Na-Faraday rotation filtering: the optimal point

Abstract

Narrow-band optical filtering is required in many spectroscopy applications to suppress unwanted background light. One example is quantum communication where the fidelity is often limited by the performance of the optical filters. This limitation can be circumvented by utilizing the GHz-wide features of a Doppler broadened atomic gas. The anomalous dispersion of atomic vapours enables spectral filtering. These, so-called, Faraday anomalous dispersion optical filters (FADOFs) can be by far better than any commercial filter in terms of bandwidth, transition edge and peak transmission. We present a theoretical and experimental study on the transmission properties of a sodium vapour based FADOF with the aim to find the best combination of optical rotation and intrinsic loss. The relevant parameters, such as magnetic field, temperature, the related optical depth, and polarization state are discussed. The non-trivial interplay of these quantities defines the net performance of the filter. We determine analytically the optimal working conditions, such as transmission and the signal to background ratio and validate the results experimentally. We find a single global optimum for one specific optical path length of the filter. This can now be applied to spectroscopy, guide star applications, or sensing.

Figure 1

(a) general scheme of the discussed Faraday filter: an atomic vapour cell is placed between two crossed linear polarizers (wire-grid type shown). A magnetic field (B) leads to a Zeeman split of the involved levels, which then act differently on both circular polarization components. An overall turn of the polarization results in the transmission through the second polarizer (b) calculated (green) and measured (blue, dots) transmission spectrum of the D₂ transition of sodium for 153°C and 0.2 T. Optical rotation (blue, dashed), Doppler spectrum (red, OD approx. 5). (c) experimental setup of Na-FADOF (d) density plot of the transmission for a temperature of 153°C for various magnetic fields, Na-D₁transition. (e) same for the D₂ transition. The red dashed line corresponds to the transmission spectrum in (b).

Figure 2

(a) Various contributions to the total FADOF transmission signal: Red, Dashed: Sodium D₁-line, Doppler transmission for zero detuning, in resonance with the D₁-line as a function of the magnetic fields. Effective transmission only due to the turned polarization (brown), and resulting FADOF transmission (green solid line) including Doppler transmission and rotation filtering. The equivalent noise bandwidth, describes the background contribution vs. the peak transmission (ENBW, blue). The optimal point for the given temperature is defined, where the ratio of the FADOF transmission and the ENBW is maximized (dashed, black vertical line). It lays between the minimum ENBW and the maximum for the FADOF transmission. (b) normalized representation of the optical rotation in the Poincare sphere with rising magnetic field. RC/LC: right and left-hand circular polarized light, LVP/LHP: linear vertical and horizontal polarized light. (c) and (d) same for the D₂-line.

Figure 3

(a) different FADOF transmission spectra for different magnetic fields and temperatures. Labels correspond to the locations in b). (b) Density plot of the peak transmission of the D₁-FADOF in dependence to the magnetic field, and the temperature (green lines denote 10, 50 and 90% transmission). Further lines indicate the ENBW (white, 1 GHz spacing), the optimal working conditions (orange), and the transition between a transmission peak at the line centre, respectively the outer rim of the Na-spectrum (red line). (c) summarized peak transmission and the ENBW in dependence of the length of the cell. The encircled points correspond the to the orange line in (b). (d) (e) and (f) same for the D₂-line.

Figure 4

(a) ratio of FADOF transmission and ENBW, depicted for the optimum points from Fig. 3a. A global optimum point can be associated to the maximum of the quotient of the FADOF transmission and the ENBW. (b) same for the D₂-line.