Polarization-controlled focusing of surface plasmon polaritons is investigated experimentally and theoretically with a novel system.
3 November 2014, SPIE Newsroom. DOI: 10.1117/2.1201410.005655
http://spie.org/x110658.xml
Surface plasmon polaritons (SPPs) are collective electromagnetic excitations that arise from the interaction between light and free electrons in a metal.1 SPPs can be detected with a THz time domain spectroscopy (TDS) system, with which both amplitude and phase information can be obtained.2, 3 Measurements made with THz-TDS, however, are time-consuming and have limited detection areas. A high-speed THz-SPP imaging system that can fully characterize the functionality of an SPP device is therefore required.
SPPs can be manipulated at sub-wavelength scales by modulating the phase, amplitude, and polarization of the incident light.4–6 SPPs excited by THz radiation are weakly confined on the metal surface. SPPs can thus be applied to sub-wavelength optics to enable microscopy and other imaging beyond the diffraction limit.
We have developed a high-speed THz-SPP imaging system (shown schematically in Figure 1) that is based on the THz holographic imaging technique.7, 8 We have used this system to investigate the focusing of THz-SPPs that are excited with THz radiation of different polarizations. In our system, the THz radiation is originally polarized along the x-axis. We use a THz quarter-wave plate (TQWP) or a THz half-wave plate (THWP) to generate circularly polarized, or y-polarized, THz radiation. The working frequency of the TQWP and the THWP is 0.73THz. The THz radiation is incident on the plasmonic lens, which has a semicircular slit structure fabricated on a metal foil, and the THz-SPPs are generated in the vicinity of the metal foil, as shown in Figure 1(a). We use a linearly expanded probe beam, a zinc telluride crystal, and an imaging module to detect the focused THz-SPPs. With our system we are able to achieve amplitude and phase image with a resolution of about 18μm.
Figure 1. Schematic diagram of the (a) plasmonic lens and (b) terahertz surface plasmon polariton (THz-SPP) imaging system. WP: Waveplate. QWP: Quarter-wave plate. TQWP: THz QWP. THWP: THz half-wave plate. ZnTe: Zinc telluride. θ: Angle between the radial direction and the THz-SPP propagating path. ϕ: Azimuth.
We simulate the focusing property of the THz-SPPs with the scalar approximation of the Huygens-Fresnel principle, which is valid for distances greater than the wavelength.9 As shown in Figure 1(a), the THz-SPP field at (x, y) is the result of the interferences of THz-SPPs emitted by the secondary sources at (x ′ , y ′ ) along the slit, and can be written as 
where θ is the angle between the radial direction and the THz-SPP propagating path, 
, and Ez(x′, y′) is the complex amplitude of the secondary source. This equation can be used to derive the distribution of the THz-SPP field that is excited by THz radiation with different polarization. For the x-polarized, y-polarized, and circularly polarized THz radiation, the excited THz-SPPs along the slit can be written as Ez(x′, y′)= sin ϕ, Ez(x′, y′)= cosϕ, and Ez(x′, y′)= sinϕ+exp(±iπ/2) cos ϕ, respectively, where the azimuth (ϕ) satisfies 0≤ϕ≤π and the ± sign represents the left circularly polarized (LCP) and right circularly polarized (RCP) THz radiation, respectively.
where θ is the angle between the radial direction and the THz-SPP propagating path, , and Ez(x′, y′) is the complex amplitude of the secondary source. This equation can be used to derive the distribution of the THz-SPP field that is excited by THz radiation with different polarization. For the x-polarized, y-polarized, and circularly polarized THz radiation, the excited THz-SPPs along the slit can be written as Ez(x′, y′)= sin ϕ, Ez(x′, y′)= cosϕ, and Ez(x′, y′)= sinϕ+exp(±iπ/2) cos ϕ, respectively, where the azimuth (ϕ) satisfies 0≤ϕ≤π and the ± sign represents the left circularly polarized (LCP) and right circularly polarized (RCP) THz radiation, respectively.
The simulated and experimental amplitude images of THz-SPPs, which we obtained for the 0.73THz x-polarized THz radiation, are shown in Figure 2(a) and (c), respectively. The THz-SPPs are focused in the center of the semicircular slit because the SPPs generated on the secondary sources along the slit are in-phase and interfere constructively in the center after experiencing the same optical path length. Cross sections through the focal spots are quantitatively compared in Figure 2(e). The spectral peak shown has a full width at half-maximum of 800μm. The simulated and experimental phase images we measured—shown in Figure 2(b) and (d)—clearly display a Gouy (i.e., on-axis longitudinal) phase shift around the focal spot. The longitudinal phase distribution through the focal spots—see Figure 2(f)—takes on a phase shift of π/2 because of the surface nature of THz-SPPs. We previously published a detailed discussion of the dispersion characteristics of our plasmonic lens.7 For the 0.73THz y-polarized THz radiation, the THz-SPP field—excited by the upper quarter slit—is out of phase with the one excited by the lower quarter slit. We find that the focal spot is split in the y-direction, as clearly seen in the simulated and experimental amplitude images shown in Figure 2(g) and (h). The transverse amplitude profile through the center is similar to the Hermite-Gaussian beam, and the phase takes on a π phase shift through the center, which causes the focal spot split.
Figure 2. Simulated (a) amplitude and (b) phase images for x-polarized THz radiation. The corresponding experimental (c) amplitude and (d) phase images are also shown. (e) Transverse amplitude profile. (f) Longitudinal phase distribution. (g) Simulated and (h) experimental amplitude images for the y-polarized THz radiation.
Simulated amplitude images of THz-SPPs that we excited with the 0.73THz LCP and RCP THz radiations are shown in Figure 3(a) and (b), respectively. The THz-SPPs are focused around the center, but with a transverse shift in the y-direction. The corresponding experimental amplitude images are shown in Figure 3(c) and (d), in which the transverse shift of the focal spot can be seen clearly. We also show cross sections through the focal spot in Figure 3(e) and (f) so that the transverse shift can be quantitatively compared. We find that there is a good agreement between the experimental and simulation results. The transverse shift that we observe is about ±70μm for both the LCP and RCP THZ radiation. This transverse shift of the focal spot originates from the spiral phase distribution along the semicircular slit, shown schematically in Figure 3(g) and (h). We can estimate10 the transverse focal shift by 
, where λsp is the wavelength of the THZ-SPPs. The estimated value we calculate is about ±65μm, which is in good agreement with our simulation and experimental results.
, where λsp is the wavelength of the THZ-SPPs. The estimated value we calculate is about ±65μm, which is in good agreement with our simulation and experimental results.
Figure 3. Simulated amplitude images for the (a) left circularly polarized (LCP) and (b) right circularly polarized (RCP) THz radiation. The corresponding experimental amplitude images for the (c) LCP and (d) RCP THz radiation are also shown. Cross section of the focal spots for the (e) LCP and (f) RCP THz radiation. Schematic diagrams of the phase distribution are shown in (g) and (h).
We have developed a THz-SPP imaging system with which we can experimentally observe the Gouy phase shift, the split of the focal spot, and the transverse shift of the focal spot. We can explain these phenomena clearly with the phase distribution of the THz-SPPs. Results from simulations we performed are in good agreement with our experimental results. In the future, we hope to demonstrate polarization-based demultiplexing, guiding, and switching plasmonic devices with our novel SPP imaging system.
This work was supported by the 973 Program of China (grant 2013CBA01702), the National Natural Science Foundation of China (grants 11204188, 61205097, 91233202, 11374216, and 11174211), the Program for New Century Excellent Talents in University (NCET-12-0607), and the Scientific Research Base Development Program of the Beijing Municipal Commission of Education.
Yan Zhang, Sen Wang, Xinke Wang
Capital Normal University
Beijing, China
Yan Zhang is a professor in the Department of Physics. His research interests include optical information processing, THz spectroscopy and imaging, and surface plasmon optics. He has published more than 150 peer-reviewed journal articles.
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