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
Achromatic Fresnel optics combine a diffractive zone plate and a refractive lens with opposite chromatic aberrations , which is very useful in visible, x-ray, and even in de Broglie wave imaging. However, one has to know the dispersion properties of the elements by a white-light point source in detail , especially those of Fresnel zone plates (FZPs), which have been found in a series of applications in photonics—optical imaging, optical monitoring, optical communication, space navigation [3–7], and x-ray imaging [8–11]—and also have been considered, fabricated, and measured in various ways [12–17]. Here we report on how to consider and realize a suitable quasi-point lighting source with higher efficiency, simpler and better color rendering, and wonderful coherency by using nanocarbon. This is the first time to our knowledge that it has been used in scientific experiments to demonstrate the chromatic phenomena of a refractive lens, a diffractive Fresnel phase (binary) zone plate (FPZP), and a squared zone plate, and to compare with those of other light sources, including a light-emitting diode (LED), a He-Ne laser, and a semiconductor laser diode (LD) under stigmatism and with different astigmatisms. Thus, understanding is clearer regarding the field of visible optics, and the study of the dispersion phenomena for electromagnetic waves could also be extended to that of quantum waves.
We have realized and reported in earlier work that the laser-induced white-light emission from nanocarbon could be a white-light point source . 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  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 . There are several examples of research concerning this [19–28], especially as seen in Ref  or , 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  with good color rendering and the supercontinuum with small dimensions [19–21]. 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 . 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], 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.
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, 20]. Hence it has both better color rendering and a smaller dimension.
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 . 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.
Before demonstrating the chromatic aberrations under astigmatism, the theoretical expression for the circular FPZP could be derived from Refs. [13, 14, 16]; but for the square, we have to rederive it. The final expression is
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 . 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, 20]), 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.
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.
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