3.1. Manufacturing Results
The manufacturing results were consistent with the design, which was due to the step-by-step etching method for the bilayer micropyramid transferring. The results of the manufacturing are shown in
Figure 5. The designed and experimental parameters of the fabrication are shown in
Table 4.
The base side-lengths of the bottom and top structure were
m and
m, and the height was
m and
m, which deviated very little from the designed size. The only difference lied in the fabrication compared to the design, where a
m spacing occurred between the two micropyramids. The red line means the contour line of the layered interface. The two red squares demonstrate the base side-lengths of the bottom and top structure, respectively, in
Figure 5. The preparation of the bilayer micropyramid was different from that of the single-layer micropyramid. First, the material of each layer was diverse, which led to a great difference in the anti-etching characteristic of each layer. The bilayer micropyramid array could not be formed in a one-step process with a single etching parameter as in the manufacturing of single-layer microstructures. Second, in order to ensure the continuity of the structure profile between layers, it was necessary to consider the stress matching between the layers. Before the bilayer micropyramid array transfer process, the thickness of the resist, the silicon nitride, and the silicon oxide thin film was 3
m, 2
m, and 2
m, respectively. The thickness matched the ratio of the etch rates, which ensured the preparation of the bilayer micropyramid array in accordance with the design. The manufacturing results proved that the step-by-step etching method was suitable for the preparation of the bilayer micropyramid array.
3.2. Characterization of the Focusing Properties
The comparison of the intensity profiles of the PNJ generated from the numerical simulations and the actual experiments is shown in
Figure 6 and
Figure 7. The maximum light intensity, decay length, FWHM, and focal distance generated from the simulation and experiment are shown in
Table 5.
Taking the results in
Figure 6 and
Figure 7 and
Table 5 into account, it simultaneously provided evidence to illustrate that the design followed the total internal reflection theorem, enhancing the intensity of the emergent optical field. Furthermore, the bilayer thin film inside the micropyramid structure extended the field intensity range benefits from the interference effects. All the parameters of the simulation and experiments satisfied the theoretical design values.
The distribution of the normalized intensity along the
z-axis characterizes the optical modulation of the bilayer micropyramid. The light intensity increased to
-times the initial one and was maintained in a certain area, which was stronger than the intensity of the simulation (
-times the initial one), as shown in
Figure 6a,b. The decay length of the actual experiments was 10.08 wavelengths, as shown in
Figure 6b, which was different from the homogeneous micropyramid whose
appeared near the apex [
23,
28,
37,
49]. The focal distance
f reached three-times the wavelengths, which means the
position broke through the locality of the near-field, bringing convenience to the manipulation of microparticles (as shown in
Table 5).
The simulated results showed good agreement with the actually measured ones. The experimental position of maximum intensity was basically the same as that of simulation with a deviation of only
. The simulated intensity had a wider range (to
), but its intensity was lower than the test value. It should be noted that the measured FWHM value of ~
was very close to the diffraction limit, which was far better than the simulation result, as shown in
Figure 7 and
Table 5. The difference in the focusing characteristics came from the replication deviation caused by the manufacturing. The structural gap produced by the actual preparation enhanced the light field coupling effect between the microstructures, which was one reason for the stronger intensity and smaller light spot, as proven by Gao [
50]. The simulation calculation pointed out the direction for fabrication and measurement, and the analysis of the simulation results helped explain the formation mechanism of the BMP-PNJ.
The experimental images of the two nearest BMP-PNJs are presented in
Figure 8. The maximum light intensity, decay length, FWHM, and focal distance are shown in
Table 5.
The two nearest bilayer micropyramid structures formed similar focused light field distributions. The difference in the decay length and focal distance were in the range of half a wavelength. Although the values were slightly different, the trend of change was very similar, as shown in
Figure 8a–c. It is worth noting that the left BMP-PNJ test showed that it broke the diffraction limit as one distinguishing feature of PNJs. These comparisons showed that although the results were similar, there were still some nonuniformities in the experimental process.
The effect of TIR theory can be illustrated by the comparison of the three BMP-PNJ types. The intensity profiles generated from the TIR, for the same length and same height PNJ, are shown in
Figure 9. The maximum light intensity, decay length, FWHM, and focal distance are shown in
Table 6.
As can be seen from
Figure 9a, when the base angle was smaller than the critical angle, which means without the TIR effect, the decay length was reduced to less than one half, and the maximum light intensity was only
in the case of the same base width dimensions. When the height of the micropyramid was the same as the TIR design, the decay length and the maximum light intensity both significantly reduced. What is noteworthy is that the focal length was increased nearly threefold.
Figure 9b further shows the numerical comparison of the decay length in accordance with TIR theory or not. The sum of the latter two types’ decay lengths was not comparable with that of the TIR-designed PNJ. The FWHMs are demonstrated in
Figure 9c. The base length determined the size of the focal spot. When the base length was long enough, there were two noticeable side lobes, which limited the resolution of the BMP-PNJ. Therefore, the use of TIR theory played a significant part in extending and enhancing the photonic nanojet.
Table 6 provides the corresponding numerical proof.
The power flow (time-averaged Poynting vector) plots for the three BMP-PNJs are shown in
Figure 10. When the incident wave entered the microstructure, the propagation direction was changed because of the effect of total internal reflection; even some light waves transmitted laterally, and other light waves converged at the pyramid tip along the sidewall of the structure (as illustrated in the red ellipse). This means that the incident energy was concentrated inside the structure. When the light wave propagated to the interface of the film layer, the incident wave interfered with the reflected wave, thus slowing down the convergence of the power flow and radiating the focusing effect to the far-field (as illustrated in the blue ellipse), which is presented in
Figure 10a.
The other two PNJ designs without TIR theory were much weaker in the light intensity and decay length. Many light waves entered the bottom of the micropyramid and then passed out, losing much energy, as seen in
Figure 10b,c. There was no obvious interference effect inside the bilayer microstructure due to the lack of the TIR effect converging the waves. Subsequently, the light waves diverged rapidly after transmission, resulting in transverse propagation in the region away from the tip of the micropyramid, which was also quite different from the TIR-designed BMP-PNJ.
Given the above, the use of TIR theory was crucial to obtain the most extended and intense photonic nanojet. Based on the power flow plots, it is obvious that the enhancement of light intensity was caused by total internal reflection. The direction of energy flow also illustrated the effect of interference effects on the extension of the decay length.