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By utilizing a vector network analyzer, the field distributions on the surface of a three-dimensional woodpile photonic crystal with a straight waveguide or a bend waveguide buried under the surface were measured in the microwave regime. The information of field profile and propagation characteristics of the guided modes can be successfully extracted from the surface near-field measurement. This work indicates that the near-field detection can become a promising means for experimental characterization of three-dimensional photonic crystal devices in supplement to the usual transmission spectrum measurement.
©2007 Optical Society of America
1. Introduction
Photonic crystals (PCs) have the capability to control the propagation of light. They have opened the way to a wide range of integrated optical components that are of crucial importance for new telecommunications applications that rely heavily on devices such as waveguides [1–5] or microcavities [6–9] to control the transmission and the exchange of optical data. The characterization of such devices is generally based on the analysis of the transmitted or the scattered light, meaning that often only the global nature of the device is probed. So far, the main research method is to measure the transmission spectrum, especially for three-dimensional (3D) photonic crystal study. However, transmission spectrum usually does not embody the detailed wave propagation characterization and field information. Since the most interesting features of these components stem from their ability to confine optical fields, it is important to study how light interacts locally with the component. One efficient way to probe the local optical properties of the component is to use scanning near-field optical microscopy (SNOM). [10] SNOM is to move a probe tip in the range of the evanescent field (thus in the proximity of the sample surface) and collect the information of the evanescent field. In the near-field zone, there are two field components: one is the propagation wave, the other is the evanescent wave. The evanescent wave can reflect the very subtle information of light interaction with the local surface of certain objects. As a result, by collecting the evanescent wave information, SNOM can have very high spatial resolution that far exceeds the diffraction limitation. Several groups have reported SNOM investigations of two-dimensional photonic crystal slabs. [11–22] Recently Lu et. al realized the field distribution scanning on the imaging plane and object plane for two-dimensional and three-dimensional microwave photonic crystal negative refraction by a vector network analyzer. [23–26] In this work, we used an Agilent vector network analyzer to scan the surface of a woodpile 3D PC in which a straight waveguide or a bend waveguide was shallowly buried to investigate the propagation characterization and field mode information of microwave in these waveguides.
Fig. 1. Schematic structure of (a) the woodpile 3D PC; (b) an x-type straight waveguide by removing a single rod in xy plane; (c) a bend waveguide as depicted by the red color in xy plane
2. Experimental setup
The crystal shown in Fig. 1(a) consists of square shaped alumina rods with a refractive index of 3.0 and dimensions of 0.32cm×0.32cm×30cm. The center-to-center separation between the rods is a=1.1cm and the filling ratio of rods is about f=0.29. The band gap along the rod extension direction extends from 10.9 to 13.5 GHz, and the complete band gap lies in the range between 11.1 and 13.3 GHz. As described in reference [5], waveguides in the 3D woodpile PC structure can be generally classified as 3 kinds: x-type, y-type and z-type. In this paper, we focus on the x-type waveguide as shown in Fig. 1. The straight x-type waveguide in xy plane shown in Fig. 1(b) is formed by removing one single rod. The bend waveguide in xy plane shown in Fig. 1(c) is formed by removing one section of one rod in one layer and removing one section of another rod in the adjacent layer above. There are 16 layers, namely, 4 cells, under the layer containing waveguides. Above the layer containing waveguides, we can add layers layer by layer according to the scanning result, and see how the field pattern changes. In general, the layer number can not be too many because if waveguides were buried too deeply, the localized field information cannot be detected due to the too strong inhibition of wave propagation by the band gap of this 3D PC and thus too weak field signal at the surface.
We built a microwave field scanning setup based on the Agilent vector network analyzer. The source is a dipole antenna connected to the network analyzer. The detector is another dipole antenna fed back to the network analyzer. The detector is mounted on an XYZ scanner to map the electric field. The minimum scanning step of the scanner is 1μm. A custom program was developed to synchronize the scanning and measurement. In our measurement, we set the frequency ranging from 11.0 GHz to 13.5 GHz, during which data at 801 frequency points were extracted. The scanning step was 2 mm. and the S-parameter value, S21, was measured, which corresponds to the transmission coefficient. In the experiment, the source antenna was inserted into the waveguide and the detector antenna was placed 1 mm away from the upper surface of our woodpile 3D PC, which allows for detection of the microwave near-field signals. We mapped the field distribution using the X-Y robot. If we want to measure the transmission spectrum, it will be all right to insert the detector antenna into the other port of the waveguide.
Fig. 2. The transmission spectrum of x-type straight waveguide (black line) and x-type bend waveguide (red line)
3. Results and discussion
We first measured the transmission spectra of the straight waveguide and bend waveguide to determine the frequency range of waveguide band. The results are shown in Fig. 2, respectively. The straight waveguide lies in the 17th layer (counting from the bottom side) of a total 34-layer crystal, and for the bend waveguide the input waveguide lies in the 17th layer and the output waveguide lies in the 18th layer. The straight waveguide band ranges from 11.696 to 13.284 GHz. The bend waveguide band ranges from 11.637 to 13.145 GHz. Therefore, the bend does not cause too much change on the frequency range of pass band except that the transmission efficiency of the bend waveguide decreases comparing with the straight waveguide. A careful design of an optimal bend section structure is expected to improve the transmission efficiency of such a bend waveguide. When scanning the field distribution, the frequency range was set as 11.0GHz ~ 13.5GHz , and this can guarantee that there exits modes in the waveguides.
After determining the frequency range, we performed the near-field scanning. We measured many cases, where the covering layer number above the waveguide changes gradually, from 3 layers to 4 layers, 5 layers, 6 layers, 7 layers, 8 layers and more. It is found that 7 layers is the optimal layer number to obtain the clearest waveguide localized field distribution. When the covering layer has less layers, especially less than one cell, 4 layers, the upper wall of the waveguide has poor confining capability. Stable localized waveguide mode cannot form in the waveguide and the field will scatter and disperse away from the waveguide central axis to a large area. As a result, the field almost homogeneously distributes on the scanning plane, and it cannot distinguish the waveguide mode field. However, when the covering wall is too thick, the localized degree of the guided mode is too high to transfer the waveguide mode field information across the covering wall to the surface of the photonic crystal. The calculated field patterns for the xz center-axis plane of the input and out waveguide clearly support this point. Figure 3(a) and (c) display the calculated field patterns in the xz center-axis plane of the input and output waveguide by the finite-difference time-domain (FDTD) method, respectively. For visual convenience and clarity of comparison, Figure 3(b) and (d) show the field patterns together with the structure contour of the photonic crystal corresponding to Fig. 3(a) and (c), respectively. From Fig. 3(a)–(d), it can be seen that the field at a certain position outside the waveguide decay suddenly to an extremely weak intensity. A close examination at the data of field profile shows that the suddenly decaying position is just 7 layers away from waveguide axis. This distance can be set as the effective modal width of the waveguide mode. Therefore, it is not surprising that both the experimental and theoretical results indicate that the optimal scanning plane is 7 layers above the waveguides.
Fig. 3. Calculated field patterns: (a) for the xz center-axis plane of the input waveguide without the structure contour of the photonic crystal; (b) for the xz center-axis plane of the input waveguide with the structure contour; (c) for the yz center-axis plane of the output waveguide without the structure contour; (d) for the yz center-axis plane of the output waveguide with the structure contour.
Figure 4(a) and (b) show a typical result of the scanned and simulated field distributions for a straight waveguide with 7 covering layers at the frequency of 12.95 GHz. The scanned and simulated results are consistent with each other. The result of Fig. 4 shows that the propagating wave is well confined to the waveguide channel and has a dominant stationary mode configuration. The scanned field can well reflect the intrinsic characteristic of localized optical field and propagation property of the photonic crystal waveguide mode. From Fig. 4 one can also find that the near field exhibits a certain degree of dissipation away from the waveguide center. This dissipation is much more pronounced than at the waveguide layer. The reason is that the observation plane is 7 layers away from the waveguide axis. Strictly speaking, the current measurement is not the true near-field detection in regard to the waveguide axis. Nonetheless, our experiments clearly show that it is possible to diagnose and discern buried functional structures by collecting the information of fields at the surface of a photonic crystal. The near field observation offers a promising way for efficient optical characterization of photonic crystal devices in addition to the usual optical transmission measurement.
Fig. 4. (a) Scanned field distribution of a straight waveguide at the frequency f=12.95 GHz with 7 layers covering above the waveguide layer. The dotted line represents the contour of the rods. (b) The simulated field distribution of waveguide at f=12.95 GHz with 7 layers above the waveguide layer. The field intensity is in unit of dB in (a) and (b).
Fig. 5. Experimental and theoretical results of the near-field patterns at the surface plane with 7 covering layers and 8 covering layers at the frequencies correspond to Peak a, Peak b and Peak c in Fig. 2. The field intensity is in unit of dB in (a) ~ (l).
We have considered a wide range of detection frequencies of microwave for this straight waveguide structure. Through systematic experimental measurements and theoretical calculations, we find that the major characteristics of field patterns are basically the same for each frequency within the frequency range of one oscillation peak in the transmission spectrum curve in Fig. 2.
Now we proceed to investigate the bend waveguide structure that is embedded in the 3D woodpile photonic crystal. Figure 5 presents the experimentally scanned and theoretically calculated field patterns at the surface plane of a buried bend waveguide with 7 and 8 covering layers, respectively. Frequencies at the three typical oscillation peaks: Peak a (12.22 GHz), Peak b (12.6 GHz), and Peak c (13.03 GHz) are considered.
Because the bend waveguide is composed of two waveguides which are positioned at two adjacent layers, the position of the optimal observation plane that is the 7th layer above the two waveguide layers is different. Consequently, we considered two photonic crystal structures in our field measurement experiments and simulations: one has 7 covering layers above the input waveguide layer [see the cases in Fig. 5(a-f)]; the other has 7 covering layers above the output waveguide layer, or equivalently 8 covering layers above the input waveguide layer [see the cases in Fig. 5(g-l)]. We can see that for different oscillation peaks the field pattern exhibits different features, especially at the bend section of the waveguide. As we know the oscillation of the transmission spectrum is caused by Fabry-Perot interference that originates from the reflection at the two ends of the waveguide. The different field patterns indicate that the propagation behavior of wave within the bend waveguide is very different for different oscillation peaks. The field pattern of Peak b clearly shows a strong localization of field intensity and an obvious radiation pattern centered around the bend section. In contrast, the field patterns for Peak a and Peak c do not exhibit such a feature. These features indicate that Peak b might correspond to a cavity state of the bend section that is excited by the incident guided wave. It is known that a cavity mode can radiate field all around the space, leading to a dispersed field pattern that is consistent with Fig. 5(b) and (h). The strong radiation effect at the bend section will cause a high propagation loss and reduce the power of electromagnetic waves entering the output waveguide channel. Therefore, through scanning the near-field, the propagation process and form of electro-magnetic wave in waveguide are clearly illustrated. Comparing the experimental results and theoretical results, one can find that the main features in the theoretical results have been embodied in the experimental results. The fairly good agreement between theory and experiment further supports the idea that the near-field measurement can become a useful technique to probe the detailed information about field profile characteristics and wave propagation behavior for photonic crystal waveguides.
4. Summary
In summary, by using the network analyzer we have measured and analyzed the near-field distribution on the surface of 3D microwave woodpile photonic crystal structures with a straight waveguide and a bend waveguide shallowly buried under the surface. It is found that the measured near-field information can well reflect the major features of the internal field profile at the waveguide layer, such as the strong confinement of optical field around the waveguide axis, the propagation behavior of electromagnetic waves through a waveguide bend, and the scattering of optical fields by the sharp bend section and their dispersion away from the bend section into the surrounding space. Our work indicates that the near-field scanning technique can offer a promising means to probe the detailed information about the field distribution and wave propagation behavior within photonic crystal devices, and it can become a very useful supplemental tool to the usual analysis method of transmission spectrum measurement for these integrated optical devices. Combination of the two analysis tools can help to bring a deeper insight into the optical properties of these devices.
Acknowledgments
The authors would like to acknowledge the financial support of the National Natural Science Foundation of China at Nos. 10404036 and 10525419, and the National Key Basic Research Special Foundation of China at No. 2006CB921702.
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