEP_ between two interfering pulses can be also measured by _SSRI_ and _SRI_. The difference in _CEP_ can be calculated from Equation (13), where \(\varphi(\omega_{0})\) and the \(GD\) are derived from spectral phase of the recorded interferogram. It can be used effectively to observe a phenomenon which introduces variation to the _CEP_ of the pulses only in the sample arm, when certain properties of the sample object are modified. Another useful application of these methods is using them to determine the jitter of _CEP_ between the arms. For instance, from the blurriness of the interference pattern, one can deduct that how stable the fringe position and density during the integration time of the detector is [96]. Not only the relative _CEP_ of a pulse, but also the _CEP drift_ of a pulse train, can be determined. The most advanced device relies solely on a multiple-beam interferometer (_MBI_) and a spectrograph [97, 98]. The advantage of using spectrally resolved interferometry is that besides properties of the detector, the system is practically free of wavelength conditions, including the bandwidth, the spectral range or the central wavelength. This technique offers not only the measurement of the pulse-to-pulse _CEP drift_, but also seems to be fast enough to apply feedback to lasers with prohibitively low pulse energy for regular _CEP_ stabilization schemes. Moreover, this scheme allows simultaneous monitoring of intracavity refraction and linear dispersion for a virtually unlimited range of mode-locked lasers, including monolithic designs where such insight is otherwise difficult to obtain [54]. Instead of using Michelson and Mach-Zehnder interferometers, a resonant ring layout was implemented to keep information of the pulse phase for several round trips (see Figure 12a). After a part of the initial pulse makes one round trip in the _MBI_, at the output--if the ring length is carefully aligned--it will interfere with the next pulse of the train. The rest of the pulse before the initial one is still in the system, and it also contributes to the interference, although with a lower intensity. This effect is similar to the principle of the Fabry-Perot interferometer, and it will result in a weighted averaging for many subsequent pulses. In the spectral domain, spectral interference fringes will appear, very similarly to the case of _SRI_. If the _MBI_ is free from second and higher-order dispersion, the fringe pattern could be described simply by two parameters: fringe position (_i.e._, \(\varphi(\omega_{0})\)) and spacing (_i.e._, _GD_). This could be important in those cases where fast detection and response is required, most notably, for _CEP_ stabilization.