Metrology of complex refractive index for solids in the terahertz regime using frequency domain spectroscopy

Abstract

Frequency domain spectroscopy allows an experimenter to establish optical properties of solids in a wide frequency band including the technically challenging 10 region, and in other bands enables metrological comparison between competing techniques. We advance a method for extracting the optical properties of high-index solids using only transmission-mode frequency domain spectroscopy of plane-parallel Fabry-Perot optical flats. We show that different data processing techniques yield different kinds of systematic error, and that some commonly used techniques have inherent systematic errors which are underappreciated. We use model datasets to cross-compare algorithms in isolation from experimental errors, and propose a new algorithm which has qualitatively different systematic errors to its competitors. We show that our proposal is more robust to experimental non-idealities such as noise or apodization, and extract the complex refractive index spectrum of crystalline silicon as a practical example. Finally, we advance the idea that algorithms are complementary rather than competitive, and should be used together as part of a toolbox for better metrology.

Metrology of complex refractive index for solids in the terahertz regime using frequency domain spectroscopy

“…This kind of methodology can allow future intercomparisons between algorithms using a standardised test which allows for comparison to exact analytic results. To ensure that fair comparisons can be drawn and our conclusions replicated, our analysis tools, data, and code for each technique discussed in the paper have been published under the GNU general license [27].…”

“…To allow reasonable cross-comparison between theoretical and experimental work, we chose two Gaussians of different amplitudes and widths to approximate the observed absorption function in real data of Si etalons (see Results section of this work). Our model data can be replicated trivially using our code published under the GNU general license [27]. Experimental data is still invaluable in showing how our data analysis fails in real samples -and how it should be improved in future.…”

“…Although extracting ( ) is beyond the scope of this paper, we anticipate applications of this feature of the algorithm to study imperfections in samples over large surfaces or volumes. All of our data and analysis techniques are published for free under the GNU general license [27].…”

Giant non-linear susceptibility of hydrogenic donors in silicon and germanium

“…We ignored a factor for the phase matching, which is unity if the length of the sample L ≪ L c , where the coherence length L c = πc /(3 ω in [ n out − n in ]). Si:P at room temperature has a nearly constant n = 3.4153 in the range from 1 THz to 12 THz 33 , leading to typical values of L c ≈ 10 cm. The factor x = 6.9 × 10 23 W/cm 2 × THz × cm −2 for silicon.…”

Photodiodes for Terahertz Applications

“…There have been several proposed technological solutions for generation of THz radiation, for example, Schottky diode multiplier chains [3], CMOS based transistors [4]- [6], Gunn diodes [7], IMPATT diodes, quantum cascade lasers [8] [9], photoconductive switches [10]- [12] and high-speed photodiodes [13]- [15]. Key THz applications such as spectroscopy [16], imaging [17] [18], metrology [19] and communications [20] impose differing sets of requirements on the THz source and detector. For example, THz spectroscopy and metrology require a wide bandwidth tunable source with a spectral linewidth narrow enough to resolve spectral features of interest and a high enough power level to pass through a sample under test and be detected [21].…”