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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 4 — Feb. 14, 2011
  • pp: 3434–3439
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High-resolution computer-generated reflection holograms with three-dimensional effects written directly on a silicon surface by a femtosecond laser

Kristian J. Wædegaard and Peter Balling  »View Author Affiliations


Optics Express, Vol. 19, Issue 4, pp. 3434-3439 (2011)
http://dx.doi.org/10.1364/OE.19.003434


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Abstract

An infrared femtosecond laser has been used to write computer-generated holograms directly on a silicon surface. The high resolution offered by short-pulse laser ablation is employed to write highly detailed holograms with resolution up to 111 kpixels/mm2. It is demonstrated how three-dimensional effects can be realized in computer-generated holograms. Three-dimensional effects are visualized as a relative motion between different parts of the holographic reconstruction, when the hologram is moved relative to the reconstructing laser beam. Potential security applications are briefly discussed.

© 2011 OSA

1. Introduction

Computer-generated holograms (CGHs) were first demonstrated in 1967 by Lohmann and Paris [1

1. A. W. Lohmann and D. P. Paris, “Binary fraunhofer holograms, generated by computer,” Appl. Opt. 6(10), 1739–1748 (1967). [CrossRef] [PubMed]

]. Originally they were fabricated by a complicated procedure involving several steps including lithography, usually making it an extensive and time-consuming process. However, recently femtosecond lasers have been used for direct writing of CGHs, e.g. inside glasses [2

2. L. Ran and S. Qu, “Self-assembled volume vortex grating induced by femtosecond laser pulses in glass,” Curr. Appl. Phys. 9(6), 1210–1212 (2009). [CrossRef]

4

4. Y. Li, Y. Dou, R. An, H. Yang, and Q. Gong, “Permanent computer-generated holograms embedded in silica glass by femtosecond laser pulses,” Opt. Express 13(7), 2433–2438 (2005). [CrossRef] [PubMed]

] and by evaporation of metal films on glass substrates [5

5. Q.Z. Zhao, J. R. Qiu, X. W. Jiang, E. W. Dai, C. H. Zhou, and C. S. Zhu, “Direct writing computer-generated holograms on metal film by an infrared femtosecond laser,” Opt. Express 13(6), 2089–2092 (2005). [CrossRef] [PubMed]

]. The original lithographic method is suitable for mass production of holograms, while the direct-writing method provides a quick way to make “one of a kind” holograms, which opens up for new applications, such as anti counterfeiting, beam shaping [2

2. L. Ran and S. Qu, “Self-assembled volume vortex grating induced by femtosecond laser pulses in glass,” Curr. Appl. Phys. 9(6), 1210–1212 (2009). [CrossRef]

,3

3. Z. Guo, S. Qu, and S. Liu, “Generating optical vortex with computer-generated hologram fabricated inside glass by femtosecond laser pulses,” Opt. Commun. 273(1), 286–289 (2007). [CrossRef]

], and optical keys [6

6. C. G. Trevino-Palacios, A. Olivares-Perez, and O. J. Zapata-Nava, “Security system with optical key access,” Proc. SPIE 6422, 642218–642224 (2007). [CrossRef]

]. CGHs written directly with a femtosecond laser are particularly suitable for security applications: The holograms that may include a unique code are easy to reconstruct but hard to replicate, since a femtosecond laser or a similar tool is needed to produce the tiny spots forming the hologram. The small (millimeter) size of the hologram also makes it possible to hide the hologram or produce it on small items, while the much larger reconstructed image is readily visible.

Since early on, three-dimensional (3-D) effects have been incorporated in CGHs in the form of binary Fourier holograms [7

7. B. R. Brown and A. W. Lohmann, “Computer-generated Binary Holograms,” IBM J. Res. Develop. 13(2), 160–168 (1969). [CrossRef]

,8

8. J. P. Waters, “Three-Dimensional Fourier-Transform Method for Synthesizing Binary Holograms,” J. Opt. Soc. Am. 58(9), 1284–1288 (1968). [CrossRef]

] and kinoforms [9

9. L. B. Lesem, P. M. Hirsch, and J. A. Jordan Jr., “The Kinoform: A New Wavefront Reconstruction Device,” IBM J. Res. Develop. 13(2), 150–155 (1969). [CrossRef]

], and also more recently in a holographic video display system [10

10. T. Yamaguchi, G. Okabe, and H. Yoshikawa, “Real-time image plane full-color and full-parallax holographic video display system,” Opt. Eng. 46(12), 125801 (2007). [CrossRef]

,11

11. P.-A. Blanche, A. Bablumian, R. Voorakaranam, C. Christenson, W. Lin, T. Gu, D. Flores, P. Wang, W.-Y. Hsieh, M. Kathaperumal, B. Rachwal, O. Siddiqui, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “Holographic three-dimensional telepresence using large-area photorefractive polymer,” Nature 468(7320), 80–83 (2010). [CrossRef] [PubMed]

]. In this experiment, a femtosecond laser is used to write CGHs directly on a silicon surface, giving a reflection hologram. This method is generally applicable to inscription on any flat reflecting surface including metal surfaces. The experiment uses a femtosecond laser because of its unique capabilities within micro-structuring. The minimal heat transfer during laser processing enables the fabrication of very small structures with sizes down to and even below the laser wavelength [12

12. P. P. Pronko, S. K. Dutta, J. Squier, J. V. Rudd, D. Du, and G. Mourou, “Machining of sub-micron holes using a femtosecond laser at 800 nm,” Opt. Commun. 114(1-2), 106–110 (1995). [CrossRef]

,13

13. K. Vestentoft, J. A. Olesen, B. H. Christensen, and P. Balling, “Nanostructuring of surfaces by ultra-short laser pulses,” Appl. Phys., A Mater. Sci. Process. 80(3), 493–496 (2005). [CrossRef]

]. In this experiment, spots with a diameter down to 3 μm have been made, which enables a resolution of 111 kpixels/mm2 (~8500 dpi). In addition, to the best of our knowledge, the present investigation is the first demonstration of the incorporation of 3-D effects into directly written CGHs. The 3-D effects appear with translation of the CGH, which causes relative motion between different parts of the hologram originating from different object planes.

2. Experimental

In the experiment, a Ti:Sapphire laser system delivering 100 fs pulses with a central wavelength of 795 nm at a repetition rate of 1 kHz is used. The beam is focused onto the sample surface using an aspheric lens with a focal length of 10 mm. With a pulse energy of 50-100 nJ and a beam diameter before the lens of ~10 mm, the theoretical Gaussian focal spot size, ω0, is ~0.5 μm, hence the theoretical fluence is 6.5-13 J/cm2. A gentle flow of helium is applied through a nozzle enclosing the focusing beam to prevent breakdown in the air and remove laser-generated debris. For the present work, silicon was selected because it is easy to obtain flat, uniform samples, and it is relatively inexpensive and has an acceptable reflectivity in the visible region [14

14. D. F. Edwards, “Silicon (Si),” in Handbook of Optical Constants of Solids, E.D. Palik, ed. (Academic, Orlando, Fla., 1985).

], but the CGHs can be written on any surface with a high reflectivity. The sample is mounted on a 3-D translation stage, which is controlled by a computer that also controls whether the laser is on or off based on the position of the stage. This is done via an inhibit signal sent to the Pockels cell that switches the pulses in and out of the regenerative amplifier.

The CGHs are calculated as Fresnel holograms [15

15. J. P. Waters, “Holographic image synthesis utilizing theoretical methods,” Appl. Phys. Lett. 9(11), 405–407 (1966). [CrossRef]

] such that they include focusing and a spatial offset. The focusing enables the realization of the holographic image without the use of other optics such as lenses, while the offset prevents the holographic image from overlapping with the directly reflected beam. The holograms are calculated in a finite grid corresponding to the chosen pixel size and hologram dimensions. The real part of the complex electric field of the object wave is used for the final hologram, which is equivalent to the so-called “bipolar intensity” [16

16. M. Lucente, “Interactive computation of holograms using a look-up table,” J. Electron. Imaging 2(1), 28–34 (1993). [CrossRef]

,17

17. H. Yoshikawa, “Fast Computation of Fresnel Holograms Employing Difference,” Opt. Rev. 8(5), 331–335 (2001). [CrossRef]

], when the reference beam is perpendicular to hologram plane. The term “bipolar intensity” was introduced by Ref. 16 to account for the fact that this quantity can assume both positive and negative values. A binary bit pattern is then constructed by setting all pixels in the grid with values below the median level to 0 and the rest to 1. The holograms are created by transferring this binary bit pattern onto the sample by selective ablation of single pixels, which significantly reduces the reflectivity in those areas. No pre- or post-treatment of the sample is necessary. The holographic images are reconstructed using a He-Ne laser at 633 nm or a frequency-doubled Nd:YAG laser at 532 nm (500 mW).

3. Results and discussion

3.1 Three-dimensional effects

The 3-D effects are incorporated in the calculation of the holographic interference pattern. Different depths are assigned to different parts of the object from which the CGH is calculated. Figure 1
Fig. 1 Perspective image of the 3-D object that is the basis of the CGH calculation. The object is shown from the front (a) and from the right-hand side, and in both cases a bit from above.
shows the virtual object used for calculating the CGH seen from two different horizontal angles. It consists of the letters “IFA”, where each letter is placed at a different depth. In Fig. 1 (a) the object is viewed from the front and in (b) from the right-hand side. In both cases they are viewed a bit from above to visualize the three-dimensionality of the object. As can be seen, viewing the object from different angles changes the apparent separation of the letters. A holographic reconstruction of the object behaves in the same way, so when the CGH is reconstructed on a screen and a 2-D projection of the object is seen, a change in viewing angle causes a change in the relative position of the letters. The viewing angle is changed by translating the hologram relative to the reconstruction beam. It should be noted, that the angle of incidence of the reconstruction beam on the CGH is irrelevant as the holographic reconstruction – from a fixed point on the CGH – always appears at the same position relative to the directly reflected beam.

To demonstrate this, a rectangular hologram with a size comparable to that of the virtual object (1.8mm x 10.8mm) has been calculated from the object in Fig. 1. The CGH bit pattern is shown in Fig. 2
Fig. 2 Visualization of 3-D effects in directly written CGHs. Top: Rectangular CGH bit pattern of the 3-D object shown in Fig. 1. Bottom: Images of the holographic reconstruction made with a He-Ne laser from the on-axis (right) and off-axis (left) ends of the CGH. The hologram used for the reconstruction was made with a pitch of 6 μm.
together with images of the holographic reconstruction from the two ends of the CGH. In the calculation, the object is placed in front of the right-hand side of the CGH, which means that the reconstruction from the right side is on-axis and the letters are separated with the original spacing. The reconstruction from the left side of the hologram, on the other hand, is off-axis and there is larger separation of the letters. A smooth translation between the two outer positions causes the reconstruction to change smoothly between the two outer positions. Figure 3
Fig. 3 (Media 1) Video of holographic reconstruction of 3-D object when the CGH is translated from right to left and back smoothly, causing the letters to move relative to each other.
displays a movie of the evolution of the holographic reconstruction as the CGH is translated from right to left and back.

The object is given a small offset in the vertical direction to position the reconstructed image just above the reflection spot, which is why the letters are misaligned in the vertical direction. This could easily be avoided by also assigning different vertical positions to the letters in the calculation of the CGH. Since the 3-D objects are virtual objects, the CGH calculations can be chosen not to include shadowing of elements in the background by elements in the foreground. This way all parts of the hologram will help to reconstruct all the different elements of the 3-D object.

The distance from the CGH where the holographic reconstruction is in focus is determined by the distance between the object and hologram planes in the calculation of the CGH. However, when introducing 3-D effects by varying the depth of the object, the focus distance also varies. Still, the depth of focus (i.e. the range in which the reconstruction is sharp) is larger than the total depth span of the object, so blurring is not visible.

3.2 Resolution

To minimize the size of the ablated spots and thereby the minimum available pitch, the pulse energies are chosen to be fairly low. This is possible in the present work, because we have chosen to write only reflection holograms on the surface, as opposed to the combined reflection and transmission holograms formed by evaporation of a thin metal film [5

5. Q.Z. Zhao, J. R. Qiu, X. W. Jiang, E. W. Dai, C. H. Zhou, and C. S. Zhu, “Direct writing computer-generated holograms on metal film by an infrared femtosecond laser,” Opt. Express 13(6), 2089–2092 (2005). [CrossRef] [PubMed]

]. This enables smaller ablation spots and thereby a higher resolution of the CGH.

The images are sharper due to the increase in information in the hologram, which means that more detailed objects can be successfully reconstructed. To demonstrate this, a hologram of the seal of Aarhus University was generated with a pitch of only 3 µm corresponding to a resolution of 111 kpixels/mm2 (~8500 dpi). Figure 4
Fig. 4 SEM images of the CGH pattern with a pitch of 3 µm written on silicon. (a) Large part of the hologram showing the bit pattern. (b) Zoom in on a few ablated spots.
shows scanning-electron-microscope (SEM) images of the silicon sample with the directly written CGH. Panel (a) shows a relatively large area of the hologram with the produced bit pattern, while (b) shows a magnified image of a few ablated spots. The spots have a diameter of 2.5-3 μm. This can be compared to the theoretical ablation diameter obtained from d 2=2ω0 2ln(F/Fth) [18

18. J. M. Liu, “Simple technique for measurements of pulsed Gaussian-beam spot sizes,” Opt. Lett. 7(5), 196–198 (1982). [CrossRef] [PubMed]

,19

19. J. Byskov-Nielsen, J.-M. Savolainen, M. S. Christensen, and P. Balling, “Ultra-short pulse laser ablation of metals: threshold fluence, incubation coefficient and ablation rates,” Appl. Phys., A Mater. Sci. Process. 101(1), 97–101 (2010). [CrossRef]

], where d is the ablation diameter, ω0 the spot size, F the fluence and Fth the threshold fluence. Assuming a fluence of 6.5 J/cm2 and a threshold fluence of 0.52 J/cm2 [20

20. J. Bonse, K.-W. Brzezinka, and A. J. Meixner, “Modifying single-crystalline silicon by femtosecond laser pulses: an analysis by micro Raman spectroscopy, scanning laser microscopy and atomic force microscopy,” Appl. Surf. Sci. 221(1-4), 215–230 (2004). [CrossRef]

], d should be only 1.1 μm. The reason for the larger spots is most likely aberrations in the lens in combination with deviation from a perfectly Gaussian beam profile, which also explains the slight ellipticity of the spots. However, as can be seen in Fig. 4 (b), the spots have a central ablated region with a diameter of about 1.4 μm, i.e. close to the theoretical ablation diameter. Most importantly, the reflectivity is reduced significantly at all the ablated spots, which is the key feature for forming the binary hologram. Figure 5
Fig. 5 (a) The seal of Aarhus University. (b) Image of the holographic reconstruction made from a hologram with a pitch of 3 µm using a frequency-doubled Nd:YAG laser at 532 nm for the reconstruction. The image is 20 cm in diameter. The bright area in the bottom right corner is scattered light from the reflection spot, most of which was blocked by a beam dump.
shows the seal of Aarhus University (a) and an image of the holographic reconstruction (b), which shows that even this relatively detailed object can be reconstructed quite well with a high resolution hologram.

The hologram also acts as a two-dimensional diffraction grating. From the diffraction-grating equation, the distance between diffraction spots is for small angles inversely proportional to the grating period, or in this case the hologram pitch. So, an increase in resolution (i.e. a decrease in pitch) increases the separation between diffraction orders. Since the holographic reconstructions are also generated at higher orders, this implies that larger holographic images can be created without overlapping when the resolution is increased.

4. Conclusions

An infrared femtosecond laser has been used to write computer-generated holograms (CGHs) directly on a silicon surface to produce reflection holograms. A pitch of only 3 µm, corresponding to a resolution of 111 kpixels/mm2 (~8500 dpi), has been achieved, which enables the generation of relatively large and detailed holographic images. 3-D effects have been implemented in the directly-written CGHs by assigning different depths to different parts of the object in the calculation. The 3-D effects appear as a relative motion of the different object parts when translating the CGH or the reconstruction beam. Increasing the resolution and introducing 3-D effects both add to the complexity of a CGH and hence may be used for increasing the level of security when using the holograms in anti counterfeiting and optical keys.

Acknowledgments

This work was supported by The Danish Council for Independent Research | Natural Sciences (FNU).

References and links

1.

A. W. Lohmann and D. P. Paris, “Binary fraunhofer holograms, generated by computer,” Appl. Opt. 6(10), 1739–1748 (1967). [CrossRef] [PubMed]

2.

L. Ran and S. Qu, “Self-assembled volume vortex grating induced by femtosecond laser pulses in glass,” Curr. Appl. Phys. 9(6), 1210–1212 (2009). [CrossRef]

3.

Z. Guo, S. Qu, and S. Liu, “Generating optical vortex with computer-generated hologram fabricated inside glass by femtosecond laser pulses,” Opt. Commun. 273(1), 286–289 (2007). [CrossRef]

4.

Y. Li, Y. Dou, R. An, H. Yang, and Q. Gong, “Permanent computer-generated holograms embedded in silica glass by femtosecond laser pulses,” Opt. Express 13(7), 2433–2438 (2005). [CrossRef] [PubMed]

5.

Q.Z. Zhao, J. R. Qiu, X. W. Jiang, E. W. Dai, C. H. Zhou, and C. S. Zhu, “Direct writing computer-generated holograms on metal film by an infrared femtosecond laser,” Opt. Express 13(6), 2089–2092 (2005). [CrossRef] [PubMed]

6.

C. G. Trevino-Palacios, A. Olivares-Perez, and O. J. Zapata-Nava, “Security system with optical key access,” Proc. SPIE 6422, 642218–642224 (2007). [CrossRef]

7.

B. R. Brown and A. W. Lohmann, “Computer-generated Binary Holograms,” IBM J. Res. Develop. 13(2), 160–168 (1969). [CrossRef]

8.

J. P. Waters, “Three-Dimensional Fourier-Transform Method for Synthesizing Binary Holograms,” J. Opt. Soc. Am. 58(9), 1284–1288 (1968). [CrossRef]

9.

L. B. Lesem, P. M. Hirsch, and J. A. Jordan Jr., “The Kinoform: A New Wavefront Reconstruction Device,” IBM J. Res. Develop. 13(2), 150–155 (1969). [CrossRef]

10.

T. Yamaguchi, G. Okabe, and H. Yoshikawa, “Real-time image plane full-color and full-parallax holographic video display system,” Opt. Eng. 46(12), 125801 (2007). [CrossRef]

11.

P.-A. Blanche, A. Bablumian, R. Voorakaranam, C. Christenson, W. Lin, T. Gu, D. Flores, P. Wang, W.-Y. Hsieh, M. Kathaperumal, B. Rachwal, O. Siddiqui, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “Holographic three-dimensional telepresence using large-area photorefractive polymer,” Nature 468(7320), 80–83 (2010). [CrossRef] [PubMed]

12.

P. P. Pronko, S. K. Dutta, J. Squier, J. V. Rudd, D. Du, and G. Mourou, “Machining of sub-micron holes using a femtosecond laser at 800 nm,” Opt. Commun. 114(1-2), 106–110 (1995). [CrossRef]

13.

K. Vestentoft, J. A. Olesen, B. H. Christensen, and P. Balling, “Nanostructuring of surfaces by ultra-short laser pulses,” Appl. Phys., A Mater. Sci. Process. 80(3), 493–496 (2005). [CrossRef]

14.

D. F. Edwards, “Silicon (Si),” in Handbook of Optical Constants of Solids, E.D. Palik, ed. (Academic, Orlando, Fla., 1985).

15.

J. P. Waters, “Holographic image synthesis utilizing theoretical methods,” Appl. Phys. Lett. 9(11), 405–407 (1966). [CrossRef]

16.

M. Lucente, “Interactive computation of holograms using a look-up table,” J. Electron. Imaging 2(1), 28–34 (1993). [CrossRef]

17.

H. Yoshikawa, “Fast Computation of Fresnel Holograms Employing Difference,” Opt. Rev. 8(5), 331–335 (2001). [CrossRef]

18.

J. M. Liu, “Simple technique for measurements of pulsed Gaussian-beam spot sizes,” Opt. Lett. 7(5), 196–198 (1982). [CrossRef] [PubMed]

19.

J. Byskov-Nielsen, J.-M. Savolainen, M. S. Christensen, and P. Balling, “Ultra-short pulse laser ablation of metals: threshold fluence, incubation coefficient and ablation rates,” Appl. Phys., A Mater. Sci. Process. 101(1), 97–101 (2010). [CrossRef]

20.

J. Bonse, K.-W. Brzezinka, and A. J. Meixner, “Modifying single-crystalline silicon by femtosecond laser pulses: an analysis by micro Raman spectroscopy, scanning laser microscopy and atomic force microscopy,” Appl. Surf. Sci. 221(1-4), 215–230 (2004). [CrossRef]

OCIS Codes
(090.1760) Holography : Computer holography
(140.3390) Lasers and laser optics : Laser materials processing
(140.7090) Lasers and laser optics : Ultrafast lasers
(220.4000) Optical design and fabrication : Microstructure fabrication

ToC Category:
Holography

History
Original Manuscript: December 22, 2010
Revised Manuscript: January 27, 2011
Manuscript Accepted: January 28, 2011
Published: February 7, 2011

Citation
Kristian J. Wædegaard and Peter Balling, "High-resolution computer-generated reflection holograms with three-dimensional effects written directly on a silicon surface by a femtosecond laser," Opt. Express 19, 3434-3439 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-4-3434


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References

  1. A. W. Lohmann and D. P. Paris, “Binary fraunhofer holograms, generated by computer,” Appl. Opt. 6(10), 1739–1748 (1967). [CrossRef] [PubMed]
  2. L. Ran and S. Qu, “Self-assembled volume vortex grating induced by femtosecond laser pulses in glass,” Curr. Appl. Phys. 9(6), 1210–1212 (2009). [CrossRef]
  3. Z. Guo, S. Qu, and S. Liu, “Generating optical vortex with computer-generated hologram fabricated inside glass by femtosecond laser pulses,” Opt. Commun. 273(1), 286–289 (2007). [CrossRef]
  4. Y. Li, Y. Dou, R. An, H. Yang, and Q. Gong, “Permanent computer-generated holograms embedded in silica glass by femtosecond laser pulses,” Opt. Express 13(7), 2433–2438 (2005). [CrossRef] [PubMed]
  5. Q.Z. Zhao, J. R. Qiu, X. W. Jiang, E. W. Dai, C. H. Zhou, and C. S. Zhu, “Direct writing computer-generated holograms on metal film by an infrared femtosecond laser,” Opt. Express 13(6), 2089–2092 (2005). [CrossRef] [PubMed]
  6. C. G. Trevino-Palacios, A. Olivares-Perez, and O. J. Zapata-Nava, “Security system with optical key access,” Proc. SPIE 6422, 642218–642224 (2007). [CrossRef]
  7. B. R. Brown and A. W. Lohmann, “Computer-generated Binary Holograms,” IBM J. Res. Develop. 13(2), 160–168 (1969). [CrossRef]
  8. J. P. Waters, “Three-Dimensional Fourier-Transform Method for Synthesizing Binary Holograms,” J. Opt. Soc. Am. 58(9), 1284–1288 (1968). [CrossRef]
  9. L. B. Lesem, P. M. Hirsch, and J. A. Jordan., “The Kinoform: A New Wavefront Reconstruction Device,” IBM J. Res. Develop. 13(2), 150–155 (1969). [CrossRef]
  10. T. Yamaguchi, G. Okabe, and H. Yoshikawa, “Real-time image plane full-color and full-parallax holographic video display system,” Opt. Eng. 46(12), 125801 (2007). [CrossRef]
  11. P.-A. Blanche, A. Bablumian, R. Voorakaranam, C. Christenson, W. Lin, T. Gu, D. Flores, P. Wang, W.-Y. Hsieh, M. Kathaperumal, B. Rachwal, O. Siddiqui, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “Holographic three-dimensional telepresence using large-area photorefractive polymer,” Nature 468(7320), 80–83 (2010). [CrossRef] [PubMed]
  12. P. P. Pronko, S. K. Dutta, J. Squier, J. V. Rudd, D. Du, and G. Mourou, “Machining of sub-micron holes using a femtosecond laser at 800 nm,” Opt. Commun. 114(1-2), 106–110 (1995). [CrossRef]
  13. K. Vestentoft, J. A. Olesen, B. H. Christensen, and P. Balling, “Nanostructuring of surfaces by ultra-short laser pulses,” Appl. Phys., A Mater. Sci. Process. 80(3), 493–496 (2005). [CrossRef]
  14. D. F. Edwards, “Silicon (Si),” in Handbook of Optical Constants of Solids, E.D. Palik, ed. (Academic, Orlando, Fla., 1985).
  15. J. P. Waters, “Holographic image synthesis utilizing theoretical methods,” Appl. Phys. Lett. 9(11), 405–407 (1966). [CrossRef]
  16. M. Lucente, “Interactive computation of holograms using a look-up table,” J. Electron. Imaging 2(1), 28–34 (1993). [CrossRef]
  17. H. Yoshikawa, “Fast Computation of Fresnel Holograms Employing Difference,” Opt. Rev. 8(5), 331–335 (2001). [CrossRef]
  18. J. M. Liu, “Simple technique for measurements of pulsed Gaussian-beam spot sizes,” Opt. Lett. 7(5), 196–198 (1982). [CrossRef] [PubMed]
  19. J. Byskov-Nielsen, J.-M. Savolainen, M. S. Christensen, and P. Balling, “Ultra-short pulse laser ablation of metals: threshold fluence, incubation coefficient and ablation rates,” Appl. Phys., A Mater. Sci. Process. 101(1), 97–101 (2010). [CrossRef]
  20. J. Bonse, K.-W. Brzezinka, and A. J. Meixner, “Modifying single-crystalline silicon by femtosecond laser pulses: an analysis by micro Raman spectroscopy, scanning laser microscopy and atomic force microscopy,” Appl. Surf. Sci. 221(1-4), 215–230 (2004). [CrossRef]

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