Frequency Tunable High-Order Harmonics
4.2 Experimental Setup and Methods
This experiment was carried out as part of a collaboration with CELIA (centre lasers intenses et applications) in Bordeaux and funded by Laserlab Europe. We were given access to the Eclipse laser facility. Eclipse is a titanium-doped sapphire laser, operating at a repetition rate of 10 Hz at around 800 nm. It provides a total pulse energy of 200 mJ, which is split between two laboratories, each receiving 100 mJ. To avoid non-linear effects when propagating through air, the beam arrives in the laboratories uncompressed and is then compressed down to 30–40 fs in each lab individually. The compressor and all beam paths thereafter are under vacuum to avoid ionisation in air and other nonlinearities.
Figure 4.1 shows a schematic of the setup used at CELIA.
After the beam enters the lab, there is an option to attenuate the remaining 100 mJ of IR using a waveplate and a polariser. The beam then propagates through the key setup of this experiment, which has been added to the usual beamline in this laboratory. This assembly for temporal field synthesis is described in more detail later on in this section.
Following the field synthesis setup, the pulses enter the standard setup of the labora-tory at CELIA, which is entirely under vacuum. First, the pulses are compressed to between 30 fs and 40 fs, depending on the input and the compressor grating settings. The compressor gratings are gold coated and the compressor has a transmission efficiency of 65%.
After exiting the compressor, the beam is sent to a custom deformable mirror. The mirror setup has been developed by engineers at Imagine Optic and ISP System in col-laboration with CELIA. It was designed specifically for the high power, low repetition rate laser system in use. The reflective dielectric coating for the membrane has a band-width of 215 nm and a damage threshold of 170 mJ/cm2. The setup works in conjunction with a Shack-Hartmann wavefront analyser (HASO by Imagine Optic), which receives a small proportion of the beam transmitted by a beamsplitter. After analysing the current wavefront, the software provides the settings for the 47 step motors that change the sur-face of the deformable mirror, and therefore the wavefront. Note that this feedback is too slow for real-time feedback and the wavefront was usually only analysed and set once a day. The corrected wavefront allows for a better focus.
The majority of the beam is reflected by the beamsplitter and sent towards the high harmonic generation setup. The beam first passes through a motorised iris before being focussed by a spherical mirror with a focal length of 2 m. The gas jet used for this ex-periment was 100µm in diameter, which was mounted on a 3-axis motorised translation
Figure 4.1: Schematic of the laboratory at the Eclipse laser facility. A 10 Hz, 200 mJ Ti:Sapph laser provides 100 mJ pulses to two separate experiments. A waveplate (WP) and a polariser are used to control the power into the experimental setup. A pair of quartz wedges, two quartz plates and another polariser are used for field synthesis (described in more detail in fig. 4.3). The compressor and everything thereafter operates under vacuum. The deformable mirror is used to change the wavefront of the beam based on feedback from the wavefront analyser (described in more detail in the body of this section).
The beam is then focussed into a gas jet and imaged by a spherical grating into the detector assembly.
The imaging setup is shown in more detail in fig. 4.2.
stage in order to be able to optimise the harmonic generation.
After the gas jet, both the fundamental IR beam and the harmonic beam pass through a 500µm slit. The harmonics are then imaged into the plane of a micro-channel plate (MCP) detector assembly by an XUV flat-field grating (Hitachi). The gold-coated grating has 1200 lines/mm and was designed for an angle of incidence of 87◦ (grazing-incidence angle 3◦). Figure 4.2 shows the XUV spectrometer setup in more detail.
The assembly for temporal field synthesis (depicted in detail in figure 4.3) consists of a pair of quartz wedges, two quartz plates and a polariser. Since quartz is a birefringent
Figure 4.2: Schematic of the XUV spectrometer. The IR beam is shown in red, the harmonic beam is shown in purple. After the gas jet, the beams pass through a 500µm slit. After reflection off a gold mirror, the harmonic beam is imaged onto the plane of a micro-channel plate (MCP). The phosphor screen, adjacent to the MCP, is then imaged onto a camera (not shown). The fundamental IR is blocked by a zero-order block.
Figure 4.3: Schematic of the temporal field synthesis setup. The quartz wedges (optical axes at 45◦ to polarisation of input pulse) project the input pulse along the two axes of the crystal and introduce a delay between the two copies of the pulse. Changing the wedge insertion changes the delay and the relative phase between the two copies. The two quartz plates introduce the bulk of the overall delay between the two copies, before the polariser projects the two copies back onto the original polarisation axis.
material, the refractive index seen by any incident radiation depends on the polarisation relative to the axes of the crystal. This property is used here to achieve the temporal field synthesis mentioned in the background section of this chapter (section 4.1). The quartz wedges and plates are oriented with their axes at 45◦ with respect to the incoming laser polarisation. As a result, the incident laser pulses are projected onto the two axes of the quartz crystals. The two copies, one travelling along the ordinary axis, the other travelling along the extraordinary axis, therefore experience a different refractive index.
This difference in refractive index leads to a temporal delay between the two copies. The polariser at the end of the setup projects both copies onto the same axis again, resulting in a synthesised field. The two quartz plates were chosen for the coarse adjustment of the time delay between the two copies. The quartz wedges were used to fine tune the phase difference between the two copies by changing the insertion, and therefore the total length of quartz the pulse travels through.
The two quartz plates used in this experiment had a thickness of L1 = 1.01 mm and L2 = 0.48 mm, respectively. Each of the quartz wedges varies in thickness from Ltn = 0.50 mm on the thin side to Ltk = 1.50 mm on the thick side. All quartz crystals used had a cut angle of Θ = 90◦. The refractive indices of quartz at a central wavelength of 800 nm are no(800 nm) = 1.5383 for the ordinary axis and ne(800 nm, 90◦) = 1.5472 for the ex-traordinary axis, giving group velocities of vg(o) = c/1.5544 and vg(e) = c/1.5639, where the denominators are the so called group indices. Using the following equation for the induced time delay between pulses propagating along the ordinary and the extraordinary axes:
we get a time delay of approximately 31.6 fs per mm of quartz. Note that depending on the relative alignment of the ordinary and extraordinary axes of the quartz plates and the wedges, the delays introduced by each element either add up or subtract. As a result, a number of different coarse delays are possible, depending on the exact configuration of the quartz plates and quartz wedges.
A change in phase delay of π between the two copies is achieved by a change in beam path length through quartz of 43.5µm, which corresponds to a change in wedge insertion of around 2.2 mm. Note that in the experiment (as opposed to computer simulations) it is not possible to change the phase delay independently of the group delay. The amount of additional quartz required to shift the phase delay by π introduces a group delay of 1.4 fs.