OSA's Digital Library

Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 26 — Dec. 25, 2006
  • pp: 12872–12879
« Show journal navigation

Spatial coherence measurements of a 13.2 nm transient nickel-like cadmium soft X-ray laser pumped at grazing incidence

Y. Liu, Y. Wang, M. A. Larotonda, B. M. Luther, J. J. Rocca, and D. T. Attwood  »View Author Affiliations


Optics Express, Vol. 14, Issue 26, pp. 12872-12879 (2006)
http://dx.doi.org/10.1364/OE.14.012872


View Full Text Article

Acrobat PDF (203 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The spatial coherence of a 13.2 nm transient collisional Ni-like Cd soft X-ray laser pumped at 23 degrees grazing incidence was measured in a series of Young’s double-slit experiments. We observed pronounced fringe visibility variations associated with microstructures in the beam’s intensity profile. The transverse coherence length was measured to be about 1/20 of the beam diameter and did not significantly improve with longer plasma columns. The equivalent incoherent source size is determined to be 10 µm and the laser’s peak spectral brightness ~3×1023 photons/sec/mm2/mrad2 within less than 0.01% spectral bandwidth.

© 2006 Optical Society of America

1. Introduction

Recently table-top high repetition rate lasers operating in the vicinity of 13.5 nm have been demonstrated to produce average powers in excess of 1 µJ [1

1. Y. Wang, M. A. Larotonda, B. M. Luther, D. Alessi, M. Berrill, V. N. Shlyaptsev, and J. J. Rocca, “Demonstration of high-repetition-rate tabletop soft-x-ray lasers with saturated output at wavelengths down to 13.9 nm and gain down to 10.9 nm,” Phys. Rev. A 72, 053807 (2005). [CrossRef]

, 8

8. G. Vaschenko, C. Brewer, F. Brizuela, Y. Wang, M. A. Larotonda, B. M. Luther, M. C. Marconi, J. J. Rocca, C. S. Menoni, E. H. Anderson, W. Chao, B. D. Harteneck, J. A. Liddle, Y. Liu, and D. T. Attwood, “Sub-38 nm resolution tabletop microscopy with 13 nm wavelength laser light,” Opt. Lett. 31, 1214–1216 (2006). [CrossRef] [PubMed]

]. The lasers, which operate on the 13.2 nm line of Ni-like Cd and the 13.9 nm line of Ni-like Ag, are excited by heating a pre-created plasma with a 6-8 ps optical laser pulse impinging at grazing incidence. This pumping geometry takes advantage of refraction of the pump beam in the plasma to increase the fraction of the pump energy absorbed in the gain region as compared to the conventional normal incidence pumping geometry [9

9. J. J. Rocca, Y. Wang, M. A. Larotonda, B. M. Luther, M. Berrill, and D. Alessi, “Saturated 13.2 nm highrepetition-rate laser in nickellike cadmium”, Opt. Lett. 30, 2581–2583 (2005). [CrossRef] [PubMed]

,10

10. R. Keenan, J. Dunn, P. K. Patel, D. F. Price, R. F. Smith, and V N. Shlyaptsev, “High-repetition-rate grazing-incidence pumped x-ray laser operating at 18.9 nm,” Phys. Rev. Lett. 94, 103901 (2005). [CrossRef] [PubMed]

]. Refraction has the advantage that it allows one to define the electron density at which the pump energy is absorbed based on only two parameters, the grazing incidence angle θ and the laser pump wavelength: θ=(n e/n cp)1/2 [8–10

8. G. Vaschenko, C. Brewer, F. Brizuela, Y. Wang, M. A. Larotonda, B. M. Luther, M. C. Marconi, J. J. Rocca, C. S. Menoni, E. H. Anderson, W. Chao, B. D. Harteneck, J. A. Liddle, Y. Liu, and D. T. Attwood, “Sub-38 nm resolution tabletop microscopy with 13 nm wavelength laser light,” Opt. Lett. 31, 1214–1216 (2006). [CrossRef] [PubMed]

], where n e is the maximum electron density within the amplification region and n cp is the critical density at the wavelength of the pump. Hence when the grazing angle is changed, different parts of the density profile formed by the pre-pulse are preferentially heated. At a selected incidence angle of 23 degrees and an incident wavelength of 800 nm, the pump energy is most efficiently coupled in the region where the electron density is n e=2.6×1020 cm-3, where large amplification can be obtained in transitions of Ni-like ions with wavelengths near 13.5 nm. This in turn significantly decreases the pump pulse energy required to operate the lasers in the gain saturated regime, allowing their operation at table-top scale and at increased repetition rate.

Several measurements of the spatial coherence of soft x-ray lasers excited using the conventional normal incidence geometry have been reported in the literature [12

12. R. A. London, “Beam optics of exploding foil plasma x-ray lasers,” Phys. Fluids 31, 184 (1988). [CrossRef]

, 13

13. H. Tang, H. Daido, M. Kishimoto, K. Sukegawa, R. Tai, S. Mosesson, M. Tanaka, P. Lu, T. Kawachi, K. Nagashima, K. Nagai, T. Norimatsu, K. Murai, H. Takenaka, Y. Kato, K. Mima, and K. Nishihara, “Spatial coherence measurement of 13.9 nm Ni-like Ag soft x-ray laser pumped by a 1.5 ps, 20 J Laser,” Jpn. J. Appl. Phys. 42, 443–448 (2003). [CrossRef]

]. It is of interest to study the coherence of soft x-ray lasers pumped at grazing incidence. Here we discuss the measurement of the spatial coherence of a 13.2 nm transient Ni-like Cd laser pumped at grazing incidence using classical Young’s double-slit interference experiments. In the experiments we used a series of double-slits with different separations, which characterize the transverse coherence length. We also investigated the coherence with different plasma lengths. Similar experiments have been done with a 13.9 nm Ni-like Ag laser pumped at normal incidence [13

13. H. Tang, H. Daido, M. Kishimoto, K. Sukegawa, R. Tai, S. Mosesson, M. Tanaka, P. Lu, T. Kawachi, K. Nagashima, K. Nagai, T. Norimatsu, K. Murai, H. Takenaka, Y. Kato, K. Mima, and K. Nishihara, “Spatial coherence measurement of 13.9 nm Ni-like Ag soft x-ray laser pumped by a 1.5 ps, 20 J Laser,” Jpn. J. Appl. Phys. 42, 443–448 (2003). [CrossRef]

]. Although 13.2 nm and 13.9 nm are both close to the 13.5 nm peak wavelength of standard Mo/Si multilayer coatings used in EUVL, the unsymmetrical shape of the reflectivity curve results in a > 50% reflectivity at 13.2 nm but < 15% reflectivity at 13.9 nm. As a result, the Cd laser is more advantageous for EUVL applications.

2. Experimental setup

Fig. 1. Young’s double-slit experiment setup for measuring the spatial coherence of a 13.2 nm soft x-ray laser.

The experimental setup of the coherence measurements is illustrated in Fig. 1. We used Young’s double-slit interferometry to measure the degree of spatial coherence of the laser beam. A set of slit pairs with separations of 30, 50, and 75 microns was used in the experiments. The width of each individual slit is 5 microns. The slits were placed at 105 mm from the laser target. A 0.2 µm thick self-supported Zr filter was used to block the Ti:sapphire laser and visible/ultraviolet radiations from the plasma. The 45-degree folding mirror is coated with Mo/Si multilayer, which has ~50% reflectivity at 13.2 nm and a spectral bandwidth of ~1 nm (FWHM). The interferograms were recorded with an EUV sensitive CCD camera having a back-illuminated 2048×2048 array of 13×13 µm2 pixels. The total path length from the double-slit to CCD is 330 mm. The multilayer and Zr filters sufficiently prevent most unwanted wavelengths from reaching the CCD and allow us to record clean interferogram in a single shot. Given the fact that the 13.2 nm laser line has a linewidth of only about 0.001 nm, although it strongly dominates the spectrum, there is still a low level of background (typically 10% of the 13.2 nm radiation) in the CCD readouts originating from those EUV wavelengths falling into the 1-nm bandwidth of the multilayer. Assuming the background radiation from the plasma is isotropic, for each interferogram we recorded the background by moving the slit away from the soft x-ray laser beam path and repeated the shot under the same experimental condition. We then obtained a clean interferogram by subtracting the background from the original one. This process also automatically removes the uniform thermal dark current of the CCD.

3. Interferograms and interpretations

A typical interferogram recorded using a double slit with 30 µm separation is shown in Fig. 2(a). The double-slit was placed horizontally, in the direction perpendicular to the target, thus diffraction and interference pattern occurred in the vertical direction. We integrated the interferogram along both horizontal and vertical directions. The vertical one [Fig. 2(b)] can be seen as a lineout of the laser beam intensity profile, sampled by the slits. It provides useful information on beam size and divergence angle. The horizontally integrated one [Fig. 2(c)] is the overall double-slit interference pattern, from which an ‘average’ fringe visibility can be obtained. The high fringe visibility in Fig. 2(c) implies a high degree of spatial coherence for 30 µm separation.

A noticeable feature of the interferograms is the pronounced intensity irregularity, with many local intense spots in them. Those spots were observed in all the interferograms, regardless of slit orientation and Cd target length. Their peak intensities and positions changed randomly from shot to shot. Their presence causes complications on the analysis of the interferograms. For typical double-pinhole/slit coherence measurements, the relationship between fringe visibility V and the spatial coherence factor µ12 is [14

14. A. Lucianetti, K. A. Janulewicz, R. Kroemer, G. Priebe, J. Tümmler, W. Sandner, P. V. Nickles, and V. I. Redkorechev, “Transverse spatial coherence of a transient nickel like silver soft-x-ray laser pumped by a single picosecond laser pulse,” Opt. Lett. 29, 881–883 (2004). [CrossRef] [PubMed]

]

V=2I1I2I1+I2μ12
Eq. (1)

where I1 and I2 are the beam intensities at the two individual slits. The fringe visibility V can be directly obtained from the interferogram as V=(I max-I min)/(I max+I min), where I max and I min are the intensity maxima and minima in the interferogram. Usually, the double-slit is positioned such that I 1I 2, which leads to the simple relationship V=|μ12|. However, in general cases when I 1I 2, Eq. (1) implies V<|µ12|, meaning measured fringe visibility would always underestimate the real degree of spatial coherence. As the difference between I 1 and I 2 becomes larger, the discrepancy between fringe visibility V and coherence factor will also become larger. In our experiments, the randomly located hot spots present in the beam microstructure make it practically impossible to position the slit so that I 1I 2 can be satisfied across the whole slit. The relative strength of I 1 and I 2 is also varying therefore the factor 2I1I2(I1+I2) can not be fully determined. The characteristic size of those spots at the double-slit plane, estimated by their sizes on the CCD and a simple geometric reduction, is around 100 µm. This is comparable to the slit separations used in the experiments. While two slits separated by 30 µm (the smallest separation used in experiments) may still sample those ~100 µm spots with roughly the same intensities, it is more likely that double-slits with 50 µm and 75 µm separations will see increasingly different intensities on individual slits. Such intensity difference will cause visibility variation even though |µ12| could still be essentially constant.

Fig. 2. (a). A typical two-slit interferogram recorded by the CCD for a 30 µm slit separation. The double-slit is placed horizontally (x-direction). (b) Integration of (a) in the vertical direction, which gives a lineout of the laser beam intensity profile. Intensity irregularities, or microstructures, are clearly observed. (c) Integration of (a) in the horizontal direction, which gives an ‘average’ interference pattern, whose fringe visibility is a measure of the spatial coherence.

We indeed observed fringe visibility variations in recorded interferograms. Figure 3 illustrates fringe patterns obtained using 4-mm-long target and horizontally placed (perpendicular to target surface) double-slits with separations of 30 (a), 50 (b), and 75 µm (c). For each separation, we first obtained an average fringe visibility (red lines) by integrating the whole interferogram, as described in earlier paragraph. We then manually scanned the interferogram along the slit orientation and picked a small region where the visibility is highest (blue lines in fig.). Consistent with the above discussions, the variation of fringe visibility with 30 µm double-slit is relatively small, where the best/average visibility is 0.69/0.59. The visibility variation becomes larger with 50 and 75 µm double-slits, where best/average visibility is 0.52/0.23 and 0.31/0.13, respectively. Although we could not rule out the possibility that |µ12| itself is varying in space, following the above discussion we believe the highest visibility observed is a more accurate representation of|µ12|, while the average visibility underestimates it.

Fig. 3. (a).-3 (c). Interference fringes with average visibility (red), obtained by integrating the whole interferogram, and fringes with highest visibility (blue), picked by manually scanning the interferogram. For comparison the fringe patterns are normalized in intensity and overlap each other. The slit separations are (a) 30, (b) 50, and (c) 75 µm. (d) Experimental data (Δ,∇) of fringe visibilities at different slit separations and theoretical predictions based on van Cittert-Zernike theorem. The source size is 10 µm [blue, corresponding to highest visibilities in (a-c)] and 15 µm (red, corresponding to average visibilities).

Having deduced values of |µ12| for different separations, we can estimate the size of an equivalent incoherent source using van Cittert-Zernike theorem [14

14. A. Lucianetti, K. A. Janulewicz, R. Kroemer, G. Priebe, J. Tümmler, W. Sandner, P. V. Nickles, and V. I. Redkorechev, “Transverse spatial coherence of a transient nickel like silver soft-x-ray laser pumped by a single picosecond laser pulse,” Opt. Lett. 29, 881–883 (2004). [CrossRef] [PubMed]

]. Assuming the source has a parabolic-like intensity profile of I=I0cosh-2(x/a) [15

15. M. Born and E. Wolf, Principles of Optics, 7th Edition (Cambridge University Press, 1999)

], to produce similar |µ12|function at the double-slit plane, the source size (FWHM) is 10 µm (Fig. 3(d), blue curve). For comparison, using the average visibility data (red Δ) results in a source size of 15 µm FWHM (red curve). The above results are for horizontally placed slits; vertically placed slits (parallel to target plane) gave similar results. The spatial coherence properties seem to be the same in both directions.

The above results show that a good degree of spatial coherence exists on a lateral size roughly the same as those microstructures found in the intensity profile, but much smaller than the beam diameter. It has been recently suggested that these microstructures are the results of interference between many independent spatial modes when the EUV laser possesses good temporal coherence and short pulse duration [18

18. M. A. Larotonda, Y. Wang, M. Berrill, B. M. Luther, J. J. Rocca, M. M. Shakya, S. Gilbertson, and Z. Chang, “Pulse duration measurements of grazing incidence pumped high repetition rate Ni-like Ag and Cd transient soft x-ray lasers,” Opt. Lett., (2006), In press [CrossRef] [PubMed]

, 19

19. A. Klisnick, O. Guilbaud, D. Ros, K. Cassou, S. Kazamias, G. Jamelot, J.-C. Lagron, D. Joyeux, D. Phalippou, Y. Lechantre, M. Edwards, P. Mistry, and G. J. Tallents, “Experimental study of the temporal coherence and spectral profile of the 13.9nm transient X-ray laser,” J. Quant. Spectrosc. Radiat. Transf. 99, 370–380 (2006). [CrossRef]

]. They could also be the results of those independent modes experiencing non-uniform gain inside the plasma and exiting the plasma at different angles due to refraction. These microstructures are important when using the laser as the illuminator in a microscope or in interferometry applications.

4. Spatial coherence versus plasma length

Based on amplified spontaneous emission (ASE), the improvement of spatial coherence of soft x-ray lasers largely depends on the formation of an elongated plasma column with large length-to-diameter ratio, for which the Fresnel number (N F=a2/λL) is small. A small Fresnel number reduces the number of spatial modes that can get effective amplification inside the gain media (plasma), thus providing a practical mode selection mechanism [15

15. M. Born and E. Wolf, Principles of Optics, 7th Edition (Cambridge University Press, 1999)

, 20

20. O. Guilbaud, A. Klisnick, K. Cassou, S. Kazamias, D. Ros, G. Jamelot, D. Joyeux, and D. Phalippou, “Origin of microstructures in picosecond X-ray laser beams,” Europhys. Lett. 74, 823–829, (2006). [CrossRef]

]. With even longer plasma length and strong refraction, refractive anti-guiding can further reduce the mode number and result in essentially full spatial coherence from a soft x-ray laser [21

21. P. D. Gasparyan, F. A. Starikov, and A. N. Starostin, “Angular divergence and spatial coherence of X-ray laser radiation,” Phys. Usp. 41, 761–792 (1998). [CrossRef]

]. In our experiments, we compared interferograms recorded with same double-slits, but varying target lengths from 2 mm to 4 mm. As described in section 3, the interferograms contain information on beam intensity, divergence, and spatial coherence. With increasing target lengths, we observed increase of beam intensity, as expected. However, in the present experiment we did not observe noticeable improvement of spatial coherence with longer targets. As an example, Fig. 4 shows the comparison of two interferograms using a 50 µm separation double-slit, one recorded with 2 mm long target, the other 4 mm.

Fig. 4. Comparisons of beam intensity lineout (a) and integrated interference pattern (b) when the Cd target length is 2 mm (blue) and 4 mm (red). The CCD readouts are not normalized, thus providing a real comparison of beam intensity. There is no noticeable improvement of either spatial coherence, or beam quality when the target length is longer.

As shown in Fig. 4, the fringe visibility is essentially unchanged with longer target. Furthermore, the beam quality also showed limited improvement, with little change on the divergence angle. If we treat the 4 mm plasma column as a 2 mm ‘source’ with another 2-mm long amplifier following it, the amplifier seems to amplify all spatial modes without preference. The lack of mode selection mechanism is an indication that the plasma lacks the high uniformity and cylindrical symmetry of the plasmas generated by fast capillary discharges, where rapidly improved spatial coherence is observed as a function of plasma column length [21

21. P. D. Gasparyan, F. A. Starikov, and A. N. Starostin, “Angular divergence and spatial coherence of X-ray laser radiation,” Phys. Usp. 41, 761–792 (1998). [CrossRef]

]. Fluctuations in the plasma, such as “hose-type” random transverse displacements of the lasing medium, can also lead to decreased spatial coherence [22

22. Y. Liu, M. Seminario, F. G. Tomasel, C. Chang, J. J. Rocca, and D. T. Attwood, “Achievement of essentially full spatial coherence in a high-average-power soft-x-ray laser,” Phys. Rev. A 63, 033802 (2001).

]. A more uniform plasma of longer length should allow for improved coherence. It can also be expected that a great improvement of the spatial coherence of this type of laser can be obtained by seeding the laser with a high coherence beam, possibly from another laser as in the double target setup [23

23. P. Amendt, M. Strauss, and R. A. London, “Plasma fluctuations and x-ray laser transverse coherence,” Phys. Rev. A. 53, R23–R26 (1996). [CrossRef] [PubMed]

], a cascaded amplifier setup with spatial filter in between, or a high-order harmonic source. In fact, a very recent experiment demonstrated that high harmonic seeding of a 32.6 nm wavelength Ne-like Ti soft x-ray laser amplifier pumped at grazing incidence achieved essentially full spatial coherence [24

24. M. Nishikino, M. Tanaka, K. Nagashima, M. Kishimoto, M. Kado, T. Kawachi, K. Sukegawa, Y. Ochi, N. Hasegawa, and Y. Kato, “Demonstration of a soft-x-ray laser at 13.9 nm with full spatial coherence,” Phys. Rev. A 68, 061802 (2003). [CrossRef]

]. Such technique can yield compact high repetition rate soft x-ray lasers with full spatial and temporal coherence.

5. Summary

In summary, comprehensive spatial coherence measurements were performed for a 13.2 nm Cd laser pumped by grazing incidence. We observed significant microstructure in the beam intensity profile, whose influence on the coherence measurements is discussed. The transverse coherence length is found to be about 1/20 of the laser beam diameter.

Acknowledgments

We thank Mark Berrill (Colorado State University) for useful information on hydrodynamic simulation of the laser. This work was supported by the Engineering Research Centers Program of the National Science Foundation under NSF Award Number EEC-0310717.

References and links

1.

Y. Wang, M. A. Larotonda, B. M. Luther, D. Alessi, M. Berrill, V. N. Shlyaptsev, and J. J. Rocca, “Demonstration of high-repetition-rate tabletop soft-x-ray lasers with saturated output at wavelengths down to 13.9 nm and gain down to 10.9 nm,” Phys. Rev. A 72, 053807 (2005). [CrossRef]

2.

H. C. Kapteyn, M. M. Murnane, and I. P. Christov, “Extreme Nonlinear Optics: Coherent X Rays from Lasers,” Phys. Today , 58, 39–44 (2005). [CrossRef]

3.

K. A. Goldberg, P. Naulleau, P. Denham, S. B. Rekawa, K. Jackson, E. H. Anderson, and J. A. Liddle, “At-wavelength alignment and testing of the 0.3 NA MET optics,” J. Vac. Sci. Tech. B 22, 2956–2961 (2004). [CrossRef]

4.

P. P. Naulleau, “Advanced EUV Lithography capabilities at Lawrence Berkeley National Laboratory’s Advanced Light Source,” Proceedings, SEMI Technology Symposium2004.

5.

P. P. Naulleau, K. A. Goldberg, E. H. Anderson, P. Denham, B. Hoef, K. Jackson, A. Morlens, and S. Rekawa, “EUV microexposures at the ALS using the 0.3-NA MET projection optics,” Microlithography 2005, paper [5751-04]. i.b. Proc. SPIE 5374, 881–891 (2004).

6.

Y. Liu, A. Barty, E. Gullikson, J. S. Taylor, J. A. Liddle, and O. Wood, “A dual-mode actinic EUV mask inspection tool,” in Emerging Lithographic Technologies IX, R. Scott Mackay, ed., Proc. SPIE5751, 660–669 (2005). [CrossRef]

7.

W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, “Soft X-ray microscopy at a spatial resolution better than 15 nm,” Nature 435, 1210 (2005). [CrossRef] [PubMed]

8.

G. Vaschenko, C. Brewer, F. Brizuela, Y. Wang, M. A. Larotonda, B. M. Luther, M. C. Marconi, J. J. Rocca, C. S. Menoni, E. H. Anderson, W. Chao, B. D. Harteneck, J. A. Liddle, Y. Liu, and D. T. Attwood, “Sub-38 nm resolution tabletop microscopy with 13 nm wavelength laser light,” Opt. Lett. 31, 1214–1216 (2006). [CrossRef] [PubMed]

9.

J. J. Rocca, Y. Wang, M. A. Larotonda, B. M. Luther, M. Berrill, and D. Alessi, “Saturated 13.2 nm highrepetition-rate laser in nickellike cadmium”, Opt. Lett. 30, 2581–2583 (2005). [CrossRef] [PubMed]

10.

R. Keenan, J. Dunn, P. K. Patel, D. F. Price, R. F. Smith, and V N. Shlyaptsev, “High-repetition-rate grazing-incidence pumped x-ray laser operating at 18.9 nm,” Phys. Rev. Lett. 94, 103901 (2005). [CrossRef] [PubMed]

11.

B. M. Luther, Y. Wang, M. A. Larotonda, D. Alessi, M. Berrill, M. C. Marconi, J. J. Rocca, and V. N. Shlyaptsev, “Saturated high-repetition-rate 18.9-nm tabletop laser in nickellike molybdenum,” Opt. Lett. 30, 165–167 (2005). [CrossRef] [PubMed]

12.

R. A. London, “Beam optics of exploding foil plasma x-ray lasers,” Phys. Fluids 31, 184 (1988). [CrossRef]

13.

H. Tang, H. Daido, M. Kishimoto, K. Sukegawa, R. Tai, S. Mosesson, M. Tanaka, P. Lu, T. Kawachi, K. Nagashima, K. Nagai, T. Norimatsu, K. Murai, H. Takenaka, Y. Kato, K. Mima, and K. Nishihara, “Spatial coherence measurement of 13.9 nm Ni-like Ag soft x-ray laser pumped by a 1.5 ps, 20 J Laser,” Jpn. J. Appl. Phys. 42, 443–448 (2003). [CrossRef]

14.

A. Lucianetti, K. A. Janulewicz, R. Kroemer, G. Priebe, J. Tümmler, W. Sandner, P. V. Nickles, and V. I. Redkorechev, “Transverse spatial coherence of a transient nickel like silver soft-x-ray laser pumped by a single picosecond laser pulse,” Opt. Lett. 29, 881–883 (2004). [CrossRef] [PubMed]

15.

M. Born and E. Wolf, Principles of Optics, 7th Edition (Cambridge University Press, 1999)

16.

R. A. London, M. Strauss, and M. D. Rosen, “Modal analysis of x-ray laser coherence,” Phys. Rev. Lett. 65, 563–566 (1990). [CrossRef] [PubMed]

17.

D. Attwood, Soft X-rays and Extreme Ultraviolet Radiation: Principles and Applications (Cambridge University Press, 1999)

18.

M. A. Larotonda, Y. Wang, M. Berrill, B. M. Luther, J. J. Rocca, M. M. Shakya, S. Gilbertson, and Z. Chang, “Pulse duration measurements of grazing incidence pumped high repetition rate Ni-like Ag and Cd transient soft x-ray lasers,” Opt. Lett., (2006), In press [CrossRef] [PubMed]

19.

A. Klisnick, O. Guilbaud, D. Ros, K. Cassou, S. Kazamias, G. Jamelot, J.-C. Lagron, D. Joyeux, D. Phalippou, Y. Lechantre, M. Edwards, P. Mistry, and G. J. Tallents, “Experimental study of the temporal coherence and spectral profile of the 13.9nm transient X-ray laser,” J. Quant. Spectrosc. Radiat. Transf. 99, 370–380 (2006). [CrossRef]

20.

O. Guilbaud, A. Klisnick, K. Cassou, S. Kazamias, D. Ros, G. Jamelot, D. Joyeux, and D. Phalippou, “Origin of microstructures in picosecond X-ray laser beams,” Europhys. Lett. 74, 823–829, (2006). [CrossRef]

21.

P. D. Gasparyan, F. A. Starikov, and A. N. Starostin, “Angular divergence and spatial coherence of X-ray laser radiation,” Phys. Usp. 41, 761–792 (1998). [CrossRef]

22.

Y. Liu, M. Seminario, F. G. Tomasel, C. Chang, J. J. Rocca, and D. T. Attwood, “Achievement of essentially full spatial coherence in a high-average-power soft-x-ray laser,” Phys. Rev. A 63, 033802 (2001).

23.

P. Amendt, M. Strauss, and R. A. London, “Plasma fluctuations and x-ray laser transverse coherence,” Phys. Rev. A. 53, R23–R26 (1996). [CrossRef] [PubMed]

24.

M. Nishikino, M. Tanaka, K. Nagashima, M. Kishimoto, M. Kado, T. Kawachi, K. Sukegawa, Y. Ochi, N. Hasegawa, and Y. Kato, “Demonstration of a soft-x-ray laser at 13.9 nm with full spatial coherence,” Phys. Rev. A 68, 061802 (2003). [CrossRef]

25.

Y. Wang, E. Granados, M. A. Larotonda, M. Berrill, B. M. Luther, D. Patel, C. S. Menoni, and J. J. Rocca, “High brightness injection seeded soft x-ray laser amplifier using a solid target,” Phys. Rev. Lett. 97, 123901 (2006). [CrossRef] [PubMed]

OCIS Codes
(030.1640) Coherence and statistical optics : Coherence
(140.7240) Lasers and laser optics : UV, EUV, and X-ray lasers
(340.7440) X-ray optics : X-ray imaging

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: September 29, 2006
Manuscript Accepted: November 5, 2006
Published: December 22, 2006

Citation
Y. Liu, Y. Wang, M. A. Larotonda, B. M. Luther, J. J. Rocca, and D. T. Attwood, "Spatial coherence measurements of a 13.2 nm transient nickel-like cadmium soft x-ray laser pumped at grazing incidence," Opt. Express 14, 12872-12879 (2006)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-26-12872


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. Y. Wang, M. A. Larotonda, B. M. Luther, D. Alessi, M. Berrill, V. N. Shlyaptsev, and J. J. Rocca, "Demonstration of high-repetition-rate tabletop soft-x-ray lasers with saturated output at wavelengths down to 13.9 nm and gain down to 10.9 nm," Phys. Rev. A 72, 053807 (2005). [CrossRef]
  2. H. C. Kapteyn, M. M. Murnane and I. P. Christov, "Extreme Nonlinear Optics: Coherent X Rays from Lasers," Phys. Today,  58, 39-44 (2005). [CrossRef]
  3. K. A. Goldberg, P. Naulleau, P. Denham, S. B. Rekawa, K. Jackson, E. H. Anderson and J. A. Liddle, "At-wavelength alignment and testing of the 0.3 NA MET optics," J. Vac. Sci. Tech. B 22, 2956-2961 (2004). [CrossRef]
  4. P. P. Naulleau, "Advanced EUV Lithography capabilities at Lawrence Berkeley National Laboratory's Advanced Light Source," Proceedings, SEMI Technology Symposium 2004.
  5. P. P. Naulleau, K. A. Goldberg, E. H. Anderson, P. Denham, B. Hoef, K. Jackson, A. Morlens, and S. Rekawa, "EUV microexposures at the ALS using the 0.3-NA MET projection optics," Microlithography 2005, paper [5751-04]. i.b.Proc. SPIE 5374, 881-891 (2004).
  6. Y. Liu, A. Barty, E. Gullikson, J. S. Taylor, J. A. Liddle, and O. Wood, "A dual-mode actinic EUV mask inspection tool," in Emerging Lithographic Technologies IX, R. Scott Mackay, ed., Proc. SPIE 5751, 660-669 (2005). [CrossRef]
  7. W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, "Soft X-ray microscopy at a spatial resolution better than 15 nm," Nature 435, 1210 (2005). [CrossRef] [PubMed]
  8. G. Vaschenko, C. Brewer, F. Brizuela, Y. Wang, M. A. Larotonda, B. M. Luther, M. C. Marconi, J. J. Rocca, C. S. Menoni, E. H. Anderson, W. Chao, B. D. Harteneck, J. A. Liddle, Y. Liu, D. T. Attwood, "Sub-38 nm resolution tabletop microscopy with 13 nm wavelength laser light,"Opt. Lett. 31, 1214-1216 (2006). [CrossRef] [PubMed]
  9. J. J. Rocca, Y. Wang, M. A. Larotonda, B. M. Luther, M. Berrill, and D. Alessi, "Saturated 13.2 nm high-repetition-rate laser in nickellike cadmium", Opt. Lett. 30, 2581-2583 (2005). [CrossRef] [PubMed]
  10. R. Keenan, J. Dunn, P. K. Patel, D. F. Price, R. F. Smith, and V N. Shlyaptsev, "High-repetition-rate grazing-incidence pumped x-ray laser operating at 18.9 nm," Phys. Rev. Lett. 94, 103901 (2005). [CrossRef] [PubMed]
  11. B. M. Luther, Y. Wang, M. A. Larotonda, D. Alessi, M. Berrill, M. C. Marconi, J. J. Rocca, and V. N. Shlyaptsev, "Saturated high-repetition-rate 18.9-nm tabletop laser in nickellike molybdenum," Opt. Lett. 30, 165-167 (2005). [CrossRef] [PubMed]
  12. R. A. London, "Beam optics of exploding foil plasma x-ray lasers," Phys. Fluids 31, 184 (1988). [CrossRef]
  13. H. Tang, H. Daido, M. Kishimoto, K. Sukegawa, R. Tai, S. Mosesson, M. Tanaka, P. Lu, T. Kawachi, K. Nagashima, K. Nagai, T. Norimatsu, K. Murai, H. Takenaka, Y. Kato, K. Mima, K. Nishihara, "Spatial coherence measurement of 13.9 nm Ni-like Ag soft x-ray laser pumped by a 1.5 ps, 20 J Laser," Jpn. J. Appl. Phys. 42, 443-448 (2003). [CrossRef]
  14. A. Lucianetti, K. A. Janulewicz, R. Kroemer, G. Priebe, J. Tümmler, W. Sandner, P. V. Nickles, and V. I. Redkorechev, "Transverse spatial coherence of a transient nickel like silver soft-x-ray laser pumped by a single picosecond laser pulse," Opt. Lett. 29, 881-883 (2004). [CrossRef] [PubMed]
  15. M. Born and E. Wolf, Principles of Optics, 7th Edition (Cambridge University Press,1999)
  16. R. A. London, M. Strauss and M. D. Rosen, "Modal analysis of x-ray laser coherence," Phys. Rev. Lett. 65, 563-566 (1990). [CrossRef] [PubMed]
  17. D. Attwood, Soft X-rays and Extreme Ultraviolet Radiation: Principles and Applications (Cambridge University Press, 1999)
  18. M. A. Larotonda, Y. Wang, M. Berrill, B. M. Luther, and J. J. Rocca, M. M. Shakya, S. Gilbertson, and Z. Chang, "Pulse duration measurements of grazing incidence pumped high repetition rate Ni-like Ag and Cd transient soft x-ray lasers," Opt. Lett., (2006), In press [CrossRef] [PubMed]
  19. A. Klisnick, O. Guilbaud, D. Ros, K. Cassou, S. Kazamias, G. Jamelot, J.-C. Lagron, D. Joyeux, D. Phalippou, Y. Lechantre, M. Edwards, P. Mistry, and G. J. Tallents, "Experimental study of the temporal coherence and spectral profile of the 13.9nm transient X-ray laser," J. Quant. Spectrosc. Radiat. Transf. 99, 370-380 (2006) [CrossRef]
  20. O. Guilbaud, A. Klisnick, K. Cassou, S. Kazamias, D. Ros, G. Jamelot, D. Joyeux, and D. Phalippou, "Origin of microstructures in picosecond X-ray laser beams," Europhys. Lett. 74, 823-829, (2006) [CrossRef]
  21. P. D. Gasparyan, F. A. Starikov and A. N. Starostin, "Angular divergence and spatial coherence of X-ray laser radiation," Phys. Usp. 41, 761-792 (1998). [CrossRef]
  22. Y. Liu, M. Seminario, F. G. Tomasel, C. Chang, J. J. Rocca, and D. T. Attwood, "Achievement of essentially full spatial coherence in a high-average-power soft-x-ray laser," Phys. Rev. A 63, 033802 (2001).
  23. P. Amendt, M. Strauss, and R. A. London, "Plasma fluctuations and x-ray laser transverse coherence," Phys. Rev. A. 53, R23-R26 (1996). [CrossRef] [PubMed]
  24. M. Nishikino, M. Tanaka, K. Nagashima, M. Kishimoto, M. Kado, T. Kawachi, K. Sukegawa, Y. Ochi, N. Hasegawa, and Y. Kato, "Demonstration of a soft-x-ray laser at 13.9 nm with full spatial coherence," Phys. Rev. A 68, 061802 (2003). [CrossRef]
  25. Y. Wang, E. Granados, M. A. Larotonda, M. Berrill, B. M. Luther, D. Patel, C. S. Menoni and J. J. Rocca, "High brightness injection seeded soft x-ray laser amplifier using a solid target," Phys. Rev. Lett. 97,123901 (2006). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Figures

Fig. 1. Fig. 2. Fig. 3.
 
Fig. 4.
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited