Effects of stray lights on Faraday rotation measurement for polarimeter-interferometer system on EAST

Understanding plasma stability and confinement requires detailed information regarding the electron density, current density distribution, and poloidal magnetic field. One approach to resolving the internal magnetic field is taking advantage of the Faraday rotation effect which occurs when light travels through a magnetized plasma. Faraday rotation arises from the fact that the left-handed wave (L-wave) and right-handed (R-wave) circularly polarized waves have different refractivity indices in magnetized plasma. Based on this principle, one can launch collinear light beams with orthogonal (R and L) circular polarization and measure their phase difference upon transmission through a plasma with respect to an external reference. Polarimeter/interferometer (POINT) systems based on this principle have been demonstrated to work successfully on several plasma experiments including RTP,¹ MST,² J-TEXT,³ C-Mod,⁴ Experimental Advanced Superconducting Tokamak (EAST),⁵ and so on. In future long-pulse, burning plasma devices, this approach is expected to be an important diagnostic tool, particularly for ITER.⁶ A single detector is used for measuring the density-induced phase shift as well as the rotation of the polarization plane when a third laser serves as a local oscillator (LO).¹ Faraday rotation-induced phase shift (typically a few degrees) is usually 10⁻² times the density-induced phase (roughly thousand degrees) due to the small difference in the refractive indices for the R- and L-waves. Cross talk due to the optical configuration for the combined interferometer-polarimeter measurements must be minimized to achieve accurate determination of small Faraday effect. One complicating issue is that multiple reflections among detectors, laser sources, focusing lens, and vacuum windows can significantly influence measurement results. This problem is amplified when one uses retro-reflectors (generating a collinear return beam with zero spatial offset) installed inside the device to accommodate a double-pass configuration. For the double-pass optical setup, multiple reflections generating standing waves are possible between detectors, sources, and retro-reflectors due to the fact that these reflecting surfaces form a cavity. These spurious oscillations have been reported for different systems installed on JET,⁷ RFX,⁸ and TEXTOR. Any unwanted light from direct feedback or spurious reflections can adversely affect polarimetry measurements when the ability to resolve small phase shift (<1°) is critical. In order to suppress the unwanted feedback signal between retro-reflectors and detectors, we have developed and tested an optical isolator positioned in front of the detector. In this way, the standing-wave-induced phase shifts have been reduced from 5°-10° to 1°-2°, which indicates that the optical isolator is effective in reducing reflections from the detector. Any residual feedback may arise from other feedback loops, such as between lasers and detectors and between lasers and retro-reflectors, which need to be further identified. In this article, we present the bench test results from using an optical isolator to establish the methodology to quantify the errors induced by standing waves. The comparison for plasma measurement with/without an optical isolator shows that this approach is effective in reducing the feedback from detectors.

The diagnostic approach used employs two orthogonal waves, the left-handed (L) and right-handed (R) circularly polarized far-infrared (FIR) lasers (nominal wavelength 432), that are collinear to probe the plasma.⁹ Due to plasma birefringence, each beam experiences a different value of refractive index. This difference causes the two beams to travel at different velocities and leads to a phase delay upon traversing the plasma. By measuring this phase delay using a heterodyne detection scheme, the Faraday effect can be resolved and is equal to half the measured phase difference. The electric field of two probe beams for the left-handed wave E_L and the right-handed wave E_R can be expressed by

where ω_R,L are the laser frequencies for L and R waves [frequency difference (ω_L − ω_R)/2π ∼ 1-2 MHz], $φR,L$ are their phase shifts experienced when the waves traversal the plasmas, and A is the amplitude of the electric field, respectively. The electric field of the local oscillator (LO) signal provided by a third laser beam can be written as

By mixing three frequency offset waves into a single mixer, we obtain ∼$ER+EL+Eo2$⁠, we can have three beat frequencies, intermediate frequency (IF),

where $Δω1=(ωR−ωL)$ is the frequency difference of the R and L waves which carries the information of L and R wave phase difference for the Faraday rotation measurement, and $Δω2=(ωL−ωo)$ is the frequency difference of the L wave and LO, and $Δω3=(ωR−ωo)$ is the frequency difference of the R wave and LO, which gives the L and R wave phase shift for interferometer measurement, respectively. By using this three-wave heterodyne approach, one can simultaneously determine the Faraday rotation and density by measuring phase shifts at three IF carriers.⁸ 

The multichord, horizontally viewing, far-infrared (FIR) polarimeter-interferometer system on EAST has been developed (see details in Ref. 9). The POINT (POlarimeter-INTerferometer) system used on the Experimental Advanced Superconducting Tokamak (EAST) exploits the Faraday-effect using the 3-wave laser technique discussed above where two frequency-offset (∼1 MHz), orthogonal, linearly polarized waves are combined and used to probe the plasma after being subdivided into 11 chords by beam splitters. Probe beams are transformed into circularly polarized counter-rotating R-beam and L-beam by using a quarter-wave plate before traversing vacuum windows. Then the beams are incident on the corner-cube retro-reflectors (CCRs) mounted on the inner vacuum wall and reflected back along the same path with opposite direction. After passing the plasma and windows again, the circularly polarized probe beams are combined with the local oscillator (LO) beam and then incident on the Schottky planar-diode mixers. The three IF signals are demodulated digitally to obtain Faraday rotation; L wave and R wave phases change in the plasma. The schematic for one chord optical layout is shown in Fig. 1.

The stray lights or multiple-reflection lights, which are unwanted lights, are additional terms in measurements, comparing the standard formula in Eqs. (1) and (2). For a simplicity without losing generality, we represent signals as follows:

where $ϵ≪1$ is the ratio of unwanted light to the signal and $φLs$ and $φRs$ are the phase shift of unwanted light for L and R waves, respectively. Thus, we have the intensity of mixer signals I_m = (E_L + E_R)² and

where the second order term ε² is dropped for Δω₁ term and I₀ = 2A². Equation (5) can be rewritten by combining the second term and the third term as

where the Faraday rotation phase is $ΦF=φR−φL2$ and the density phase is $ΦI=φR+φL2$⁠. Φ_Fs and Φ_Is are the Faraday phase and density phase arising from unwanted lights, respectively.

From Eq. (6), we have a measured total phase shift (Ψ) associated with IF (Δω₁),

Therefore, the measured phase not only depends on Faraday rotation but also on unwanted lights as shown in Eq. (7). For ε = 0, the measured phase is two times of Faraday rotation phase as we expected. For a very small Faraday rotation angle, Eq. (7) can be approximately reduced to

It is clear that for ε = 10%, unwanted light could result in 5° phase change which is almost comparable to the Faraday rotation angle for some chords. Since the density phase shift (ϕ_I) is large and has multiple fringes, the second term in Eq. (8) can result in the periodic modulation of the Faraday rotation signal when plasma density phase changes with time. During the discharge flat, errors associated with unwanted lights are difficult to observe if the density remains stable as the second term in Eq. (8) becomes a constant. The suppression of unwanted light is necessary to achieve accurate Faraday-effect measurements.

To illustrate the effects of unwanted lights on Faraday rotation measurement on a test bench, we introduce the interferometry phase shift by a moving reflecting mirror (equivalent to retro-reflectors) in the system, as shown in Fig. 2. Since there is no Faraday rotation when moving a mirror, one would expect zero phase change. According to Eq. (8), one can now assume that a standing wave will be generated between the CCR and each mixer (1&2), mixer 1 and mixer 2, each mixer and lens, as shown in Fig. 2. Here we are excluding the influence of feedback between the laser and mixers as the reflected beam is too weak. In order to avoid the formation of the standing wave, reducing the multiple reflections of light beams in light path seems to be a direct and effective method. An optical isolator is placed in front of the mixer, which consists of a λ/4-waveplate, polarizer, and an extinction material as shown in Fig. 2.

In the bench experiment, the two circularly polarized probe beams are incident on the moveable mirror and then reflected to the detector serving as a double path interferometer. An opto-isolater consisting of a polarizer and ¼ waveplate can be installed in front of the detector to demonstrate effects of unwanted lights. The polarizer passes two linearly polarized waves which are focused onto the mixer. Any light back-reflecting from the detector traverses the ¼ waveplate twice so that the reflected light is perpendicular to incoming waves and rejected by the polarizer. It should be noted that both the λ/4-waveplate and polarizer are installed at an oblique angle (about 45°) to avoid having any reflected portion of the beams back-reflected on the optical path. Orientations, the wire grid must be parallel to the fast or the slow axis of the waveplate. Absorber materials are then employed to damp any unwanted light.

For the setup, where no optical-isolator is in place, a phase change is introduced by the moving mirror, as shown in Fig. 3, where the black line represents the phase change. The saw-tooth waveform results from the fringe reset of the phase comparator. It is clear that Faraday rotation (red) has a periodic modulation of approximately 7° consistent with the expectation from Eq. (8). To confirm that back-reflected lights from the detector can introduce Faraday effect phase modulation of Faraday rotation, we next install an optical isolator in front of the detector. As shown by the blue line in Fig. 3, the modulation amplitude is significantly reduced to ∼1°. The residual modulation is likely to arise from other reflecting elements in the optical path, such as the laser sources, imperfect AR coating of ¼ waveplates and lens. Nevertheless, the bench test provides us a convenient way to identify and minimize unwanted light without the need for a plasma discharge.

Measurement results clearly show that unwanted lights exist in the optical negatively impact of the Faraday effect measurement. Introducing the optical isolator can effectively eliminate the unwanted light back-reflected from the detector. It should be noted that not allstray light originates from the detectors, and further eliminating spurious reflections from all components is an important task for future improvement of the polarimetry diagnostic.

The 11 double-pass horizontal chords of the POINT system have been used to measure the electron density and current density profile, an essential diagnostic tool for the EAST tokamaks.⁵ Internal magnetic field measurement provides critical information on the safety factor (q) by providing internal constraints on the equilibrium reconstruction fitting code (EFIT).¹⁰ Unwanted light effects can introduce systematic errors in Faraday rotation measurement which in turn affect the accuracy of the equilibrium reconstruction. To illustrate the standing wave effects on the Faraday rotation measurement in EAST, phase data for a typical plasma shots can be seen in Fig. 4. Both Faraday rotation phase and density phase for the channel 8 (CH8: Z = −17 cm) and channel 9 (CH9: Z = −25.5 cm) are shown.

Figures 4(a) and 4(b) plot the density and Faraday rotation for channel 8 for two different EAST discharges. For shot 66 347 shown in blue, the Faraday rotation signal has a visible modulation during density ramp-up at early times (0-2 s) and ramp-down (8-10 s). During these times, there is approximately a 1 fringe change in the density phase. As described in Eq. (8), this changing density can lead to a modulation of the Faraday phase when feedback effects are present. The observed modulation in the Faraday phase, ∼2° pk-to-pk, is also consistent with the bench test described previously where the moving mirror introduces phase modulation in the Faraday signal. The modulation amplitude is approximately 2° while Faraday rotation reaches ∼8° at flattop. The modulation is not observable during flattop since there is no temporal change in the plasma density. However finite errors may still exist depending on the saturated value of density phase [see Eq. (8)]. The maximum errors could be 2°, which introduces up to a 25% systematic error for this channel. This error increases when the plasma Faraday rotation angle is reduced.

To suppress any potential feedback from the mixer, we install an optical isolator in front of the mixer in CH8 for shot 70 474 (in red). The modulations induced by unwanted lights during density ramp-up phase are largely reduced as expected, while density time evolution for two shots is comparable. This confirms that the feedback from the mixers, at least in part, is responsible for the most modulation of Faraday rotation. In addition, this feedback can be partly suppressed by installing an optical isolator in front of the mixer. These results are shown in Figs. 4(b) and 4(d). For the 11-channel POINT system, the distance between adjacent channels is very close and a complicate optic layout may (with many optical components) introduce additional light from different reflecting surfaces for each channel. These stray lights must also be minimized to achieve more accurate measurements. Nevertheless as long as feedback signals come from the mixers, an optical isolator can be used to minimize the unwanted signals. Experimental results clearly demonstrate that the optical isolator is very beneficial for suppressing feedback.

We have developed a simple model [Eq. (8)] to describe the impact of unwanted light on the Faraday rotation measurements for the POINT system. The bench test confirms the model and experimental results from EAST can be qualitatively described. It is found that an optical isolator can be used to minimize the feedback signals from the mixer. For a double-pass system where a corner-cube retro-reflector is used, any residual feedback may introduce errors associated with this unwanted light. In the future, a quantitative model has to be developed to help us to quantify the contribution of unwanted lights to Faraday rotation measurements so that these errors can be subtracted for accuracy of measurements.

This work is supported by the National Magnetic Confinement Fusion Program of China with Contract No. 2014GB106002 and the National Nature Science Foundation of China with Contract Nos. 11375237 and 11505238. This work was in part supported by the U.S. Department of Energy, Office of Science, and Office of Fusion Energy Sciences through Grant No. DE-SC0010469. This work was also partially supported by the JSPS-NRF-NSFC A3 Foresight Program in the field of Plasma Physics (NSFC No. 11261140328) and supported in part by the Collaborative Research Program of the Research Institute for Applied Mechanics, Kyushu University.