This paper reports a novel approach to the direct observation of Bloch surface waves, wherein a layer of fluorescent material is deposited directly on the surface of a semi-infinite periodic layered cell. A set of surface nano-gratings is used to couple pumping light to Bloch surface waves, while the sample is rotated until the pumping light meets the quasi-phase matching conditions. This study investigated the directional propagation of waves on stripe and circular one-dimensional grating structures by analyzing the dispersion relationship of the first two eigen modes. Our results demonstrate the efficacy of the proposed scheme in visualizing Bloch surface waves, which could be extended to a variety of other devices.
© 2016 Optical Society of America
The development of photonic crystal structures has prompted interest in Bloch surface states at the surface of semi-infinite super lattice structures . The surface state is located in the bandgap region of one-dimensional photonic crystals [2, 3], and researchers have proposed numerous methods for the computation of mode [4–8]. The roundtrip phase of Bloch surface waves (BSWs) confined to the top layer is highly sensitive to the thickness of the cap layer, due to the effects of multiple reflections from periodic dielectric layers beneath. Thus, the thickness of the cap layer is an important factor in device tuning, with considerable influence over the field distribution and the mode propagation vector in the resulting devices . The complex coupling effect between surface modes at the edges of a two-dimensional photonic crystal and continuum modes in a vacuum were discussed in [9, 10]. In [11, 12], the researchers conducted experiments to observe fine coupling effects between reflections from 1D photonic crystal layers and surface modes. This confined mode features superluminal propagation similar to that of surface plasmon waves at a metal/dielectric interface. Moreover, the all-dielectric environment greatly reduces loss and expands the operating bandwidth . This makes it possible to implement designs involving two-dimensional flat optics utilizing all-dielectric surface states [7, 14–16]. Researchers have developed a wide range of applications involving resonant sensors, which have proven comparable to sensors using surface plasmon waves [17–19]. Near-field scanning optical microscopy has been used to examine Bloch surface waves directly . In this study, we deposited a layer of fluorescent dye as an imaging layer in order to illustrate the propagation paths of BSWs using gratings as a coupling component. The outward emission of rays from the grating region indicates the direction of BSWs. The propagation constant of the proposed structure is based on the formulation proposed in . Our experimental observations are in strong agreement with simulation results. The proposed imaging platform is suitable for the design of two-dimensional optical devices such as BSW waveguides and resonators . This imaging method could also be used in the development of two-dimensional metasurface devices [14, 16].
2. Experiment setup
The structure of the samples used in this study are presented in Fig. 1. As shown in Fig. 1(a), the planar periodic structure comprises layers of TiO2 (n = 2.58 for λ = 532nm) (73nm thickness) and SiO2 (n = 1.5) (119nm thickness), as well as a cap layer of TiO2 (196nm thickness). 1D poly(methyl methacrylate) (PMMA) gratings were produced using electron-beam lithography. As shown in Fig. 1(b), we fabricated two sets of circular gratings with a periodicity of 340nm. One circular PMMA grating was patterned on the 1D photonic crystal substrate and another was patterned on a film of Au (50nm thickness) over a regular glass substrate. A layer of 4-(dicyanomethylene)-2-t-butyl-6-(1,1,7,7-tetramethyljulolidyl-9-enyl)-4H-pyran (DCJTB) dissolved in Tris-(8-hydroxyquinoline) aluminum (Alq3) was deposited on the surface of the sample. The device was then examined using a fluorescence optical microscope (FOM). As shown in Fig. 1(a), we employed a pumping laser at a wavelength of 532nm with TM polarization incidental to the surface of the sample at a specified angle. The stripe grating was rotated until it met the quasi-phase matching conditions.
3. Results and discussion
Figure 2 presents the outward emission of rays, wherein differences in pitch Λ indicate the various incident angles (θ, ϕ) required to meet phase matching conditions. The incident angle θ was set to 58°. The rotational angles ϕ are denoted in the figure caption with a ϕ error range of +/−2°. The outward emission angle is specified as ψ. The grating pitch range from 300nm to 550nm and the length of the grating region is 50μm. The gratings are indicated by white dashed squares and the emission patterns excited by the gratings are in red. The three white lines in the dashed squares indicate the orientation of the stripe gratings. The momentum matching conditions are illustrated in Fig. 2(g). According to the emission patterns, the propagation path of BSW is straight and directional, similar to the propagation effects induced by small defects excited by surface plasmon waves . The coupling conditions are explored later in a discussion of the corresponding dispersion curves.
Figure 3 presents the optical paths through circular gratings excited by BSW and SPP modes, respectively. Figures (a) and (b) were obtained from a 1D PC substrate and an Au thin film substrate, respectively with incident angle θ set to 58°. The horizontal red line in Fig. 3(b) indicates a defect resulting from patterning bugs in the lithography controller. Nonetheless, the directionality of BSW propagation and SPP mode are clearly illustrated. Figure 3(c) presents the intensity profile of the white dashed line. The main paths are denoted as “1” and the unclear paths are denoted as “2”.
We followed the simulation procedures used in  to obtain the correct propagation constant for the proposed substrate, the resolved dispersion curves of which are presented in Fig. 4. The dispersion curves include the curves of a 1D PC-Air interface, 1D PC-PMMA interface and an equivalent asymmetrical slab waveguide, which are later used for comparison. kBSW-air is the propagation k-vector at the air/1D PC interface, whereas kBSW-pmma is the propagation k-vector at the PMMA/1D PC interface. We were unable to obtain a solution for the 1st mode with a wavelength exceeding 610nm because a field with a longer wavelength cannot be fit within the space available in the cap. At 532nm, kBSW-air = 1.18ko (denoted as”dark star” in figure) and the composite k values (using the set incident angle and various grating pitches in Fig. 2) were fitted using Eq. (1) below. A directional beam was created when the composited k values (ranging from 1.17ko~1.23ko) fit to kBSW-air of the 1st mode. Outward emission angle ψ (defined in Fig. 2) was derived according to vector analysis in the k-space, and a comparison of simulation and experiment results is presented in Fig. 5. The emission path is rather difficult to judge due to the blurred boundaries. Nonetheless, it is clear that the principle of momentum matching fits perfectly in this scenario.
At the appearance of the directional beams, the images of pumping light scattering revealed nothing. This corresponds to the fact that the maximum field intensity in this design is located within the cap layer and does not necessarily extend into the air. Figure 6 presents the field profiles of the 1st mode at 532nm (kBSW-air = 1.18ko) and the 2nd mode at 620nm (kBSW-air = 2.22ko), i.e. the emission peak wavelength. We used the term “second” mode for the second set of curves despite the fact that these curves are the first mode for wavelength longer than 610nm. The 2nd mode profile at 532nm is similar to that shown in Fig. 6(b), showing very little field extension into the uniform upper medium. Thus, the k-vectors of the 2nd modes at the two types of interface (BSW-air and BSW-pmma) present similar kx values. The different field distributions of the 1st mode at 532nm and 2nd mode at 620nm facilitate the observation of BSW modes. A higher field amplitude (> 40%) extends into the air region (Fig. 6(a)), thereby guaranteeing pumping light of higher intensity in the fluorescence layer. The lower field amplitude at the cap/ air interface @ 620nm (< 10%, Fig. 6(b)) results in most of the fluorescence being emitted back to the air due to low coupling efficiency in this BSW mode.
One might question whether the proposed BSW modes in Fig. 6 are indeed similar to the modes of the slab waveguide based on a three-layer dielectric scheme. Calculations were performed on the asymmetrical slab waveguide in accordance with the methodology outlined in , from which we derived the dispersion curves of the 1st and 2nd modes, as shown in Fig. 4. The average optical refractive index of the multi-film substrate was ~1.94 (, where t indicates the thickness of the layer). A 197nm cap layer of TiO2 is adjacent to the air. In Fig. 4, kslab-1 = 1.93*ko @532nm (denoted as “bright star”) does not fit our observations of the stripe or circular grating structures. A slab waveguide mode is therefore intrinsically different from a BSW mode in that the former requires total internal reflection at both boundaries whereas the latter is associated with multiple reflections (with a phase shift) from each periodic layer.
Figure 7 illustrates the phase matching conditions of the circular grating on the 1D PC substrate, where the red circle with radius “kG” represents the momentum diagram of the circular gratings, which is shifted horizontally due to a tilt in the incident angle of θ = 58°. The two black circles represent the first two BSW modes @532nm at the Air/PC interface (1.18ko and 2.37ko respectively). The crossing points between the red circle and the two black circles indicate the propagation directions of the excited BSWs within the circular grating. The fitted angles between the propagation directions of the 1st order and 2nd order modes and the horizontal line are respectively designated as θ1 (48°) and θ2 (22°). These values are in good agreement with the emission patterns in Fig. 3(a) with θ1 (49°+/−4°) and θ2 (22.5°+/−1.5°). The ratio of the field exposed to air over the maximum field value within the cap layer is far larger for mode 1 than for mode 2. Thus, the fluorescence emission excited by mode 1 far exceeds that excited by mode 2. As for the SPP mode, the theoretical kspp value at the air/Au film interface presents only one black circle with a radius of 1.09*ko. In this case, the fitted path is at angle (θ1 = 42°), such that the phase matching conditions allow for only two symmetrical directions. As shown in Fig. 3(b), θ1 of the emission path is 41° with error range of +/−2°. Again, the experimental observations of the SPP mode are in good agreement with theoretical computations.
This paper describes the directionality of Bloch surface waves on a 1D photonic crystal substrate, as observed from a layer of fluorescent material. We used the calculated dispersion relationship of BSWs based on the field continuity conditions located in the photonic bandgap region for the examination of emission patterns. We used stripe and circular gratings as coupling elements. This platform could be used to facilitate the design of other two-dimensional planar optical elements.
We would like to thank Prof. Zhaowei Liu from Univeristy of San Diego, California for his input on phase matching diagrams and Prof. Shuo-Yen Tseng from National Cheng-Kung University, Taiwan for discussion on slab waveguide mode. We would also like to thank the Ministry of Science and Technology, Taiwan for funding the project under grant “104-2112-M-110 −007-“.
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