Micro‐demultiplexer of Coupled Resonator Optical Waveguide Fabricated by Microspheres

Abstract

A micro-demultiplexer of a coupled resonator optical waveguide composed of polystyrene microspheres is fabricated by a self-assembly technique in colloidal suspension on a lithographically patterned substrate. The spectrum of propagating light taken at the 60°-branch (Point 2) shows sharper peaks than that taken at Point 1 while the spectrum taken at the 30°-branch (Point 3) shows broader peaks. How does light propagate within a chain of transparent spheres? In the case of microspheres with diameters of a few micrometers, the feature of an optical resonator should be included in the discussion because the diameters are nearly the same order of magnitude as the wavelength of light. In microspheres, light goes around the circumference of those with whispering gallery modes (WGMs), and indicates a spectrum that has sharp and discrete peaks.1-4 Moreover, waveguides that utilize a weak coupling between resonators, such as microrings, microdisks, or microspheres, are called coupled-resonator optical waveguides (CROWs).3, 5, 6 By controlling the coupling efficient, this concept can be applied to on-chip optical buffer memory.7-9 Another particularly appealing feature of CROWs is the possibility of making loss-less and reflection-less bends with a wavelength-scale curvature because the microresonators can couple at an arbitrary point on the circumference of light going around. When we use microspheres as the microresonators, CROWs allow us to utilize a self-assembly phenomenon in colloidal suspension to align and connect microspheres with non-elaborate processing.10-15 Moreover, if we use a lithographically patterned substrate which is formed lines of dimples in order to trap the microspheres, we can fabricate arbitrary-shape waveguides for on-chip optical circuits. Since the prevalent waveguide concepts16-19 require very elaborate technology to fabricate such sharp bends, or require a delicate assembling technique, the CROW concept might partly replace the prevalent concepts. In this article, we utilize a self-assembly phenomenon in colloidal suspension on a lithographically patterned substrate to align and connect microspheres, and we observe the optical properties of propagated light through bended or branched chains of transparent microspheres, and we perform a finite-difference time domain (FDTD) simulation to explain the optical properties. By using microspheres doped with CdSe nanocrystals, Möller and co-authors show the accuracy of microsphere's diameter should be better than <0.05% in order to induce resonance and coupling among the microspheres.3 Hara and co-authors found that their numerical model is consistent with the experimental results of transparent polystyrene-microsphere chains fabricated in air or in a vacuum.2 On the other hand, the polystyrene-microsphere chains fabricated by a dewetting process in colloidal suspension show long-range propagation of about 20 microspheres even though the deviation of the diameters exceeds 1.1%.20-24 In the case of straight chains, this long-range propagation can be explained by the concept of a photonic nanojet that consists of focused spots with elongated shapes by spherical or cylindrical resonators. Chen and co-authors have shown that the nanojets can be periodically reproduced along a chain of microspheres.25, 26 This quasiperiodic pattern of coupled nanojets, termed nanojet-induced modes (NIMs), has been observed in chains of polystyrene microspheres,20, 24 and the NIMs are rather tolerant to the presence of disorder and show broad peaks. However, in the case of bended or branched chains, some theoretical26-28 and experimental29 studies have been reported based on the WGMs concept, yet the propagation mechanism is not been understood sufficiently. When we use a far-field imaging technique to observe light propagating within microsphere chains, the objective lens of a conventional microscope collects the scattered light, which is only a portion of the propagation light.20, 24 Contrary to this, the guide-collection-mode near-field scanning optical microscopy (NSOM) technique can be used to directly observe propagation light that is confined to high-index dielectric materials with wavelength-scale spatial resolution.29-33 Therefore, we use the guide-collection-mode NSOM to observe the optical properties of microsphere CROWs. Microsphere CROWs with a branched structure were fabricated by a self-assembly technique10-15 in colloidal suspension on a lithographically patterned substrate. Figure 1a shows a scanning electron microscopy (SEM) image of a typical patterned substrate with a cleaved cross-section surface. Dimples with tetragonal symmetry were patterned on Si (001) substrates by means of electron-beam lithography and inductive-coupled-plasma reactive-ion-etching. The dimples have an inverse shape of a frustum of a tetragonal pyramid; they are arranged for the template of CROWs and are spaced 2.0 μm apart from center to center. Figure 1b shows a schematic of the self-assembly technique. First, we placed a glass coverslip on the substrate's left with a small gradient (1–2°). The gap between the coverslip and the substrate should be less than 100 μm. Next, a colloidal suspension of polystyrene microspheres was put inside the gap and then slowly evaporated. After that, the microspheres in the meniscus would be dragged by the capillary force and could be definitely trapped in the dimples. The diameter of the microspheres is also 2.0 μm. This technique has been described in detail in Ref.14 Figure 1c indicates the SEM images of ordered chains of microspheres that have 30°-, 60°- and 90°-branched structures. Since the pitch of the dimples and the diameter of the microspheres are the same, the microspheres trapped in the nearest neighbors are closely connected to each other. Fabrication of microsphere CROWs by a self-assembly technique. To fabricate the microsphere CROWs of branched structures, we use a lithographically patterned substrate as a template, and we utilize a self-assembly technique in colloidal suspension. a) SEM image of the patterned substrate with cleavage cross-section surface. The dimples have an inverse shape of the frustum of a tetragonal pyramid, and the square is 1.5 μm × 1.5 μm. The size of square is larger than that in Ref.29 for strong trapping. b) Schematic of the self-assembly technique to arrange the microspheres on a patterned substrate. The movement of the meniscus is indicated by the arrow, and the polystyrene microspheres could be definitely trapped in the dimples. c) SEM image of microsphere CROWs made of chains of microspheres. The microsphere CROWs have 30°-, 60°-, and 90°-branched structures, which are some of the elements of basic design for optical circuits in the future. In this article, we note the 30°- and 60°-branched structures (left, upper). To understand the light propagation within the CROWs, we observed the propagation light by the guide-collection-mode NSOM technique. Figure 2a is a schematic of the experimental setup. The light source was the luminescence emitted from dye-doped fluorescent polystyrene microspheres (FL-PSMSs) that had an emission maximum in the wavelength of 508 nm and that were excited by violet light (λ = 406 nm) through the objective lens as depicted in Figure 2a. The reason why we used fluorescent microspheres as a light source is that it is easy to couple incident light to the chains of transparent microspheres. The propagation light was collected by a cantilevered optical fiber probe and was detected by a charge-coupled device (CCD) detector.32 Observation of light propagation. Spectra of propagated light through a microsphere CROW were measured by a guide-collection-mode NSOM technique. a) Experimental setup of guide-collection-mode NSOM. The excitation light is illuminated through the objective lens of a conventional optical microscope. The diameter of the focal point is ∼10 μm. Light emitted from a fluorescent microsphere propagates within the CROW and is collected by an optical fiber probe. The spectra of light are measured by a monochromator and CCD detector. b) Conventional optical microscope image of microsphere CROWs with branched structure. c) Spectra of propagated light taken at the points indicated in b. Figure 2b is an optical microscope image of CROWs, and indicates the points where the propagation light was collected. A FL-PSMS is next to the edge of CROW; it was found by supplementary observation with conventional fluorescence microscopy (data not shown). This is the only FL-PSMS in the focal point of excitation light. Therefore, this is the only light source of luminescent light in NSOM observation. The luminescent light propagates to Point 1 through the CROW and also propagates from Point 1 to Points 2 and 3, which are at the 60°- and 30°-branched CROWs, respectively. Light collects at those points, and the spectra taken at the points are plotted in Figure 2c. For reference, the luminescence spectrum of the FL-PSMSs dispersed in water, which shows the same spectrum as the dye itself, is plotted by a light-cyan line. Moreover, the scattering spectrum for a single transparent microsphere calculated using the Mie theory is plotted by an orange line. The labels TEn,l and TMn,l denote the polarization type (transverse electric and magnetic) and the angular (n) and radial (l) quantum numbers, respectively. In Figure 2c, the spectra taken at Points 1 and 2 show some sharp peaks, which indicate TM peaks of WGMs,29 although those are red-shifted. Here, we notice that the spectrum taken at Point 2 shows sharper peaks than that taken at Point 1. On the other hand, the spectrum taken at Point 3 shows rather broad peaks, which seem to be not associated with WGMs. In other words, the spectrum taken at Point 1 involves WGMs and other components, and the results suggest that the microsphere at the branching point in the branched microsphere CROW splits the WGMs and other component. This splitting of WGMs and other components is the most important point of this article. The relative intensity of light with a 488 nm wavelength (TM16,1) are I2/I1 = 0.41 and I3/I1 = 0.36 where I1, I2, and I3 denote the light intensity taken at Point 1, 2, and 3, respectively. Because the I2/I1 is larger than the I3/I1 in the wavelength of WGM peak, this result indicates the branched microsphere CROW selects out light of a wavelength from the luminescent light that has a broad peak. The rest of I1 should be scattered and lost. Moreover, in TM15,1 peak (λ = 515 nm), I2/I1 and I3/I1 are 0.43 and 0.28. This result suggests the propagation efficiency is slightly different among the different modes of WGMs, and suggests there is a kind of demultiplexing function, i.e., the demultiplexing function selects out one WGM component from other WGM components.29 Next, we discuss the splitting function of branched microsphere CROWs and its mechanism. To shape the FDTD simulation model accurately, we observed the CROWs by high-resolution SEM (HR-SEM). Figure 3a and b are the HR-SEM images of the CROWs’ branching point which are composed of polystyrene and borosilicate glass microspheres, respectively. In Figure 3a, we note that the neighboring microspheres are connected by microjoints though Figure 3b shows that the neighboring microspheres are perfectly separated. In these figures, we did not use any bonding agents for curing, unlike the case in Ref.15 except for the polystyrene microspheres dispersed in pure water. Since Figure 3a and b were taken in vacuum, water as a simple substance should have evaporated. However, in the case of polystyrene microspheres, water molecules should exist and should be preserved among the chain polymer with the “strong absorbed” state at the vicinity of surface. Then, the surface of polystyrene is partly dissolved, and the volume of microsphere should be increased. This is called swelling effect. After that, when the dewetting process progresses, the partly dissolved polystyrene concentrates around the contact points of the microspheres due to capillary forces. From these results, the most likely origin of the microjoints is some swelling effect of polystyrene within the suspension. For both WGM and NIM light propagation, these microjoints might be able to increase the optical coupling between microspheres. Therefore, the joint's influence should be also included in the FDTD simulation model. HR-SEM image of branching point of microsphere CROWs. a) Polystyrene microspheres. The gaps of neighboring microspheres should have been filled with small amounts of viscous liquid (partly dissolved polystyrene), after which the microjoints should form. The diameter of a microjoint is about 300 nm. b) Borosilicate glass microspheres. The microjoints are not found. Figure 4a is a schematic of the model for FDTD simulation, and indicates the mechanism of light propagation. A small oscillating dipole is set between the fluorescent microsphere and the transparent one. Figure 4b–d are the intensity mapping of the electric field of propagating light calculated by the FDTD method, and indicate the cases where the dipole is parallel to the x, y, and z axes indicated in Figure 4a, respectively. The simulation was performed with a 488 nm wavelength (TM16,1), and a 300 nm microjoint diameter. As Figure 4b shows, a resonant mode of WGM appears around the circumferences of the microspheres and the WGM component propagates to the 60°- and 30°-branches. On the other hand, Figure 4c,d show that WGM's resonance is rather weak, and show that a large electric field appears across the center of the microspheres. Because the y- and z-direction dipoles cannot cause resonance with the TM polarization of WGMs,34 the electric field in Figure 4c,d indicates light propagation with NIMs in which the microspheres act as ball-type lenses. Moreover, it was shown that the diameter of propagating light is enlarged when light propagates through odd microspheres.24 Actually, Figure 4c indicates larger diameter of electric field at x = 6 μm than that at x = 4 μm. Therefore, the next microsphere of 30°-branch should be able to collect the light with better efficiency. Here, we note that almost all of the NIM component propagates to the 30°-branch, and little propagates to the 60°-branch. As a result, only the WGM component indicated in Figure 4b can propagate to the 60°-branch. Since the WGM components have sharp peaks in the spectrum, the NSOM spectrum taken at the 60°-branch should indicate sharp peaks. On the other hand, the NSOM spectrum taken at the 30°-branch should indicate broad peaks because the spectrum includes the NIM component. Then, we see that the FDTD simulation supports the results of NSOM observation and explains the splitting function of the branched microsphere CROW. From this, we can conclude that the splitting function is attributed mainly to the difference in propagation efficiency of the NIM component between the 30°- and 60°-branches. FDTD simulation of light propagation within a branched microsphere CROW. FDTD simulation was performed, including consideration of the influence of microjoints as found by HR-SEM. a) Schematic of the model for FDTD simulation. b–d) Intensity mappings of propagating light simulated on the model in which the polarization of the light source is parallel to the x, y, and z axes, respectively, indicated in a. In a, the WGM component is indicated by red lines, and the NIM component is indicated by green ones. In conclusion, we found that the microsphere CROW of 30°- and 60°-branched structures fabricated by a self-assembly technique on a lithographically patterned substrate acts as a kind of micro-demultiplexer. Our results suggest that the microspheres’ branching chain itself has a splitting function, which splits the WGM and NIM components. This microsphere branching chain can be applicable to fabricate smaller demultiplexers in optical circuits than those of the photonic crystal waveguide16, 17 since the microsphere chain has no cladding region. Fabrication of Microsphere CROWs: The aqueous dispersions of polystyrene microspheres were purchased from Duke Scientific Corp. (Palo Alto, CA). The microspheres were 2.001 ± 0.025 μm in diameter, with 1.2% variation coefficient, a density of 1.05 g cm−3, and a refractive index of 1.59 at 589 nm. The mean diameter of the microspheres was certified by the National Institute of Standards and Technology (NIST). The fluorescent microspheres were also made of polystyrene and were green-dyed with a wavelength emission maximum of 508 nm. The mean diameter of the fluorescent microspheres was nearly equal to that of the nonfluorescent microspheres. The fluorescent microspheres were combined with the nonfluorescent microspheres by mixing the two dispersions at a mixing ratio of 1: 700. This mixture of dispersions was diluted with pure water, and the concentration of dispersed microspheres was adjusted to 0.3 wt%. This colloidal suspension was put inside the gap between the substrate and the glass coverslip, and then slowly evaporated under conditions of controlled temperature (22 °C) and humidity (∼40%) in an automatically controlled box. NSOM Observation and FDTD Simulation: To excite fluorescent microspheres, a 406 nm laser light from a GaN-based semiconductor laser diode (Neoark Corp., Hachioji, Japan) was used. Fiber probes were fabricated from a multimode optical fiber by melting and pulling techniques. The nominal aperture size was 300 nm. The fiber was bent, and was equipped with NSOM (MultiView4000, Nanonics Imaging Ltd., Jerusalem, Israel) as a cantilever. Since the bending angle of the fiber probe we used was rather low (∼45°), we could collect both TM and TE polarized lights.29 The distance between the probe and specimen was kept constant by a tapping-mode feedback system. The detection system of light was assembled by Horiba Ltd., Tokyo Japan, and the CCD multichannel detector used in this study was iDus DV420A-0E of Andor Technology (Belfast, Northern Ireland). FDTD simulation was performed by the FDTD Solutions system of Lumerical Solutions, Inc. This study was carried out as a collaborative project between the Institute of Multidisciplinary Research for Advanced Materials of Tohoku University and the National Institute for Materials Science. This study was financially supported by a Grant-in-Aid for Scientific Research (B) (19310092) from the Ministry of Education, Culture, Sports, Science, and Technology of the Japanese Government.