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Abstract
On-chip optical tweezers based on evanescent fields overcome the diffraction limit of the free-space optical tweezers and can be a promising technique for developing lab-on-a-chip devices. While such trapping allows for low-cost and precise manipulation, it suffers from unavoidable contact with the device surface, which eliminates one of the major advantages of the optical trapping. Here, we use a 1D photonic crystal cavity to trap nanoparticles and propose a novel method to control and manipulate the particle distance from the cavity utilizing a self-induced back-action (SIBA) mechanism and electrical-double-layer (EDL) force. It is numerically shown that a 200 nm radius silica particle can be trapped near the cavity with a potential well deeper than 178kBT by 1 mW of input power without any contact with the surface and easily moved vertically with nanometer precision by wavelength detuning.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Optical trapping has attracted strong interest owing to its versatile and noninvasive characteristics and remarkable value in biological and physical applications [1–5]. Nevertheless, traditional optical tweezers based on a focused laser beam are bulky and expensive apparatus which suffer from diffraction limit and cannot be used for sub-wavelength particles. On the other hand, low-cost on-chip optical trapping beyond diffraction limit can be realized by the near-field counterparts based on the evanescent field of photonic structures [6–8].
Among the near-field optical tweezers cavity-based systems, such as micro ring resonator and photonic crystal cavities, have a robust trapping capability due to the field enhancement through the resonant buildup in the cavity which leads to an effective and efficient system in contrast with the other techniques [9–12].
A number of experiments in recent years have utilized from intensity buildup of a cavity and self-induced back-action (SIBA) mechanism [13,14]. The cavity builds up to a higher optical intensity applied to the particle within the structure, relaxing input power requirements. On the other hand, SIBA mechanism relaxes requirements from the viewpoint of optical intensity experienced by the particle. The key physics behind SIBA is that the position of the particle changes the resonance wavelength of the cavity. Consequently, any movement of the particle dynamically affects the buildup of intracavity intensity, and thus, optical field seen by the particle in the trapped position can be decreased by an appropriate detuned input wavelength [15]. In this context, an effective trapping of a 250 nm radius dielectric particle in a photonic crystal cavity has been reported with very low intracavity powers (less than 120 μW) [14].
While such near-field trapping allows for efficient manipulation of nanoparticles in on-chip devices, there is a common issue for all of the near-field trapping schemes including waveguide-, cavity- and plasmonic-based systems. The near-field optical trapping is based on an evanescent field, leads to an attractive force to the surface. This phenomenon causes unavoidable physical contact of the trapped particle with the device, that eliminates one of the major benefits of the optical trapping. Such contact can disrupt many biological processes [16], and can even lead to shape distortion of biological samples [17]. An ideal integrated optical trap should operate with an ultralow trapping power and be able to manipulate trapped particles away from any surface.
In this paper, for the first time to the best of our knowledge, a method is proposed for trapping particles near an optical cavity without any physical contact by utilizing SIBA mechanism and interparticle forces. Also, using this method we can move the trapped particle in vertical direction and manipulate the particle distance from the cavity surface.
2. Structure
The device structure, shown in Fig. 1, includes a 1D photonic crystal cavity embedded in a silicon (Si) waveguide. The core of the waveguide is formed by patterning the Si layer on a SOI wafer. The width of the waveguide, w, is 500 nm and its height, h, is 220 nm. The optical cavity is made by two mirror sections, each consists of five holes with radius ri and period Λi (i = 1, 2, . . ., 5), in which the holes radii and the periods are chosen in a way that reported in published studies to obtain a high quality factor cavity [18]. The entire chip is immersed in water that serves as top cladding. The trapping sample in all calculations and simulations is a 200 nm radius silica particle.
Fig. 1 (a) Schematic diagram of the 1D photonic crystal trapping system. (b) Cross-section view and (c) top view of the structure. Geometry parameters are: w = 500 nm, h = 220 nm, l = 80 nm, r1 = 100 nm, r2 = 130 nm, r3 = 160 nm, r4 = 160 nm, r5 = 160 nm, Λ1 = 360 nm, Λ2 = 400 nm, Λ3 = 440, Λ4 = 440 nm and Λ5 = 440 nm.
The electromagnetic fields and optical forces are calculated by a full-wave analysis of the structure in COMSOL Multiphysics applying 3D finite element method taking into account material dispersion and absorption. The resonance wavelength and the quality factor of the cavity with no particle in its proximity are λr = 1557.95 nm and Q = 2.57 × 103, respectively. Figure 2 shows distribution of |E|2 on top surface and in lateral cross section of the cavity at the resonance wavelength.
3. Exerted forces on the particle
3.1. Optical trapping force
A particle exposed to an optical field, experiences an optical force given by [19]:
where 〈TM〉, n and dS are the time-averaged Maxwell stress tensor, the unit vector normal to the outer surface enclosing the particle of interest, and the differential surface element, respectively.Normally, trapping force of an evanescent field exerted on a particle increases with approaching of the particle to the surface of the trapping unit. But, using SIBA mechanism which is present in the cavity-based systems, it can be possible to change the profile of the exerted force versus particle distance depending on the input wavelength. In a cavity-based system with SIBA mechanism, coupling of light inside the cavity is modulated by the position of the trapped object over the cavity, forming a back-action from the particle on the cavity field. Since for any position of the particle only a particular wavelength can resonate inside the cavity, detuning the wavelength of the input laser can change the trapping behavior of the cavity [20].
Figure 3 demonstrate effect of the particle distance in the resonance wavelength of the cavity. As seen, approaching of the particle to the cavity causes red-shifting in the resonance wavelength of the cavity.
Fig. 3 Transmission spectra of the photonic crystal cavity for different particle distances. The trapping sample is a 200 nm radius silica particle.
Figure 4 shows the optical trapping force, FOp,z, exerted on the particle versus particle distance from the cavity surface for different input wavelengths with input power of 1 mW. As shown in this figure, detuning of the input wavelength changes profile of the trapping force, but it is attractive for all distances and wavelengths, consequently leads the particle to contact with the surface of the cavity. In order to have a contactless trapping, a repulsive force is required near the cavity surface in which combination of these forces results a balance point above the cavity.
Fig. 4 Optical trapping force exerted on the 200 nm radius silica particle in the z direction versus d for different wavelengths. The input power is 1 mW.
3.2. Intermolecular forces
According to DLVO theory [21,22], there are two interparticle forces between objects immersed in a liquid, the van der Waals (vdW) and the electrical double layer (EDL) forces [22]:
The vdW force Exerted on a sphere particle near a flat surface can be calculated by [22]:
where A is the Hamaker constant related to the properties of the interacting objects, γ is the geometric factor, r is the particle radius, and d is the distance between the particle and the surface. The Hamaker constant for the used materials (a silica particle immersed in water near a Si surface) can be approximated by 2 × 10−20 J [22], therefore the force is attractive for this situation. The vdW force is comparatively weak and quickly vanishes at longer distances between interacting parts.The EDL is the result of charge accumulation at the surface of an object inside a liquid, and refers to two parallel layers of charge, surrounding the object. When an object is immersed in a liquid, its surface becomes charged due to chemical interactions on the surface and the first layer of charge is formed. Value of the surface charge depends on the object material and solution properties such as ionic strength. The surface charge interacting with dissolved ions inside the solution, forms the second layer that surrounds the charged particle. This second layer is made of free ions that move in the fluid under the influence of electric attraction and thermal motion, so it is called the “diffuse layer” [22–24]. The characteristic length of the decay of the EDL is represented by the Debye length which depends solely on the properties of the solution, not on any property of the surface such as its charge or potential [22]. The Debye length is on the order of one to a few tenths of nanometers. For a solution containing 10 μM ionic strength of a monovalent solution (such as KCl or NaCl), the Debye length is approximately 100 nm. Higher ionic strengths allow for the shielding of the double layer and reduce the Debye length.
As a result of EDL effect, similarly charged surfaces of two objects and their resulting defuse layers in the solution repel each other electrostatically. So, by a proper choosing of the parameters we can utilize the EDL force as the repulsive force that is required to form a contactless trapping system mentioned above.
The EDL force exerted on a particle near a flat surface is given by [22]:
where κ−1 is the Debye length and Z is the interaction constant, defined by [22]:where ε0, εr, e, kB, T and ψ0 are the vacuum permittivity, relative permittivity of the solution, elementary charge, Boltzmann constant, temperature in Kelvin and surface potential, respectively. Surface potential ψ0 is related to the surface charge σ [22]:where C is the ionic concentration in molar unit. We assume that the aqueous solution is made by NaCl with ionic strength of 150 μM that results a Debye layer of about 25 nm [22] and surface charge of −0.002 C/m2 for the silica particle and Si cavity [24]. Also, temperature T, is assumed to be 300 K (room temperature) in the structure. Consequently, the surface potential would be 58 mV for the mentioned parameters. Although, the surface charge and potential of the Si cavity can be adjusted using an external source in order to detune the EDL force. Since our focus is on the particle distance bigger than 5 nm (d ≥ 5 nm), we neglect other interparticle forces such as Steric force which are revealed in very short distances from surfaces [22].Figure 5 illustrates attractive vdW and repulsive EDL forces exerted on the 200 nm radius silica particle immersed in the solution. As shown in this figure, the EDL force is dominant and the resulting force, FDLVO, can serve as the repulsive force which is required for the contactless trapping. Considering the density of silica (ρ = 2.65 g/cm3) [25] and particle size (r = 200 nm), gravity force exerted on the particle is around 9 × 10−16 N that can be neglected.
Fig. 5 Interparticle forces exerted on the 200 nm radius silica particle immersed in the solution over the cavity in the z direction versus d. The ionic strength of the solution is 150 μM and the Debye length is 25 nm.
It should be mentioned that in our structure, the surface near the trapped particle is not perfectly flat due to the holes and finite width of the waveguide. Therefore, we use the correction factor γ, approximated by 0.5 [22], in the Eqs. (3) and (4). These equations are initial approximations, but in a real experiment the EDL force as dominant force can be adjusted by an external source.
3.3. Total exerted force and potential
Figure 6 depicts total exerted force, FTot = FOp,z + FDLVO, on the particle for different wavelengths. As shown in the figure, attractive optical trapping force is dominant in long distances and total exerted force is attractive. With approaching the particle to the cavity, the repulsive EDL force increases, the total force reaches to zero and a balance point will be formed. If the particle come closer to the cavity, the EDL force will be dominant and the total exerted force will be repulsive that returns the particle to the balance point. In addition, as seen in the figure, the balance point of the particle over the cavity varies by wavelength detuning, so the trapped particle can simply move vertically over the cavity from approximately d = 55 nm to d = 25 nm by detuning of the input wavelength from 1558.2 nm to 1558.8 nm. For a bigger displacement, a wider detuning range in the input wavelength together with other adjustment of the input power and solution properties should be considered.
Fig. 6 Total exerted force on the 200 nm silica particle over the cavity for different wavelengths in the z direction versus d. The input power is 1 mW.
Changing of the particle size affects both of the trapping and interparticle forces. As an initial approximation, optical trapping force, FOp,z, on a nanoparticle is proportional to r3 [7] and according to Eq. (4), FEDL as the dominant interparticle force is proportional to r. So, absolute values of these forces change in a same way but not in a same rate with respect to r. Therefore, for a different particle size, the forces should be recalculated and it may need other sort of parameters (the solution properties, input power and detuning range) to achieve contactless trapping with tunable balance point.
Figure 7 shows the total potential of the particle with input power of 1 mW. As depicted in the figure, the 200 nm radius silica particle can be stably trapped with a depth of at least 178 kBT with 1 mW of input power without any contact with the cavity surface. The particle needs a high kinetic energy (at least 178kBT) to overcome the strong repulsive EDL force and make a contact with the surface of the device. Regarding to the figure, moving of the particle is realized with small changes in the potential well of the particle. The depth points in this figure belong to the balance points in Fig. 6.
4. Conclusion
In conclusion, a 1D photonic crystal cavity was used to trap nanoparticles and a method was proposed to realize contactless on-chip trapping that can manipulate particle distance from the cavity utilizing SIBA mechanism (reducing trapping force near the surface) and EDL force (preparing repulsive force near the surface). We numerically showed that a 200 nm radius silica particle can be stably trapped with a potential well deeper than 178kBT by 1 mW of input power without any contact with the cavity surface and easily moved in the vertical direction near the cavity with nanometer precision by detuning of the input wavelength. This scheme is very promising to be integrated into the lab-on-a-chip systems to form multifunctional analysis devices.
Funding
Sahand University of Technology (SUT) (30-17496).
Acknowledgments
We thank Professor Aleksandra Radenovic and her group (LBEN) at EPFL and Electromagnetics and Photonics Research Group (EPRG) at Sahand University of Technology for their support and discussion.
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