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We present the experimental demonstration of imaging of a point source by negative refraction at near-infrared frequencies using a hybrid photonic crystal device. The photonic crystal device, fabricated by patterning holes in 260nm silicon-on-insulator, integrates a triangular-lattice photonic crystal with a large photonic bandgap and square-lattice photonic crystal with negative refraction. Experimental results show that the output of a line-defect photonic bandgap waveguide provides a nearly ideal point source and then is imaged through the photonic crystal by negative refraction.
©2007 Optical Society of America
1. Introduction
Recently, the work on metamaterial [1] and “perfect lenses” [2] revived Veselago’s left-handed materials [3] and triggered intensive discussion on them. Meanwhile, negative refraction and imaging by negative refraction [4, 5, 6] were also demonstrated using 2D photonic crystals (PhCs) by dispersion-engineering. More recently, we experimentally achieved subwavelength imaging by a 3D PhC flat lens exhibiting full 3D negative refraction [7, 8]. However, most of the work was carried out in the microwave regime. Similar results are also envisioned in the optical regime, e.g., near infrared (NIR) or visible light, by down-scaling the dimensions of suitable structures. As a matter of fact, most of the PhC structures demonstrated in the microwave regime were originally proposed for visible light applications. However, due to fabrication and observation challenges some of the corresponding results have not been realized in the optical regime. For 3D negative refraction imaging in visible light or NIR regime, the main challenge lies in 3D nano-structure fabrication, which is extremely difficult to achieve using current technologies. The development of advanced fabrication techniques may address this issue in the future. For the time being, 2D nano-PhCs can be readily fabricated in a large variety of materials. On the other hand, for demonstration of 2D negative refraction subwavelength imaging in visible light or NIR regime, there are still challenges in constructing a device to provide an ideal point source, which is also the object of the imaging system, and finding an approach to observe the imaging process inside a planar device.
Fig. 1. (a). The band structure of the triangular-lattice PhC to achieve the PBG waveguide. (b). The simulation of light (amplitude) propagating in the PBG waveguide.
The first experimental evidence of negative refraction at NIR wavelengths by a PhC was reported by Berrier, et al [9]. In their work, a conventional waveguide on the object side is used as the feed of a point source (object and input) and another waveguide on the image side works as a detector. The evidence of negative refraction imaging was obtained by measuring the transmission at different frequencies because good imaging gives rise to high coupling efficiency. Direct verification of imaging of a point source by negative refraction using a PhC at NIR frequencies was achieved in recent work [10], where a tapered waveguide is used as the feed of a point source (object) and an array of waveguides as detectors for the image field, and the image size was achieved to be 1.7λ. In order to demonstrate subwavelength imaging, a precondition is to supply a subwavelength object. The size of point objects provided by conventional waveguide feeds is often larger than λ due to the deterioration by leakage radiation and sidewall roughness.
Herein, we propose a line-defect photonic bandgap (PBG) waveguide to achieve a nearly ideal point source (object) and demonstrate negative refraction imaging of a point source at NIR frequencies using a hybrid PhC device that employs two dispersion properties of PhCs, namely photonic bandgap and negative refraction.
Fig. 2. Dispersion diagrams of the square-lattice PhC designed to achieve negative refraction imaging. The lattice constant is a and air hole diameter is 2r=0.85a. The equi-frequency dispersion contours extend over the first and second Brillouin zones.
2. Design and simulation of the device
To achieve high index contrast and thereby photonic bandgaps and negative dispersion, the device is designed in a 260 nm silicon-on-insulator (SOI) slab. A J-coupler [11] is used to couple light from a conventional waveguide into the PBG waveguide and to change propagation direction 90° for easy observation. The photonic bandgap is attained in a triangular-lattice PhC with lattice constant a = 560 nm and air hole diameter 2r = 480 nm. It has a very wide photonic bandgap between the first and the second bands, see Fig. 1(a). The photonic bandgap has ideal control over the leakage radiation, so the size of the object is dependent on the width of the defect and can go down to 150nm (0.1 λ) or even smaller as shown in Fig. 1(b). Negative refraction is achieved in a square-lattice PhC with negative curvature of dispersion contours [12]. The lattice constant is designed to be a = 420nm and air hole diameter is 2r = 0.85a. Figure 2 shows the dispersion relation of the PhC and negative refraction is expected at frequency ω = 0.24~0.29 (2πc/a) (centered at λ = 1550 nm).
Two dimensional finite-difference time-domain (FDTD) simulation results verify the feasibility of the design. Figures 3(a) and 3(b) illustrate the design and simulation of the device, respectively. Working wavelength, 1550 nm, and effective index of 260nm-SOI slab for TE modes, 3.0, are applied in the simulation. According to the simulation results, the size of the imaged object from the PBG waveguide is only 210nm. Light emanating from the object is first focused inside the flat lens, and then focused on the other side of the flat lens forming an image. The size of the simulated image is 1.2 μm or 0.76λ.
3. Device fabrication and experimental results
In the fabrication process, we used direct-write electron-beam lithography to pattern the feed waveguide, J-coupler, PBG waveguide, and negative refraction PhC into 260nm-SOI. The pattern, developed in polymethyl methacrylate (PMMA), was transferred into the silicon layer by a dry etching process with an inductively coupled plasma (ICP) system. Figure 4(a) shows the scanning electron microscope (SEM) picture of the device we fabricated. The components as shown from the top to the bottom are the J-coupler, PBG waveguide, negative-refraction PhC, and a 3 μm wide buffer. The width of the buffer is approximately equal to the image distance according to the FDTD simulation. The lattice constants are very close to the designed values, and the air hole diameters of the PhCs are slightly larger than the designed values: 488nm for the triangular-lattice PhC and 373nm for the square-lattice PhC. The fabrication error may lead to frequency shift for observing the optimal imaging. To this end, a tunable laser (Agilent 8164A Light Measurement System) with working wavelengths spanning from 1260 nm to 1640 nm was fed into the device. An NIR microscope and camera captured the scattered light from the device surface at different wavelengths.
Fig. 3. (a). The layout of the hybrid PhC device. (b). The simulation of amplitude for the negative refraction imaging of a point source through the designed PhC.
Figure 4(b) shows the experimental result observed at λ = 1499 nm [corresponding to normalized frequency 0.28— the red line as shown in Fig. 2(b)] when the image is located at the edge of the slab. The J-coupler focuses NIR light from the feed waveguide into the PBG waveguide, then partial light propagates through the PBG waveguide, supplying a point object (labeled as spot 1) for the negative refraction PhC. Due to impedance mismatch, there is light scattered at both ends of the PBG waveguide, and very small amount of light propagates along the interface between the two PhCs. Then, the PhC focuses light from the object and forms another bright spot on the other side of the PhC. The bright spot labeled as 2 is the image of spot 1. By tuning the working wavelengths away from 1499 nm, the spot becomes broader because the negative refraction PhC is highly dispersive and has different imaging distance for different working wavelengths. In other words, at other wavelengths imaging by negative refraction may also occur, but the location of the image is away from the edge. In addition, this spot cannot be attributed to other mechanisms, e.g. self-collimation, because a collimated beam diverges very fast in the buffer area due to diffraction. By comparing the image size with the dimension of the device, the image size is measured to be about λ by full-width at half maximum, and is limited by the microscope resolution. Subwavelength resolution imaging is expected to be observed using near-field scanning optical microscopy (NSOM) technology. Note that most image pixels of the source are saturated due to high light intensity, which makes spot 1 look larger than spot 2.
For comparison, we fabricated another device containing the same components except for the negative refraction PhC, see Fig. 4(c). We repeated the experiment and found that spot 2 disappears at λ = 1499 nm [Fig. 4(d)]. Moreover, we could not observe a bright spot on the image side at any wavelength in the tunable range. This result further confirms that negative refraction is responsible for the formation of the image (spot 2). Although this structure is designed to work for TE modes, negative refraction for TM modes is also achievable by using a triangular-lattice PhC as demonstrated in Ref. [10].
Fig. 4. (a). SEM picture of the device used to demonstrate negative refraction imaging. (b) Imaging by negative refraction using a square-lattice PhC. (c) SEM picture of the device with the negative refraction PhC removed. (d) Radiation from the device shown in (c).
4. Summary
To summarize, in this paper we numerically simulated and experimentally demonstrated negative refraction imaging of a point source in the NIR regime. The results were achieved in a hybrid PhC, which integrated a PBG PhC and negative refraction PhC. Experimental results showed that the output of a line-defect PBG waveguide provided a nearly ideal point object (source), which was then imaged through the PhC by negative refraction.
References and links
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