1. Introduction

Surface plasmon polaritons (SPPs) are surface electromagnetic waves coupled with collective oscillation of electrons at a metal/dielectric interface. They allow the two-dimensional control of light and have strong electromagnetic field enhancement in the near-field. Thus, SPPs are important for applications in many nano-photonic fields, such as high harmonic generation [1], subwavelength optics [2–5], near-field imaging and sensing [6], nanoparticle manipulations [7], etc. Recently, it has been demonstrated that the plasmonic focusing in near-field with a subwavelength focal spot could be achieved by using a laser illuminating on axially symmetric nano- or micro- metallic structures called plasmonic lens [8–10]. Normally, the structure of the plasmonic lens is a single annular nanoslit or multiple concentric slits fabricated on an optically opaque metallic film. SPPs can be excited at all azimuthally directions near the nanoslits and propagate toward the geometric center, when the nanoslits are illuminated with a radially polarized laser beam. Therefore, the electric field component of SPPs interferes constructively at the center of the plasmonic lens and forms a sharp focal spot [10].

However, such structure of the plasmonic lens also induces two additional effects that have to be avoided for a lens. One is that the intensity of light transmission through the nanoslits is usually strong, sometimes even stronger than the focal spot. The other is that the excited SPPs propagate both towards and away from the geometric center, causing the considerable loss of SPPs. To eliminate the two effects, we designed a new plasmonic lens consisting of two groups of the concentric semitransparent annular grooves that differ in the groove periodicity. The inside group serves as a converging lens to focus SPPs, the outer group serves as a Bragg reflector to block the SPPs out-propagating. When a linearly polarized laser was incident from the bottom of the plasmonic lens, two tightly focused spots in the near-field without any other obvious light transmission were obtained by a scanning near-field optical microscope (SNOM). By raising the radius of half of every groove, we delayed the phase of the corresponding SPPs byπ, and obtained a single focal spot. Theoretical simulations using finite-difference time-domain (FDTD) method confirmed that about 1 time increment of SPP light intensity was obtained for the plasmonic lens with a Bragg reflector in comparison to that with only a converging lens.

2. Experiments

A 75-nm thick gold film was deposited onto a glass substrate by e-beam evaporation. Annular groove rings were fabricated by a Focused Ion Beam (FIB, FEI dual beam SEM/FIB NOVA 200 Nanolab system) on the gold film. The schematic diagram of the experimental setup is illustrated in Fig. 1(a) . The sample was illuminated from the bottom by a linearly polarized laser beam with the wavelength of 671-nm. Because only a vertically incident light could excite the SPPs when the period of the grooves equals to the SPPs wave length, the illuminating light is normally incident light without focusing. The beam was generated by a semiconductor laser. The diameter of the beam is about 1.5 mm. The two-dimensional (2D) intensity distribution of SPPs was measured by a SNOM (Nanonics) [11, 12]. The probe of the SNOM is an Al-coated, tapered cantilever optical fiber, with an apex diameter of 100-nm. The collection of SPP light is acquired by an Avalanche Photo Diode (APD) system.

 

Fig. 1 (a) Schematic diagram of the experimental setup. Vertical arrows at the bottom points the incident direction of the illuminating light, the horizontal arrow points the polarized direction of the incident light; (b) Scanning electronic microscope image of the plasmonic lens; (c) Scanning electronic microscope image of the phase delayed plasmonic lens.

Download Full Size | PDF

Figure 1(b) presents the scanning electron microscope image of the fabricated plasmonic lens structure, which gives the period of the inner converging lens about 634-nm, the outer reflector 317-nm. Figure 1(c) presents the scanning electron microscope image of a phase delayed plasmonic lens structure, where the radius of half of every groove is 320nm bigger than the other half.

3. Results and discussions

The free propagating light cannot excite SPPs at a metal/air interface directly, for the conservation of energy and momentum cannot be satisfied. In our work, we used periodic metallic structures to couple free propagating light to SPPs in the metal/air interface. The SPPs is excited by a combination of normally incident light and concentric annular grooves with the period satisfying the following formula$\left(\omega /\text{c}\right)\sin \theta \pm n2\pi /\lambda =k$, a is the period of the grooves, and k is the SPP wave vector. In our experimental configuration, the incident angle θ is 0, thus the period a of the plasmonic lens should be the wavelength λ_spp of the SPPs at the gold/air interface [13]. The λ_spp at gold/air interface can be calculated by the following formula${\lambda }_{\text{spp}}={\lambda }_0\sqrt{\left({\epsilon }_r+1\right)/{\epsilon }_r}$, λ₀ is the wavelength of illuminating light. ${\epsilon }_r$ is the real part of the relative dielectric constant of gold. For a 671-nm incident light in this experiment, the obtained λ_spp is about 640-nm. Hence, the plasmonic lens designed here consists of 10 concentric annular grooves with the period of a (640-nm), which can efficiently excite SPPs at the gold/air interface when the 671-nm laser beam is normally incident from the bottom of the sample. Surrounding the 10 grooves is another 9 ones with the period of a/2 (320-nm). These grooves, serving as a Bragg reflector, can reflect out-propagating SPPs generated from inside grooves back to the geometric center and thus enhance the intensity of the focal spots [14–17].

The film should be thin enough to make sure that the incident light from the bottom could partially penetrate and excite SPPs at gold/air interface. Meanwhile, the film should also be thick enough to prevent excessive light transmission, reduce background noise around the focal spot. Together with the finite-difference time-domain (FDTD) calculation, the thickness of the gold film was set as 75-nm, the depth of the grooves about 25-nm for the inner converging lens and about 15-nm for the outer reflector.

The depth of the grooves and the thickness of the metallic film were measured by an atomic force microscopy (AFM), as shown in Fig. 2 . Figure 2(a) shows the topographical image of the plasmonic lens structure; Fig. 2(b) shows a cross-sectional profile along the dash line in Fig. 2(a). The average depth of outer grooves is 14.5-nm, the inner 23.4-nm. The thickness of the gold film obtained by measuring an intentionally fabricated transparent slit on the film is 74.0-nm. The corresponding parameters of the phase delayed plasmonic lens are all the same.

 

Fig. 2 (a) Atomic force microscopy (AFM) image of the plasmonic lens. (b) Cross-section image of the lens along the dash line in (a), indicating the depth of the grooves.

Download Full Size | PDF

The intensity distribution of SPPs was measured by SNOM at a constant height of about 80-nm height above the sample in order to reduce the damage of the sample. The decay length of the SPP field into the air is calculated to be about 400-nm so that SPPs can be detected at 80-nm height with decent signal-to-noise ratio. Along the polarized direction, two focal spots with the separation of 580-nm were obtained above the center of the plasmonic lens, as shown in Fig. 3(a) . Different from plasmonic lens only consists of transparent annular slits, no obvious transmission of light field were detected in the whole illuminating region, as we predicted. To obtain further insight on the focusing mechanism, we also performed numerical calculations using the FDTD method to simulate the optical intensity distribution above a model with the same structure as we designed [18]. Figure 3(b) shows the simulated optical intensity distribution in the plane at the height of 80-nm above the plasmonic lens. Two focal spots with the separation of 320-nm were obtained in the center along the polarized direction. Both in the experiments and simulations, the SPP field are preferentially generated along the polarized direction of the illuminating light, because only the polarized component perpendicular to the grooves could excite SPPs. Because the film is not smooth enough, the resulting scattering of light on the surface cause some differences between the experimental results and the simulations, the experimental results shown in Fig. 3(a) does not show obvious polarization direction preference as shown in the simulations.

 

Fig. 3 (a) SNOM image in near-field of the area with periodic grooves, bright regions correspond to high intensity. (b) Electric field distribution of the plane about 80-nm above the plasmonic lens on a thickened substrate. (c) Normalized experimental and theoretical cross sections through the center of the plasmonic lens along the polarized direction. The solid line indicates the experimental results. The dash line indicates the numerical results.

Download Full Size | PDF

For comparison, the transverse profiles of the measured energy density distribution and the numerically computed results by the FDTD method were depicted in Fig. 3(c). In the experimental results depicted by the solid line, the peak intensity is about 4-5 times of the background noise above the grooves. For comparison, the intensity of the incident laser beam is also detected by the SNOM system when using the incident laser beam directly incident on the fiber tip. The results indicate that the peak intensity of the spots is as strong as the incident laser beam. The average full-width at half-maximum (FWHM) of the focal spots is about 330-nm, within the subwavelength range for the incident light. In the simulating results depicted by the dash line, the peak intensity of the focal spots is 4-6 times of the side lobes. The average FWHM of the focal spots is 200-nm. The difference between the experimental and theoretical results is mainly attributed to the big probe aperture and the long distance away from the surface. The vibration in the scanning and the field disturbance by the probe tip also result in some differences.

There are two components contribute to the total energy density distribution |E|², namely the longitudinal electric field component |Ez|² (with respect to the focusing plane) and radial electric field component |Er|². |Ez|² was calculated to be several tens of times stronger than |Er|² for a SPP mode [10]. Two focal spots, or in other word, a null at the center of the plasmonic lens can be understood by considering two SPP waves originating from two opposite points along the circumference of a annular groove and propagating towards the center. Because of uniform distribution of the illuminating light, these two SPPs arrive at the center with the same amplitude and accumulating the same phase, and therefore |Er|² will interfere constructively. |Ez|², however, will interfere destructively at the center because the two SPP waves arrive at the center with their Ez pointing in the opposed z-direction. On the other hand, owing to the symmetry of fundamental mode propagating in the fiber core of the SNOM probe, the detected signal of the apertured SNOM fiber probe is proportional to$\left|{\nabla }_{\perp }{E}_z\right|$ [19,20]. Consequently, the experimental results show a null at the center. For the same reason, if illuminating with a radially polarized light, |Ez|² will interfere constructively at the center because the two SPP waves arrive at the center with Ez pointing in the same z-direction, resulting in a single focal spot.

Here, we proposed a new structure to produce a single focal spot still using a linearly polarized light. The radius of half part of every circle is designed to be bigger than the other half by 320-nm. Because the SPPs wavelength is 640-nm for the 671-nm illuminating light, the phase of the SPPs excited on the upper half region (See Fig. 1c) was delayed by π comparing to the SPPs excited on the other half. Hence, |Ez|² interferes constructively at the center because the two SPP waves exited in the opposite position of the same groove arrive at the center with Ez pointing in the same z-direction, resulting in a single focal spot. Figure 4 shows the SNOM image at the height of 80-nm above the plasmonic lens. As expected, a single focal spot is obtained experimentally (Fig. 4a, Fig. 4b) and theoretically (Fig. 4c). The average FWHM of the focal spots is about 200-nm (Fig. 4d).

 

Fig. 4 (a) SNOM image in near-field of the area with periodic grooves, bright regions correspond to high intensity; (b) SNOM image of the white square region in (a); (c) Electric field distribution of the plane about 80-nm above the phase delayed plasmonic lens; (d) Normalized experimental and theoretical cross sections through the center of the plasmonic lens along the polarized direction. The solid line indicates the experimental results. The dash line indicates the numerical results.

Download Full Size | PDF

To testify the enhancement effect of the surrounding plasmonic Bragg reflector, we also calculated electric field intensity distributions at 80-nm height above a converging lens without Bragg reflector surrounding. The cross section of the SPPs field through the center of the plasmonic lens along the polarized direction is shown in Fig. 5 . In the normalized coordinatometer, the solid and dash lines with the peak values of 1.0 and 0.51, indicate the model with and without the Bragg reflector surrounding, respectively. Thus, the intensity of the focal spots is almost doubled by using the Bragg reflector. For comparison, we also simulated the process of the previous works, and obtained the intensity of the focus. The strength of the plasmonic focal field is about 10 times of that in the previous works.

 

Fig. 5 Intensity distribution of |E_z | ² along the polarization direction through the center of the plasmonic lens at 80-nm height above the structure; Solid line and dash circle line are calculated above the plasmonic lens with and without Bragg reflector of SPPs surrounding, respectively. The lines are shown with the same coordinatometer; the maximum intensities of each line are 1.0 and 0.51, respectively.

Download Full Size | PDF

4. Conclusion

In summary, by illuminating a converging lens surrounded by plasmonic Bragg reflector, two focal spots of SPPs with the separation of 580-nm were detected by using a SNOM. No obvious light transmission was detected in the illuminating region. The average FWHM of the focal spot is 330-nm, within the subwavelength range for the incident light. Using FDTD method, we demonstrated the intensity of the focal spots is almost doubled by using the plasmonic Bragg reflector. By raising the radius of a half of every groove by 320-nm, the two focal spots turned into a single one with a 200-nm FWHM. This type of plasmonic lens offers potential applications at many regions like subwavelength optics, near-field imaging and sensing, lithography and nanoparticle manipulations, etc.