Plasmonic Nanopores: Optofluidic Separation of Nano-Bioparticles via Negative Depletion

In this chapter, we review a novel “ optofluidic ” nanopore device enabling label-free sorting of nano-bioparticles [e.g., exosomes, viruses] based-on size or chemical composition. By employing a broadband objective-free light focusing mechanism through extraordinary light transmission effect, our plasmonic nanopore device eliminates sophisticated instrumentation requirements for precise alignment of optical scattering and fluidic drag forces, a fundamental shortcoming of the conventional optical chromatography techniques. Using concurrent optical gradient and radial fluidic drag forces, it achieves self-collimation of nano-bioparticles with inherently minimized spatial dispersion against the fluidic flow. This scheme enables size-based fractionation through negative depletion and refractive-index based separation of nano-bioparticles from similar size particles that have different chemical composition. Most remarkably, its small (4 μ m (cid:1) 4 μ m) footprint facilitates on-chip, multiplexed, high-throughput nano-bioparticle sorting using low-cost incoherent light sources.


Introduction
Optical chromatography (OC) is an increasingly adapted technique for labelfree sorting and analysis of bioparticles including cells, bacteria, fungi [1][2][3][4]. It exploits a lightly focused Gaussian laser beam within a microfluidic channel to create opposing optical scattering and fluidic drag forces. One can leverage these controllable forces to realize selective fractionation of bioparticles in a heterogeneous mixture based on size, morphology or chemical composition (i.e., refractive index variation) [5,6]. OC technique was first implemented in size-based fractionation of inorganic materials such as polystyrene beads. Later, researchers employed this technique for size-based fractionation and sorting of organic particles including human blood constituents including erythrocytes, monocytes, granulocytes, and lymphocytes [2,5]. Subsequently, differentiation of micronscale bioparticles with subtle differences [4,7], including those with size differences as small as 70 nm [8], are shown. In addition to size-based separation, OC technique also offers refractive index-based fractionation capability, allowing separation of bioparticles with minuscule differences in chemical composition, such as Bacillus anthracis and Bacillus thuringiensis [4] and cells with single gene modifications [3]. Most recently, precise separation capability of OC technique is utilized in realization of multi-stage fractionation approaches enabling network-based microfluidic purification [9,10]. On the other hand, conventional OC technique suffers from powerful laser beam requirements to create sufficiently strong optical scattering forces [2], as well as multiple off-chip and bulky optical multi-axis positioners that are needed to realize well-controlled laser beam profiles precisely aligned against the fluidic flow [5]. Furthermore, separate sets of light sources and optical components are needed for each processing channels, preventing multiplexed high-throughput operation [10].
In a recent publication, we introduced a novel plasmonic nanopore device that eliminates the shortcomings of the conventional OC technique [11]. Here, we review this hybrid Optofluidic PlasmonIC (OPtIC) device merging light focusing and fluidic flow through a tiny (4 μm Â 4 μm footprint) plasmonic microlens housing an integrated nanopore channel. Based on a subwavelength-thick ($ 200 nm) suspended device structure, our optofluidic approach opens the door to practical, scalable, and high-throughput on-chip particle sorting.

OPtIC microlens design
In Figure 1a, an OPtIC device that consists of a periodic nanohole array (NHA) defined in a suspended multilayer membrane is shown. The mechanically robust membrane consists of a free-standing 100 nm thick silicon nitride (Si 3 N 4 ) substrate coated with 100 nm thick gold (Au) and a 5 nm thick titanium (Ti) adhesion layer. The total thickness of the microlens is h = t Au + t Ti + t Si3N4 = 205 nm, whereas the lateral dimension of the finite size NHA is 4 μm Â 4 μm. Recent research findings suggest that (quasi)periodic arrays of nanoplasmonic apertures behave as microconvex lenses focusing broadband incoherent light beams to spot sizes comparable to wavelength of light [11][12][13]. Such tight light focusing capability can be harnessed to realize sufficiently strong optical scattering forces suitable for OC using collimated broadband light sources [14,15]. In addition, the finite-size plasmonic NHAs can focus light over a broad wavelength range with focusing characteristics dictated by the lateral dimension of the array and nearly insensitive to sub-structural imperfections [13]. In this respect, our plasmonic nanopore device provides a distinct nanofluidic integration capability through small modifications in the NHA design without degrading its light focusing characteristics. The periodic NHA shown in Figure 1a consists of d = 150 nm diameter openings with a periodicity of a = 380 nm. Enhanced light transmission through the periodic nanohole around this center nanoaperture occurs through the extraordinary optical transmission (EOT) effect [16][17][18][19]. The enlarged central nanopore with d c = 500 nm exhibits orders of magnitude smaller fluidic resistance with respect to the neighboring nanoholes, enabling efficient nanofluidic flow through it. The OPtIC device uses inlet and outlet fluidic ports that are on the opposite sides of the NHA [20,21], as depicted in Figure 1b. This design facilitates microfluidic access from either side of the membrane [22]. In our simulations, 50 μm distance in between of the inlet and outlet fluidic ports is chosen to provide a clear path for the focused light beam [20]. Figure 1b depicts the cross-sectional view of nanofluidic flow pattern across the OPtIC device calculated using steady-state finite-element method (FEM) simulations (COMSOL Multiphysics). The overall size of the computational domain in Figure 1b is 50 μm Â 50 μm Â 40 μm. The inlet fluidic flow is directed towards the central aperture, where flow velocity is largest along the optical (z) axis in the vicinity of the optical focal point, whereas an almost symmetric behavior is observed towards the outlet port. The observed fluidic flow pattern can be understood through the Hagen-Poiselle law, where the pressure-driven flow across a cylindrical aperture with hydraulic diameter r H and thickness h occurs with a volumetric flow rate given by Q = Δp/R H (in m 3 s À1 ). Here, Δp is the pressure gradient across the aperture and R H = 8μh/πr H 4 (in PaÁs 3 m À1 with μ = 8.9 Â 10 À4 PaÁs being dynamic viscosity of water) is the hydraulic resistance [23]. Since the hydraulic resistance is inversely proportional to the 4 th power of hydraulic radius, it is two orders of magnitude smaller across the central aperture with respect to the rest of the holes in the NHA. Hence, convective fluidic flow, which follows the least resistance path, is through the central nanoaperture, as shown in our simulations. In summary, the OPtIC device forces nano-bioparticles to flow towards its focal point, where the dynamic flow trajectories of the particles are aligned with the optical axis of the plasmonic microlens.
A close-up cross-sectional view of the OPtIC device is given in Figure 1c, where the fluidic flow is in the -z direction within the close vicinity of the focal point (f 0 away from microlens top) as explained above. In this configuration, the collimated light incident from bottom along the +z direction is focused by the plasmonic microlens along the optical axis. Here, the focusing pattern, the amplitude-squared electric field ($|E| 2 ), is calculated through finite-difference time-domain (FDTD) simulations for incident light at λ = 655 nm. Forces acting on two different size nano-bioparticles within the focal point region are depicted on the right of the Figure 1c. Here, the optical scattering force (F s ) is inherently aligned against the fluidic drag force (F d ) along the optical axis for both particles. In addition, thermoplasmonic drag force (F tp ) caused by electromagnetic heating acts in parallel to F s . This will be explained in detail later. In addition to radial drag forces (F d,r ) due to the fluidic flow, the optical gradient forces (F g ) collimate particles along the optical axis, thus providing a robust mechanism for their precise alignment along the optical axis. Figure 1c depicts that large particles with diameters above a threshold are driven against the fluid flow (i.e. in the +z direction) provided that F s is sufficiently larger than F d . This is also true for particles with larger refractive indices. Thus, particles with larger diameters and/or higher refractive indices are rejected by the OPtIC device. In contrast, particles with smaller diameters and/or lower refractive indices are propelled through the central nanopore and leave the system from the outlet port. This mechanism provides a complete separation capability for smaller nanobioparticles (e.g. exosomes) in a heterogeneous mixture through negative depletion. Clogging of the central aperture is prevented by the microlens itself since it keeps the larger particles away from the surface.
Optical radiation force acting on nano-bioparticles can be divided into scattering F s and gradient F g components, as discussed above, which act along and perpendicular to the optical axis, respectively. While F s acts against F d , F g is directed towards the optical axis. Their magnitudes are given by [14]: where P is incident light power, n m is surrounding medium's refractive index, c is the speed of light and Q s,g is a respective dimensionless parameter representing optical pressure transfer efficiency due to reflection/refraction at material interfaces. It can be analytically calculated for simple beam profiles such as lightly focused Gaussian beams acting on a spherical particle. On the other hand, scenarios that use complex beam profiles or target smaller particles with diameters comparable to the optical wavelength (e.g. d $ 1 μm), the ray optics approximation cannot be used. Instead, a Maxwell stress tensor (MST) approach should be adopted [24,25].
where E and H are electric and magnetic field vectors, ε and μ are the electric permittivity and magnetic permeability of the medium, whereas δ ij is the Kronecker delta symbol. Using MST, the net optical radiation force on a small particle in an arbitrary field profile can be calculated through assuming a bounding box small enough to confine the particle as in [25].
with S being box surface wheren j is a unit vector along one of the principal axes.

Focusing efficiency of OPtIC microlens
The central nanopore opening plays a key role in precise alignment of fluidic flow along the optical axis and determining the threshold rejection diameter. On the electromagnetic part, it also controls the focusing characteristics of the OPtIC microlens. Hence, it should be ensured that the focusing behavior does not deteriorate for an admissible d c range [13]. Focusing patterns of the microlens illuminated by plane waves with λ = 655 nm for various d c values are given in Figure 2a.
Compared with the cases of no central nanopore (i.e., d c = 0 nm) and a uniform NHA (where d c = 150 nm), the enlarged aperture (d c = 500 nm) has a negligible effect on light focusing behavior, i.e., maximum intensity (|E| 2 ), spot size and depth of field (DoF). Moreover, focusing behavior does not significantly degrade for a large d c of 800 nm, as seen on the rightmost panel of Figure 2a.
The dashed horizontal lines in Figure 2a, corresponding to focal point, indicate that the focal length (f D ) is minimally affected by the change of d c , where it is 5.32 μm for d c up to 500 nm, and slightly increases to 5.56 μm for d c = 800 nm. Intensity profiles along the focal axis (i.e., z = f D , dashed lines in Figure 2a) are presented in Figure 2b. It is clearly seen that the OPtIC microlens brings incident light to a tight focal spot with a full width at half maximum (FWHM) of 1.12 μm for d c ≤ 150 nm, whereas FWHM tends to slightly increase for d c ≥ 500 nm, as it becomes 1.24 μm and 1.80 μm for d c = 500 nm and 800 nm, respectively. Thus, the focusing characteristics of the microlens is remarkably stable for a broad range of d c . Variation of optical intensity along the optical axis (z-direction) for different d c is shown in Figure 2c, where almost identical behavior is observed for relatively small size central nanopores (d c ≤ 150 nm). DoF also shows little variation for d c up to 500 nm. Only, a slight increase in focal distance is observed when d c = 800 nm. The light focusing mechanism of OPtIC microlens relies on the periodic arrangement of smaller nanoholes around the central one. The EOT effect occurs when the Bragg condition is met, i.e., G = iG x + jG y, where i and j are the corresponding (i, j) grating orders [16,18]. The transmission spectra shown in Figure 2d is obtained using E-field monitors on the focusing side of the microlens. EOT resonance occurs at λ = 650 nm (55 nm FWHM) for the (1,0) grating coupled condition. This confirms that the light focusing behavior is due to interference of inphase wave components emanating from the periodic NHA [13]. For the NHA with a large central nanopore (d c = 500 nm), deviation of the EOT peak compared to the NHA without a central opening (d c = 0 nm) is relatively small, although a larger background transmission is observed. However, further increase in the central nanopore dimensions (d c = 800 nm) leads to non-resonant light transmission, manifesting itself as enhanced background signal, as shown in Figure 2d (top curve). In the light of the above discussion regarding the fluidic flow around the focal point (see Figure 1) and light focusing behavior of NHA, an OPtIC microlens with 9 Â 9 NHA of d = 150 nm and a = 380 nm, along with a central nanopore opening of d c = 500 nm is adopted for label-free sorting of nano-bioparticles.
An important observation in Figure 2a is the checkerboard-like pattern just above the OPtIC microlens surface, which arises from plasmonic Talbot effect, that is diffractive self-imaging of smaller-diameter nanoholes [13,26]. On the other hand, intensity right over the central aperture is significantly enhanced for d c ≥ 500 nm due to diffractive light transmission through it. These two effects are compared in Figure 3 using near field phase maps where each small nanohole transmits waves with almost identical amplitude and phase, giving rise to in-phase interference around the focal point. Closer inspection of Figure 3 reveals that the checkerboard pattern is not disrupted when the central aperture is absent (Figure 3a) or is larger than the surrounding nanoholes in the array (Figure 3c). Light intensity around the central nanopore opening increases with increasing d c , as seen in Figure 2a. This observation is confirmed in Figure 2c where a secondary peak in light intensity close to the microlens surface appears. This peak is less intense than the peak around the focal point for smaller size central nanopores (d c ≤ 150 nm). However, it is significantly enhanced for larger size nanopore (d c ≥ 500 nm). The high intensity region around the nanopore opening may lead to increased optical scattering force F s , causing undesired rejection of smaller/lowerrefractive index particles that managed to pass the focal region and carried towards the central nanopore. However, in addition to tailoring the central nanopore dimension, one can also take advantage of Stokes flow [1,9,11], where the fluidic drag forces scale with the relative velocity of nano-bioparticles (u) with respect to the flow rate (v) of medium (i.e., F d ∝|u-v|). As fluidic velocity v is approximately three orders of magnitude higher close to the central nanopore opening with respect to that of the focal point (Figure 1b), fluidic drag forces F d are significantly larger too. Hence, optical scattering force F s around the nanopore region cannot repel particles that were below the critical diameters. As a result, in the following sections, interplay of forces only around the focal point is considered in the assessment of sorting efficiencies of the OPtIC microlens.

Broadband operation of OPtIC microlens
In the preceding section, we showed that the OPtIC nanopore device can focus collimated monochromatic light at λ = 655 nm (close to the EOT resonance peak) into a tight spot. However, broad spectrum operation is also desirable to utilize lowcost broadband incoherent light sources, such as light emitting diodes (LEDs) and halogen bulbs. Hence, development of microlenses that exhibit minimal chromatic aberration is critical [13]. Here, we examine the broadband light focusing behavior of the OPtIC nanopore device with d c = 500 nm over a wavelength range spanning from 600 nm to 780 nm. Figure 4a shows that f D decreases monotonically with increasing λ with a maximum deviation (Δz max ) that is below 200 nm ($λ/33) between 620 nm and 680 nm, which resides within the FWHM of the EOT peak (Figure 2d). Below the short-wavelength tail of the EOT peak, Wood's anomaly [19,27] leads to longer f D for λ = 600 nm at the transmission minimum (Figure 2d).
Optical intensity variation along the focal plane (dashed lines in Figure 4a) is shown in Figure 4b. Focal point has a FWHM of 1.08 μm, 1.12 μm, 1.24 μm and 1.28 μm at λ = 620 nm, 633 nm, 655 nm and 680 nm, respectively. In addition, the DoF calculated from Figure 4c shows small variations within the same spectral window (620 nm < λ < 680 nm). However, the DoF is considerably larger at the wavelength of 600 nm that resides outside the EOT spectral window. Therefore, light focusing characteristics over a sufficiently broad range of wavelengths hinges on the (1,0) resonance transmission (EOT) peak.
Using the Rayleigh-Sommerfeld (R-S) formula [13,28,29], the focal length of the finite-size NHA microlens can be calculated: where I and I 0 are the intensity values calculated at a distance above the lens along the optical (z) axis and the peak intensity, respectively. Here, ρ is the aperture radius and n is the refractive index of the surrounding medium. Comparison of the solid black curve obtained from FDTD simulations to the gray dots calculated via the R-S formula Eq. (4) are in very good agreement for λ between 620 nm and 680 nm, as seen in Figure 4d. The shaded area bounded by the solid blue lines in Figure 4d indicates that DoF does not change significantly within the same wavelength range, even though incorporation of an enlarged central aperture breaks the NHA periodicity. Minimal modulation in the focal length and spot size is also shown in Figure 4d (the solid black and orange curves, respectively). Thus, the OPtIC microlens exhibits minimal chromatic aberration within the FWHM spread of the EOT peak, offering a well-defined broadband light focusing characteristic.

Influence of thermo-plasmonic forces
As conventional wisdom suggests, surface plasmon generation is accompanied by electromagnetic heating, which evokes heat-induced fluid dynamics. The local temperature elevation in the vicinity of the OPtIC microlens induces a buoyancedriven convective fluid flow (Archimedes force) against the reverse main flow stream, resulting in a thermo-plasmonic drag force that drives particles away from the microlens surface [30,31]. A comprehensive review of this physical mechanism thermo-induced fluid motion -can be found elsewhere [32,33]. In this work, thermo-plasmonic drag forces are calculated using Multiphysics FEM simulations, which incorporate electromagnetic (EM) wave, heat transfer and Navier-Stokes equations. Here, we solve the EM wave Equation [34].  [11].
where k 0 = 2π/λ 0 is free-space wavelength and ε(r) is spatial distribution of ε at λ 0 . The calculated E-field is used to find the heat source density q(r) = 0.5Re[JÁE * ], which is employed to find the total heat power using Q = Ð q(r)dv, J being the induced current density in metal [34]. Solving the heat transfer equation simultaneously with the incompressible Navier-Stokes relations, where ρ, K, c p and η are the density, thermal conductivity, constant pressure specific heat capacity and dynamic viscosity of the fluidic medium, respectively. T (r) and v(r) are the temperature and the fluidic velocity where ∇Á v = 0. Calculations are performed using material parameters that are adopted from the work of Roxworthy et al. [33]. Provided that the EM induced temperature gradient and convective fluid flow distribution are obtained through Eqs. (5)- (7), the volumetric thermo-plasmonic force F tp and F d can be calculated through the Boussinesq approximation [31,33,35].
and Stoke's equation where g denotes the gravitational acceleration constant and β is the thermal expansion coefficient of the water.
Steady-state 2D temperature spatial distributions in the x-y (Figure 5a) and x-z planes (Figure 5b) are calculated using Eqs. (5)- (9). To demonstrate the dynamical properties of the thermal-induced fluid convection, the temperature distribution is deliberately overlaid on a vertical 2D slice of convection velocity profile within the same x-z plane (Figure 5b). In our FEM simulations, the wavelength and power of the excitation light beam is assumed to be 633 nm and 20 mW, respectively. The ambient temperature is T 0 = 20°C. The ambient temperature near and across the microlens surface is considerably increased due to endogenous heat generation via dissipative losses. Because light transmitting through the central aperture is mostly diffractive in nature and lightly coupled to the surface plasmon polariton (SPP) modes of the NHA, a relatively small temperature increase takes place close to the enlarged aperture region. On the contrary, a significant amount of heat is generated outside the central aperture area, which is attributed to non-radiative damping of SPPs launched on the metal/dielectric interface. Due to the large differences in the heat conductivity of Au and water, heat dissipation occurs slowly along the optical axis of the microlens within the solution environment. This results in reduction of the mass density of ambient water, leading to an upward-directed convective fluidic flow that possesses the features of a toroidal Rayleigh-Bénard flow [33], as represented by the arrows in Figure 5b. Here, v is along the optical axis in the +z direction, exerting a drag force on the suspended nano-bioparticles that directs them away from the microlens surface. Our calculations show that the maximum heat induced convective flow velocity is v max = 900 nm/s, whereas the flow velocity is v = 360 nm/s at the focal point.

Label-free sorting of nano-bioparticles
OPtIC nanopore device enables both size-and refractive-index based separation of nano-bioparticles by utilizing a delicate balance of counteracting forces, i.e., F s , F d , F tp and W (gravitational force). Since these forces act along the optical axis within the focal point region, selective particle elution can be readily achieved by adjusting the net force F net = F s + F d + F tp + W [11]. We calculated F net for varying spherical bioparticles with a mass density of 1.05 g/cm 3 and refractive index of 1.55. The direction of F net as a function of distance from the microlens (0 ≤ z ≤ 6 μm) and particle diameter (100 nm ≤ d ≤ 1.0 μm) is shown in Figure 6a and b. In both cases, incident light power is 20 mW and wavelength 633 nm, and the fluidic flow velocities at the focal point v(z = f D ) are 1.3 μm/s and 3.0 μm/s. The red and blue shaded regions in Figure 6a and b correspond to the positive (F s + F tp > F d + W, blue shaded region) and negative (F s + F tp < F d + W, red shaded region) net forces, respectively.
F net is always negative for d ≤ 200 nm, as indicated by the white dashed line on the left in Figure 6a. Nano-bioparticles smaller than this threshold diameter, d < d th = 200 nm can travel a path along the optical axis and pass through the nanopore opening towards the outlet port. Particles with diameters larger than d th experience stronger optical scattering and thermo-plasmonic drag forces (F s + F tp ) relative to the fluidic drag and gravitational forces (F d + W). Therefore, they are retained in the top chamber. Hence, under the above-stated flow and illumination conditions, small particles (d ≤ 200 nm) get separated from relatively large bioparticles. The OPtIC nanopore device offers selective particle fractionation by adjusting either the incident light power or bulk fluidic flow rate. At a fixed incident light power of 20 mW, when v(z = f D ) is increased to 3.0 μm/s, the threshold particle diameter d th is shifted to 350 nm (Figure 6b). By further tuning, relative contributions of acting forces can be tailored for selective separation of nanobioparticles with diameters up to 500 nm, as larger particles cannot physically pass through the nanopore opening (d c = 500 nm).
Size-based separation is not adequate when similar size bioparticles of different origins need to be separated. As indicated in Eq. (1), the optical radiation force acting on particles is a function of both particle radius and refractive index. In this respect, particles comparable dimensions can be separated based on their refractive indices [4,7]. In general, refractive index is intimately linked to the internal structure and chemical makeup of the nano-bioparticles [e.g., exosomes, viruses]. A recent research study has shown that implementation of optical chromatography based on refractive index differences yield successful differentiation of cells with single gene modifications [3]. We calculated forces (F s , F tp , F d , W) acting on the nanoparticles (d = 200 nm) as a function of refractive index (1.33 < n e < 1.6) at the focal point (z = f D = 5.32 μm). A fluidic flow rate of v(f D ) = 1.9 μm/s and 100 mW monochromatic light illumination at 633 nm is assumed. Solid red and black curves in Figure 6c depicts optical scattering F s and the net drag (i.e., F nd = F d -F tp ) forces, respectively. The dashed curves represent contribution of the gravitational force (W). In our calculations, n e is varied from n water = 1.33 to n ps = 1.6 (polystyrene beads). As depicted in Figure 6c, at the flow rate (1.9 μm/s), the magnitude of F s increases with n e and F s balances F nd when n e = 1.46 (indicated by the vertical dashed line). For smaller n e , drag force originating from the primary fluidic flow dominates the opposing forces (F s + F tp ). Thus, the OPtIC microlens can be employed for selective separation of nano-bioparticles with a threshold of n e = 1.46, corresponding to the refractive index of phospholipids and proteins.
It is known that exosomes (nanovesicles composed mostly of water enclosed by a thin phospholipid membrane) have lower refractive indices n e in the range of 1.37-1.39 [36][37][38], which is closer to n e = 1.33 of water. In contrast, virions are tight assemblies of nucleic acids, proteins and lipids with higher n e around 1.48 [39]. For an exosome-like bioparticle (d = 200 nm) with n e $ 1.38, F s can be as small as 4 aN, which is two orders of magnitude smaller than the corresponding value for n e = 1.48 ($400 aN) for a similar size virion. Hence, our OPtIC nanopore device can selectively separate exosomes from similar size virions with high efficiencies.
The threshold n e can be readily tuned, as in the case of particles size, by adjusting the fluidic flow velocity and/or light power. Figure 6d shows that the threshold refractive index can be tuned to n e = 1.54 when the fluidic flow rate is halved to 0.95 μm/s and light power is reduced to 20 mW. Since OPtIC nanopore devices can be operated by directly incident light using an objective-free focusing mechanism, a number of them can be implemented on a planar chip. One can combine multiple OPtIC devices to achieve multi-stage sequential fractionation of nano-bioparticles to realize highly specific size and refractive index-based separation.

Radial lining-up of nano-bioparticles
A major limitation of conventional OC is the difficulty of aligning fluidic flow against a lightly focused Gaussian beam in a precise manner [6]. Our OPtIC nanopore device employs a self-collimation mechanism effortlessly aligning fluidic flow along the optical axis of the microlens. This self-collimation capability, liningup particles against the scattering force, is demonstrated in Figure 7. We calculated radial components of the optical gradient (F g-r ), fluidic drag (F d-r ) and thermoplasmonic (F tp-r ) forces at the focal point z = f D . We analyzed 200 nm (Figure 7a) and 600 nm (Figure 7b)   restoring mechanism (F ∝ À x) within AE1 μm away from the optical axis. Nanobioparticles that deviate from the optical axis are pushed back towards it (x = 0) by these radial restoring forces. This leads to minimal spatial dispersion of the nanobioparticles in the radial direction. As shown in Figure 7b, larger particles (d = 600 nm) experience at least an order of magnitude larger optical gradient forces. This enables precise alignment of larger particles against the optical scattering force at the focal point, a critical requirement for selective rejection of particles above a threshold diameter.
As shown in Figure 7, nanoparticles in the focal are mainly retained along the optical axis by the optical gradient force F g-r , which is significantly stronger than F d-r . Optical gradient force F g-r is relatively stable and readily tuned using light intensity. Hence, self-collimation mechanism employed by our OPtIC nanopore device is robust against fluctuations in the fluidic flow rate.

Conclusion
In this chapter, we reviewed a facile optofluidic nanopore platform for the purposes of optical chromatography of nano-bioparticles based on their size and/or refractive index (chemical composition). Consisting of a finite-size periodic plasmonic nanohole array on a suspended membrane, this OPtIC nanopore device with an enlarged central aperture facilitates precise alignment of optical scattering, thermo-plasmonic drag, and fluidic drag forces against each other for the purposes of OC. Its self-collimation mechanism eliminates the need for sophisticated and bulky optic components (e.g., lasers, microscope objectives, multi-axis stages, etc.) that are commonly used in conventional OC techniques. Furthermore, our plasmonic microlens opens the door to use of incoherent light source, such as LEDs, for the purposes of OC by readily focusing collimated broadband light into a tight spot. This lensing mechanism provides a robust separation capability that is insensitive to structural variations of the central nanopore. We demonstrated size-based selective sorting of nano-bioparticles, such as exosomes, with a tunable threshold diameter using incident light power or fluidic flow rate. In addition, refractiveindex based separation of identical size nano-bioparticles are shown. Similar to sizebased separation, the refractive-index (material composition) based separation mechanism is readily tunable through incident light power and fluidic flow rate.