2.1.

Generation Principle of IPB

A schematic diagram of our all-fiber IPB generator is shown in Fig. 1. In the generator, one end of a graded index multimode fiber (MMF) with a specific length is fused with a single-mode fiber (SMF); the other end of the MMF is polished and plated with nanogold film, and then surface plasma structure is prepared on the gold film. When the device is working, the optical field radiating from the SMF is first expanded in the MMF and subsequently irradiates the plasma structure to excite plasmon waves; then the excited plasmon waves will couple into the free space via the plasma structure and produce the subwavelength IPB. In this scheme, expanding the optical field using the MMF aims to provide more space for the flexible design of the plasma structures. In Fig. 1(a), the plasma structure illustrated is a nanoring slot with inner radius and external radius being $r_1$ and $r_2$, respectively. Figure 1(b) shows the schematic diagram of the measurement system for measuring the far-field transversal optical intensity distributions generated by the fiber plasma structure. The single-wavelength laser is coupled into the IPB generator through an SMF, and the imaging system is a Nikon microscope that consists of a 100× objective lens with $\mathrm{NA}=0.9$, a tube lens (TL), and a charge-coupled device (CCD) with a single pixel $7\mu \mathrm{m}\times 7\mu \mathrm{m}$. The IPB generator is fixed on a high-precision displacement table. During the movement of the displacement table, the imaging system can observe the far-field intensity distribution of the IPB with different propagation distances.

Fig. 1

(a) 3D schematic diagram of the all-fiber far-field IPB generator. SMF is a single-mode fiber and MMF is a graded index multimode fiber. $r_1$ and $r_2$ in the inset are the inner and external radii of the nanoring slot plasma structures, respectively, and the white circular region denotes the area of the gold film that has been etched. (b) Measurement system for observing the far field of the IPB generated by the fiber-integrated plasma structure.

Assuming that $f(x,y)$ is the mode field distribution function at the output face of the MMF (i.e., $z=0$ plane) and $C(x,y)$ is the aperture function of the plasma structure, according to the Rayleigh–Sommerfeld diffraction formula, the output optical field can be expressed as

Considering that the center of the nanoring slot is located on the central axis of the MMF, and the width of the slot is much smaller than the wavelength, i.e., $\mathrm{\Delta }r=r_2-r_1=\lambda$, the aperture function $C(x,y)$ can be rewritten as

Fig. 2

Normalized intensity distributions of the output optical field simulated via the analytic equation. (a) Normalized intensity distribution in the $x-z$ plane. (b1)–(b4) Normalized intensity distributions on the $x-y$ plane with different transmission distances of 4, 5, 6, and $7\mu \mathrm{m}$, respectively. (c1)–(c4) Normalized intensity distributions on the $x$ axis extracted from the results of (b1)–(b4), respectively.

2.2.

Experimental Generation of IPB via Nanoring Slot

As shown in Fig. 1, the optical field needs to be expanded to provide more space to design the structure. For the nanoring slot structure with an inner radius of $7\mu \mathrm{m}$, if the optical field is not expanded via MMF, the radius of the mode field in the SMF core should be much less than $7\mu \mathrm{m}$, which means that the structure cannot be illuminated at all. Therefore, the length of the fused MMF will affect the far-field distribution of the output light. We calculate the optimal fusion length of the MMF by Rsoft simulation. The SMF and the MMF selected in the simulation are the Coherent 980-xp SMF (Coherent Company) and OM1 graded refractive index MMF (Yangtze Optical Fibre and Cable Joint Stock Limited Company), respectively. The simulation results are displayed in Fig. 3. Figure 3(a) is the normalized intensity distribution of the optical field in the $x-z$ plane when the light is coupled from the SMF to the MMF, from which we can see that fusing a $250\text{-}\mu \mathrm{m}$ long MMF to the SMF can achieve an optimal beam expansion. Figures 3(b) and 3(c) are the normalized intensity distributions of the optical field on the $x-y$ plane and along the $x$ axis after being expanded by the $250\text{-}\mu \mathrm{m}$ long MMF. The blue curve in Fig. 3(c) is the simulation result extracted from Fig. 3(b).

Fig. 3

Normalized intensity distributions of the optical field of the MMF. (a) Normalized intensity distribution on the $x-z$ plane. (b) Normalized intensity distribution on the $x-y$ plane after being expanded by $250\mu \mathrm{m}$ MMF. (c) Normalized simulation and experimental intensity distributions on the $x$ axis after being expanded by $250\mu \mathrm{m}$ MMF.

Based on the simulation results, we fused a $250\text{-}\mu \mathrm{m}$ long MMF to the SMF and polish the end surface of the MMF. Then we measured the normalized intensity distribution of the optical field along the $x$ axis; the experimental result is shown as the red curve in Fig. 3(c). It can be seen that the experimental result is highly consistent with the simulation result, and the optical field follows Gaussian distribution with an FWHM of $20\mu \mathrm{m}$. The surface morphology of the MMF end surface, as shown in Fig. 4(a), is measured using a 3D morphometer microscope (sneox-IFU90). By extracting the surface height distribution in the horizontal direction of the MMF end surface, it can be seen that the surface height drop is only 20 nm in the center region of the MMF end surface with a $40\text{-}\mu \mathrm{m}$ diameter, as shown in Fig. 4(b), which is suitable for processing plasma structures. The scanning electron microscope (SEM) image of the fabricated nanoring slot with $r_1=7\mu \mathrm{m}$ and $r_2=7.2\mu \mathrm{m}$ is shown in Fig. 4(c).

Fig. 4

Sample characterization. (a) 3D morphology measurement result of the polished fiber end surface. (b) Morphology measurement results along the $x$ axis of the polished fiber end surface. (c) SEM images of the fiber end surface and the nanoring slot.

In the experiment, a 980-nm wavelength laser is selected as the incident light. During the measurement process, the all-fiber IPB generator is fixed on an electronically controlled nanodisplacement table, and the fiber end surface is defined as the original plane ($z=0$). The nanodisplacement table is used to move the end surface of the subwavelength beam generator with a precision of 200 nm step by step, so the intensity distribution of the output optical field at different transmission distances can be observed and recorded experimentally. Figures 5(a1)–5(a4) show the observed light-intensity distributions on the $x-y$ plane at different distances (4, 5, 6, and $7\mu \mathrm{m}$) from the fiber end surface. Then the intensity distributions along the $x$ axis of the four corresponding planes are extracted from Figs. 5(a1)–5(a4) and compared with the simulation results, as shown in Figs. 5(b1)–5(b4), where the red curves are the experimental results and the blue curves are the simulation ones. The FWHM of the experimental results are 378 nm ($0.385\lambda$), 428 nm ($0.436\lambda$), 450 nm ($0.459\lambda$), and 504 nm ($0.514\lambda$), respectively. Therefore, the generated optical field with subwavelength resolution ($<\lambda /2$) when the propagation distance is $<6\mu \mathrm{m}$ fits well with the theory. Meanwhile, we extract the light-intensity distributions along the $x$ axis of different transmission distances in the range of $4\mu \mathrm{m}\le z\le 10\mu \mathrm{m}$ with 200 nm step precision, and then splice the extracted results to obtain the intensity evolution of the light along the propagation direction, as shown in Fig. 5(c). It clearly reveals that the output light generated by the plasma nanoring slot is an IPB, and the intensity evolution is in high agreement with the simulation result shown in Fig. 2(a). Figure 5(d) shows the simulation and experimental results of the FWHM of the main lobe of the IPB at different transmission distances. It can be seen that the FWHM obtained from experimental measurements increases with the propagation distance, and the FWHM of the IPB is smaller than $\lambda /2$ under $z\le 6\mu \mathrm{m}$. This trend is consistent with the simulation results. However, the FWHMs of the experimental results is slightly larger than that of the simulation results, which may be due to imperfections in the device fabrication process.

Fig. 5

(a1)–(a4) Observed intensity distributions of the output light on the $x-y$ plane at $z=4$, 5, 6, and $7\mu \mathrm{m}$, respectively. (b1)–(b4) Comparison of the simulation and experimental results of the normalized light-intensity distributions along the $x$ axis of $z=4$, 5, 6, and $7\mu \mathrm{m}$ planes. (c) Experimental result of the intensity distribution of the output light on the $x-z$ plane. (d) Variation of the FWHM of the IPB’s main lobe with the propagation distance in different environments. (e) Normalized intensity distributions on the center axis of the IPB in a blood serum environment with different absorption losses.

We further find that the FWHM remains subwavelength-scale, even though the propagation distance from the fiber end surface reaches $10\mu \mathrm{m}$. This makes the beam ideal for realizing noninvasive single-point illumination or targeted stimulation of subcellular structures inside a living cell, such as organelles, biomolecules, or nanosized pharmaceutical particles, thus allowing for the study of relevant life processes at the single-cell level through light–matter interactions on a subwavelength scale. It should be noted that, however, the above experimental results are obtained in the air environment. Usually, cells can only survive in liquid environments such as cell culture fluid, blood, and biological tissue fluid. Therefore, it is necessary to study the output optical field of our all-fiber IPB generator in a liquid environment. However, due to the lack of a water immersion objective, we do not have the experimental conditions to measure the intensity distribution of the output optical field when the device is placed in a liquid environment. Fortunately, the correctness of the theoretical formula (1) is fully proven by the fact that the experimental results are in good agreement with the simulation results when the device is placed in the air environment. Therefore, we can also effectively evaluate the transmission evolution of the output light theoretically when the generator is placed in a liquid environment. For this, the variations of the FWHM of the main lobe with the transmission distance when the device is placed in blood serum and glycerol solutions were simulated, respectively. The simulation results are shown as the green and orange solid lines in Fig. 5(d). In the simulation, the refractive index of glycerol and blood serum solutions are chosen to be 1.473 and 1.344.³⁹ It can be seen that by placing the device in a medium with a refractive index greater than that of air, such as blood serum and glycerol, the FWHM of the IPB will be further reduced, and even if the transmission distance reaches $10\mu \mathrm{m}$, the FWHM will still be smaller than half of the wavelength, so it is expected to achieve light–matter interactions in a living cell with higher precision. Moreover, in order to evaluate the influence of the transmission loss of the blood serum environment on the evolution of the IPB beam, we calculated the evolution of the normalized intensity on the center axis of the IPB beam during its propagation in a blood serum environment with different absorption coefficients $\alpha$; the simulation results are shown in Fig. 7(e). It can be seen that since the distance of the optical field propagation is only at a 10 mm scale, the effect of loss on the intensity evolution is negligible.

2.3.

Generation of Subwavelength Beam with Sidelobe Suppression Characteristic

Although it has been demonstrated that the fiber end integrated nanoring slot can generate an IPB with subwavelength resolution effectually, the obtained IPB is accompanied by strong sidelobes, which may limit its field of view and, hence, potential applications. Suppressing the strong sidelobes can overcome this deficiency. For sidelobe suppression, Hu et al.⁴⁰ have proposed a sharp-edge diffraction element consisting of a pair of moonlike sharp-edged apertures, which can generate an optical superoscillation with low sidelobe in a particular dimension. Motivated by this, we designed and fabricated a nanopetal plasma structure structure on the end surface of the fiber to produce a subwavelength beam with sidelobes suppressed in two dimensions. The design process of the nanopetal structure is depicted in Fig. 6(a). Initially, the central axis of the fiber is considered as the center of the circles $C_1$ and $C_2$ with radii $r_1=7\mu \mathrm{m}$ and $r_2=5\mu \mathrm{m}$, respectively. Then, the circles $C_3$, $C_4$, $C_5$, and $C_6$ are obtained by shifting $C_2$ along the negative $x$ axis, positive $x$ axis, positive $y$ axis, and negative $y$ axis with the displacement $d=4\mu \mathrm{m}$; finally, the gold film in the parts of circles $C_3$, $C_4$, $C_5$, and $C_6$ that do not intersect with circle $C_1$ are etched off to form the nanopetal structure. The aperture function of this nanopetal structure is

Fig. 6

(a) Schematic of the nanopetal structure etched on the fiber end surface. (b) SEM image of the nanopetal plasma structure. (c) and (d) Simulation and experimental results of the optical intensity distribution with a propagation distance of $6\mu \mathrm{m}$, respectively.

The SEM image of the nanopetal structure etched on the fiber end surface is presented in Fig. 6(b). Figures 6(c) and 6(d) illustrate the simulation and experimental intensity distribution of the output light of the nanopetal structure with a transmission distance of $6\mu \mathrm{m}$ from the fiber end surfaces, i.e., $z=6\mu \mathrm{m}$. The results clearly show that it can effectively suppress the sidelobes of the output field in two dimensions, i.e., in both the $x$-axis and $y$-axis directions.

To evaluate the generated subwavelength beam with sidelobe suppression in more detail, we first experimentally measure the output light-intensity distributions along the $x$ axis with transmission distances of 4, 5, 6, and $7\mu \mathrm{m}$ from the end surface of the fiber and compare them with theoretical simulation results. The comparison results are shown in Fig. 7. It can be seen that the FWHMs of the main lobe are 407 nm ($0.415\lambda$), 411 nm ($0.419\lambda$), 516 nm ($0.527\lambda$), and 529 nm ($0.540\lambda$) at 4, 5, 6, and $7\mu \mathrm{m}$, respectively. It can be found that before $5\mu \mathrm{m}$, the FWHM of the generated IPB is smaller than half of the wavelength.

Fig. 7

Normalized intensity distributions along the $x$ axis of the nanopetal plasma structure with different transmission distances. (a) $4\mu \mathrm{m}$, (b) $5\mu \mathrm{m}$, (c) $6\mu \mathrm{m}$, and (d) $7\mu \mathrm{m}$, respectively. (e) and (f) Comparison of the sidelobe suppression effect of the nanoring slot and nanopetal plasma structures. The proportional value is defined as the ratio of the maximum light intensity of the first-order sidelobe to that of the main lobe.

Then to provide a clear demonstration of the sidelobe suppression effect of the nanopetal structure on the $x$-axis direction, we extracted the ratio between the maximum intensity of the first-order sidelobe and the maximum intensity of the main lobe from the light-intensity distributions along the $x$ axis. The extracted results of the output IPBs from both the nanoring slot and nanopetal structures are shown in Figs. 7(e) and 7(f), in which Fig. 7(e) is the result obtained via theoretical simulation and Fig. 7(f) is the result extracted from the experimental results. The simulation results show that within the range of $4\mu \mathrm{m}\le z\le 9\mu \mathrm{m}$, the ratio of the output beam of the nanopetal structure is smaller than that of the nanoring slot along the $x$ axis. Especially at the distance of $z=7\mu \mathrm{m}$, the ratio of the output beam of the nanopetal structure decreases to 8%, implying that the nanopetal structure has a significant sidelobe suppression effect along the $x$ axis. The experimental results can demonstrate the sidelobe suppression effect of the nanopetal structure in the same transmission distance range. However, both the output beams of the nanopetal and the nanoring slot exhibit higher experimental sidelobe strengths compared to the simulated results. This discrepancy may be attributed to imperfections in the device preparation process. Nevertheless, these imperfections do not prevent the ability of the nanopetal structure to suppress the sidelobes in the $x$-axis direction. Since for the output beam of the nanopetal structure, the maximum intensity of the first-order sidelobe locates on the 45-deg axis, we further investigated the ratio between the maximum intensity of the first-order sidelobe and the maximum intensity of the main lobe from the light-intensity distributions along the 45-deg axis, and show the theoretical and experimental results in Figs. 7(e) and 7(f). It is shown that on the 45-deg axis, the ratio of the output beam of the nanopetal structure is larger than that of the nanoring slot. This implies that the sidelobe suppression effect of the nanopetal structure in the $x$-axis direction comes at the expense of sidelobe enhancement in the 45-deg-axis direction.