Figure 2.9: (a) Spectral lines of the 32.8-nm laser beams for increasing pump pulse energies. (b) Angular distributions of the 32.8-nm laser beams for some pump energies corresponding to (a).
the increase of the pump energy results in higher peak intensity which may exceed the ionization threshold of Kr9+ and generate an overionization re-gion to reduce the gain volume. Over-ionization took place from the central region outwardly in the channel and may reduce the density barrier of the plasma waveguide by increasing the electron density in the central region.
Nonetheless, the transverse intensity distribution of the guided pump pulse also further ionized the outer region of the waveguide to increase the electron density barrier which maintained the guiding condition. mboxThe interfer-ometry and relayed imaging system showed that the guiding of the pump pulse in the channel was sufficiently good and the waveguide structure was also sustained even at high pump energy. The propagation of the amplified EUV laser beam is thus guided by the gain volume which had a depressed gain column in the vicinity of the optical axis to produce an annular EUV laser beam.
2.3 Summary
Our laboratory has continually endeavored to improve the performance of
light source TLS∗ IAMS† NCUk TPS∗
commissioning 1993 2007 2012 2014
apparatus synchrotron tabletop tabletop synchrotron mechanism bremsstrahlung ASE†† ASE bremsstrahlung
pulse duration (ps) 100 5 [28] 5 19 [44]
repetition rate (Hz) ≈ 106 10 10 ≈ 106
wavelength (nm) tunable 32.8 32.8 tunable
peak spectral brightness¶
at 32.8 nm
7.9×1014[32] 7.9×1023[45] 1.2×1025[5] 5×1018§[46]
∗ TL(P)S: Taiwan Light(Photon) Source
† IAMS: Institute of Atomic and Molecular Sciences, Academia Sinica
k NCU: National Central University
†† ASE: amplified spontaneous emission
¶ spectral brightness: photons/sec/mm2/mrad2 in 0.1% bandwidth
§ EPU100 beamline of Taiwan Photon Source
Table 2.1: Comparison of the EUV laser in this work with that in the previous work and the synchrotron radiations in Taiwan.
EUV lasers these years, fabricating optically preformed plasma waveguides with axicon ignitor-heater scheme [4, 40], seeding of high harmonic genera-tion [43] and characterizing the polarizagenera-tion state and coherence property [32]
are some efforts we made in this field.
In this thesis, we observe dramatic enhancement of collisionally excited EUV lasing in optical-field-ionized Ni-like krypton plasmas at 32.8 nm. Ex-perimental datarevealing the pump energy dependence of the EUV outputs suggests that the lasing is near saturation. At pump energy of 600 mJ, the spectral brightness reaches 1.2 × 1025 photons/sec/mm2/mrad2 in 0.1%
bandwidth. Table 2.1 shows the comparison of our EUV laser with that in the previous work and with the synchrotron radiations of Taiwan’s National Synchrotron Radiation Research Center.
On grounds of the introduction of the optically-preformed plasma
waveg-2.3. Summary
uide technique, not only the spectral brightness of the EUV radiation is sig-nificantly enhanced, but also the corresponding energy conversion efficiency is raised to an unprecedented level. For comparison, we review some represen-tative achievements here. By virtue of precise pressure control in a capillary waveguide, conversion efficiencies of greater than 10−6 at 30 nm were ob-tained [47]. Similar efficiencies were observed in grazing-incidence pumped transient collisional EUV lasing at 32.6 nm [48], 13.9-nm laser excited by a slab-pumped Ti:sapphire laser [49] and 32.8-nm laser adopting optically preformed plasma waveguide technique [4]. Energy yields of higher-order harmonic radiations in the spectral range of 31–17 nm were measured up to several tens of nJ, corresponding to conversion efficiencies of as high as 10−7 in each harmonic [50]. As the harmonic approaches the regime with higher photon energies, say ∼ 10 nm, only a small fraction of pump energy as low as 10−11– 10−8 could be converted into x-ray photons [51, 52, 53, 54].
In this work, the pulse energy of 32.8-nm EUV lasing pumped by a 100-TW laser system in an optically preformed plasma waveguide reaches 6 µJ at an energy conversion efficiency of around 10−5 [5].
Chapter 3
Holographic Processes
A lensless imaging process which is now known as holography was proposed in 1948 by Dennis Gabor to improve the resolution in electron microscopy [55].
Gabor found that the information about both the amplitude and phase of the waves diffracted or scattered from an object can be fully recorded when a coherent reference wave exists simultaneously, which totally contradicts the conventional dogma of optical recording as simple intensity measurement of optical radiations can only store the information of the amplitude distribution the object carries. In holography, the phase information of the object wave buried in a coded form, an interference pattern or simply named a hologram, can ultimately be used to acquire the image of the original object. We review the basic principles behind holographic processes in this chapter and discuss the inherent conundrum of phase ambiguity to be tackled in the next chapters.
3.1 Amplitude and Phase Recording
All the recording media, either chemical or digital, respond only to the light intensity that impinges on it. For that reason, we need the phase infor-mation carried by the object wave to somehow be converted into intensity variations for recording purposes. Interferometry is an ingenious thought on that implementation. Think of a reference wave of known amplitude and phase is interfering with the original object wave of unknown wavefront on the recording medium, as shown in Figure 3.1. Note that the wavefront of the reference wave is not necessarily plane, wavefronts of arbitrary shape will do as long as they are mutually coherent with the object field. If complex amplitude of this reference wave is described as
ER(x, y) = aR(x, y) exp [jψR(x, y)] (3.1)
Figure 3.1: Holographic recording∗.
with real amplitude aR and phase ψR, while the object wave to be recon-structed is written as
EO(x, y) = aO(x, y) exp [jψO(x, y)] (3.2) with real amplitude aO and phase ψO. The intensity of the interfering field of two complex waves is thus
I(x, y) =
EO(x, y) + ER(x, y) 2
= EO(x, y)EO∗(x, y) + ER(x, y)ER∗(x, y) + EO(x, y)ER∗(x, y) + ER(x, y)EO∗(x, y)
= a2O(x, y) + a2R(x, y)
+ 2 aO(x, y) aR(x, y) cos
ψO(x, y) − ψR(x, y)
. (3.3)
The first two terms of Eq.(3.3) contain no information about the object phase at all. It is the third term that codes the phase information in a decipherable way to be retrieved during the holographic reconstruction. Now, the question remains is how we reconstruct the object wave EO(x, y) given the interferometric recording.