1. Introduction

Computational techniques such as digital holographic microscopy (DHM) provide for high-resolution lensless imaging that can capture both the amplitude and phase of light waves [1–8]. These digital holography techniques explicitly reproduce the propagation of light waves through an imaging volume. Computational imaging provides many benefits, such as being able to change the focus after capturing an image or removing aberrations numerically. Because all recording media (e.g., CCD or CMOS cameras) respond only to the intensity of light, gathering phase information requires a mutually coherent reference wave. The interference of this known reference wave and an unknown object wave form a hologram in the recording plane. The phase and amplitude of the object wave is therefore recovered and can be propagated through space when processed digitally. Along with other lensless [9] or incoherent [10] imaging techniques, DHM has significant potential for biological imaging and sensing [11]. For example, DHM has been used for high-resolution microscopy without lenses [12], simulating differential interference contrast microscopy [13,14], imaging of particles and microorganisms [15], tracking cells [16], as well as profiling surfaces and other microscopic objects [17]. Holography has many applications, including data storage [18].

Parallel to these significant advances in digital imaging technology, the field of plasmonics is pursuing complementary goals via nano-optical engineering for optical sensing [19], high-resolution imaging [20–22], surface-enhanced spectroscopy [23], optical tweezing [24], and even as a holographic recording medium [25]. Surface plasmons (SPs) are electromagnetic surface waves bound to a metal-dielectric interface by coupling light to free electrons [26] and are characterized by sub-wavelength field confinement, greatly enhanced fields, and short wavelengths. To more fully characterize, control, and exploit the potential of these surface waves, there is significant interest in developing the two-dimensional equivalents of standard optical elements such as plasmonic mirrors, beam-splitters, and interferometers [27]. For example, directly visualizing SP interactions with various objects in-plane could aid in the development of plasmonic biosensors [19]. Therefore, in-plane plasmon diffraction [28], refraction [29], reflection [30], wavefront shaping [31], and plasmonic lenses [32–35] have been demonstrated. Unfortunately, these have typically relied on complex nano-fabrication techniques [36], hindering efficient, simple, and direct in-plane imaging with surface plasmon waves.

Previously, we demonstrated lensless, in-plane plasmonic imaging by applying digital holographic techniques in the plane of surface plasmon propagation [37]. While other in-plane plasmonic imaging techniques [30,38,39] capture the intensity of the plasmons, holographic reconstruction also records the phase. Furthermore, while related digital techniques have been used for tweezing [40], scanning [41], and to study apertures [42], out-of-plane diffraction patterns [43,44], and prism-coupled plasmons [45], capturing and digitally reconstructing both the intensity and the phase of plasmon waves for imaging and sensing applications over a surface has not been fully explored. Therefore, in-plane digital holographic techniques offer many unique research opportunities. However, our previous work [37] also had several important drawbacks such as the need for a complex dual-probe Near-Field Scanning Optical Microscope (NSOM) or using a lithographically-defined fluorescent screen. Our previous experiments and holographic reconstructions also suffered from what is known as the “Twin Image” problem, wherein the object wave reconstruction is overlapping with its complex conjugate, oftentimes causing significant interference. Because of these drawbacks, the potential for high-resolution imaging and real-time plasmonic sensing applications was limited.

In this work, we show the plasmonic equivalent of lensless, in-line DHM, which we call digital plasmonic holography, with iterative phase retrieval algorithms to remove the twin image. Supported by computational modeling, we present high-resolution, direct in-plane plasmonic imaging without the need for plasmonic lenses, nano-structured surfaces, or other in-plane optical elements. Since in-plane digital plasmonic holography directly visualizes and measures plasmon interaction with surface objects, it can also be used for sensing purposes. In particular, we use leakage radiation microscopy [38] to capture an intensity image of plasmons propagating over a surface, sample the image along a 1D line, and use iterative phase retrieval and digital holographic algorithms to remove the Twin Image and extract the phase of the plasmon waves scattered by various test objects. Recent out-of-plane plasmonic holography schemes also tackle Twin Image interference [46] but the reconstruction process relies on 2D Fourier transforms. In-plane plasmonic holography, on the other hand, only requires a 1D hologram to reconstruct the 2D field, as discussed below, thereby offering potential advantages for high-speed data acquisition and processing. With in-plane plasmonic holography, both the reference wave and the object wave are surface plasmon waves, removing the need for an external reference beam. Therefore, plasmonic holography as described here may provide a valuable new tool for nano-imaging and plasmonic sensing.

2. Method

A hologram $H({x,y} )$ is the recorded interference pattern between a known reference wave $R({x,y} )$ and an unknown, but mutually coherent, object wave $O({x,y} )$ as given here:

But recording media (digital or otherwise) are sensitive only to the hologram intensity ${|{H({x,y} )} |^2}$ as follows:

If this hologram intensity is recorded digitally, the unknown object wave can be extracted through various techniques [47]. In our specific case, with small, isolated, and transparent object particles, the object intensity term ${|{O({x,y} )} |^2}$ will be smaller than the reference intensity ${|{R({x,y} )} |^2}$. and can typically be ignored. The slowly-varying reference intensity ${|{R({x,y} )} |^2}$ is then removed with a digital high-pass filter, which can further suppress ${|{O({x,y} )} |^2}$. This leaves the two interference cross terms, i.e., the object wave $O({x,y} )$ and its so-called twin image [1]. These two terms can’t be separated algebraically and much effort has gone into reducing the interference effects of the twin image [48]. Various options are directly applicable here, such as iterative techniques [49] and recording multiple holograms [50] at different distances, as are discussed below. Furthermore, since the object wave and reference wave propagate over a surface as 2D plasmon waves, our holograms are sampled along a 1D line or curve. A 1D hologram can therefore be used to reconstruct a 2D field, just as a 2D hologram recorded on a digital camera or piece of film can be used to reconstruct a 3D light field. Please see supporting information for more information on 1D versus 2D holography.

The holographic pattern over the surface is imaged directly via plasmon leakage radiation microscopy [38]. This is a powerful imaging technique that captures light radiated at the surface plasmon resonance (SPR) angle by using a high numerical aperture (NA) lens [51] and has been used for biological imaging [52]. An image is produced that directly represents the intensity of plasmons at the surface [53]. In our experiments, these leakage radiation images were then analyzed as in-plane plasmonic holograms. Figure 1 shows the leakage radiation image process. Our microscope setup (see supporting information for a full schematic) contains a 50x upper objective (air, NA = 0.55) and a 100x lower objective (oil, NA = 1.40). The upper microscope objective provides the illumination source as a 660 nm wavelength laser. Direct transmission through a 50 nm thick silver film on a substrate generates no plasmon waves [Fig. 1(a)] whereas illuminating a small nano-feature will scatter Hankel-type plasmons in a circularly-symmetric pattern [54].

 

Fig. 1. Experimental scheme. (a) Illuminating a thin metallic film will have partial direct transmission. The sample here is a smooth, template-stripped 50-nm thick Ag film. The objective lens used is a 100x (NA = 1.40) oil-immersion lens. (b) When illuminating a small 200 nm diameter particle embedded in the surface (inset), surface plasmon waves are launched as from a point source. These leak into the high-NA objective lens at the surface plasmon resonance angle. (c) Image of the back-aperture (Fourier plane) of the directly transmitted light, the diameter reflecting the NA of the upper illuminating microscope. (d) Fourier plane image obtained by illuminating the embedded particle showing a clear ring of leakage radiation. (e) The Fourier plane is filtered with an annular aperture, selectively passing the plasmon leakage radiation. (f) Image-plane view, directly from the microscope camera, showing a clear leakage radiation image of the plasmon waves from the illuminated point source. The features are discussed in the text. (g) A simplified experimental schematic.

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These plasmons will leak at the surface plasmon resonance angle as shown in Fig. 1(b) and are collected by the high-NA lower objective. This is clearly seen in the back-aperture (Fourier) plane of the lower objective. Figure 1(c) shows a bright illumination disc, the diameter corresponding to the NA=0.55 upper illumination objective. When the laser is focused on the nano-feature, plasmons are generated and leak at a specific angle, as shown in Fig. 1(d). Furthermore, this plasmon leakage can be spatially filtered with an annular aperture (Thorlabs) placed in the physical Fourier plane, blocking all of the directly transmitted light and only passing the light emitted at the SPR angle. Figure 1(f) shows a raw image-plane picture of the sample surface taken by the CCD camera (PCO Pixelfly), clearly demonstrating plasmon generation radiating out from the source over the surface. The laser is horizontally polarized, and the circular fringes are due to interference between plasmonic and non-plasmonic sources, e.g., between the leakage radiation and the dipole-like emitter at the nano-feature [38]. For the most part, these circular fringes could be ignored or filtered out. The radially-propagating plasmonic wave forms the illumination source or reference wave $R({x,y} )$ for in-plane digital plasmonic holography. Figure 1(g) shows a simplified and not to scale experimental schematic with illumination from an upper objective, plasmon leakage radiation, collection with a high-NA lower objective, filtering with the annular aperture, and imaging on a camera. The images in Figs. 1(c), 1(d), and 1(e) were taken with the camera located in a conjugate aperture plane. More details are given in the supporting information.

3. Results and discussion

Figure 2 shows digital plasmonic holography with source and object waves. Hankel-type plasmons [54] were emitted from the single “source” nano-features and provide the point-source reference wave $R({x,y} )$ which in turn scattered from the various objects, generating the object wave $O({x,y} )$. Importantly, the object wave is generated by in-plane scattering from the object illuminated “edge-on” by the plasmonic reference wave, i.e., the object is not externally illuminated in any way. The holographic image, i.e., the interference between the object and reference waves, leaked through the film into the microscope as shown in Fig. 2(a). Due to the circular geometry of the reference wave, polar coordinates were used for $R({\rho ,\phi } )$ and $O({\rho ,\phi } )$.

 

Fig. 2. Leakage radiation plasmonic holography. (a) The reference plasmon wave illuminates an object, thereby creating the object plasmon wave. The coherent interference of the two is the hologram leakage image. (b) Brightfield optical microscope image of the experimental setup showing the 200 nm diameter reference launch point and the 1 µm diameter microsphere objects. (c) “Darkfield-like” optical microscope image after the annular aperture of the reference point and several objects. (d) Leakage hologram image of the plasmons, showing clear interference between the reference and object waves. (e) Zoomed-in region of the image showing the object wave interference pattern. The dashed lines represent where the hologram is sampled. (f) Raw hologram sampled from the image. (g) Reconstruction of the hologram showing the point-like object. The inset shows the reconstructed phase around the object.

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The samples consisted of a smooth template-stripped silver film [55] with embedded 200 nm “source” polystyrene nanospheres (Bang’s Labs) and with dropped-and-dried 1 µm diameter “object” polystyrene microspheres (Bang’s Labs) over the surface. First, a 50 nm silver film was deposited via thermal deposition chamber (Oxford Vacuum Science) onto a silicon wafer with the dispersed 200 nm “source” nanospheres. This covered and embedded the nanospheres into the silver. A drop of UV-curable optical adhesive (Norland 61) was then used to strip the pockmarked film from the silicon with a glass coverslip. The 1 µm diameter “object” microspheres were then dropped-and-dried onto the smooth silver surface and the sample was placed into the microscope setup. See supporting information for more experimental and sample fabrication procedures.

Figure 2(b) shows the optical image from the upper microscope objective of both “source” and “object” particles. A 660 nm laser was focused onto one of the 200 nm “source” nanospheres from the upper objective, generating the reference plasmon wave that propagated over the surface and interacted with the 1 µm “object” microspheres. The plasmons then leak into the lower objective. Direct white-light transmission from the upper objective is also blocked by the annular aperture, producing a dark-field-like image that is helpful in identifying objects on the sample, as shown in Fig. 2(c). The full leakage image, after blocking the direct laser transmission, is recorded in an image plane of the lower microscope. The plasmonic hologram is shown in Fig. 2(d). A zoomed-in portion, showing the scattered object wave more closely, is shown in Fig. 2(e). While the leakage radiation image does provide the intensity of the plasmons in the plane, the phase information is missing and therefore needs to be extracted via holographic reconstruction. Since we are considering the in-plane propagation of the surface plasmons, a one-dimensional circumferential hologram of the plasmonic intensity is extracted from the leakage image [the dashed line in Figs. 2(d) and 2(e)] and is shown in Fig. 2(f). The hologram is back-propagated in the plane, towards the source, thereby reconstructing the amplitude and phase of the plasmonic field. Since in-plane plasmonic holograms are analyzed along a one-dimensional line, not a two-dimensional surface as is typically the case for imaging, it has potential for very high-speed data acquisition of plasmonic images.

Previously we used the plasmonic equivalent [56] of the angular spectrum technique [1] to back-propagate in-plane plasmonic holograms [37]. For a circular geometry, an analogous method using a helical wave spectrum [57] can also be applied [37], as it is again here. Briefly, the plasmonic field ${E^{SP}}({\rho ,\phi } )$ is given in polar coordinates, centered on the source, and propagated radially inward with $\rho < a$, with a being the radius where the hologram is captured, using the Fourier series relation given here:

In this case, $H_n^{(2 )}$ are Hankel functions of the second kind defining the transfer function $\frac{{H_n^{(2 )}({{k_{SP}}a} )}}{{H_n^{(2 )}({{k_{SP}}\rho } )}}$ whereas $E_n^{SP}({\rho = a} )$ is the transform in polar coordinates of the hologram recorded at $\rho = a$. This is given as:

While a single object is still recovered relatively clearly, as in Fig. 2 and in our previous work [37], the twin image noise is still present and should be removed, especially for quantitative phase imaging or sensing applications. In conventional “in-line” digital holography, the twin image interference cannot be directly removed from a single intensity image [48,60]. Relative phase shifts between the object and the reference waves [7], iterative phase-retrieval techniques [49], or combining multiple recordings at different distances [50] are therefore necessary. In our case, since we already have the in-plane intensity of the plasmon wave with a single leakage image, this information can be used to iteratively extract the unknown phase of the plasmonic field as the holograms are propagated, thereby removing the twin image term and leaving only the object wave after reconstruction. In other words, the intensity profile can provide a constraint on the holographic reconstruction process. Therefore, to remove the twin image term in Eq. (2), we adapted a “dual-plane” iterative phase retrieval technique [61] to a “dual-radius” geometry. The iterative phase-retrieval algorithm proceeded as follows. For a single leakage image [e.g., Fig. 2(d)], we extracted the hologram intensity at two radii, producing a pair of circular holograms. The field, or the square-root of the hologram intensity, was then propagated inward using the helical spectrum, as before, but from the outer radius to the inner radius. The propagated phase was kept, and the reconstructed intensity was replaced with the measured hologram intensity. This corrected inner hologram (measured intensity, propagated phase) was then propagated outward to the outer radius. Propagation in the outward direction uses a slightly modified Eq. (3) transfer function, shown in the supporting information as Eq. SE1. The propagated phase was again kept while the reconstructed intensity was replaced with the measured hologram intensity. This corrected outer hologram (measured intensity, propagated phase) was then propagated to the inner radius, repeating the process. This is essentially a standard Gerchberg-Saxton iterative phase retrieval algorithm [62] adapted to our one-dimensional helical wave spectrum propagation technique. Please see the supporting information for more information on this algorithm. After a number of iterations, the field was then propagated fully towards the center source, reconstructing a full in-plane image of the plasmonic field.

Simulations of this iterative phase retrieval algorithm are shown in Fig. 3. A plasmonic hologram is first simulated by interfering two separate Hankel-type, point source plasmon waves over a surface [Fig. 3(a)] using MATLAB software. This simulation also includes the non-plasmonic circular fringes seen in Fig. 1(f) and appears qualitatively similar to the experimental leakage images shown in Fig. 2. The hologram intensity is extracted at the two marked radii producing the pair of inner and outer holograms as shown in Fig. 3(b). If only a single hologram radius is used, as done experimentally in Fig. 2(g), the object is reconstructed with significant twin image interference, shown in Fig. 3(c). If the dual-radius iterative technique is used, the twin image interference is removed as shown in Fig. 3(d). Typically only <50 iterations are required to reduce the intensity of the twin image interference by a factor of ∼10 [Fig. 3(e)]. Multiple objects can also be more accurately recovered. Figures 3(f) and 3(g) show three point objects arranged around the center. With a single radius technique, the objects are barely visible, and the twin image of one overlaps the real image of another [Fig. 3(f)]. With iterative phase recovery, the three objects are much more clearly defined [Fig. 3(g)]. In these simulations, the phase of the object wave forming the hologram can be easily adjusted, as done in Fig. 3(h). The phase of the reconstruction is more accurately extracted using the dual radius technique, critical for sensing applications.

 

Fig. 3. Computer simulations and verification of iterative phase retrieval algorithm. (a) Simulation of two point sources, the reference and the object, showing qualitative similarities to the experimental in-plane plasmonic holograms. (b) Two holograms are extracted along two radii and are used to constrain the intensity of the hologram propagation. (c) Reconstruction only using the outer radius, showing twin image interference. (d) Using the dual-radius iterative technique, the twin image and surrounding interference is removed. (e) Plot of the relative twin image intensity versus iterations. (f) A more complicated reconstruction from three point-like objects showing significant twin image interference that (g) is largely removed with iterative phase retrieval.

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Figure 4 shows the dual-radius iterative phase retrieval on a set of experimental data. Figure 4(a) shows a section of the same hologram shown in Fig. 2 of a single object. At the same (arbitrary) intensity scaling, the dual-radius iterative technique clearly increases the brightness and contrast of the reconstructed spot, removing much of the residual twin image noise. Another area of the sample contained more objects. The bright-field optical microscope image is shown in Fig. 4(c) and the leakage image is shown in Fig. 4(d). Two holograms are extracted at the marked inner and outer radii and then plotted, as raw data, in Fig. 4(e). Using only the outer radius reconstructs the objects rather poorly, shown in Fig. 4(f), whereas the dual-radius iterative technique shown in Fig. 4(g) shows the reconstructed objects.

 

Fig. 4. Experimental hologram reconstruction. (a) The same object and holographic reconstruction shown in Fig. 2(g). While the object appears as a bright spot, twin image noise remains. (b) Same data, but reconstructed with the dual-radius iterative phase retrieval technique. The object brightness and contrast increases. (c) Another region of the sample with more objects. (d) The raw leakage radiation image, showing where two concentric holograms were extracted. (e) Plot of the raw hologram data at the two radii. (f) Reconstruction of the object wave using only a single radius and (g) using the dual-radius iterative technique.

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Iterative phase retrieval can be used for real-time plasmonic sensing applications, as shown in Fig. 5. In our case, instead of a liquid-based [63] or gas-based [64] molecular sensing experiments as is often done with plasmonic sensors, we simply employed a second 532 nm heating laser that would selectively heat the various objects. This allowed us to heat only one object and keep other objects as sensing reference baselines. Simulations shown in supporting information as well as our previous work [37] confirm that changes in the refractive index of one object can be detected in the plasmonic hologram. Typical power levels of the green heating laser were 50 ∼ 250 mW at the laser, corresponding to 0.5 ∼ 2.4 mW at the upper objective after passing through several optics, beam combiners, beam splitters, and filters. This is shown schematically in Fig. 5(a). After heating, the green laser was filtered with a steep long-pass filter (Semrock) shown in Fig. 1(g), still allowing the red imaging laser through to the camera. In a typical experiment, full-frame movies of the leakage images were captured at ∼7 frames per second over the course of ∼75 seconds. The green heating laser was turned on after establishing a ∼15 second baseline and turned off again at ∼55 seconds. A zoomed-in region of a typical holographic leakage image is shown, both before [Fig. 5(b)] and after [Fig. 5(c)] heating the object with the green laser. The small phase shift in the holographic fringes is enhanced by viewing the difference between these two images, shown in Fig. 5(d). Two circular holograms were extracted from each of the frames in the sensing movie and processed. Sample holograms are shown before and after heating in Fig. 5(e). In time, these holograms will shift, as shown in the waterfall plot in Fig. 5(f). The location of laser heating is marked. The phase of the objects is reconstructed, as shown previously in Fig. 2(g), and plotted in time. Figure 5(g) shows a representative real-time sensing experiment, reconstructed from the data in Fig. 5(f). The phase of the reconstructed object changes as it is heated with the green laser. A second object is used as a baseline, and shows no shift in the reconstructed phase. This is seen in the raw holograms in Fig. 5(e), where the heated object fringes appear and shift at the circumferential angle $\phi \sim 45^\circ $ whereas the reference object’s fringes appear and don’t shift at the circumferential angle $\phi \sim 180^\circ $. Another sample in Fig. 5(h) shows a similar effect, with a significant phase shift in the heated object with respect to the reference object. Several effects are likely contributing to the measured phase shifts including thermal expansion or melting of the polystyrene bead. Some of these phase shifts appear permanent, indicating a deformed or melted bead, as shown in 5g as “Sample 1”. Lower laser powers on a different sample, shown in 5g as “Sample 2”, produced a reversible effect in the measured phase, perhaps indicating thermal expansion, local changes in refractive index, or melting and reforming of the polystyrene sphere. Because of the in-plane imaging aspect of digital plasmonic holography, a reference object can be used to ensure that we are measuring only changes in a single object. To summarize, we are detecting changes in the phase of the reconstructed image at the location of the heated test object, as shown earlier in Fig. 2(g). As the test object is heated by the second laser, this reconstructed phase changes in a measurable way, either because of thermal expansion, refractive index changes, or by simply melting. A second nearby object that is not heated acts as the baseline in the recorded phase vs time plots in Figs. 5(g), 5(h) and could be used to remove any background artifacts. These results demonstrate that in-plane digital plasmonic holography with iterative phase retrieval can be used for real-time plasmonic sensing.

 

Fig. 5. Experimental sensing results. (a) Schematic showing the second 532 nm green laser that was used for heating one object for sensing experiments. (b) Raw leakage image, with the green laser filtered out, of an object both before and (c) after heating. (d) The slight phase shift in the holographic fringes are apparent by taking the difference of the two images. (e) The phase shift is also apparent in a before and after heating hologram slice, particularly at circumferential angle $\phi \sim 45^\circ $ where the heated object was placed. (f) A waterfall plot of the hologram slices in time, showing the effects of heating when the green laser was activated. (g) Recovered phase of the object, plotted along with another nearby object that wasn’t illuminated and became a phase reference. The heated object shows a large permanent shift in the reconstructed phase in time [sample 1]. Another sample, at lower powers, shows a smaller, but reversible, phase shift [sample 2]. (h) Another example with a different sample and two objects, again showing the heated object responding with a large phase shift and the unheated object remaining steady.

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4. Conclusion

We have shown that iterative phase-retrieval technique can be used with digital plasmonic holograms imaged via leakage radiation microscopy. Using the intensity images to extract the phase of various objects over a surface can then be used for real-time plasmonic sensing. Heating one object on a sample shows a large phase shift whereas a nearby reference object remains steady, indicating that digital plasmonic holographic sensing can be used in an imaging format. Furthermore, digital plasmonic holography captures information about in-plane scattering of plasmon waves from surface objects. In this regard, in-plane plasmonic holography can be complementary to conventional digital holography since objects are imaged from two orthogonal points of view. Plasmons image an object through its “edge” in-plane whereas conventional holography images objects through their thickness, i.e., perpendicular to the object plane. Plasmons are also only sensitive to objects within ∼100 nm of the surface, providing unique sensing capabilities. In-plane holography doesn’t require a reference beam external to the sample or external to the microscope, thereby eliminating mechanical noise that may occur if the reference beam moves relative to the object beam. Finally, in-plane reconstruction only requires a 1D hologram, thereby providing potential opportunities for high-speed data acquisition and processing. These unique advantages of digital plasmonic holography may therefore enable new studies of plasmon / nanoparticle interactions and provide researchers with valuable new tools for nano-imaging, plasmonic phase imaging or interferometry, characterizing plasmonic devices, or new forms of plasmonic sensing.