Tapered Fabry-Perot Filter Measures Wavelength
There are many applications of a simple, elegant technique to separate and measure the wavelengths present in an optical signal. Indeed, an important component of the history of spectroscopy has been the ongoing search for improved approaches to spectral analysis. Recently, a team from Cornell University in Ithaca, N.Y., analyzed and demonstrated a particularly straightforward approach: a solid, tapered Fabry-Perot etalon.
Figure 1. Radiation incident on the top of the tapered Fabry-Perot interferometer is split into its component wavelengths. λ0, the nominal wavelength for the λ/4 layers, is typically the wavelength in the center of the measurement range.
The concept involves two mirrors separated by a wedge-shaped spacer (Figure 1). Because the transmission of a Fabry-Perot filter is a function of the spacing between the mirrors, the transmission of the tapered filter varies spatially across its surface. Although conceptually simple, the device must be carefully designed to minimize its transmission bandwidth. Also, only one wavelength within the measurement range must be transmitted through a given location on the filter. That is, the range of wavelengths measured must not exceed the interferometer's free-spectral range, a requirement complicated by the fact that the free-spectral range varies with location across the filter's surface.
The first requirement -- that of minimizing the interferometer's bandwidth or maximizing its finesse -- is met by maximizing the reflectivity of the Fabry-Perot mirrors or, in this case, choosing high- and low-index materials (nH and nL in Figure 1) with maximum contrast. The researchers used TiO2 and SiO2, respectively.
They addressed the second requirement by performing a matrix analysis of the filter and designing their experimental device so that there was only one location on its surface where a transmission peak occurred for any wavelength between 479 and 597 nm. They first deposited four λ/4 periods (eight layers in total) of alternating TiO2 and SiO2 onto a microscope slide by electron-beam evaporation. Next, they deposited the wedge of SiO2 by translating a shutter (i.e., one edge of a slit) at a constant rate across the slide's surface while the SiO2 evaporation rate was steady. Finally, they deposited the remaining fixed-thickness layers of SiO2 and TiO2.
Figure 2. Each curve is the experimental transmission at a given location on the tapered Fabry-Perot's front surface along the X-axis. The broad curves are the experimental ("measured") and theoretical ("simulated") reflectivities of the individual dielectric mirrors.
To quantify the performance of their filter, the scientists measured its transmission at eight locations across its surface, each corresponding to 14 nm of increased thickness of the spacer. Each location has a distinct transmission maximum (Figure 2). But the experimental results differed in several ways from the prediction of the matrix analysis. The seemingly random variation in transmission peaks probably is due to nonuniformity in the slope of the wedge thickness, the scientists believe.
Although the analysis predicted that the individual peaks would have a bandwidth of ~15 nm, the observed bandwidth was closer to 25 nm. They attribute this discrepancy to inadequate thickness monitoring during the deposition of the TiO2-SiO2 mirrors. This theory is substantiated by a comparison of the predicted and measured reflectivity of the mirrors alone, also shown in Figure 2. The experimental curve, taken before the wedge was applied to the microscope slide, is significantly narrower and shifted ~15 nm to the longer wavelengths than the predicted curve.
- fabry-perot etalon
- A nonabsorbing, multireflecting device, similar in design to the Fabry-Perot interferometer, that serves as a multilayer, narrow-bandpass filter.
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