4.2.1 How to make femtosecond pulse interference

It is well known that the shorter the pulses, the smaller the area over which the pulses overlap at relatively large angles and with little coherence. For two beams crossed at an angle θ, the size of the overlap area is given by L = cτ(sinθ/2)⁻¹, where c is the speed of light in the medium and τ is the pulse duration.³⁰ For example, for a 120 femtosecond duration and a 30° crossed angle, the beams overlap only within a strip approximately 140 μm wide. The number of interference fringes produced by two beams is independent of the angle and, for transform-limited pulses, is roughly 2cτ/λ, where λ is the optical wavelength.³⁰ With 120-femtosecond pulses at 800 nm, only approximately 90 interference fringes can be produced.

Currently, there are two beam delivery approaches to achieve interference of femtosecond pulses. The first approach is to split the source beam by a mirror beam splitter (MBS), with an optical delay in order to achieve the spatial and temporal interference of femtosecond laser pulses. The second is to split the source beam by a diffractive beam splitter (DBS), which can divide one laser beam into several beams with equal intensity (illustrated in Fig. 4.1), and then to use a confocal imaging system in which no optical delay is needed. For the first approach, precise adjustments of the optical delay for each optical path are needed by observing the sum-frequency generation, or third-harmonic generations,¹¹ to obtain the temporal overlap of the femtosecond pulses; additionally, when the interference of more than two beams is needed, a complicated optical set up is required, the precise adjustment of which is very difficult. For the second approach, the optical set up is quite simple and temporal overlap can be achieved without any adjustment.³⁰

The intrinsic difference between the two beam delivery approaches is that, in the case of diffraction off a grating (in the case of MBS), short pulses become tilted, whilst pulses that correspond to different diffraction orders (in the case of DBS) have parallel pulse fronts. Figure 4.2 illustrates this difference.^10,30 When the source beam is split by an MBS (Fig. 4.2a), the width of the overlapping area is cτ/sin(θ/2) because the pulse fronts of the two beams are not parallel. When the source beam is split by a DBS (Fig. 4.2b), the width of the overlapping area can reach the beam diameter of the incidence light because the wave fronts of the two beams are parallel. Thus, if a larger overlapping area is required, the second beam delivery approach is a better choice. The disadvantage of the second beam delivery approach, however, is that the power density in the interference plane is lower compared to the first beam delivery approach because the interference area in the second approach is larger than that of the first. It is hard to induce periodic structures on high damage threshold materials for the second approach.

For classification purposes, microstructures induced by using an MBS beam delivery are referred to as microstructures induced by two-beam femtosecond laser interference. Similarly, microstructures induced by using a DBS beam delivery are referred to as microstructures induced by multibeam femtosecond laser interference.

4.2.2 Distribution of optical intensity in the interfered region

To investigate the interference patterns formed by multiple non-coplanar laser beams, we have taken a four-beam interference setup as an example, to deduce the optical intensity distribution within the region of interference.

Extending the different beam interferences is straightforward. Based on electromagnetic wave theory, the plane wave can be expressed as E = Aexp[−i(ωt−k•r)], which can be analyzed in coordinate as:

[4.1]

where A, k and ω are amplitude, wave vector and angular frequency of the plane wave, respectively, and α, β and γ are the azimuth angles of the plane wave. In Fig. 4.3 (inset), four laser beams, located in two orthogonal planes, irradiate a sample with incident angles of θ₁, θ₂, θ₃ and θ₄, respectively. The azimuth angles of the four beams can be calculated for this figure; see Table 4.1.

Substituting the azimuth angles of the four beams taken from Table 4.1 into Eq. [4.1], the complex amplitude of the four laser beams can be deduced as:

[4.2]

The complex amplitude of the sum oscillation for the four beams in the interfering field is then:

[4.3]

If we assume that the four beams have equal light intensity and approach the sample with the same angle of incidence (i.e., A₁ =A₂ = A₃ = A₄=A and θ₁ = θ₂ = θ₃ = θ₄ = θ), then, by combining Eqs. [4.2] and [4.3], we obtain:

[4.4]

and

[4.5]

where, ‘*’ represents the complex conjugate.

Finally, we can get the distribution of light intensity within the interfering field:

[4.6]

Using the relation cos α = (e^iα + e ^−iα)/2, Eq. [4.6] can be simplified to:

[4.7]

Using a similar procedure, the distribution of light intensity for two- and five-beam interference can also be deduced as:

[4.8]

[4.9]

From Eqs. [4.7], [4.8] and [4.9], we can see that for two- and four-beam interference, the intensity distribution is independent of z, while for five-beam interference, it is not. Thus, the structures are basically independent of depth, that is, the same structure is observed in any xy plane in the case of the interference of four beams or less. However, with five-beam interference, the central beam has a different wave vector in the z axis. As a result, the structures obtained by five-beam interference is periodic in the z axis as well as in the x and y axes.

The interference fringe interval can be derived from the distribution of light intensity. For example, for two-beam interference, the period of the fringes, Λ, is given by:

[4.10]

When θ equals 90°, the interference fringes have a minimum period, which is half the wavelength.

4.3.1 Experimental setup

For their experimental setup (schematically shown in Fig. 4.1a), most studies have used a regeneratively amplified Ti:sapphire laser with a wavelength of 800 nm, a pulse duration of 30–200 fs, and a pulse repetition of 1–1000 Hz. A single laser beam is split into two beams that are then redirected at approximately equal incident angles onto a sample surface, focused by two lenses. After the optical paths are adjusted to realize perfect overlap of the two beams both spatially and temporally, the sample surface is adjusted to be approximately normal to the perpendicular bisector of the two incident beams, so that the sample surface becomes the laser interfering plane. A single shot of the femtosecond laser with controlled energy for each interfered beam completes the encoding process.

4.3.2 Formation of periodic microstructures

Fabrication of surface relief gratings is the most common application for the femtosecond laser interference technique. The fabrication of surface relief gratings on a variety of transparent dielectrics including silica glass, sapphire, etc. have been extensively investigated by the Hosono group.^{11−14, 19, 20} Figure 4.4 shows surface relief gratings encoded on amorphous SiO₂ bulk glass by irradiation with crossed femtosecond-laser pulses with different incident angles (θ, 10°, 45° and 80°, respectively). The period of grating, d, varies with θ, that is, it is 2.5 μm for 10°, 0.58 μm for 45° and 0.43 μm for 80°. These correspondences confirm the relation for two-beam interference at the surface, according to Eq. [4.10]. In addition, by double exposure,¹³ dual-structured gratings can be achieved (as shown in Fig. 4.5).

Our group (at the Shanghai Institute of Optics and Fine Mechanics) has fabricated surface relief gratings containing noble metal nanoparticles using two-beam femtosecond laser interference.¹⁵ Au₂O-doped glass samples were first irradiated by two 800 nm interfered femtosecond laser pulses at room temperature and then heat-treated at 550°C to allow Au nanoparticle precipitation in the laser irradiation areas. One-dimensional periodic arrays of the Au nanoparticles were controlled by changing the pulse energy and the incident angle between the interfered laser pulses.

Kaneko et al. demonstrated fabrication of a submicron grating in a metal ion-doped polymer by two-beam femtosecond laser interference with two-photon photoreduction.¹⁶

As well as being used for the fabrication of surface relief gratings, two-beam femtosecond laser interference can also induce volume gratings inside transparent materials. Si et al. have fabricated volume gratings inside bulk azodye-doped polymers and perylene-orange-doped hybrid inorganic-organic materials.^17,18 The diffraction efficiency of the first-order Bragg gratings can be up to 90%. Figure 4.6 shows a volume and surface relief gratings fabricated in azodye-doped PMMA and the diffraction patterns.

It is much more difficult to fabricate volume-type gratings on the surface of non-photosensitive materials than it is to fabricate surface relief gratings. Kawamura et al.¹⁹ attribute this to two reasons: first, the nonlinear interaction between a strong laser pulse and a material would deteriorate its coherency; second, free carriers cause enhanced optical absorption. It is known that the peak frequency of the absorption band caused by free carriers, or plasma, which are created almost simultaneously by irradiation from a femtosecond laser pulse, is proportional to (carrier concentration)1/2. This implies that the optical absorption coefficient increases in the infrared (IR) region if the laser is powerful enough to generate carriers. The relaxation time of free carriers is nearly equivalent to the laser pulse duration so that, if the laser pulse duration is stretched, the volume gratings are likely to be encoded inside the material. Kawamura et al. used chirped (0.5–5 ps) IR laser pulse interference to induce volume gratings inside SiO₂ glass.¹⁹ By moving the focal spot of the interfering laser beam, multi-layer gratings can be induced. Recently, Kawamura et al. have also demonstrated fabrication by a distributed-feedback color center laser in single lithium fluoride crystals, encoding gratings inside crystals using chirped femtosecond laser pulses interference.²⁰

Li et al. have also fabricated multi-layer volume gratings inside nonphotosensitive glass by using common femtosecond pulses,²¹ though their results are not consistent with Kawamura’s analysis (see above) and further investigation is required.

4.4.1 Experimental setup

The setup for this experiment is shown schematically in Figs 4.1b and 4.3. A regeneratively amplified Ti:sapphire laser with a wavelength of 800 nm, a pulse duration of 30–200 fs and a pulse repetition of 1 kHz is used as the irradiation source. A DBS (the key element of this setup) splits the incident laser beam into several beams. The split beams are made parallel by a lens, L₁, and are then selected by an aperture array to obtain an aimed interference pattern. The selected beams are gathered by an objective, L₂, and create interference in a focused region, where the sample is placed. The temporal and spatial overlap of the five beams’ pulses is perfectly achieved on the focal plane of L₂; no adjustment for the pulses’ temporal overlap is needed. The distance between L₁ and L₂ is adjusted to make each beam’s plane wave after lens L₂. The outer beams (of equal intensity) are placed symmetrically around the central beam, and make an angle with it. Irradiation power and duration can be adjusted to obtain clear periodic structures.

As examples, three types of samples were tested: a commercial silicon wafer (2 mm thickness), a commercial metallic (Ni) foil (20 μm thickness) and a thin metallic (Al) film deposited on a transparent quartz plate (200 nm thickness) were used. All the experiments were carried out at room temperature in ambient atmosphere.

The fabricated structures were observed by an optical microscope and a scanning electron microscope (SEM). The diffraction characteristics of the fabricated structures were also investigated using an He-Ne laser with a wavelength 633 nm, and with a diode-pumped all solid state laser with a wavelength of 532 nm.

4.4.2 Formation of periodic microstructures on silicon wafer

The formation of periodic microstructures on a silicon surface is important for its application in optoelectronic devices. Many types of micrometer-scale surface structures have been fabricated on the surface of silicon when irradiated by pulsed lasers.³³⁻³⁶ Mazur’s group, for example, created a silicon surface covered with a semi-ordered pattern of sharp conical microspikes by irradiating the surface with a femtosecond laser in the presence of halogen-containing gases.^35,36

The fabrication of periodic microstructures on silicon wafers has been demonstrated using the interference of five femtosecond laser beams.³⁷ The typical input laser power (incident DBS) was set at 100 mW, whilst the exposure time was ~5 s. Figure 4.7 shows optical and SEM images of the microstructures fabricated by such five-beam femtosecond laser pulses. As can be seen, spots with a diameter of about 300 μm were fabricated in a one-step exposure process (~ 5 s) (Fig. 4.7a). By scanning the silicon wafer, the fabricated spots can be aligned. The detailed structures in the spot are shown in Fig. 4.7b, c and d. A four-fold symmetrical structure was induced on the silicon surface. The period of the array structures was about 2.5 μm. As the exposure time was up to 5 s with a laser power of 300 mW and a 1 kHz repetition rate, the ablated surface deposited much oxidized debris (as shown in Fig. 4.7 d).

The structures in Fig. 4.7 can be employed as a diffractive beam splitter, as shown in Fig. 4.8. To investigate the diffraction characteristics of the fabricated structures, a diode-pumped all solid state laser with a wavelength of 532 nm was coupled with a 10× optical objective into the structures and the diffraction patterns were recorded by a digital camera; see Fig. 4.8a. With a 532 nm laser wavelength, the induced structure works as a reflective beam splitter. Figure 4.8b shows the diffraction patterns of the periodic structures obtained. Two-order diffraction spots were observed for the periodic structures on a silicon surface. The first-order diffraction efficiency can be defined as the ratio of the averaged power of the first-order diffraction to the power of the zero-order diffraction. The measured diffraction efficiencies of the first-order diffraction spot were 4.84% (for a wavelength of 532 nm) for the periodic structures. The diffraction patterns can be changed by interval and by the shape of the structures, which are related to the laser energy, angle of the beams, focal length and focusing of the lens, irradiation time, laser wavelength, etc.

As already mentioned, there is much debris on the surface of the laser-structured area, which reduces its reflectivity. After washing the surface in an aqueous solution of HF acid to remove the debris, the first-order diffraction efficiency increased to 5.48%.

It should be noted that, with a wavelength of 532 nm, there is a high absorption level for silicon within the absorption spectra of the silicon sample (Fig. 4.9). But where there is ‘strong’ absorption, there is also ‘strong’ reflection, and the calculated reflectivity of Si from its optical constants is 37.34% with a wavelength of 532 nm. For IR light with a wavelength of more than 1200 nm, absorption is very low, so that the induced structures can be used as transmission beam splitters for that IR light. In addition, the spectrum ‘after structuring’ shows a higher optical density than that before structuring, because the sample itself acts as a grating, and diffraction losses therefore appear as additional absorption.

4.4.3 Formation of periodic microstructures on metal foil and metal film

For some technological implementations, such as when micrometer-order array holes are necessary, metal materials are required for use in microfabrication. In the case of metal materials with high heat conductivities, the fabrication of micron-order structures by use of ultrashort pulse lasers have unique advantages.³⁸⁻⁴⁰ By applying femtosecond laser pulses, the heat-affected zone is in the region of microns in size, allowing the creation of small lateral structures. However, short-pulse irradiation is not necessarily enough to such a small size. The theoretical limit for the smallest spot size achievable is defined by the numerical aperture of the imaging optics and the wavelength of the laser radiation. By decreasing the wavelength, Békési et al. employed a UV femtosecond laser to fabricate micron holes on a metal foil.⁴¹ By employing an alternative method, an IR femtosecond laser interference technique, we were able in our experiments to fabricate micrometer-order array holes on both metal foil and metal film.⁴² With the same experimental setup, we irradiated five-beam interfered femtosecond beams onto Ni-foil and onto Al-film deposited on a glass substrate, using a 150 mW laser (incident DBS), and with an exposure time of ~10 s; the structures fabricated on the Ni-foil are shown in the SEM images in Fig. 4.10. As with the structures fabricated on a silicon wafer, spots with a diameter of about 300 μm were fabricated on the Ni-foil in a one-step exposure process, and four-fold symmetric array holes were induced (with a period of about 2.5 μm). The depth of the ablated holes was about 10 μm (as measured by an optical microscope). As can be seen in Fig. 4.10b, the wall of holes is not very regular, which may be the reason for the longer ablation duration. Based on a two-temperature diffusion model, Chichkov et al. investigated the ablation behaviors of metal during femtosecond laser irradiation³⁷ and proposed that the ablation process could be considered as a direct solid-vapor transition, since very short time scales are involved in the ablation. In our case, the five-beam interference of femtosecond laser pulses produced a periodically modulated light field (the interference pattern) with a distribution of enhanced and weakened intensity. The enhanced optical intensity heated the lattice on a picosecond time scale,³⁸ resulting in the creation of vapor and plasma phases followed by a rapid expansion, and finally forming periodic hole structures on the metal foil.

Figure 4.11 shows the optical and SEM images of array holes fabricated by five-beam interfering femtosecond laser pulses on an Al-film. Similar four-fold symmetric structures were formed on the metal film. The period of the structures was also about 2.5 μm. In the more detailed SEM image in Fig. 4.11b, a particular ‘bead in the hole’ structure can be observed. Beads with a diameter of less than 900 nm are held in each hole. This structure is probably formed by surface tension: during ablation by interfering femtosecond laser pulses, the film is shrunk and torn, forming the ‘bead in the hole’ structure.

The structures in Fig. 4.11 work as diffractive beam splitters, as shown in Fig. 4.12. To investigate the diffraction characteristics of the structures, we coupled a diode-pumped all solid state laser (wavelength 532 nm) with an optical objective lens onto the structures on the metal film, and the diffraction patterns were recorded by a digital camera (see Fig. 4.12a); the experimental setup is presented in Fig. 4.12b. Four-order diffraction spots were observed for the array holes. Here, the diffraction efficiency can be defined as the ratio of the averaged power of every order of diffraction spots to the power of the incident light. The measured diffraction efficiencies of all the order diffraction spots are shown in Fig. 4.12c.

Nakata et al. reported the generation of a nano-sized hollow bump array of gold thin film after uniformly spaced melting and inflation of the film induced by a single shot of four interfering femtosecond laser beams,²⁵ and they investigated the transition procedure of the induced periodic structures with increasing laser fluence.

Books

Rullière, Claude Femtosecond laser pulses: Principles and experiments. 2nd, Springer Press; 2003. http://www.google.com/books [available at].

Journal articles

1. Kryukov, P.G. Ultrashort-pulse lasers. Quantum Electronics. 2001; 31:95–119.

2. Bloembergen, N. From nanosecond to femtosecond science. Reviews of Modern Physics. 1999; 71:S283–S287.

3. von der Linde, D., Sokolowski-Tinten, K. The physical mechanisms of short-pulse laser ablation. Applied Surface Science. 2000; 154–155:1–10.

Useful websites

Hosono-Kamiya Laboratory, http://www.khlab.msl.titech.ac.jp

Mazur group, https://mazur-www.harvard.edu

Prof. Kawata’s Cyber Lab, www.skawata.com

1. DiDomenica, M. Small-signal analysis of internal (coupling-type) modulation of lasers. Journal of Applied Physics. 1964; 35:2870–2876.

2. Hargrove, L.E., Fork, R.L., Pollack, M.A. Locking of He-Ne laser modes induced by synchronous intracavity modulation (diffraction by phonons in crystals E). Applied Physics Letters. 1964; 5:4–5.

3. Yariv, A. Internal modulation in multimode laser oscillators. Journal of Applied Physics. 1965; 36:388–391.

4. Fork, R.L., Green, B.I., Shank, C.V. Generation of optical pulses shorter than 0.1 psec by colliding pulse mode locking. Applied Physics Letters. 1981; 38:671–672.

5. Fork, R.L., Shank, C.V., Yen, R., Hirliman, C.A. Femtosecond optical pulses. IEEE Journal of Quantum Electronics. 1983; QE-19:500–506.

6. Morgner, U., Kärtner, F.X., Cho, S.H., Chen, Y., Haus, H.A., Fujimoto, J.G., Ippen, E.P. Sub-two-cycle pulses from a Kerr-lens mode-locked Ti:sapphire laser. Optics Letters. 1999; 24:411–413.

7. Morgner, U., Ell, R., Metzler, G., Schibli, T.R., Kärtner, F.X., Fujimoto, J.G., Haus, H.A., Ippen, E.P. Nonlinear optics with phase-controlled pulses in the sub-two-cycle regime. Physical Review Letters. 2001; 86:5462–5465.

8. Gallman, L., Sutter, D.H., Matuschek, N., Steinmeyer, G., Keller, U., Iaconis, C., Walmsley, I.A. Characterization of sub-6-fs optical pulses with spectral phase interferometry for direct electric-field reconstruction. Optics Letters. 1999; 24:1314–1316.

9. Bahk, S.-W., Rousseau, P., Planchon, T.A., Chvykov, V., Kalintchenko, G., Maksimchuk, A., Mourou, G.A., Yanovsky, V. Generation and characterization of the highest laser intensities (10²² W/cm²). Optics Letters. 2004; 29:2837–2839.

10. Nakata, Y., Okada, T., Maeda, M. Lines of periodic hole structures produced by laser ablation using interfering femtosecond lasers split by a transmission grating. Applied Physics A. 2003; 77:399–401.

11. Kawamura, K., Ito, N., Sarukura, N., Hirano, M., Hosono, H. New adjustment technique for time coincidence of femtosecond laser pulses using third harmonic generation in air and its application to holograph encoding system. Review of Scientific Instruments. 2002; 73:1711–1714.

12. Kawamura, K., Ogawa, T., Sarukura, N., Hirano, M., Hosono, H. Fabrication of surface relief gratings on transparent dielectric materials by two-beam holographic method using infrared femtosecond laser pulses. Applied Physics B. 2000; 71:119–121.

13. Kawamura, K., Sarukura, N., Hirano, M. Periodic nanostructure array in crossed holographic gratings on silica glass by two interfered infrared-femtosecond laser pulses. Applied Physics Letters. 2001; 79:1228–1230.

14. Kawamura, K., Sarukura, N., Hirano, M., Hosono, H. Holographic encoding of fine-pitched micrograting structures in amorphous SiO₂ thin films on silicon by a single femtosecond laser pulse. Applied Physics Letters. 2001; 78:1038–1040.

15. Qu, S., Qiu, J., Zhao, C., Jiang, X., Zeng, H., Zhu, C., Hirao, K. Metal nanoparticle precipitation in periodic arrays in Au₂O-doped glass by two interfered femtosecond laser pulses. Applied Physics Letters. 2004; 84:2046–2048.

16. Kaneko, K., Sun, H., Duan, X., Kawata, S. Two-photon photoreduction of metallic nanoparticle gratings in a polymer matrix. Applied Physics Letters. 2003; 83:1426–1428.

17. Si, J., Qiu, J., Zhai, J., Shen, Y., Hirao, K. Photoinduced permanent gratings inside bulk azodye-doped polymers by the coherent field of a femtosecond laser. Applied Physics Letters. 2002; 80:359–361.

18. Qian, G., Guo, J., Wang, M., Si, J., Qiu, J., Hirao, K. Holographic volume gratings in bulk perylene-orange-doped hybrid inorganic-organic materials by the coherent field of a femtosecond laser. Applied Physics Letters. 2003; 83:2327–2329.

19. Kawamura, K., Hirano, M., Kamiya, T., Hosono, H. Holographic writing of volume-type microgratings in silica glass by a single chirped laser pulse. Applied Physics Letters. 2002; 81:1137–1139.

20. Kawamura, K., Hirano, M., Kurobori, T., Takamizu, D., Kamiya, T., Hosono, H. Femtosecond-laser-encoded distributed-feedback color center laser in lithium fluoride single crystals. Applied Physics Letters. 2004; 84:311–313.

21. Li, Y., Watanabe, W., Yamada, K., Shinagawa, T., Itoh, K., Nishii, J., Jiang, Y. Holographic fabrication of multiple layers of grating inside soda–lime glass with femtosecond laser pulses. Applied Physics Letters. 2002; 80:1508–1510.

22. Kondo, T., Matsuo, S., Juodkazis, S., Misawa, H. Femtosecond laser interference technique with diffractive beam splitter for fabrication of three-dimensional photonic crystals. Applied Physics Letters. 2001; 79:725–727.

23. Kondo, T., Matsuo, S., Juodkazis, S., Mizeikis, V., Misawa, H. Multiphoton fabrication of periodic structures by multibeam interference of femtosecond pulses. Applied Physics Letters. 2003; 82:2758–2760.

24. Nakata, Y., Okada, T., Maeda, M. Fabrication of dot matrix, comb, and nanowire structures using laser ablation by interfered femtosecond laser beams. Applied Physics Letters. 2002; 81:4239–4241.

25. Nakata, Y., Okada, T., Maeda, M. Nano-sized hollow bump array generated by single femtosecond laser pulse. Japanese Journal of Applied Physics. 2003; 42:L1452–L1454.

26. Zaidi, S.H., Brueck, S.R.J. Multiple-exposure interferometric lithography. Journal of Vacuum Science & Technology B. 1993; 11:658–666.

27. Choi, J.O., Akinwande, A.I., Smith, H.I. 100 nm gate hole openings for low voltage driving field emission display applications. Journal of Vacuum Science & Technology B. 2001; 19:900–903.

28. Pati, G.S., Heilmann, R.K., Konkola, P.T., Joo, C., Chen, C.G., Murphy, E., Schattenburg, M.L. Generalized scanning beam interference lithography system for patterning gratings with variable period progressions. Journal of Vacuum Science & Technology B. 2002; 20:2617–2621.

29. Solak, H.H., David, C. Patterning of circular structure arrays with interference lithography. Journal of Vacuum Science & Technology B. 2003; 21:2883–2887.

30. Maznev, A.A., Crimmins, T.F., Nelson, K.A. How to make femtosecond pulses overlap. Optics Letters. 1998; 23:1378–1380.

31. Cai, L.Z., Yang, X.L., Wang, Y.R. All fourteen Bravais lattices can be formed by interference of four noncoplanar beams. Optics Letters. 2002; 27:900–902.

32. Valentine, J., Li, J., Zentgraf, T., Bartal, G., Zhang, X. An optical cloak made of dielectrics. Nature Materials. 2009; 8:568–571.

33. Fauchet, P.M., Siegman, A.E. Surface ripples on silicon and gallium arsenide under picosecond laser illumination. Applied Physics Letters. 1982; 40:824–826.

34. Lu, Y.F., Choi, W.K., Aoyagi, Y., Kinomura, A., Fujii, K. Controllable laser-induced periodic structures at silicon–dioxide/silicon interface by excimer laser irradiation. Journal of Applied Physics. 1996; 80:7052–7056.

35. Her, T.H., Finlay, R.J., Wu, C., Deliwala, S., Mazur, E. Microstructuring of silicon with femtosecond laser pulses. Applied Physics Letters. 1998; 73:1673–1675.

36. Wu, C., Crouch, C.H., Zhao, L., Carey, J.E., Younkin, R., Levinson, J.A., Mazur, E., Farrell, R.M., Gothoskar, P., Karger, A. Near-unity below-band-gap absorption by microstructured silicon. Applied Physics Letters. 2001; 78:1850–1852.

37. Zhao, Q.Z., Qiu, J.R., Jiang, X.W., Zhao, C.J., Zhu, C.S. Formation of array microstructures on silicon by multibeam interfering femtosecond laser pulses. Applied Surface Science. 2005; 241:416–419.

38. Chichkov, B.N., Momma, C., Nolte, S., von Alvensleben, F., Tuenermann, A. Femtosecond, picosecond and nanosecond laser ablation of solids. Applied Physics A. 1996; 63:109–115.

39. Simon, P., Ihlemann, J. Ablation of submicron structures on metals and semiconductors by femtosecond UV-laser pulses. Applied Surface Science. 1997; 110:25–29.

40. Pronko, P.P., Dutta, S.K., Squier, J., Rudd, J.V., Du, D., Mourou, G. Machining of sub-micron holes using a femtosecond laser at 800 nm. Optics Communications. 1995; 114:106–110.

41. Békési, J., Klein-Wiele, J.-H., Simon, P. Efficient submicron processing of metals with femtosecond UV pulses. Applied Physics A. 2003; 76:355–357.

42. Zhao, Q.Z., Qiu, J.R., Zhao, C.J., Jiang, X.W., Zhu, C.S. Formation of array holes on metal-foil and metal-film by multibeam interfering femtosecond laser beams. Chinese Physics. 2005; 14:1181–1184.

43. Mailis, S., Zergioti, I., Koundourakis, G., Ikiades, A., Patentalaki, A., Papakonstantinou, P., Vainos, N.A., Fotakis, C. Etching and printing of diffractive optical microstructures by a femtosecond excimer laser. Applied Optics. 1999; 38:2301–2308.

44. Zergioti, I., Mailis, S., Vainos, N.A., Papakonstantinou, P., Kalpouzos, C., Grigoropoulos, C.P., Fotakis, C. Microdeposition of metal and oxide structures using ultrashort laser pulses. Applied Physics A. 1998; 66:579–582.

45. Chrisey, D.B., Pique, A., Fitz-Gerald, J., Auyeung, R.C.Y., McGill, R.A., Wu, H.D., Duignan, M. New approach to laser direct writing active and passive mesoscopic circuit elements. Applied Surface Science. 2000; 154–155:593–600.

46. Bähnisch, R., Groß, W., Menschig, A. Single-shot, high repetition rate metallic pattern transfer. Microelectronic Engineering. 2000; 50:541–546.

47. Bohandy, J., Kim, B.F., Adrian, F.J. Metal deposition from a supported metal film using an excimer laser. Journal of Applied Physics. 1986; 60:1538–1539.

48. Zhao, Q.Z., Qiu, J.R., Zhao, C.J., Jiang, X.W., Zhu, C.S. Optical transfer of periodic microstructures by interfering femtosecond laser beams. Optics Express. 2005; 13:3104–3109.

49. Adrian, F.J., Bohandy, J., Kim, B.F., Jette, A.N. A study of the mechanism of metal deposition by the laser-induced forward transfer process. Journal of Vacuum Science & Technology B. 1987; 5:1490–1494.