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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 2 — Jan. 23, 2006
  • pp: 932–937
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Dispersion phenomena demonstrated by a nanocarbon white point source

Shaomin Wang, Laigui Hu, Binzhi Zhang, Jie Wang, and Daomu Zhao  »View Author Affiliations


Optics Express, Vol. 14, Issue 2, pp. 932-937 (2006)
http://dx.doi.org/10.1364/OPEX.14.000932


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Abstract

Emission from nanocarbon as a point white-light source is studied in several scientific experiments, i.e., a demonstration of chromatic phenomena of a refractive lens, a diffractive Fresnel phase zone plate (FPZP), and a squared zone plate. Results show that white light from nanocarbon exhibits good coherent properties and can be an ideal point light source in comparison with other normal lighting sources, e.g., a light-emitting diode (LED), a He-Ne laser, and a semiconductor laser diode (LD). Dispersion and even diffraction phenomena could be analyzed this way as well.

© 2006 Optical Society of America

1. Introduction

We have realized and reported in earlier work that the laser-induced white-light emission from nanocarbon could be a white-light point source [2

2. S. Wang, L. Hu, B. Zhang, D. Zhao, Z. Wei, and Z. Zhang, “Electromagnetic excitation of nanocarbon in vacuum,” Opt. Express 13, 3625–3630 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-10-3625. [CrossRef] [PubMed]

]. The dimensions of a white spot could be in the order of micrometers if the prepared nanostructured carbon is excited by a focused laser, e.g., a semiconductor laser (LD) beam [18

18. S. Wang, Y. Shen, J. Xu, L. Hu, J. Zhu, D. Yang, H. Zhang, Y. Zeng, and J. Yao, “Deep-ultraviolet emission from an InGaAs semiconductor laser,” Appl. Phys. Lett. 84, 3007–3009 (2004). [CrossRef]

] whose intensity is over a threshold (1 kW-1 MW/cm2) in vacuum, and the energy is absorbed and transformed into white and bright light emission with an efficiency higher than 80%. Such a quasi-point source is smaller than the focused laser beam waist. Second, if the nanocarbon with metal substrate is in a vacuum and excited by a microwave, we can also get a C2 molecular white spectrum [2

2. S. Wang, L. Hu, B. Zhang, D. Zhao, Z. Wei, and Z. Zhang, “Electromagnetic excitation of nanocarbon in vacuum,” Opt. Express 13, 3625–3630 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-10-3625. [CrossRef] [PubMed]

]. There are several examples of research concerning this [19–28

19. P. Fischer, C. T. A. Brown, J. E. Morris, C. López-Mariscal, E. M. Wright, W. Sibbett, and K. Dholakia, “White light propagation invariant beams,” Opt. Express 13, 6657–6666 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-17-6657. [CrossRef] [PubMed]

], especially as seen in Ref [19

19. P. Fischer, C. T. A. Brown, J. E. Morris, C. López-Mariscal, E. M. Wright, W. Sibbett, and K. Dholakia, “White light propagation invariant beams,” Opt. Express 13, 6657–6666 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-17-6657. [CrossRef] [PubMed]

] or [20

20. A. Saliminia, S. L. Chin, and R. Vallèe, “Ultra-broad and coherent white light generation in silica glass by focused femtosecond pulses at 1.5 μm,” Opt. Express 13, 5731–5738 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-15-5731. [CrossRef] [PubMed]

], which utilized the supercontinuum in transparent materials to get a white point source. Our source is different from those used in prior research: a halogen bulb [19

19. P. Fischer, C. T. A. Brown, J. E. Morris, C. López-Mariscal, E. M. Wright, W. Sibbett, and K. Dholakia, “White light propagation invariant beams,” Opt. Express 13, 6657–6666 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-17-6657. [CrossRef] [PubMed]

] with good color rendering and the supercontinuum with small dimensions [19–21

19. P. Fischer, C. T. A. Brown, J. E. Morris, C. López-Mariscal, E. M. Wright, W. Sibbett, and K. Dholakia, “White light propagation invariant beams,” Opt. Express 13, 6657–6666 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-17-6657. [CrossRef] [PubMed]

]. It has both the characteristics, i.e., a small dimension and better color rendering. In this paper, the key is to design and develop a suitable white-light point source to demonstrate the dispersion phenomena of these refractive and diffractive optical imaging elements.

2. Dispersion properties of a refractive lens

In this section we select laser excitation and the improved nanostructured carbon with a transmission electron microscopy (TEM) image as shown in Fig. 1(a). The diameter of carbon particles is around 30 nm. If we magnify one of the particles [smaller square in Fig. 1(a)], the subnanostructure is clear in [Fig. 1(b)] where the disordered graphitic crystallites can be seen and is similar to that of a carbon onion [29

29. R. L Vander Wal, A. J. Tomasek, and T. M. Ticich, “Synthesis, laser processing, and flame purification of nanostructured carbon,” Nano Lett. 3, 223–229 (2003). [CrossRef]

]. When we use a lasing area 1 μm × 5 μm, power of 100 mW, wavelength of λ = 820 nm, and a LD beam focused by an aberrationless lens to excite the nanocarbon in the vacuum, then a stable white quasi-point lighting source with a diameter of about 5 μm is thus created. Compared with the other white-light point source (i.e., the supercontinuum) [19–21

19. P. Fischer, C. T. A. Brown, J. E. Morris, C. López-Mariscal, E. M. Wright, W. Sibbett, and K. Dholakia, “White light propagation invariant beams,” Opt. Express 13, 6657–6666 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-17-6657. [CrossRef] [PubMed]

], which can also be more effective than the traditional white-light sources white LEDs and halogen bulbs, the procedure to achieve a carbon point source is convenient and a lower-cost option. We first use the source to demonstrate the dispersion properties of a refractive lens both under stigmatism [Fig. 1(c)] and with astigmatism (the lens inclined with an angle about 10°) [Fig. 1(d)] and compare them with those of a common white LED with the emission area 0.4 mm × 0.4 mm [Figs. 1(e) and 1(f)]. Obviously, the new one is much better.

Fig. 1. Demonstration of dispersions of a refractive lens (by using light emission from nanocarbon) with focal length f = 302 mm and diameter Φ = 60 mm under stigmatism and with astigmatism and compared with the case of white LED. (a) TEM image of the nanoscaled carbon spheres. (b) The magnification of the squared area in (a). The chromatic phenomenon of the lens near and closer to the lens is shown in (c), and that of the case with astigmatism is shown in (d). If the lighting spot is replaced by a white LED, the corresponding phenomena are given in (e) and (f).

3. Dispersion properties of diffractive FPZPs

Now we demonstrate the dispersion characteristics of diffractive FPZPs by using this new white quasi-point source. The scheme is shown in Fig. 2(a), where the sources, a white LED with a common size (0.4 mm × 0.4 mm), a He-Ne laser with a wavelength of 633 nm, the power of 1 mW diffracted by a pinhole with Φ = 35 μm, a LD with a wavelength of 635 nm, and the power of 100 mW with lasing area 1 μm × 100 μm, are adopted for comparison with the new one. The refractive lens with a focal length of f = 302 mm and diameter Φ = 60 mm acts as a collimated lens, i.e., l 1 = f. Two kinds of FPZPs (π phase-changing for 635 nm) are prepared; one of them is circular and the second is square. For the circular one, the total zones are 2N = 200, r 1 = 0.68 mm, the principal focal length is fc = 710 mm, and the width of the outermost zone is Δr N = 34 μm; for the square, 2N = 200, d 1 = 0.53 mm, the principal focal length is fs = 440 mm, and Δd N = 27 m. The combined resolving power of the arrangement that depends on the size of light source, the outermost zone width, and the recorder (Kodak film) are designed reasonably except for the LED. Figure 2(b) shows the spectra of these four different sources measured by a high-resolution spectrometer (Ocean Optics, USB-2000, US). Nanocarbon and LED are white lightings but with different color rendering; the He-Ne laser and LD are monochromatic lasers but with different modes. The spectra indicate that the light from nanocarbon is closer to sunlight, which is quite different from the light from other sources, including those in prior research [19

19. P. Fischer, C. T. A. Brown, J. E. Morris, C. López-Mariscal, E. M. Wright, W. Sibbett, and K. Dholakia, “White light propagation invariant beams,” Opt. Express 13, 6657–6666 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-17-6657. [CrossRef] [PubMed]

, 20

20. A. Saliminia, S. L. Chin, and R. Vallèe, “Ultra-broad and coherent white light generation in silica glass by focused femtosecond pulses at 1.5 μm,” Opt. Express 13, 5731–5738 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-15-5731. [CrossRef] [PubMed]

]. Hence it has both better color rendering and a smaller dimension.

Fig. 2. Scheme of the demonstration set-up using four kinds of light sources. (a) Setup with four different quasi-point sources: white-light spot induced by a focused LD beam, a common white LED, a typical He-Ne laser, and a LD; they are followed by a space l 1, a lens (f = 302 mm) for collimation (l 1 = f), a FPZP (circular or square), a distance l 2, and a screen (recoded by Kodak film), respectively. (b) The spectra of these four sources.

Let us start from the simplest, the case of stigmatism; i.e., collimated beams from these four kinds of quasi-point sources are normally incident on the square phase plate. Figures 3(a), 3(b), and 3(c) are the main results in this section produced by the nanocarbon light source with the distances l 2 ≈ 438 mm, 440 mm, and 442 mm, respectively. Here l 2 is the distance between the screen and zone plates that we chose, which is nearly proportional to the inverse of the wavelength. The chromatic phenomenon is clear and opposite to that of refractive lens [Fig. 1(c)] because the focal length of FZPs is also proportional to the inverse of the wavelength, which is opposite to the behavior of refractive lens [1

1. Y. Wang, W. Yun, and C. Jacobsen, “Achromatic Fresnel optics for wideband extreme-ultraviolet and X-ray imaging,” Nature 424, 50–53 (2003). [CrossRef] [PubMed]

]. For comparison, Figures 3(d), 3(e), and 3(f) are produced by a He-Ne laser, a LD, and a LED, respectively. It is clear to us that the nanocarbon as a white quasi-point lighting source has higher efficiency, better color rendering, and better coherency (than that of white LEDs), and it is simpler.

Fig. 3. Chromatic phenomena of a square FPZP under stigmatism (using light from the four kinds of quasi-point source with normal incidence). (a), (b), and (c) are main results illuminated by the collimated white light of the nanocarbon, with the distances between screen and zone plates l 2 = 438 mm, 440 mm, and 442 mm, respectively. (d) The phenomena formed by the He-Ne laser diffracted by a pinhole Φ = 35 μm (Airy disk). (e) The phenomena formed by the LD, single-mode in x direction, and multi-mode in y direction. (f) The phenomena formed by the white LED.

Before demonstrating the chromatic aberrations under astigmatism, the theoretical expression for the circular FPZP could be derived from Refs. [13

13. S. Wang, X. Jiang, Q. Lin, E. Bernabeu, J. Alda, and V. Martin, “Astigmatism for an inclined Fresnel zone plate,” Optik 93, 190–192 (1993).

, 14

14. S. Wang and D. Zhao, Matrix Optics (CHEP-Springer Press, Beijing, 2000).

, 16

16. A. R. Jones, “The focal properties of phase zone plates,” Brit. J. Appl. Phys. (J. Phys. D) 2, 1789–1791 (1969).

]; but for the square, we have to rederive it. The final expression is

E(ζ,η,z,λ)=iE0(λ)λzeikze(λ)m=02N1{()md1md1mexp[ik2z(xζ)2]dxd1mcosθd1mcosθexp{ik2z[(yη)2+y2tan2θ]}dy}
+iE0(λ)λzeikzm=02N1{()md1m+1d1m+1exp[ik2z(xζ)2]dxd1m+1cosθd1m+1cosθexp{ik2z[(yη)2+y2tan2θ]}dy},
(1)

that means, the superposition of the diffraction among the zones and the interference between nonphased and phased fields with different colors (polychromatic) is a generalized grating or optical array [30

30. S. Wang and L. Ronchi, “Principles and design of optical arrays,” Prog. Optics 25, 279–348 (1988). [CrossRef]

]. Where E(ζ,η,z,λ) is the optical field at the screen s with coordinates in Fig. 2(a), λ means wavelength, k = 2π/ λ denotes wave number, and eiδ(λ) indicates binary phase changing. There are several arrangements to demonstrate chromatic phenomena under different astigmatisms as shown in Fig. 4.(a) The square FPZP is inclined at an angle of θ ≈ 10° and is illuminated by the collimated light from the excited nanocarbon under l 2 ≈ 440 mm [Fig. 4(a)]. (b) A comparison with the LED [Fig. 4(b)]. (c) The square FPZP is rotated axially at an angle of 45°, inclined with an angle of θ ≈ 35°, and illuminated by the light from white quasi-point source under l 2 ≈ 439 mm [Fig. 4(c)]. (d) l 2 ≈ 441 mm [Fig. 4(d)]. Change another circular FPZP with a diaphragm as shown in Fig. 4(e) just behind and illuminated by the light from a nanocarbon, and a photo is taken at l 2 = fc/ 3 ≈ 237 mm [Fig. 4(f)], and the zone plate with the diaphragm is inclined at an angle of θ ≈ 40° [Fig. 4(g)]. A series of fresh, unknown, and important information has been included in these pictures, which we feel is going to be recognized in the near future.

4. Summary and conclusions

In conclusion, the dispersion properties of a refractive lens and diffractive FPZPs are demonstrated by using a quasi-point white-light source, i.e., the laser-induced white-light emission from a nanocarbon. When compared to other common lighting sources in scientific experiments (including LED, LD, He-Ne laser and those in prior work [19

19. P. Fischer, C. T. A. Brown, J. E. Morris, C. López-Mariscal, E. M. Wright, W. Sibbett, and K. Dholakia, “White light propagation invariant beams,” Opt. Express 13, 6657–6666 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-17-6657. [CrossRef] [PubMed]

, 20

20. A. Saliminia, S. L. Chin, and R. Vallèe, “Ultra-broad and coherent white light generation in silica glass by focused femtosecond pulses at 1.5 μm,” Opt. Express 13, 5731–5738 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-15-5731. [CrossRef] [PubMed]

]), a nanocarbon light source shows the most ideal characteristics. Some of this information may also be helpful in the study of x-ray imaging and de Broglie wave imaging.

Fig. 4. Quite complete chromatic phenomena of FPZPs under different situations with three kinds of arrangements: (a) the square FPZP is inclined with an angle θ ≈ 10° and illuminated by the light from nanocarbon, (b) compared with the case of LED, (c) the square FPZP is rotated axially by an angle 45°, inclined with an angle θ ≈ 35°, and illuminated by the light from white quasi-point source when l 2 = 439 mm (inset is magnification of the center pattern) and (d) l 2 = 441 mm. Change another circular FPZP (2N = 200, fc = 710 mm, r 1 = 0.68 mm and Δr N = 34 μm) with a diaphragm like (e), and (f) illuminated by the carbon light point source and (g) the case of the FPZP with diaphragm inclined with an angle θ ≈ 40°.

Acknowledgments

J. Zhu, M. Shen, B. Wang, and Y. Zeng provided assistance on this subject. This research was supported by National Natural Scientific Foundation of China grants 60276035 and 60478041 and Space Technology Foundation of China grant 2002-HT-ZJDX-08.

References and links

1.

Y. Wang, W. Yun, and C. Jacobsen, “Achromatic Fresnel optics for wideband extreme-ultraviolet and X-ray imaging,” Nature 424, 50–53 (2003). [CrossRef] [PubMed]

2.

S. Wang, L. Hu, B. Zhang, D. Zhao, Z. Wei, and Z. Zhang, “Electromagnetic excitation of nanocarbon in vacuum,” Opt. Express 13, 3625–3630 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-10-3625. [CrossRef] [PubMed]

3.

E. Marom, E. Ben-Eliezer, L. P. Yaroslavsky, and Z. Zalevsky, “Two methods for increasing the depth of focus of imaging systems,” Proc. SPIE 5227, 8–15 (2004).

4.

M. Makowski, G. Mikula, M. Sypek, A. Kolodziejczyk, and C. Prokopowicz, “Diffractive elements with extended depth of focus,” Proc. SPIE 5484, 475–481 (2004). [CrossRef]

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S. C. Kim, S. E. Lee, and E. S. Kim, “Optical implementation of real-time incoherent 3D imaging and display system using modified triangular interferometer,” Proc. SPIE 5443, 250–256 (2004). [CrossRef]

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S. Wang, D. Zhao, X. Jiang, and F. Huang, “Laser safety monitoring consideration for the largest dam by means of the generalized three-point method,” Opt. Laser Technol. 33, 153–156 (2001). [CrossRef]

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X. Ren, S. Liu, and X. Zhang, “Fabrication of off-axis holographic Fresnel lens used as multiplexer/demultiplexer in optical communications,” Proc. SPIE 5456, 391–398 (2004). [CrossRef]

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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, 1210–1213 (2005). [CrossRef] [PubMed]

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S. Eisebitt, J. Lüning, W. F. Schlotter, M. Lörgen, O. Hellwig, W. Eberhardt, and J. Stöhr, “Lensless imaging of magnetic nanostructures by X-ray spectro-holography,” Nature 432, 885–888 (2004). [CrossRef] [PubMed]

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L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature 414, 184–188 (2001). [CrossRef] [PubMed]

11.

E. Di Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, and R. Barrett, “High-efficiency multilevel zone plates for keV X-rays,” Nature 401, 895–898 (1999). [CrossRef]

12.

I. A. Schelokov, D. V. Roshchupkin, A. S. Kondakov, D. V. Irzhak, M. Brunel, and R. Tucoulou, “Second generation of grazing-incidence-phase Fresnel zone plates,” Opt. Commun. 159, 278–284 (1999). [CrossRef]

13.

S. Wang, X. Jiang, Q. Lin, E. Bernabeu, J. Alda, and V. Martin, “Astigmatism for an inclined Fresnel zone plate,” Optik 93, 190–192 (1993).

14.

S. Wang and D. Zhao, Matrix Optics (CHEP-Springer Press, Beijing, 2000).

15.

Y. Fan, H. Ren, and S. Wu, “Electrically switchable Fresnel lens using a polymer-separated composite film,” Opt. Express 13, 4141–4147 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-11-4141. [CrossRef] [PubMed]

16.

A. R. Jones, “The focal properties of phase zone plates,” Brit. J. Appl. Phys. (J. Phys. D) 2, 1789–1791 (1969).

17.

L. J. Janicijevic, “Diffraction characteristics of square zone plates,” J. Opt. (Paris) 13, 199–206 (1982). [CrossRef]

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S. Wang, Y. Shen, J. Xu, L. Hu, J. Zhu, D. Yang, H. Zhang, Y. Zeng, and J. Yao, “Deep-ultraviolet emission from an InGaAs semiconductor laser,” Appl. Phys. Lett. 84, 3007–3009 (2004). [CrossRef]

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20.

A. Saliminia, S. L. Chin, and R. Vallèe, “Ultra-broad and coherent white light generation in silica glass by focused femtosecond pulses at 1.5 μm,” Opt. Express 13, 5731–5738 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-15-5731. [CrossRef] [PubMed]

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R. R. Alfano and S. L. Shapiro, “Emission in region 4000 to 7000 Å via four-photon coupling in glass,” Phys. Rev. Lett. 24, 584–587 (1970). [CrossRef]

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F. Wang, G. Dukovic, L E. Brus, and T. F. Heinz, “The optical resonances in carbon nanotubes arise from excitons,” Science 308, 838–841 (2005). [CrossRef] [PubMed]

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J. Xiong, D. Z. Cao, F. Huang, H. G. Li, X. J. Sun, and K. Wang, “Experimental observation of classical subwavelength interference with a pseudothermal light source,” Phys. Rev. Lett. 94, 173601 (2005). [CrossRef] [PubMed]

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D. Z. Cao and K. Wang, “Sub-wavelength interference in macroscopic observation,” Phys. Lett. A 333, 23–29 (2004). [CrossRef]

29.

R. L Vander Wal, A. J. Tomasek, and T. M. Ticich, “Synthesis, laser processing, and flame purification of nanostructured carbon,” Nano Lett. 3, 223–229 (2003). [CrossRef]

30.

S. Wang and L. Ronchi, “Principles and design of optical arrays,” Prog. Optics 25, 279–348 (1988). [CrossRef]

OCIS Codes
(090.1970) Holography : Diffractive optics
(230.6080) Optical devices : Sources
(260.2030) Physical optics : Dispersion

ToC Category:
Physical Optics

Citation
Shaomin Wang, Laigui Hu, Binzhi Zhang, Jie Wang, and Daomu Zhao, "Dispersion phenomena demonstrated by a nanocarbon white point source," Opt. Express 14, 932-937 (2006)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-2-932


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References

  1. Y. Wang, W. Yun, and C. Jacobsen, "Achromatic Fresnel optics for wideband extreme-ultraviolet and X-ray imaging," Nature 424, 50-53 (2003). [CrossRef] [PubMed]
  2. S. Wang, L. Hu, B. Zhang, D. Zhao, Z. Wei, and Z. Zhang, "Electromagnetic excitation of nanocarbon in vacuum," Opt. Express 13, 3625-3630 (2005), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-10-3625">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-10-3625</a>. [CrossRef] [PubMed]
  3. E. Marom, E. Ben-Eliezer, L. P. Yaroslavsky, and Z. Zalevsky, "Two methods for increasing the depth of focus of imaging systems," Proc. SPIE 5227, 8-15 (2004).
  4. M. Makowski, G. Mikula, M. Sypek, A. Kolodziejczyk, and C. Prokopowicz, "Diffractive elements with extended depth of focus," Proc. SPIE 5484, 475-481 (2004). [CrossRef]
  5. S. C. Kim, S. E. Lee, and E. S. Kim, "Optical implementation of real-time incoherent 3D imaging and display system using modified triangular interferometer," Proc. SPIE 5443, 250-256 (2004). [CrossRef]
  6. S. Wang, D. Zhao, X. Jiang, and F. Huang, "Laser safety monitoring consideration for the largest dam by means of the generalized three-point method," Opt. Laser Technol. 33, 153-156 (2001). [CrossRef]
  7. X. Ren, S. Liu, and X. Zhang, "Fabrication of off-axis holographic Fresnel lens used as multiplexer/demultiplexer in optical communications," Proc. SPIE 5456, 391-398 (2004). [CrossRef]
  8. 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, 1210-1213 (2005). [CrossRef] [PubMed]
  9. S. Eisebitt, J. Lüning, W. F. Schlotter, M. Lörgen, O. Hellwig, W. Eberhardt, and J. Stöhr, "Lensless imaging of magnetic nanostructures by X-ray spectro-holography," Nature 432, 885-888 (2004). [CrossRef] [PubMed]
  10. L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, "Sharper images by focusing soft X-rays with photon sieves," Nature 414, 184-188 (2001). [CrossRef] [PubMed]
  11. E. Di Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, and R. Barrett, "High-efficiency multilevel zone plates for keV X-rays," Nature 401, 895-898 (1999). [CrossRef]
  12. I. A. Schelokov, D. V. Roshchupkin, A. S. Kondakov, D. V. Irzhak, M. Brunel, and R. Tucoulou, "Second generation of grazing-incidence-phase Fresnel zone plates," Opt. Commun. 159, 278-284 (1999). [CrossRef]
  13. S. Wang, X. Jiang, Q. Lin, E. Bernabeu, J. Alda, and V. Martin, "Astigmatism for an inclined Fresnel zone plate," Optik 93, 190-192 (1993).
  14. S. Wang and D. Zhao, Matrix Optics (CHEP-Springer Press, Beijing, 2000).
  15. Y. Fan, H. Ren, and S. Wu, "Electrically switchable Fresnel lens using a polymer-separated composite film," Opt. Express 13, 4141-4147 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-11-4141. [CrossRef] [PubMed]
  16. A. R. Jones, "The focal properties of phase zone plates," Brit. J. Appl. Phys. (J. Phys. D) 2, 1789-1791 (1969).
  17. L. J. Janicijevic, "Diffraction characteristics of square zone plates," J. Opt. (Paris) 13, 199-206 (1982). [CrossRef]
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