A thin-film Fabry–Perot filter (FPF) was designed and fabricated to achieve the superprism effect. A polychromatic light, tuned at various incident angles onto the device, was used to attain more demultiplexing channels. This indicates that the FPF, which can be fabricated simply and inexpensively, can be used as a tunable demultiplexing device. Further, the transfer matrix method (TMM) and the Gaussian angular spectrum method were introduced to calculate a more-accurate spatial shift at different wavelengths and to analyze the beam-splitting phenomena in the FPF.
©2006 Optical Society of America
Wavelength-division-demultiplexing devices are used for many applications in optical communication that require components with large numbers of channels and large dispersion [1–3]. Recently, anomalous dispersion and anisotropy properties were observed near the bandgap of photonic crystals (PCs). When polychromatic light is obliquely incident in these structures, a huge deflection that is more than 500 times stronger than in conventional prisms is achieved; this phenomenon has been termed the “superprism effect” [4–8].
One-dimensional (1-D) film acts like a PC, so we chose a FPF to obtain spatial dispersion. This device is fabricated simply and cost-effectively [9,10]. Its small size suggests that it is advantageous for applications in DWDM systems. Furthermore, a fascinating spatial beam shift can be achieved at the output surface. Nevertheless, the drawback of this device is that it can demultiplex only the fixed channels. To overcome this drawback, we tuned the angle of the polychromatic light incident onto the device to change the demultiplexed wavelength range. As a result, tunable spatially separated channels are obtained.
To analyze the spatial shift of different wavelengths, Refs. [11,12] use a Wentzel-Kramer-Brillouin-type (WKB) approximation to calculate the tangential component of the group velocity vgx multiplied by the group delay τg (the total time elapsed from entering the stack to exiting the stack). In fact, this arithmetic does not take into account the properties of incident spots. However, we found in the experiment that the spatial shift depends closely on the size of the beam spots. On the other hand, WKB is more suitable for infinite periodic structures than finite, non-periodic stacks such as FPF. For getting more accurate results, TMM was used to calculate the distribution of the electric field in every layer of the stack, then to obtain the distribution of the total reflected electric field on the interface of the incident medium, and ultimately to get the displacement between the incident and the output beam spot [13,14].
As depicted in Fig. 1, the laser (s-polarization Gaussian beam) is obliquely incident on 1-D PCs, z-axis is the propagation direction, and x-axis is the direction perpendicular to the propagation direction. Here nj was assumed as the refractive index of the j th layer, dj as the physical thickness of the j th layer, and θi. as the incident angle of the central plane wave.
At first, the incident field of the Gaussian beam can be expressed as
where is the Gaussian spectrum that carries the information on the shape of the footprint centered at x=0, z=0. The tapering parameter g indicates the width of the Gaussian beams. The incident beam is centered about k⃗i = x⃗kix + z⃗kiz = x⃗k 0 sin θi + z⃗k 0 cos θi. Now the total electric field distribution in each layer can be written as a sum of the +z and -z direction plane waves as follows :
and the distribution of magnetic field can also be calculated. The amplitude Aj represents all wave components that have a propagating velocity component along the direction, and Bj represents those with a velocity component along the direction.
Using TMM, we have
From Fig. 1, we can get B0=1, Am+1=0
where M 0m+1 =M 01 ⋯M (m-1)mMm(m+1), and then the field distribution in every layer can be calculated.
3. Design and fabrication
The sample of FPF was deposited by e-beam evaporation with high-index material (TiO2) and low-index material (SiO2). The total physical thickness of the thin-film stacks was 3.66 μm arranged as Air| (HL)5 H 6L H (LH)5 | Sub, where H and L were quarter-wave layers of TiO2 (2.077 at 867 nm) and SiO2 (1.437 at 867nm), respectively, and Sub represented glass substrate BK7 with the refractive index of 1.52 at 867 nm. The physical thickness for each layer was monitored by the optical method and the background vacuum was 2.0E-3 Pa, while the partial pressure of oxygen was 1.8E-2 Pa. Meanwhile, the substrate was heated to 300°C. To meet the requirement of the output wavelength of the tunable laser in our experiment, the center wavelength for a stack at normal incidence was designed at 867 nm. The measured peak transmittance of our sample was 67% at the center wavelength and FWHM was 4 nm at normal incidence.
The setup for the measurement of the superprism effect in FPF is shown in Fig. 2(a). The change of the incident light wavelength was achieved by using a tunable Ti: sapphire laser (Tsunami Model 890); the beam from the tunable laser was attenuated by several prisms and focused by the lens to obtain a small light spot. Then the light spot in s-polarization was obliquely incident on the sample and one 1/3 inch charge-coupled device (CCD) array (MTV-03X10HC) was used for recording the position information of the light spot after exiting the thin-film stack as depicted in Fig. 2(a). To realize a large spatial separation, the CCD camera was arranged on the same side as the incident beam to detect the reflected spots. The data of detected images were processed by the Gaussian fitting method on a computer.
We can ascertain the center position of the light spot, and thus get the distance of the output beam spots at different wavelengths caused by the superprism effect.
As shown in Fig. 2(b), the value of measured shift Smeas can be obtained by processing the images obtained by CCD. In the spatial dispersive shift calculated by Sx = (Smeas - S 0)/cos(θi), θi is the incident angle of the beam and S 0 = 2Lsub∙tan(θi) cos(θi), where Lsub is the thickness of the substrate. The measurement was performed for θi = 55.2°, and the detected images of the output spots at different wavelengths are shown in Fig. 3(a).
When the wavelength increased from 730.25 nm, the left spot, which was caused by a weak reflection at the air-substrate surface, did not change position with the wavelength and was taken as the benchmark. The other spot was split into two spots as a function of the wavelength. The explanation is that the incident Gaussian beam has finite beam width and, in practice, the incident light beam is a light cone with incident angles in the range[θi - δ,θi + δ]. The spatial shift would achieve its maximum at the central angle θi and would decrease rapidly when the angle is changed, since the superprism effect in FPF is very sensitive to the incident angle. This explanation also can be proved by the previous arithmetic and the splitting distance can also be calculated when the δ is determined.
Figure 3(b) gives the measured spatial shift (solid curve) and the theoretically simulated spatial shift (dashed curve). Some differences between the experimental curve and the numerically simulated one are caused by the instability of the laser, the difference between an ideal FPF and the actual fabricated one, as well as some other errors in the experiment. At the same time, the experimental result shows that the device has higher spatial resolution than that of the conventional component, such as grating and prism in the DWDM system, and the applied wavelength ranges from 730.58 nm to 732.08 nm.
The same process is also operated for θi = 50.8° and θi = 44.6°. Their respective measured spatial shift and simulated results are given in Fig. 4, and their applied wavelength ranges from 747.01 nm to 749.25 nm in (a), and 769.9 nm to 772.06 nm in (b).
As the experimental results show, the FPF can be employed to realize spatial separation at different wavelengths and be used as a tunable spatial demultiplexer when the incident angle is varied. Thus, many more channels can be demultiplexed by a smart device such as the FPF. The device is simple to fabricate and convenient to integrate, as shown in Fig. 5. It can also get a much larger spatial shift than with conventional components such as the grating or prism. Meanwhile, this flexibility in device design and the remarkable spatial dispersion properties are interesting for optical communication systems and might lead the way to other novel systems.
This work is supported by the National Natural Science Foundation of China, Grant 60478038.
References and links
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