High-precision phase plate for targeted generation of pseudorandom femtosecond pulses

. The targeted generation of fs pulses is essential for a variety of applications and it is routinely carried out by 4f pulse shapers. However, this seemingly simple task is complicated by hidden experimental limitations, such as modulator crosstalk or pixelation. We present an approach to overcome this issue by using a high-precision phase plate with a phase change characterized with  /500 precision. We generated pseudorandom pulses using a 4f pulse shaper by using a structured PMMA plate with the high-precision predefined shape made by the SPDT machine. We study the accuracy, reproducibility, as well as the sufficiency, and limits of the method. The generated pulses are characterized using the FROG method. The reconstructed pulses’ shapes and their spectral phases are compared to the results of simulations.

Reliable generation of complex femtosecond pulses is an inherent part of many branches of ultrafast optics, such as femtochemistry or pulsed laser deposition.A less common use, which is studied in our research team, is to use complex pulses to study buried interfaces in thin films.
The (pseudo)random pulses can be generated by various methods, including the 4f pulse shaper [1].The individual wavelengths are dispersed in space and their phase or amplitude can be altered independently in the focus plane of the shaper.Typically, a spatial light modulator (SLM) can be used, where the phase of light is modulated by voltage-controlled liquid crystals.However, not only is the SML a relatively expensive device, but it can also suffer from time jitter, pixel crosstalk, pixelation and pixel boundaries influence.
Here we present a low-cost and robust alternative approach to targeted complex pulse generation by using a 4f pulse shaper, where the modulating element is a phase plate with a predefined shape.Namely, we used a plate of PMMA with a centrosymmetric structured surface prepared by the single point diamond turning (SPDT) [2].The accurate machining with a sub-micrometer precision can faithfully reproduce the predesigned shape of the plate.We were able to verify the actual shape by a set of interferometric methods: whitelight interferometry and a multi-wavelength digital holography method [3] -see Fig. 1.Hence, this allowed us to create a faithful model of the phase change along the plate used in the simulations.
By moving the plate horizontally or vertically relatively to the dispersed pulse spectrum in the 4f pulse shaper, we get a variety of pseudorandom pulses.E.g. even for the relatively simple plate in Fig. 1, moving the plate just by 1 mm causes the change in the positions of the resulting pulses maxima more than 15 fs.It means, we can get hundreds of different pulses from one phase plate.We can optimize the shapes of the plates to get a large number of non-correlated pulses.The actual pulses created in the pulse shaper were retrieved via frequency-resolved optical gating (FROG) and compared to the simulated ones -see Fig. 2. Indeed, for the phase plate shown in Fig. 1 we were able to achieve a very good agreement between the simulated and actually measured pulses, including the spectral phase -see the inset in Fig. 2. The G-error between the reconstructed and simulated FROG spectrograms range between ~2 and ~2.7% for different pulse complexities, what is result competitive to the pulses shaped by an SLM [4].
As the fabrication of such a PMMA phase plate on our in-house SPDT machine takes only ~2 minutes, we can test phase plates with various profiles.As shows Fig. 3 even very sharp changes in the phase plate profile are transferred into the pulse spectral phase in a satisfactory way.In order to test the limits of this approach to the pulse shaping, we prepared yet another phase plate with progressively narrowing steps in its profile (see Fig. 4).In order to show the space resolution, the data are plotted in the space coordinate.We see that a 0.3 mm wide step is still reproduced in the phase of the measured pulse.This distance corresponds to 3 pixels of a standard SLM.Further improvements can be expected by increasing data density or decreasing laser beam focus.
In this contribution, we have showed that the structured PMMA plate can be a competitive, low-cost and robust way of targeted complex pulse generation.At the same time, the discrepancies between the experimental and simulated pulses allowes us to track the sufficiency and the limits of the method.

Fig. 1 .
Fig. 1.Height profile of the shaping PMMA plate measured by a multi-wavelength digital holography method.Inset shows on the same x-scale the designed profile cut through the centre, the rectangle marks the position of the dispersed laser spectrum, for which the random pulse in Fig.2 was simulated and measured.

Fig. 2 .
Fig. 2. The simulated (blue) and measured and reconstructed (red) random pulse for the region of the phase plate marked by the red rectangular in Fig.1.Inset shows the spectral phase of the simulated (blue) and measured (red) pulse.

Fig. 3 .
Fig. 3.The simulated (blue) and measured (red) spectral phase of a random pulse for a phase plate with rectangular profile.

Fig. 4 .
Fig. 4. The simulated (blue) and measured (red) spectral phase of a random pulse for a phase plate with progressively narrowing steps in the profile.