Breaking the Contrast Limit in Single-Pass Fabry-Pérot Spectrometers

The development of high-resolution Fabry-Pérot interferometers has enabled a wide range of scientific and technological advances—ranging from the characterization of material properties to the more fundamental studies of quasiparticles in condensed matter. Spectral contrast is key to measuring weak signals and can reach a ${10}^3$ peak-to-background ratio in a single-pass assembly. At its heart, this limit is a consequence of an unbalanced field amplitude across multiple interfering paths, with an ensuing reduced fringe visibility. Using a high-resolution, high-throughput virtually imaged phased array spectrometer, we demonstrate an intensity-equalization method to achieve an unprecedented 1000-fold increase in spectral contrast in a single-stage, single-pass configuration. To validate the system, we obtain the Brillouin spectrum of water at high scattering concentrations where, unlike with the standard scheme, the inelastic peaks are highly resolved. Our method brings the interferometer close to its ultimate limits and allows rapid high-resolution spectral analysis in a wide range of fields, including Brillouin spectroscopy, mechanical imaging, and molecular fingerprinting.

Figure 1

(a) Schematic of the transmitted field of a VIPA etalon. The incident beam is internally reflected by a high- ($R_1\sim 99.9\%$) and a low- ($R_2\sim 96\%$) reflection coated surface. (b) The Airy function given by the output exponentially decaying field ultimately sets a limit (of approximately $10^3$) to the instrumental spectral contrast. (c) A 1000-fold increase in contrast is obtained when we assume an output field amplitude (d) of Gaussian profile. (e) Schematic of the spectrometer ($P_i$, linear polarizer; ${\pi }_i$, field observation plane). The light beam delivered by a single-mode (SM) fiber is focused by a cylindrical lens to the AR-coated window of a VIPA etalon, giving high ($>50\%$) throughput efficiency. A SLM is used to equalize the output field of the VIPA through an intensity mask of semi-Gaussian profile (f). A CCD camera acquires the spectral pattern at the Fourier plane of a spherical lens.

Figure 2

Beam shaping for high spectral contrast. (a) Comparison of the output beam of the VIPA acquired at the ${\pi }_1$ plane with the SLM-equalized beam at the ${\pi }_2$ plane. (b) Line profiles (the dashed lines) along the two beams acquired with an equal integration time. Using a transfer function of semi-Gaussian profile (c), the natural exponentially decaying beam arising at the VIPA output is converted into a Gaussian beam of an approximately 5 mm width. (d) A real-time least-squares fit is performed to achieve the optimal beam shape ($R^2>0.99$) with a loss of approximately 58%. Scale bars are in 2-mm increments.

Figure 3

Spectral contrast. The spectral profile is reconstructed using a set of calibrated ND filters. The contrast given by our spectrometer is measured to be approximately 60 dB at half FSR, corresponding to a more-than-25-dB increase with respect to the contrast given by a standard single-stage VIPA spectrometer.

Figure 4

Validation of the spectrometer. Brillouin spectra of a water-milk solution at different milk concentrations acquired in a 90° scattering geometry with both (a) the standard and (b) the equalized single-stage VIPA spectrometer. An arbitrary offset is added to the spectral profiles at each milk concentration for clarity. (c) Scattering of the green laser beam through the liquid samples. The spectrum of distilled water at room temperature has a lower Rayleigh peak than the inelastic Brillouin peaks, as shown in both configurations. As the milk concentration increases, elastic scattering prevails, overwhelming the Brillouin peaks (a). In turn, Brillouin peaks are still highly resolved at ${10}^{-4}$ milk concentration due to the higher contrast of the spectrometer (b). Spectra are acquired with a 200-ms integration time. (d) Brillouin spectrum of glycerol. Glycerol is characterized by a natural high Rayleigh peak and much weaker Brillouin peaks. ${\mathbf{k}}_{\mathbf{i}}$ and ${\mathbf{k}}_{\mathbf{s}}$ represent incident and scattering wave vectors.