Thermopile detector of light ellipticity

Polarimetric imaging is widely used in applications from material analysis to biomedical diagnostics, vision and astronomy. The degree of circular polarization, or light ellipticity, is associated with the S3 Stokes parameter which is defined as the difference in the intensities of the left- and right-circularly polarized components of light. Traditional way of determining this parameter relies on using several external optical elements, such as polarizers and wave plates, along with conventional photodetectors, and performing at least two measurements to distinguish left- and right-circularly polarized light components. Here we theoretically propose and experimentally demonstrate a thermopile photodetector element that provides bipolar voltage output directly proportional to the S3 Stokes parameter of the incident light.

M easurements of light ellipticity or the degree of circular polarization of an electromagnetic wave are highly important for the characterization of chiral molecules 1,2 , imaging of biological tissues 3 , identifying bio-organics 4,5 , studying cosmic microwave background radiation 6,7 , enhancing vision in turbid media 8,9 as well as for performing quantum cryptography and communication experiments [10][11][12] . Light ellipticity is quantified by the Stokes parameter S 3 ¼ I RCP À I LCP , where I LCP and I RCP are the intensities of the left-circularly polarized (LCP) and rightcircularly polarized (RCP) light waves in which the electric field moves along a helical trajectory, either clockwise or counterclockwise. Distinguishing the two circular polarizations with conventional photodetectors directly is inherently difficult. Traditionally, external optical components, such as polarizers and wave plates, are used to filter LCP or RCP light for detection 13,14 . Intensive investigations have been focused recently on developing integrated solutions for detecting light circular polarization. Detectors based on chiral materials, optical antennas/ metamaterials or nonlinear plasmonic structures were proposed and demonstrated with different sensitivity to LCP and RCP light [15][16][17][18][19] . However, all these detectors are still sensitive to linearly polarized light, that is, they have non-zero output when S 3 ¼ 0, and thus cannot be used to measure the S 3 Stokes parameter directly. A number of integrated on-chip photonic elements, such as polarizers 20,21 or beam splitters [22][23][24][25][26][27] , have also been proposed to separate LCP and RCP light components.
Monolithic detectors with the output directly proportional to the S 3 Stokes parameter would be the most compact and desirable solution for detecting and characterizing light ellipticity, especially if one thinks of polarimetric focal-plane-array imaging, for example, for identification of bio-organics 4,5 , astronomical observations 6,7 , or vision in turbid media 8,9 . Recently, the first monolithic photodetectors with voltage response directly proportional to the light ellipticity were reported in mid-infrared and terahertz spectral ranges 28,29 based on spin-galvanic and circular photogalvanic effect in semiconductors 30,31 . However, spin-galvanic effect in semiconductors is intrinsically small 30,31 and thus these detectors require kW cm À 2 -level optical intensity to produce detectable response.
Here we theoretically propose and experimentally demonstrate a thermopile photodetector element with electromagnetically engineered optical antennas that translate the degree of circular polarization of light into the d.c. voltage directly proportional to the S 3 Stokes parameter of the incident radiation. Our detector operation is based on the concept of antenna-coupled thermopiles which are constructed by placing the hot junction of a thermocouple at the centre of an optical antenna and have previously demonstrated sensitivity to linear or mixed light polarization [32][33][34][35] . We demonstrate our detector operation at 7-9 mm wavelength range; however, similar to other thermopile detectors, our detectors can be tailored for operation at any wavelength of interest from visible light to radio frequencies.
They provide orders of magnitude higher sensitivity, compared with the photogalvanic photodetectors 28,29 and can be manufactured into focal-plane-arrays. To the best of our knowledge our devices are the only photodetectors, other than that based on photogalvanic effect, that are sensitive exclusively to the degree of circular polarization of light.

Results
Thermopile antenna design. Consider two identical rod antennas positioned at ± 45°to the y axis on a planar substrate as shown in Fig. 1a. The dimensions of the antennas are chosen so that they have a resonance at the target wavelength of 7.5 mm. When the antenna gap is large (g4 4l), x-and y-polarized light will excite antisymmetric and symmetric plasmon modes, respectively, as shown in Fig. 1a, with resonances at exactly the same frequencies. However, as the antenna gap decreases to the subwavelength scale, a frequency gap emerges between the resonant positions of the new symmetric and antisymmetric eigenmodes of the dimer antenna 36 . The computed resonance positions of the two modes for the antenna gap of 100 nm are shown in Fig. 1b. Under LCP or RCP illumination, the symmetric and antisymmetric charge oscillations in the dimer antenna will have a relative phase delay given by the sum of the phase delay between E x and E y components of the optical field that excite them ( ± p/2 for LCP and RCP light) and the phase delay due to different detuning of symmetric and antisymmetric antenna resonances relative to the excitation light frequency. We adjusted the antenna gap size so that the latter effect produces a phase delay of Bp/2 between symmetric and antisymmetric charge oscillations for the excitation light wavelength of lE7.5 mm. The total phase difference between the symmetric and antisymmetric charge oscillations induced by circularly polarized light in the dimer antenna is then either 0 or p , depending on whether we use LCP or RCP illumination. The induced optical currents of the symmetric and antisymmetric modes then add constructively in one rod antenna in the dimer and destructively in the other. As a Light absorption (a.u.)  Fig. 1c. If a thermocouple is now placed in thermal contact with the antennas, as shown schematically in Fig. 2a, the temperature difference between the thermocouple junctions will be translated into the d.c. voltage through Seebeck effect 37,38 , which would change sign for LCP and RCP light illumination.
The voltage output of the antenna-coupled thermopile structure shown in Fig. 2a is still sensitive to linearly polarized light (for example, when incident light is polarized along one of the rod antennas). To build a thermopile element sensitive exclusively to the degree of circular polarization of light, we arrange four dimer antennas in a two-dimensional (2D) configuration that possesses D 4 symmetry (that is, the mirror symmetry and the four-fold rotational symmetry), see an example in Fig. 2b. To prove this point, we note that the temperature difference across a thermocouple number Fig. 2b is given as where T N (A) and T N (B) are the temperatures of the A and B junctions of the thermocouple N, cf. Fig. 2b, E i and E j are the components of the normally incident optical field (i, j ¼ x or y) and a where DS is the difference in the Seebeck coefficients of the two materials forming the thermocouple 37,38 . Using equation (1) and the D 4 symmetry of the antenna structure, we can show the emf voltage is given as where R¼2DS Imða yx Þ=e 0 c is the detector responsivity (V W À 1 ) and S 3 I RCP À I LCP ¼e 0 cjðE x E Ã y À E y E Ã x Þ is the S 3 Stokes parameter of the incident light 39 , see Supplementary Note 1 for details of the derivation. The dimer antenna shown in Fig. 1 and discussed above is one of the simplest plasmonic antenna designs with Imða 1 ð Þ xy À a 1 ð Þ yx Þ 6 ¼ 0. We note that our derivations of equation (2) used only general symmetry considerations so any planar antenna-coupled thermopile with the D 4 symmetry will provide voltage output given by equation (2).
Experimental implementation. For the proof-of-concept experimental demonstration, we have fabricated antenna-coupled thermopile element shown in Fig. 3a. Fabrication details are given in the 'Methods' section. The overall symmetry of the structure in Fig. 3a is similar to that in Fig. 2b   NATURE COMMUNICATIONS | DOI: 10.1038/ncomms12994 ARTICLE the size of our detector element of 24 Â 24 mm 2 , the simulation results translate into the expected thermopile responsivity under under continuous wave (CW) illumination of B15 mV W À 1 . The detailed comparison of thermocouple heating dynamics under pulsed and CW illumination is given in Supplementary  Fig. 1 and Supplementary Note 2. Figure 3c shows the simulated detector responsivity as a function of light wavelength, which shows a peak at l ¼ 7.5 mm. From equation (2) it follows that the spectral responsivity of the detector scales with the wavelength dependence of Imða 1 ð Þ xy À a 1 ð Þ yx Þ. Our dimer antennas were optimized to maximize this parameter at l ¼ 7.5 mm and its value drops as the light wavelength is tuned away from antenna resonances.
Optical characterization. To characterize the detector performance, infrared pulses with adjustable ellipticity generated by a quantum cascade laser and a quarter-wave plate (QWP) were normally incident onto the thermopile element. Details of the experimental setup are given in the 'Methods' section. The measurements were performed at lE7.9 mm, which corresponds to the peak detector responsivity measured experimentally, and with B270 W cm À 2 input light intensity. Figure 4a compares the detector voltage output with the normalized S 3 Stokes parameter of the incident light as a function of the ellipticity angle w, with w defined as sin(2w) ¼ (I RCP À I LCP )/(I RCP þ I LCP ) ¼ S 3 /I 0 (ref. 39). The bipolar voltage output of the detector is in an excellent agreement with the S 3 Stokes parameter of the incident light, as expected theoretically. We have also tested the detector response to the linearly polarized light at different polarization angles c (c ¼ 0 corresponds to the light polarization in vertical direction in Fig. 3a). The results of these measurements are shown in Fig. 4b. As expected, our detectors are virtually insensitive to linearly polarized light, as such response is forbidden by symmetry, see equation (2). The extinction ratio of our detector, defined as the ratio of the maximum detector output under linear polarization illumination (that is, the maximum signal in Fig. 4b) to the detector output under purely RCP or LCP illumination, for the same light intensity, is B1/10. The residual non-zero response in Fig. 4b may be attributed to (i) non-ideal and non-identical fabrication of the Au-Ni thermocouples in the antenna loop (Fig. 3a), which may lead to different thermal contacts and different Seebeck coefficients 41 at each thermocouple junction and (ii) distortion of the D 4 symmetry of the detector by the readout electrodes (seen the upper-left corner in Fig. 3a). We note that the second issue may be alleviated by using vertical electrodes or designing similar electrode structures at all four corners of the thermopile antenna structure.
The dependence of the thermopile output on the light intensity is shown in Fig. 4c. As expected, the detector shows linear response to the power of the optical beam. The spectral dependence of the responsivity of the detector is shown in Fig. 4d and is in a good agreement with the theoretical predictions shown in Fig. 3c. The peak detector responsivity is measured to be R ¼ 43 mV W À 1 at lE7.9 mm, which is close to the theoretical expectations presented above. Differences in the peak responsivity value and spectral position are likely the result of differences in the actual values of optical, thermal and thermoelectric parameters of the detector materials, compared with the table values assumed in the simulations, particularly taking into account the effect of nanoscale dimensions of our antenna elements 42 .

Discussion
We note that we did not aim to produce thermopile detectors with the highest possible sensitivity in this proof-of-concept demonstration. Thermopiles with orders of magnitude higher responsivity, for example, 30 V W À 1 (ref. 34), may be fabricated by using thermocouples made of semiconductor materials with large difference in their Seebeck coefficients (for example, BiSb/Sb with DSE135 mV K À 1 (refs 32,34)) and by reducing the heat mass and improving thermal isolation of thermocouple junctions (for example, by using air bridges with conventional materials 32 or graphene 43 ). Air-bridge antenna-coupled BiSb/Sb thermopile detectors have recently demonstrated noise equivalent power below 100 pW Hz À 1/2 (ref. 34) and we expect that similar levels of sensitivity could be achievable with the detectors presented here. Even in the present form, the sensitivity of our detectors is already orders of magnitude higher than that of detectors based on the circular photogalvanic effect in semiconductors 28,29 , which, to the best of our knowledge, are the only other photodetectors that have shown voltage output directly proportional to the degree of circular polarization of the incident light.
To summarize, we proposed the concept and experimentally demonstrated the operation of a novel class of antenna-coupled thermopile photodetectors that provide bipolar voltage response directly proportional to the S 3 Stokes parameter of the incident light. The detector design is completely achiral and the chirality of the incident light is translated into the direction of current and/or the sign of d.c. voltage in the detector. Given the compactness and simplicity of the photodetectors presented here and the CMOS compatibility of the thermopile photodetector technology 41,44 , we expect that our elements can be easily integrated into various polarimetry systems and be used to provide video-rate focalplane-array imaging of the S 3 Stokes parameter of light for identification of bio-organics 4,5 , astronomical observations 6,7 or vision in turbid media 8,9 .

Methods
Device fabrication. The device fabrication started from depositing a 100-nm-thick Au film (via e-beam evaporation) on the Si substrate to serve as the bottom reflector, followed by the deposition of a 2-mm-thick layer of SiO 2 (via plasmaenhanced chemical vapor deposition (PECVD)) on top of the Au film. The SiO 2 layer serves as the l/4 dielectric spacer which ensures that the wave reflected from the ground plane interferes constructively with the incident wave on the antenna surface. Au was chosen as the material for the optical antenna as well as part of the thermocouple, and was joined by Ni to form the thermocouple junction. The antenna-coupled thermopile structure was fabricated by the e-beam lithography, metal deposition and lift-off. The structure elements are made with 50-nm-thick Au antenna/thermocouple, 60-nm-thick Ni thermocouple and lastly 100-nm-thick Au electrodes. Ti (5-10 nm thick) was deposited before any Au layer to promote adhesion. The active region of the device had a footprint of 24 Â 24 mm 2 . After fabrication, the device was wire bonded to the chip carrier for testing with electrostatic discharge precautions.
Experimental setup. A tunable quantum cascade laser (Daylight Solutions) was used as the mid-infrared source. The output was 1-ms-long pulses repeated at the rate of 100 kHz. The quantum cascade laser beam was inherently linearly polarized, and was converted to be elliptical by passing through a QWP (Altechna). In this configuration, the ellipticity angle w equals the angle y between the optical axis of QWP and light linear polarization direction ðsin 2w ð Þ¼ 2Ex Ey sin p=2 ð Þ E 2 x þ E 2 y ¼ sin 2y ð ÞÞ, which can be continuously tuned. The beam was then focused onto the thermopile detector at normal incidence using a ZnSe lens with 6 inch focal length, resulting in a beam spot size of B500 mm in diameter. The thermopile emf voltage was recorded using the lock-in amplifier (Stanford Research SR830) referenced by the laser pulse trigger. Details of extracting the value of the thermopile voltage from the lock-in amplifier output are given in Supplementary Note 2. To measure the device response to linearly polarized light, QWP was replaced by a half-wave plate (Altechna) and a wire-grid polarizer.
Data availability. The data that support the findings of this study are available from the corresponding author upon request.