CEP dependence of signal and idler upon pump-seed synchronization in optical parametric amplifiers

Abstract

We study the effect of pump-seed timing fluctuations on the carrier-envelope phase (CEP) of signal and idler pulses emerging from an OP(CP)A. A simple analytical model is derived in order to provide an intuitive explanation of the origin of CEP fluctuations, while split-step simulations are performed to cover a broad range of different seeding schemes. Finally, we compare the simulation results with real observations of the CEP of idler pulses generated by an OPA. The quantitative model presented provides a key tool for designing the next generation of low-noise CEP-stable OP(CP)A-based sources. good levels of stability [7,8]. However, in order to reach high pulse energies, OP(CP)A systems have grown in size and complexity, entailing an increase in the timing jitter among the different amplification stages.In this Letter, we intend to clarify the influence of pumpseed timing fluctuations on the CEP of both signal and idler pulses emerging from an OP(CP)A. We analyze two of the most significant schemes: generation of a CEP-stable idler and amplification of a broadband stretched signal successively compressed.We start by considering the system of three coupled equations [9], which describes parametric amplification along the propagation direction, within the approximation of monochromatic plane waves and perfect phase matching. The parametric amplification process is maximized when the generalized phase Φ ϕ p − ϕ s − ϕ i is equal to π∕2 [10], in other words ϕ i ϕ p − ϕ s − π∕2. It is worth noting that the phase ϕ k (k p; s; i), represents the absolute phase (AP) of each wave, that is, the phase with respect to the lab reference frame and not the CEP of the corresponding pulses. To analytically determine the CEP of the signal and idler pulses generated in an OPA, it would be necessary to solve the aforementioned coupled equation system while considering the time dependency of the amplitude envelope of each pulse and the effect of dispersion. Unfortunately, no analytic solutions have been found in this case. However, within certain limits, it is still possible to describe analytically the effect of the pump-seed timing fluctuations on the CEP of signal and idler.Consider a white-light (WL) seeded OPA or any other parametric amplifier where the seed has been produced starting from a portion of the pump pulse via a coherent process, i.e., the seed pulse has inherited the AP from the pump pulse. During the spectral broadening, an additional term is added to the phase of the seed, but we will not consider it because such phase term has no dependence on timing fluctuations but rather on intensity fluctuations, whose effects on CEP goes beyond the scope of this paper. For small pump-seed relative arrival time fluctuations ΔT compared with the pump pulse Full control of the electric field of an ultrashort laser pulse is necessary to precisely control light-matter interaction processes happening on femtosecond (fs) and attosecond (as) time scales [1][2][3]. To describe the time-dependence of the electric field of a laser pu...

Asymmetric high energy dual optical parametric amplifier for parametric processes and waveform synthesis

“…It is known [32] that the CEP of the signal, 𝜙 𝑠 and idler, 𝜙 𝑖 of an OPA can be given by 𝜙 𝐶 𝐸 𝑃 𝑠 = −𝜔 𝑠𝑒𝑒𝑑 * 𝑇 + 𝜙 𝐴𝑃 𝑝 and 𝜙 𝐶𝐸 𝑃 𝑖 = 𝜔 𝑠𝑒𝑒𝑑 * 𝑇 + 𝜋 2 respectively, where 𝑇 is the relative arrival time difference between the seed and the pump, 𝜙 𝐴𝑃 𝑝 is the absolute phase of the pump, and p,s,i stand for the pump, signal, and idler respectively. As can be seen, the idler of an OPA is passively CEP stable while the signal has the CEP value of the pump.…”

Novel method for the angular chirp compensation of passively CEP-stable few-cycle pulses

“…In addition, the setup could be improved by coupling the idler of the first OPA stage, and not of the second stage, into the Kagome fiber. This would reduce the CEP instability, due to the shorter path length difference between pump and signal [21], and it would also improve the coupling efficiency into the Kagome fiber, as explained in the following. In the second stage, due to the higher pump intensity, we used a big beam size (∼800 µm) to avoid crystal damage and unwanted nonlinearities.…”

“…It is an efficient technique and shows good performances, but it is costly and complex. Another scheme [20] consists in using a narrowband collinear [21] or slightly non-collinear OPA [22] whose CEP-stable idler has none or negligible angular chirp compared to its natural divergence, and whose frequency is well separated from the signal. The idler, or its second harmonic, is used to pump a CEP-stable white light generation (WLG) stage in bulk materials.…”

Continuous every-single-shot carrier-envelope phase measurement and control at 100 kHz

“…Both results are comparable to values published for typical Ti:Sapphire amplifier systems [23][24][25], and comply with the demand of attosecond science experiments, although not yet reaching the limit imposed by the residual CEP noise in the oscillator (≈150 mrad). The additional CEP noise in the amplified pulses may have multiple sources, such as pulse-to-pulse intensity variations in the pump laser of the OPCPA, residual jitter in the pumpseed delay of the OPCPA and beam pointing instabilities affecting the amplification process and the broadening in the HCF [26][27][28].…”