Tuneable spectrometer for submillimeter astronomy based on silicon Fabry-Perot, preliminary results

We are studying and developing high performance spectroscopy solutions in silicon technology in the framework of the instrumental developments around the B-BOP bolometer arrays [1] and in the continuity of the former developments of the Herschel space telescope instruments and in particular its PACS instrument [2]. The integration of multi-wavelength spectroscopic capabilities close to the array of a cooled bolometer would make it possible to detect the interstellar medium (ISM) continuum by scanning and to trace its evolution in particular by the detection of characteristic lines such as the cooling line [CII] at 158µm. In this paper, we present the �rst concept under development and the preliminary results obtained in our cryogenic optical test bench. This solution is a tunable cavity Fabry-Perot (FP) with silicon mirrors driven by a cryogenic piezoelectric mechanism with a nanometric step. Each mirror is a dielectric Bragg structure, a stack of quarter-wave layers of silicon and air providing a high re�ectivity without metal losses. This solution allows extremely accurate scanning around a targeted wavelength. The �rst prototype is a relatively bulky proof of concept and future optimizations will allow it to be adapted to a focal plane array.


Introduction
The long-term project is to design a spectrometer integrated into the focal plane of a detector.For this reason, we have chosen to focus on silicon technology that is easily compatible with different detector technologies, and we decided to focus on the simplest type of interferometer, the Fabry-Perot.This kind of interferometer has no in uence on the polarization of the light and retains the spatial information as long as the beam is collimated.A Fabry-Perot interferometer is composed of two parallel mirrors perpendicularly positioned to the propagation direction of the incident wave.The light travels back and forth in the cavity and interferes constructively in transmission at the output of the cavity for selected wavelengths.This optical system transmits a comb of wavenumber in which all orders are directly dependent on the cavity size, and whose fundamental wavelength is equal to twice the cavity.
The e ciency and the resolution of this kind of interferometers depend directly on the mirror properties.
The higher the re ectivity of the mirrors, the better the transmission of the FP peaks.Furthermore, in practice, any degradation of parallelism between the two mirrors, of atness or of surface of each mirror degrade the resolution of the transmitted peaks.Our objective is to build a midresolution compact FP interferometer with the least possible absorption that is capable of transmitting several wavelengths close to each other.To develop a tunable Fabry-Perot, we choose for this concept to modify the cavity size by scanning one of the mirrors. 2 The concept of Bragg-mirror Fabry-Perot Most of the common Fabry-Perot interferometers for space applications are made of thin-sheet metal or metallic mesh mirrors.This introduce metal losses and a loss in e ciency.
The concept we propose here is a Fabry-Perot with no losses in the mirrors and has been realized by S. Bounissou during her thesis work [3].Each mirror is made of a Bragg stack of dielectric layers, here silicon and vacuum.The mirrors used here is a three layers stack silicon-vacuum-silicon.The big advantage of such mirrors is the use of dielectric materials that do not absorb the light wave.They also re ect light very e ciently over a wide band of wavelengths.
For feasibility reasons, we are targeting transmitted wavelength around 320µm.In fact, the layers composing our device are made of pure crystalline silicon and this is technically di cult to manufacture and handle thinned-layers with a thickness of less than 50µm.However, the principle we demonstrate in this paper for wavelengths around 320µm remains identical to the one we would implement for a Fabry-Perot transmitting at 158µm.The layers used here are 70.2µmthick (3λ/4) for the silicon and 80µm thick (λ/4) for the vacuum.In order to scan the wavelengths around 320µm with the best resolution, we decided to scan the rst order, which means a cavity size around /2.
As mentioned previously, to reach a good nesse, the surface of the mirrors must be as at and smooth as possible.That is why we have had the thinned silicon manufactured with high precision tools at the CEA/LETI and we built a mechanical mount to assemble the Fabry-Perot with minimum deformation of the individual sheet.
In 2019, the high performance of this concept has been proved with a Bragg mirror FP with a xed cavity.This rst sample reached more than 98% of e ciency for a resolution of over 180.Our objective is now to be able to scan the cavity between the two mirrors to transmit several wavelengths close to each other with the same interferometer.

The of scanning Bragg Fabry-Perot
The prototype we developed is made of a three piezoelectric actuators mechanism that allows one to adjust the parallelism of the Fabry-Perot and to scan the cavity.We designed this whole setup to operate under cryogenic vacuum conditions.On Fig. 2 above, we xed the mobile mirror on the blue part connected to the piezo mechanism and the other mirror on the bracket in front of the rst one.The challenge of this experiment is to reach a good parallelism of the mirrors before the vacuum and cold operations, and then, under those harsh conditions nd back the initial parallelism and adjusting it by varying the tip and tilt of the mechanism.
Many calibrations and characterization, optically and thermally are thus necessary before taking the spectral measurement of the Fabry-Perot.
Page 5/9 The measurements are performed with a cryogenic Martin-Pupplet Fourier Transform Spectrometer (FTS) with a 10cm travel.The signal is acquired by a bolometer cooled down to 300mK allowing us to get high resolution and low signal interferograms.Our optical samples are placed in the optical path between the FTS and the bolometer.For each spectrum showed below, many interferograms have been acquired with the sample in the path and another batch of measurements has been made without the sample, for reference.Therefore, we can eliminate the spectral signature of the test bench environment and retrieve the absolute spectral e ciency of our sample.
Thanks to a measurement of the single silicon sheet we use for the Bragg mirrors, we have been able to know precisely its thickness and thus feed the theoretical model with the spectral response of the two Bragg mirrors that we measured on the FTS at 77K Fig. 3.
The measured spectra of those mirrors are really close to the simulation, they have high re ectivity (more than 95%) on a wavelength range wider than 100µm.The numerical simulation plotted in this article are calculated on the model basics of the thin-lms theory developed by Abelès [4].
We then measured the response of the scanning FP with those two Bragg mirrors and saved the spectra for four different sizes of cavity in order to get four different peaks of transmission at 310µm, 320µ, 330µm and 340µm.To begin with, this rst series of measurements was carried out with the Fabry-Perot kept at room temperature in order to simplify mirror-paralleling operations.The rest of the optical bench was kept at cryogenic temperature.Figure 4 below shows the four spectra obtained with the scanning FP.By changing the cavity size of a known distance, we shift the position of the transmitted peak in accordance with the model.
With the same model used for the Bragg mirrors, we can compare the performance of our interferometer with the theoretical simulation.We see on the Fig. 5 that the experimental measurements t perfectly with the theory for the four positions.Therefore, we clearly see that the e ciencies of the transmitted wavelengths are lower than the ones simulated.We summarize the e ciency and the resolution of each peak of FP in the table below, and compare them with the expected performance: As shown on Fig. 6, the performance of the transmitted peaks are lower than expected.This can be explained by several factors.The most probable here, in addition to the possible small parallelism defects, is that the Bragg stack are a little bit deformed by the way they are assembled on their mounts (some microns of wedge).Even those small deformations have a big impact on the shape of the peak.Here, we cannot precisely t those peaks with Lorentzian curves, which con rms our hypothesis.Their shape are closer to the case of FP peak with a non-zero angle of incidence.The next step is to optimize the assembly of the Bragg mirrors in order to reduce the deformations down to less than 1µm of wedge and for the next cold measurements of this Fabry-Perot, the parallelism procedure should be ne-tuned.

Figures
Figures

Figure 1 Scheme
Figure 1

Figure 4 Transmission
Figure 4