Achieving sub-100 nm resolution over a broad visible bandwidth has long been an elusive goal in the nano-imaging of cell-surface interfaces. While metamaterial super-lenses and near-field optics have been previously demonstrated, these techniques can operate only at one wavelength, and do not provide accesses to the cell-surface interfaces. Here, we investigate a broadband 2D lens comprised of an oblate spheroidal dielectric cavity embedded just beneath a planar metal surface. The lens operates by adiabatically focusing asymmetric plasmon energies at sub-100 nm scale on the low-index side of the thin metal film formed between the cavity top and the planar metal surface. We then proposed the use of our lens in a high-resolution far-field confocal microscopy setup. Due to the surface-field nature of our lens, the presented system holds potential as an indispensable tool for cell-surface interfacial studies that require sub-100 nm hyper-spectral imaging analysis.
© 2011 OSA
Many cellular functions, such as cell proliferations, cell migrations, wound healing, and adaptive immune response are inherently linked to cell-surface interactions. However, given their biological importance, cell membranes have been surprisingly overlooked by biochemists until recently [1–4]. In particular, during cell-cell/cell-surface interactions, the role of membrane-bound receptors and lipids in regulating membrane behavior at the interfaces remains obscure , due, perhaps, to the hurdles presented in accessing these areas. Although some high-resolution microscope techniques, such as field emission scanning electron microscope (FESEM), have permitted visualizations of membrane structures with utmost details, these techniques are often restricted to static investigations under conditions that are not of physiological relevance .
Recently, there have been increased interests in visualizing cell membranes via optical means. While optical techniques are generally not comparable to FESEM in terms of spatial resolution, they offer the possibility of probing molecular activities within plasma membranes under physiological environments. Fluorescence spectral imaging, for instance, has been employed in conjunction with a lipid-phase-sensitive fluorescent probe to study lipid domain distributions on the cell surface . R. Bohme et al., on the other hand, employed a Raman spectroscopic approach to simultaneously determine multiple biomolecular components on a cell membrane in a label-free manner , thereby eliminating the possibility of perturbations to the membrane morphology by exogenous molecules . Given the chemical specificity of optical spectra, one could expect membrane studies to benefit profoundly from hyper-spectral imaging techniques. Although a conventional microscopy system coupled with a spectrometer could fulfill this goal, an equivalent system is practically non-existing in the realm of nano-scale imaging. It is the main objective of this paper to present such a system.
Generally, to achieve supra-resolution requires breakthroughs in shrinking the point-spread function (PSF) of the imaging system. In a conventional far-field microscope, the minimum attainable PSF size is limited to about half of the illuminating wavelength, which, for a visible light, is in the order of 200 nm . Such a limitation is dictated by the dispersion characteristic, , of the medium surrounding the sample, which causes the high spatial-frequency components (i.e. large ) from the sample to decay exponentially with distances and ultimately become lost in the far field. This brings about blurring as these components cannot be included in the image reconstruction - a condition best known as the diffraction limit. Nonetheless, many have attempted to achieve supra-resolution. One example is the solid immersion lens reported by Terris, et al., in which the high refractive index of the lens permitted imaging at approximately 120 nm at visible frequencies . Another more recent example is the demonstration of an antenna-based optical microscopy in the imaging of single fluorescent molecules in both dried as well as wet states . In this particular study, an 80 nm Au nano-particle was incorporated at the end face of a scanning glass fibre tip to serve as an optical antenna. During imaging, the “bright” nano-particle was brought to the near field of the sample surface and maintained at a fixed particle-sample distance of just ~5 nm so as to attain an optimal fluorescence excitation. With these regards, NSOM may be seen as a relatively more suitable hyperspectral imaging technique, since it has already been utilized to image non-contacting membrane surfaces in fluorescence as well as Raman-scattering modes [8,12,13]. Unfortunately, the inaccessibility of the interfaces between contacting membranes to the probe tip has hampered the applications of NSOM to cell-surface studies. In addition, given there exist evidences indicating reorganization of membrane receptors during cell-surface interactions , it is therefore doubtful that knowledge acquired from non-contacting membrane surfaces could be of relevance to the understanding of membrane dynamics at the cell-surface contacts. Although superlens constructed with an uniaxial metamaterial layered structure capable of transferring high spatial-frequency energies from a sample plane onto a far-field plane may be used for cell-surface studies , a drawback, however, is that high-resolution can be attained only within a very narrow range of wavelengths, where the radial propagation vector vanishes .
In the current paper, we propose a simpler approach with which sub-100nm imaging can be carried out over a broad bandwidth spanning between 400 nm – 700 nm with a flat-top optical response. More specifically, we look into a system comprising of an oblate dielectric cavity with a high major/minor ratio buried just beneath the surface of a semi-infinite metal bulk. We show that if the cavity is kept within the skin depth of the SPPs, the thin metal film so-formed between the top of the embedded cavity and the planar metal surface shall behave as a 2D plasmonic lens capable of adabiatically compressing incident SPP waves to form a narrow SPP spot. We will investigate such a cavity-SPP interaction in the second section of this paper and comment on the focusing effect invoked by the embedded dielectric cavity. In the third section, we show how a tightly focused SPP spot (~50 nm) could be obtained on the metal surface by directing a radially-converging SPP wave toward the lens. Finally, a method for tuning the position of this particular SPP spot is discussed, and a proposition is made of a far-field confocal microscopy system consisting of a scanning radially-polarised beam and our plasmonic lens. We then assess the resolving power of such a system by calculating the images of four close-spaced fluorophores placed near the center of the lens through the use of an effective PSF. The attainable resolution is estimated to range between 30 nm to 67 nm for incident-wavelengths ranging between 450 nm to 700 nm, respectively. With such a broad-band imaging capability, our lens therefore meets the desired requirements as a truly broadband imaging tool suitable for routine nano-scale cell-surface studies in either fluorescence multi-labeling mode or Raman mode.
2. Focusing of SPP by embedded oblate dielectric cavity
Let us begin by considering a system consisting of a 3-µm (major diameter) oblate dielectric cavity embedded at a depth, d, beneath a metal surface as shown in Fig. 1a . The minor diameter of the cavities is assumed to be 230 nm. Also, we assume that the cavity is made of a medium with a dielectric constant, , and the embedding material is Au with optical constants given by Johnson and Christy . The region above the planar metal interface is assumed to be water (). The field distributions around the embedded cavity were calculated by solving the related Maxwell equations in spheroidal coordinates (see Appendix), and numerically computed using MATLAB. In the calculation, the incident SPP was assumed to propagate in the positive x-direction as indicated in the figure.
First, the normalized field-strength distributions (i.e. ) on a vertical plane (i.e. xz-plane) cutting through the center of the cavity are examined. The calculated results are shown in Figs. 1b and 1c for d = 10 nm and 25 nm respectively. In this particular example, the SPP angular frequency is assumed to be - which corresponds to the vacuum wavelength of 633 nm. A general inspection reveals the fields to be mainly confined to the metal-dielectric interfaces, suggesting that these fields are plasmonic in nature. Of particular interest are the fields associated with the thin metal film region (TF in Figs. 1b and 1c) formed between the top of the embedded cavity and the planar metal interface. Due to the narrow thickness of the film, the SPPs bound to the opposing metal interfaces can interact with each other and hybridize to yield two coupled SPP modes differing in the field directions at the opposites sides of the film; a symmetric SPP mode () corresponds to cases where the transverse fields () at both sides of the film are vectorially parallel, while an anti-symmetric SPP mode () anti-parallel. Depending upon the film thickness as well as the refractive index of the bounding dielectric mediums, the two modes can have differed field strengths. In order to identify which of the SPP modes is dominant in the current case, we check the directionalities of the instantaneous evanescent fields in the vicinity of the film for d = 10 nm and 25 nm, as shown in Figs. 2a and 2b, respectively. Note that a positive value would indicate an upward pointing electric field, while a negative value represents downward field. As indicated in Fig. 2, the fields on both sides of the film are generally anti-parallel, which implies that these fields are primarily arisen from the modes . To further assert this conclusion, we proceed to examine the extension of along the z-direction at different points near the planar metal surface with a rationale that a field should decay more rapidly compared to single-interface SPPs because of its comparatively large propagation constant (see red marks in the dispersion curves shown in Fig. 2c). Indeed, the fields bounded to the metal film are found to be generally more confined and decay up to 1.5 times more rapidly compared to those at other dielectric-metal interfaces, thereby asserting the above claim that is the dominant plasmonic mode on the film. The absence of the mode is not surprising given the fact that the metal film considered here is bounded by asymmetric dielectrics ( and ), which bestow a cut-off thickness exceeding the current film thicknesses (see dispersion curves in Fig. 2c) i.e. mode can no longer propagate on the films as a pure bound mode. This observation corroborates quite well with the results of Burke, et al. studies on asymmetric metal slabs .
One beneficial consequence brought about by the unique plasmonic characteristic of the metal film is the possibility to focus SPP energies. To illustrate this point, we return to the cavity systems considered in Fig. 1a, and compute the xy-distributions of the plasmonic field amplitudes over a 3. 2 µm × 3.2 µm area just above the metal surface. The data are shown in Figs. 3a and 3b, respectively for the two cases where the cavities are embedded 10 nm and 25 nm beneath the metal interface. An interesting observation that can be made of these fields is the formation of a focal spot (denoted as FS in Fig. 3) within the circular area defined by the circumference of the embedded cavity (dashed circle in Fig. 3). In other word, the metal area directly above the cavity appears to behave as a 2D lens. In fact, the propagation of SPPs within this area was found to follow classical ray optics as shown in Fig. 3c. Generally, the effective index of the lens is not homogenous but graded radially due to the gradual changes in the film thickness (see cavity cross-section in Fig. 1a) toward the lens center C. However, to illustrate the ray behavior of SPPs, it suffices to treat the lens as to have a homogeneous effective index, as in Fig. 3c. Since the index of -SPPs is higher than that of a single-interface SPPs, the incident ray should deflect toward the C upon entering the lens. Due to mismatch in the momentum, the transmitted and incidence wave-vectors, and at the lens boundary should satisfy, , in which the modulus of the reflected wave-vectors (i.e. ) are equal to , and is the momentum transferred to the cavity system. The reflection coefficient R in the above equation can be approximated to zero, since a further study of the fields shows minimal back-reflections from the lens. This can be attributed to an adabiatic coupling between the incident SPP and the -modes owing to the gradual changes in the film thickness toward the center of the lens (see cavity cross-section in Fig. 1a). Hence, the boundary condition could be satisfied simply by equating the tangential components of and , i.e. . By virtue of a simple geometry, one sees that the angle α, sustended between and the x-axis, and the distance between the lens center C and the focus point B (see Fig. 3c) can be expressed as , and , respectively. For a system containing a deeply-embedded cavity (i.e. thick metal film), and hence , implying no focusing effect. However, if the cavity depth is shallow so that the -SPP momentum , , suggesting a deflection of the vectors toward the C and thus resulting in a pencil of converging rays crossing the x-axis, i.e. focusing. Furthermore, from the equations, one could also predict a tighter focusing with the focal position as becomes larger than . This is indeed the case according to Figs. 3a and 3b on the fact that the FS positions become closer to the lens center when the film thickness decreases, i.e. when the -SPP momentum increases. We have therefore qualitatively demonstrated that the 2D lens formed by the embedded oblate cavity follows a similar geometric optics as 3D lenses do.
3. Formation of a narrow plasmon focus by the 2D lens
As shown in Figs. 3a and 3b, the plasmonic focus (PF) formed by the 2D lens through focusing a SPP plane wave is generally not sharp and exhibits a profile that is modulated by interferences fringes arisen from converging -SPP waves crossing each others. The quality of the focus must be improved before it can be applied to a high-resolution imaging. We therefore ask if a narrow PF can be obtained by radially converging -SPP waves toward the center of the lens. To see this, we consider our 2D lens placed at the center of a ring of closely spaced SPP point sources as shown in Fig. 4a . The total SPP wave produced within the ring of SPP sources can be described as , in which is the propagation length of the surface plasmons. The phase-lags between sources will, for the moment, be assumed to be zero. Figures 4b and 4c show PFs formed at the center of the ring in the absence and presence of the 2D lens (here assumed to be a 3 µm oblate cavity with a thickness of 230 nm), respectively at a SPP frequency of . It is clear that the focus appears to be more tightly confined, when the lens is used, with a FWHM of about 67 nm (see profile in Fig. 4d), while the focus created without the lens is notably larger (FWHM = 144 nm), owing to the lack of diffraction by the short-wavelength -SPPs.
We now consider the general scheme of a high-resolution far-field microscopy system that incorporates our 2D plasmonic lens as shown in Fig. 5 . A circular slit milled through the metal slab constitutes the ring of SPP point sources by providing a means to couple free-space incident light into SPPs. A circular slit is used, instead of a grating, because of its ability to couple light at different frequencies. In order to ensure SPPs generated at the slit can converge radially toward and interact with the lens, the circular slit is positioned such that its center coincides with that of the lens. The incidence angle of the excitation beam can be altered via the xy-mirror, which also serves to ensure that SPP energies generated from samples within the lens can be collected and focused into a detection fiber. Since the fiber here acts as a point detector, the current system is thus a confocal setup.
The choice of the incident polarization is crucial in producing a narrow PF. In order to produce a single spot at the focus point, constructive interferences of SPPs must occur exactly there. This is illustrated in Fig. 5 for different incident polarizations under a normal incidence condition. Figures 6a and 6b show SPP spots obtained without and with the embedded cavity, respectively using a linearly-polarized Gaussian incident beam, while Figs. 6c and 6d using a radially-polarized Gaussian beam. A double PF is obtained under a linear polarization because opposing SPP sources on the circular slit oscillate at a 180° phase shift, and hence only at the sides of the focus point can constructive interferences occur. Next, we show that the position of the PF can be tuned by adjusting the relative phase of the SPP wave vectors at the circular slit, i,e. by introducing some phase lags between the SPP sources. This can be achieved by changing the angle of the incident beam via the xy-scanning mirror. , in this case, can be expressed as , in which, and are the inclination and azimuthal angles of the incident beam, respectively (see Fig. 5), and R is the radius of the circular slit. Simulated SPP spots produced by a 633-nm radially-polarised beam in a 2 µm × 2 µm imaging area for ranging between 0° to 3° at = 0° are displayed in Fig. 6e–6j. As can be seen, the PF shifts laterally by up to 1.12 µm for this angle range, giving a shift-per-degree-angle of 373 nm/°. Of particular interest is the focusing quality of the PF which is, in general, not significantly affected by the shifting with a FWHM maintaining at about 67 nm (see profiles in Fig. 6k). This result is extremely important as it implies no degradation of lateral resolution throughout the imaging area. We should note that the position of the PF is, however, sensitive to the wavelength with about 15% displacement for every 60 nm shifts in wavelengths. Nevertheless, this should not be a factor impeding image reconstruction so long as only signals close to the excitation wavelength are detected.
Given the sensitivity of the PF position to the inclination angle, , one must ensure the lens be mounted perfectly level, i.e. the imaging Au plane should be perfectly normal to the optical axis, so that scanning at the theoretical resolution can be attained. This can be achieved by securing the lens on a micro-meter holder, and aligning it until the position of the laser spot formed on plane P via L2 by the specular reflection from the bottom of the superlens coincides with the incident laser spot (see Fig. 5) when is set to 0°. A simple geometrical analysis will show that an alignment with a sub-radian accuracy is possible with this particular method if f2 is sufficiently long (say, ~6 cm). On the other hand, the accuracy in the lateral alignment of the circular slit to the annular beam can be relatively more relaxed since the PF position depends only on and . Positioning of the beam to the slit can be easily accomplished via markings deliberately left on the lens during fabrication.
In order to evaluate the resolving power of the current microscopy system, we attempt to compute the image of a closely-spaced square array of four fluorophores placed around the center of the lens as shown in Figs. 7a –7c. The fluorophores are assumed to emit with negligible stokes shifts (i.e. ) and are arranged with a closest fluorophore-fluorophore separation of . Simulation of far-field fluorescence images reconstructed using signals collected by the detection fiber (see Fig. 5) is calculated through the convolution , where defines the positions of each fluorophore on the lens. Due to the confocal nature of the microscopy system, both the excitation PSF, and the detection PSF, can be assumed to be identical functions as defined by the intensity distribution of the PF. Since the PF does not vary considerably in shape with position (see Fig. 6k), it will be assumed that , in which indicates the PF intensity distribution obtained under normal incidence. To demonstrate the broadband imaging capabilities of the lens, three images are calculated at three different incident vacuum wavelengths, . Typical simulation results are shown in Figs. 7d–7f for λ0 = 488, 520, and 633 nm, respectively. Note that, in each case, is adjusted to a minimum value below which individual fluorophores are judged un-resolvable in the images. In this way, we determine the maximum achievable resolutions to be 37, 43, and 60 nm at 488, 520 and 633 nm, respectively. Maximum resolutions attainable at other wavelengths are also computed in a similar fashion and are plotted in the graph shown in Fig. 7k. Curve I is the resolution-versus-wavelength curve corresponding to lens with the dielectric cavity embedded 10 nm below the planar metal surface, while curve II and III, 12.5, and 15 nm, respectively. From these curves, one can estimate a variation of at most 3% in the spatial resolution for every nano-meter error in the cavity depth during fabrication.
In addition, one should also be aware of ohmic losses in Au, which could limit the scanning area. We estimated, based on the optical constants given by Johnson and Christy , that a 19, 6.6, and 1.14-times drop in the excitation intensities can occur at λ0 = 488, 520, and 633 nm, respectively if the scanning area is doubled. Such a damping in SPP intensities can nevertheless be compensated by increasing the laser power or the power density at the wall of the radially-polarized excitation beam.
For comparison, images of the closely-spaced fluorophores obtained in the absence of the embedded oblate cavity (i.e. using only the circular slit) are shown in Fig. 7g–7i. These images generally appear as one bright patch with hardly any discernible structural details for the same incident wavelengths and values as those considered in Fig. 7d–7f.
A possible fabrication scheme for producing our 2D superlens is shown in Fig. 8 . The ultra-smooth imaging plane that is required in order to minimize in-plane SPP scatterings can be attained by the method of mica templating as shown in the diagram. A high-precision deposition technique such as ion-assisted e-beam evaporation can be employed for deposition of Au with a sub-10 nm resolution on the cleaved mica (110) plane, thereby allowing for an accurate tuning of the distance, and hence the plasmonic coupling strength, between the cavity and the imaging plane. Formation of the oblate dielectric cavity can be achieved via Au encapsulation of an oblate polystyrene micro-particle (OPM) deposited on the Au film (see Step #1 - #6). The OPM can be obtained either by the method of heat-stretching a polymer micro-sphere as reported by J. A. Champion et al. or by the technique of particle-shaping with ion-irradiation by E. Snoeks et al [18,19]. Also crucial for the correct operation of the 2D superlens is the precise centering of the circular plasmonic slit around the OPM. Such a structural accuracy can be achieved by using a dual-beam high-resolution FIB/FE-SEM system both to locate the OPM, which can first be half-embedded with Au, and to mill the slit with the ion-beam (see Step #3). Since the scanning area of our lens is 2 µm × 2 µm, a typical error of about 10 nm in the ion-beam position is tolerable. Subsequently, masked Au deposition can be applied to cap the OPM further with Au while avoiding filling up the circular slit. Finally, a layer of SiO2 coating is deposited to provide supporting strength (see Step #5). For ease of handling, the lens can be glued to a thin glass slip with an index-matching epoxy. Mica may remain attached to the lens to prevent contamination during storage, and be removed by mechanical stripping to expose the smooth imaging plane only prior to use (see Step #6).
The simulation results discussed above confirm that the 2D lens proposed here works well for sub-100nm imaging over a broad bandwidth. In particular we have provided a detailed analysis of the operating mechanism of our 2D lens. It was pointed out that the short-wavelength -SPP modes were mainly responsible for the sub-diffraction resolution. Owing to the peculiar nano-focusing ability of our lens, a narrow PF of about 50 nm in size can be obtained. Finally, we evaluate the resolving power of our proposed imaging technique at different incident wavelengths. The results indicate our system holds potential as a general tool suitable for broadband imaging of sub-cellular structures such as lipid domains at the cell-surface contacts or protein assembles. Since the SPP coupling efficiency of the circular slit is not frequency sensitive, the current lens therefore allows for multi-color excitations.
The field distributions for the cavity systems considered in this paper are calculated by solving the related Maxwell equations in oblate coordinates. Fields were computed using MATLAB software, and the validity of the Maxwell solutions was verified by asserting that the boundary conditions were satisfied at all metal-dielectric interfaces. Due to the strong interactions between the oblate cavity and the planar metal surface, we found that the boundary conditions can be reliably satisfied only if the maximum angular momentum index, m, for the spheroidal wave expansion was set at 60. Field distribution at the metal surface shown in Figs. 3a and 3b was computed according to
(calculated based on the Maxwell theory) where is the incident SPP plane wave propagating in the positive x-direction. To calculate the field distributions of the plasmonic focus (FS) obtained when the lens is situated at the center of the SPP ring, we first expressed the converging incident SPP wave near the ring center (i.e. , where R is the radius of the ring) as a summation of SPP plane waves, , in which denotes the phase lags between the SPP point sources, and is the single-interface SPP momentum. From this, the field for the FS can be expressed as, , where is a rotation operator that rotates about the z-axis by an angle with respect to the x-axis.
This project is supported by the BioMedical Research Council (BMRC No. 05/1/31/19/397). The first author would like to thank the Singapore Millennium Foundation for a postgraduate scholarship.
References and links
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