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Light propagation in two-dimensional photonic crystals illuminated by a tightly focused laser beam
Superlattices and Microstructures, Vol. 25, No. 1/2, 1999 Article No. spmi.1998.0656
Light propagation in two-dimensional photonic crystals illuminated by a tightly focused laser beam S HUN - ICHI M ATSUSHITA , F UJIO M INAMI Department of Applied Physics, Tokyo Institute of Technology, Meguro-ku, Tokyo 152 AYA I MADA , RYOKO S HIMADA , TAKAO K ODA Department of Mathematical and Physical Science, Japan Women’s University Bunkyo-ku, Tokyo 112, Japan (Received 26 October 1998)
By using a tightly focused laser beam, we have studied light propagation in two-dimensional photonic crystals consisting of closed-packed hexagonal arrays of polystyrene particles with diameter of 1 ∼ 5 µm. The light propagation is found to depend strongly on the focal point positioning, the incident beam polarization and the interaction between particles and glass substrates. c 1999 Academic Press
Key words: photonic crystals, polystyrene particles, light propagation.
Photonic crystals are artificial microstructures constructed by periodic arrays of dielectric materials. They are of great interest since these structures have the possibility of spontaneous emission control [1]. Recently, two-dimensional (2D) structures have attracted much attention because of the ease of fabrication, compared to 3D structures. Several 2D structures were proposed and some structures have already been fabricated [2]. However, the details of electromagnetic wave propagation in such 2D structures are not yet clear. In this paper, using a tightly focused Gaussian beam, we have investigated unique light propagation in 2D photonic crystals in which microspheres were self-assembled into hexagonally close-packed ordered arrays [3]. The photonic crystals used here were composed of close-packed hexagonal arrays of polystyrene (LATEX) particles with diameter of 1 ∼ 5 µm fabricated on the surface of glass substrates. For illumination of the crystals, the 632.8 nm line of a He:Ne laser was used. The laser beam was condensed into a tight spot with a diameter of less than 1 µm by a 0.5 NA objective lens. The reflected light from the crystal was collected with the same objective lens, divided by a half mirror, and detected by a photomultiplier or a charge coupled device (CCD) camera. The transmitted light was collected with another 0.5 NA objective lens and detected by a photomultiplier. First, we investigated the intensity of the reflected and transmitted lights from the photonic crystal consisting of ordered 5 µm LATEX particles. The light intensity was measured by moving the focal point in 1 µm steps along the layer. Figure 1A shows the intensity of the reflected light and B, that of the transmitted light, respectively. Both data show many sharp cone-like intensity profiles. The intensity maxima appear at the 0749–6036/99/010347 + 04
$30.00/0
c 1999 Academic Press
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Superlattices and Microstructures, Vol. 25, No. 1/2, 1999
A
B 0
0
10
10 µm
µm 20
0
10
µm
20
30
30
20
0
10
µm
20
30 30
Fig. 1. Optical transmission A, and reflection B, images for a layer of 5 µm LATEX particles. From comparison with the microscope image, the transmission and reflection maxima are found to occur during the focal positioning at the top of each LATEX sphere.
same positions for the reflection and the transmission. The spacing of neighboring cones is 5 µm and the cones form close-packed hexagonal arrays. The high reflection and transmission points are found to coincide in position with the tops of the spheres. In other words, the high reflection or transmission occurs when the incident beam is focussed just on the top of each LATEX sphere. At the contact point of two adjacent spheres and in the open space surrounded by three neighboring spheres, we can hardly observe the reflected and transmitted lights. This means that the fraction of the beam energy coupled into the crystal is much higher at these points. For the samples consisting of 1 and 3 µm LATEX particles, similar results were obtained. From now on, therefore, we present only the results for the sample composed of 5 µm LATEX particles. Next, we investigated light propagation patterns in a layer of the ordered LATEX spheres by using a CCD camera. The incident beam was focused directly on the LATEX layer, and the image of the reflected light was observed. Figure 2 shows the CCD images of the propagation patterns when the incident beam was focused at the contact point of two adjacent spheres. Figure 2A and B show the images for the polarization of the incident beam (e), chosen normal and parallel to the line connecting the centers of the two illuminated spheres (x-axis). In the CCD images, small white points in the hexagonally close-packed array indicate the top of LATEX spheres. White arrows refer to the focus point of the incident beam. As stated above, high reflection from the focus point cannot be observed here, since the incident beam energy couples with internal or surface modes of the crystal. On the other hand, bright spots are clearly seen at the neighboring contact points of the spheres. When the polarization of the incident beam is set normal to the x-axis, many bright points are found to appear at the contact points of the linear chain formed by the spheres. At a contact point further away from the focusing point, the brightness becomes weaker. Further, it can be seen from the figure that the length of light propagation along the linear chain depends strongly on the polarization of the incident beam. From an analogy to the case of a single spherical particle [4, 5], this behavior can be interpreted in terms of a model where the incident beam refracts into the spherical LATEX particles at the edge of the spheres and couples with electromagnetic wave modes propagating along the LATEX layer. Figure 3 shows the CCD image of the light propagation pattern in the layer, when the incident beam was focused directly on the open space surrounded by three neighboring spheres. The polarization of the incident beam is normal A, and parallel B, to a side (x-axis) of a triangle made up of the illuminated three spheres. Many bright spots are observed at the contact points of linear chains of spheres, especially for e ⊥ x. The bright
Superlattices and Microstructures, Vol. 25, No. 1/2, 1999
349
A
B
C
D
X Fig. 2. The polarization dependence of light propagation pattern when the incident beam is focused directly on the contact point of two spheres in an ordered LATEX array. The polarization of the incident beam is parallel A, or normal B, to x. Figure 2C and D show the schematic images of Fig. 2A and B. Black and gray circles indicate the incident beam position and the reflection spots, respectively.
A
B
C
D
X Fig. 3. The polarization dependence of light propagation pattern when the incident beam is focused directly on the open space surrounded by three neighboring spheres in an ordered LATEX array. The polarization of the incident beam is parallel A, or normal B, to x. Figure 2C and D show the schematic images of Fig. 2A and B. Black and gray circles indicate the incident beam position and the reflection spots, respectively.
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spots on the chains have the same polarization dependence as the spots appearing when the incident beam is focused directly at the contact point of spheres. Thus, it can be found that a fraction of the incident beam illuminates the contact points of the three spheres. Bright spots are also seen at the centers of triangles made up of three spheres. Further, it is noted that those spots can be observed only in some downward triangular arrays of spheres, on the trigonal symmetry axes connecting the apexes and the center of the upward triangle formed by the illuminated three spheres. From the polarization dependence, three bright spots nearest to the focus point are found to be due to leakage of the internal beam from the surface of the illuminated spheres. For the second nearest spots in the triangles, their brightness varies greatly when the incident beam is sent through the substrate. The existence of the substrate is therefore considered to be important for the appearance of these spots. In this case, the wave propagation is as follows. A fraction of the internal beam in the illuminated spheres leaks out at the contact points to the substrate, propagates in the substrate in the direction of the trigonal symmetry axes, and enters in to the spheres forming downward triangles at the contact points to the substrate. Owing to this propagation process, the second nearest bright spots appear. The validity of this picture is also borne out by the CCD images of the transmitted light. In conclusion, we have observed the images of light propagation in 2D photonic crystals composed of close-packed hexagonal LATEX particles. The light propagation patterns in the LATEX layer are affected drastically by the focal point positioning of the laser beam. It is also shown that the propagation patterns depend strongly on the incident beam polarization and the interaction between the particles and glass substrates. Acknowledgement— This work was partly supported by a Grant-in-Aid for Scientific Research from Ministry of Education, Science, Sports and Culture, Japan.
References [1] }E. Yablonovitch, J. Opt. Soc. Am. B10, 283 (1993). [2] }P. L. Gourley, J. R. Wendt, G. A. Vawter, T. M. Brennen, and B. E. Hammons, Appl. Phys. Lett. 64, 687 (1994). [3] }K. Nagayama, Mater. Sci. Eng. C1, 87 (1994). [4] }H. C. Van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957). [5] }Elsayed E. M. Khaled, Steven C. Hill, and Peter W. Barber, IEEE Trans. Antennas Propag. 41, 295 (1993).
Light propagation in two-dimensional photonic crystals illuminated by a tightly focused laser beam S HUN - ICHI M ATSUSHITA , F UJIO M INAMI Department of Applied Physics, Tokyo Institute of Technology, Meguro-ku, Tokyo 152 AYA I MADA , RYOKO S HIMADA , TAKAO K ODA Department of Mathematical and Physical Science, Japan Women’s University Bunkyo-ku, Tokyo 112, Japan (Received 26 October 1998)
By using a tightly focused laser beam, we have studied light propagation in two-dimensional photonic crystals consisting of closed-packed hexagonal arrays of polystyrene particles with diameter of 1 ∼ 5 µm. The light propagation is found to depend strongly on the focal point positioning, the incident beam polarization and the interaction between particles and glass substrates. c 1999 Academic Press
Key words: photonic crystals, polystyrene particles, light propagation.
Photonic crystals are artificial microstructures constructed by periodic arrays of dielectric materials. They are of great interest since these structures have the possibility of spontaneous emission control [1]. Recently, two-dimensional (2D) structures have attracted much attention because of the ease of fabrication, compared to 3D structures. Several 2D structures were proposed and some structures have already been fabricated [2]. However, the details of electromagnetic wave propagation in such 2D structures are not yet clear. In this paper, using a tightly focused Gaussian beam, we have investigated unique light propagation in 2D photonic crystals in which microspheres were self-assembled into hexagonally close-packed ordered arrays [3]. The photonic crystals used here were composed of close-packed hexagonal arrays of polystyrene (LATEX) particles with diameter of 1 ∼ 5 µm fabricated on the surface of glass substrates. For illumination of the crystals, the 632.8 nm line of a He:Ne laser was used. The laser beam was condensed into a tight spot with a diameter of less than 1 µm by a 0.5 NA objective lens. The reflected light from the crystal was collected with the same objective lens, divided by a half mirror, and detected by a photomultiplier or a charge coupled device (CCD) camera. The transmitted light was collected with another 0.5 NA objective lens and detected by a photomultiplier. First, we investigated the intensity of the reflected and transmitted lights from the photonic crystal consisting of ordered 5 µm LATEX particles. The light intensity was measured by moving the focal point in 1 µm steps along the layer. Figure 1A shows the intensity of the reflected light and B, that of the transmitted light, respectively. Both data show many sharp cone-like intensity profiles. The intensity maxima appear at the 0749–6036/99/010347 + 04
$30.00/0
c 1999 Academic Press
348
Superlattices and Microstructures, Vol. 25, No. 1/2, 1999
A
B 0
0
10
10 µm
µm 20
0
10
µm
20
30
30
20
0
10
µm
20
30 30
Fig. 1. Optical transmission A, and reflection B, images for a layer of 5 µm LATEX particles. From comparison with the microscope image, the transmission and reflection maxima are found to occur during the focal positioning at the top of each LATEX sphere.
same positions for the reflection and the transmission. The spacing of neighboring cones is 5 µm and the cones form close-packed hexagonal arrays. The high reflection and transmission points are found to coincide in position with the tops of the spheres. In other words, the high reflection or transmission occurs when the incident beam is focussed just on the top of each LATEX sphere. At the contact point of two adjacent spheres and in the open space surrounded by three neighboring spheres, we can hardly observe the reflected and transmitted lights. This means that the fraction of the beam energy coupled into the crystal is much higher at these points. For the samples consisting of 1 and 3 µm LATEX particles, similar results were obtained. From now on, therefore, we present only the results for the sample composed of 5 µm LATEX particles. Next, we investigated light propagation patterns in a layer of the ordered LATEX spheres by using a CCD camera. The incident beam was focused directly on the LATEX layer, and the image of the reflected light was observed. Figure 2 shows the CCD images of the propagation patterns when the incident beam was focused at the contact point of two adjacent spheres. Figure 2A and B show the images for the polarization of the incident beam (e), chosen normal and parallel to the line connecting the centers of the two illuminated spheres (x-axis). In the CCD images, small white points in the hexagonally close-packed array indicate the top of LATEX spheres. White arrows refer to the focus point of the incident beam. As stated above, high reflection from the focus point cannot be observed here, since the incident beam energy couples with internal or surface modes of the crystal. On the other hand, bright spots are clearly seen at the neighboring contact points of the spheres. When the polarization of the incident beam is set normal to the x-axis, many bright points are found to appear at the contact points of the linear chain formed by the spheres. At a contact point further away from the focusing point, the brightness becomes weaker. Further, it can be seen from the figure that the length of light propagation along the linear chain depends strongly on the polarization of the incident beam. From an analogy to the case of a single spherical particle [4, 5], this behavior can be interpreted in terms of a model where the incident beam refracts into the spherical LATEX particles at the edge of the spheres and couples with electromagnetic wave modes propagating along the LATEX layer. Figure 3 shows the CCD image of the light propagation pattern in the layer, when the incident beam was focused directly on the open space surrounded by three neighboring spheres. The polarization of the incident beam is normal A, and parallel B, to a side (x-axis) of a triangle made up of the illuminated three spheres. Many bright spots are observed at the contact points of linear chains of spheres, especially for e ⊥ x. The bright
Superlattices and Microstructures, Vol. 25, No. 1/2, 1999
349
A
B
C
D
X Fig. 2. The polarization dependence of light propagation pattern when the incident beam is focused directly on the contact point of two spheres in an ordered LATEX array. The polarization of the incident beam is parallel A, or normal B, to x. Figure 2C and D show the schematic images of Fig. 2A and B. Black and gray circles indicate the incident beam position and the reflection spots, respectively.
A
B
C
D
X Fig. 3. The polarization dependence of light propagation pattern when the incident beam is focused directly on the open space surrounded by three neighboring spheres in an ordered LATEX array. The polarization of the incident beam is parallel A, or normal B, to x. Figure 2C and D show the schematic images of Fig. 2A and B. Black and gray circles indicate the incident beam position and the reflection spots, respectively.
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Superlattices and Microstructures, Vol. 25, No. 1/2, 1999
spots on the chains have the same polarization dependence as the spots appearing when the incident beam is focused directly at the contact point of spheres. Thus, it can be found that a fraction of the incident beam illuminates the contact points of the three spheres. Bright spots are also seen at the centers of triangles made up of three spheres. Further, it is noted that those spots can be observed only in some downward triangular arrays of spheres, on the trigonal symmetry axes connecting the apexes and the center of the upward triangle formed by the illuminated three spheres. From the polarization dependence, three bright spots nearest to the focus point are found to be due to leakage of the internal beam from the surface of the illuminated spheres. For the second nearest spots in the triangles, their brightness varies greatly when the incident beam is sent through the substrate. The existence of the substrate is therefore considered to be important for the appearance of these spots. In this case, the wave propagation is as follows. A fraction of the internal beam in the illuminated spheres leaks out at the contact points to the substrate, propagates in the substrate in the direction of the trigonal symmetry axes, and enters in to the spheres forming downward triangles at the contact points to the substrate. Owing to this propagation process, the second nearest bright spots appear. The validity of this picture is also borne out by the CCD images of the transmitted light. In conclusion, we have observed the images of light propagation in 2D photonic crystals composed of close-packed hexagonal LATEX particles. The light propagation patterns in the LATEX layer are affected drastically by the focal point positioning of the laser beam. It is also shown that the propagation patterns depend strongly on the incident beam polarization and the interaction between the particles and glass substrates. Acknowledgement— This work was partly supported by a Grant-in-Aid for Scientific Research from Ministry of Education, Science, Sports and Culture, Japan.
References [1] }E. Yablonovitch, J. Opt. Soc. Am. B10, 283 (1993). [2] }P. L. Gourley, J. R. Wendt, G. A. Vawter, T. M. Brennen, and B. E. Hammons, Appl. Phys. Lett. 64, 687 (1994). [3] }K. Nagayama, Mater. Sci. Eng. C1, 87 (1994). [4] }H. C. Van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957). [5] }Elsayed E. M. Khaled, Steven C. Hill, and Peter W. Barber, IEEE Trans. Antennas Propag. 41, 295 (1993).