1. Introduction

Recently there has been extensive interest in realizing anomalous propagation behaviors of light such as negative refraction [1–4] in optical frequencies by means of deliberately designed artificial optical nanostructures. The first experimental realization of negative refraction was made by Shelby et al. in microwave frequencies by using a periodic array of copper wires and splitted–ring resonators [5]. Recently Zhang and coworkers showed that metamaterials composed of cascaded ‘fishnet’ structure [6] or silver nanowires [7] could exhibit negative index of refraction in optical frequencies. However, these metamaterials always involve some metal cells and are subject to strong energy dissipation and absorption loss in optical frequencies. An efficient way to surpass the loss problem is to use dielectric photonic crystals (PhCs) with specially designed band diagrams and equifrequency surface (EFS) contours, which allow one to realize various anomalous propagation properties such as negative refraction, superlensing, and self-collimation [8–14].

Deliberate control of the anomalous optical properties requests high precision construction of PhC structures. Microfabrication technologies such as electron-beam lithography or focused ion beam lithography are excellent candidates for this purpose as they allow drilling of air holes or other subtle nanostructures on silicon-on-insulator (SOI) wafer with accuracy on the order down to 1 nm. Several groups have reported design and realization of two-dimensional (2D) PhC structures on low-index contrast InP/GaInAsP/InP heterostructure [15, 16] or high-index contrast silicon-on-silica slab [17] and air-bridged silicon slab [18–20] that exhibit negative refraction for infrared light at around 1.55 µm.

In order to see whether full understand and control of the delicate optical properties for these negative refraction PhCs have been achieved elaborate and exhaustive optical evaluation and characterization must be implemented on the nanoscale with high precision. A high-resolution optical picture about the ray trace of an infrared light beam within the PhC structure can greatly help to disclose convincingly the unambiguous presence of negative refraction of light. So far, successful examples toward this fundamental cause are quite limited. In [18–20] the ray trace picture was observed via conventional microscope. The resolution is diffraction limited and is not able to probe the delicate information. In [16, 17] negative refraction pictures were observed by using scanning near-field optical microscopy (SNOM) technique, which in principle should allow much finer details of the race trace to be revealed. In [16], the ray trace of light in a low index contrast InP/GaInAsP/InP structure was probed, while in [17], the transmitted beam was probed in the Si/SiO2 PhC structure. In our current work, we successfully realize and visualize negative refraction of infrared light in an air-bridged silicon slab by means of SNOM technique. The structure allows for strong confinement of infrared light on the slab. Furthermore, it has a symmetric geometry that supports the TM-like and TE-like eigen modes, which can be excited and probed individually.

 

Fig. 1. (a). Photonic band structure of TE-like and TM-like bands for an air-holes square-lattice PhC slab with the air-hole diameter 0.478a (a is the lattice constant), the thickness and refractive index of the slab as 0.478a and 3.4, respectively. The normalized frequency area indicated by the red dotted lines shows the experimentally available wavelength range. (b) EFS contours of the TE-like second band for the same PhC show that negative refraction can occur in the direction around the ΓM direction.

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The paper is organized as follows. In section 2 we analyze the band structures and EFS contours of 2D air-bridged PhC slab structures, from which we can find the appropriate geometric configuration and wavelength range in which negative refraction can occur. In section 3 we continue to investigate how incident infrared light propagates in the designed PhC structure by means of three-dimensional (3D) finite-difference time-domain (FDTD) [22] simulation. A special interface layer is designed to facilitate high-efficiency coupling of light from the input linear silicon waveguide to the negative-refraction PhC structure. This feature is important for successful experimental realization and visualization of negative refraction properties. In section 4 we fabricate the designed PhC structure and characterize their optical properties by means of conventional far-field optical microscope and SNOM. The SNOM experiment unambiguously demonstrates that negative refraction of light indeed takes place in the designed 2D air-bridged PhC structure at telecommunication frequency (1.55 λ=µm). We have overcome several technical obstacles and clearly observed high-resolution negative refraction ray trace of pure TE-like modes inside the PhC structure. In section 5 we briefly summarize this paper.

2. Photonic bands and equal-frequency surface contours

In order to find an appropriate 2D air-bridged PhC slab structure that exhibit high-performance negative refraction properties, we first make a systematic numerical simulation and analysis of the band structures and EFS contours. The simulation results indicate that a PhC structure composed of a square lattice of air holes can show such properties when its surface normal is along the (11) crystalline direction of the square lattice. In other words, the incident light must be shined upon the (11) surface of the PhC structure. The geometric and physical parameters of a typical negative-refraction PhC slab structure that we design are as follows: the air hole diameter 2r is 0.478a, where a is the lattice constant, the thickness of the PhC h is 0.478a, and the refractive index of the background slab n is 3.4.

 

Fig. 2. Schematic view of the negative refraction PhC structure. (a) Top view of the whole structure with the waveguide and PhC structure with tapered air-hole interface that helps to reduce impedance mismatch. Detailed geometric parameters of the interface layer are depicted explicitly in the picture. The surface normal of the PhC structure is along the ΓM direction. The angle of incidence is fixed at 10°. (b) Side view for the same structure shows clearly the air-bridged geometry formed by using HF wet etching.

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We show in Fig. 1 the band diagram and the EFS contours calculated by 3D plane wave expansion method [21]. Figure 1(a) gives the band diagrams of TE-like and TM-like modes. Figure 1(b) shows the EFS contours of the second TE-like band that is explored to create negative refraction. In a PhC structure, the Poynting vector S is determined by the gradient of the EFS contours. The EFS contours are roughly circular around the ΓM direction at the reduced frequency (a/λ) range 0.2850~0.3156, as indicated in the red dotted line frame in Fig. 1(b). Γ=(0,0)(π/a) and M=(1,1)(π/a) are high-symmetric points in the first Brillouin zone. When the frequency increases, the EFS contours move toward the Γ point, which indicates existence of negative refraction in the regime. If the incident light is mainly parallel to the ΓM direction, the PhC will behave like an isotropic medium with a negative index of refraction in that particular frequency range. Meanwhile, in this frequency range the PhC behaves like an ordinary right-hand material for TM-like modes and no negative refraction occurs. In our case, the SOI wafer has a 220 nm thick silica top layer and 3 µm buried oxide layer, so we choose the following parameters of the 2D PhC as a=460 nm, r=110 nm (i.e., 2r/a=0.478), and the wavelength range at which negative refraction can occur is 1457–1614 nm.

 

Fig. 3. 3D FDTD simulation of the field intensity distribution in the xy plane at 1503 nm. A ray tracing is superimposed on the structure to illustrate the direction of the light. (a) Light intensity distribution of TE-like modes for PhC without tapered air-holes interface. (b) Light intensity distribution of TE-like modes for PhC with deliberately designed tapered air-holes interface. (c)Light intensity distribution of TM-like modes for PhC with tapered surface.

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3. Design and simulation

Based on the above analysis, we simultaneously designed an air-bridged PhC and an air-bridged wire waveguide based on SOI wafer, as schematically shown in Fig. 2. The surface normal of the PhC structure is parallel to the ΓM direction. The input silicon wire waveguide is inclined with respect to the surface normal by 10°. This angle is within the space orientation range in which negative refraction can occur, as can be referred to Fig. 1(b). The high index contrast air-bridged structure can achieve good optical confinement for the TE-like guided mode, but it also induces serious impedance mismatch that leads to strong reflection and scattering at the interface between the input waveguide and the PhC, as has been found in our 3D FDTD numerical simulations. To surpass this obstacle, we have designed a tapered air-holes connection layer at the input surface of the PhC structure, as shown in Fig. 2(a) to effectively reduce the reflection and scattering losses [18, 19]. The tapered air-holes grating structure has an effective refractive index that gradually varies to match with the input waveguide in one end and with the PhC structure in the other end. We used 3D FDTD method to simulate the electromagnetic field intensity distribution at wavelength 1503 nm of the whole device. Figure 3 shows the calculated results of light intensity pattern in the central xy plane of the silicon slab. Light from the source couples into the input waveguide and propagates along the waveguide, then incident on the PhC. Figure 3(a) shows the light intensity distribution for an ordinary structure without the tapered air-holes layer. One can clearly see that very little energy of light is coupled into the PhC structure from the incident line waveguide and the field pattern is so weak that it is hard to identify whether positive or negative refraction happens here. In contrast, as is clearly displayed in Fig. 3(b), the situation is greatly improved by using the tapered air-holes interface. A large fraction of light power from the input waveguide is coupled into the PhC structure and negative refraction of light beam within the PhC structure is clearly seen. Besides, the reflection or scattering of light at the input interface of the PhC is very much reduced. This clearly indicates that the designed tapered interface can reduce the interface impedance mismatch remarkably. The calculated value of negative refraction angle is -45°. On the other hand, ordinary positive refraction only occurs for TM-like modes, as is obvious from the field pattern in Fig. 3(c).

 

Fig. 4. (a). SEM picture of the PhC structure and an input waveguide. The width of the waveguide d is 2 µm. (b) Schematic of the near-field experimental setup.

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4. Experimental results

We fabricated a device following the simulated PhC structure. A 2 µm wide silicon wire waveguide (also with the air-bridged geometry) close to the interface of the PhC is used as the input infrared light beam channel. The air holes are directly written by focused-ion-beam milling and the air-bridged structure was formed by HF wet etching [23]. Figure 4(a) shows the scanning electron microscopy (SEM) picture of the fabricated PhC with the input silicon wire waveguide launching the input infrared wave along the ΓM direction of the PhC. The PhC sample has a size of about 25 µm in width and 15 µm in length. The input wire waveguide is set to incline with respect to the surface normal of the PhC sample by 10°. At the far end of the PhC structure, an air slot is introduced for the sake of optical observation.

 

Fig. 5. (a) Directly observed pattern of the radiated light of 1500 λ=nm from the top using an objective lens. (b) SNOM picture of the negative refraction of the same wavelength. In each picture, the boundary of the PhC structure is superimposed as solid lines.

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In our measurement, TE-polarized light from a tunable semiconductor laser (1500–1640 nm) was first launched into a tapered single mode fiber, then coupled to the silicon wire waveguide, and finally incident on the PhC structure. The schematic configuration of the experimental setup is depicted in Fig. 4(b). A polarizer controller was used to select a particular polarization mode (here the TE-polarization mode) in the optical fiber. The ordinary way to see the light propagation behavior is to directly observe the pattern of the radiated light from the top of the sample using a conventional microscopy objective and an infrared camera. The result is shown in Fig. 5(a). The light spot at the middle bottom part of the pattern is the radiated light from the input silicon wire waveguide. The big light spot at the center represents the scattered light at the interface between the input wire waveguide and the PhC due to impedance mismatch. There is also a small bright spot at the top right corner of the pattern, and it is recognized to result from the radiated light when the negative refraction beam hits the end facet of the PhC structure. Because the TE-like modes are strongly confined guided mode on the silicon slab and the surface fields are nonradiative and evanescent with respect to the vertical direction of the PhC slab, the far-field pattern observed and recorded by the ordinary optical microscope is not able to reveal the detailed process about how the negative refraction beam propagates inside the PhC structure unless the scattering of light by roughness and irregularity is sufficiently strong on the beam propagation path. This is indeed the case for Fig. 5(a). In fact, the small bright spot could not appear without the intentional introduction of the air slot at the far end of the PhC structure. It would not be possible to tell which way the infrared beam would refract if without the aid of this scattering light spot.

In order to observe clearly and tell unambiguously the ray trace of the negative refraction beam in the PhC structure, we used the SNOM technology (SNOM-100 Nanonics, Israel). A probe scans in the vicinity of the surface of the PhC structure and records the near-field intensity distribution. The tip has a resolution of about 100 nm, i.e., 1/15 of the wavelength. The signal is recorded by an infrared single-photon detector, which allows us to capture very weak infrared signals. The probed near field information directly reflects light propagation properties of the TE-like modes for the PhC and enables one to visualize the ray trace of the negative refraction light beam. This is because the near field at the surface is an integral part of the modal profile of the confined guided modes that exponentially decay away from the surface of the slab. We plot the SNOM picture [Fig. 5(b)] together with the directly observed microscopy pattern to facilitate a direct comparison. In the SNOM picture, a bright spot also appears at the front interface of the PhC structure, but it is much smaller than the one in Fig. 5(a). The ray trace of the incident light beam along the silicon wire waveguide and its propagation along the negative refraction direction inside the PhC structure can be clearly seen. The negative refraction angle is about -45°, which is in good agreement with the FDTD simulation presented in Fig. 3(b). The SNOM detection unambiguously discloses the negative refraction property of the designed PhC.

We recorded a variety of SNOM pictures of TE-like mode infrared light propagation in the device for wavelength range from 1500 to 1620 nm. A clear negative refraction beam is observed for wavelength range from 1500 to 1599 nm. The negative refraction feature of infrared light beam becomes much degraded, although still observable, when the input wavelength increases to 1600 nm, as shown in Fig. 6(c). The clear reason for this abrupt change is yet to be discovered by more detailed theoretical and experimental investigations. Our previous work [10] has shown that the negative refraction regime in a 2D PhC structure can transit to the ordinary positive refraction regime by crossing a narrow frequency window of self-collimation. The observed phenomenon of abrupt change might correspond to such a narrow transition window. When the input light wavelength further increases, negative refraction completely disappears, as indicated in Fig. 6(d). Because the minimum wavelength of our laser is 1500 nm, we did not observe SNOM patterns for wavelengths less than 1500 nm. Therefore, the wavelength range in which negative refraction can occur in the designed PhC structure should be broader than 99 nm.

 

Fig. 6. (Color online) SNOM pictures of electric field intensity distribution for different wavelengths. The boundary of the PhC structure is superimposed as solid lines.

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5. Conclusion

In conclusion, we have designed and fabricated a 2D air-bridged silicon PhC structure that exhibits negative refraction for TE-like guided modes at wavelength around 1550 nm. Experimentally we directly measured high-resolution pictures of the ray trace of light beam by using SNOM technology and clearly observed negative refraction of light in the designed PhC structure for TE-like confined modes in a broad wavelength range from 1500 to 1599 nm. On the other hand, ordinary positive refraction only occurs for TM-like confined modes, so the designed PhC structure can behave as an efficient beam splitter in an integrated optical circuit. The high-resolution SNOM technology can greatly help one to directly visualize the ray trace and acquire deeper understanding on various anomalous wave propagation behaviors such as super-prism, superlensing, self-collimation, and slow light in deliberately designed 2D PhC slab structures in the optical wavelengths. This in turn can help one to explore a wider regime of controlling light behaviors on the nanoscale for future basic science and high technology applications.