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To enhance the optical pressure on a thin dielectric sample, a resonance structure using graphene layers coated over a metal film on a high index prism sputtered with MgF2 was theoretically analyzed. The number of graphene layers and the thicknesses of metal and MgF2 films were optimized to achieve the highest optical pressure on the sample. Effects of three different types of metals on the optical pressure were investigated numerically. In addition, simulations were carried out for samples with various thicknesses. Our numerical results show that the optical pressure increased by more than five orders of magnitude compared to the conventional metal-film-base resonance structure. The highest optical pressure was obtained for 10 layers of graphene deposited on 29-nm thick Au film and 650 nm thickness of MgF2 at 633nm wavelength, The proposed graphene based resonance structure can open new possibilities for optical tweezers, nanomechnical devices and surface plasmon based sensing and imaging techniques.
© 2015 Optical Society of America
1. Introduction
Using optical tweezers allow fine controlling of the position of particles on a wide range of sizes in a non-invasive manner [1]. Conventional optical tweezers have been used to manipulate artificial beads, living cells and organelles with minimum damage [2–6]. Researchers used optical tweezers to investigate a wide range of interesting biological interactions such as the properties of single DNA molecules and molecules that interact with a DNA molecule. Important information concerning the biophysical properties and dynamic structures of both double-stranded and single-stranded DNA, the kinetics of DNA [7–12], polymerase [13, 14] and RNA polymerase [15–17] activity have been revealed.
Kawata et al. have experimentally shown that micron size particles can be moved in the evanescent field produced by a totally reflected beam from a prism-liquid interface [18] or a laser beam propagating in a channel waveguide [19]. The evanescent field (EF) forces acting on small spheres or dielectric films near the surface of a dielectric prism, a multimode waveguide and a prism surface covered by a dielectric and a metal layer have been theoretically analyzed before [20–24]. However, conventional and plasmonic optical tweezers still have drawbacks. They have low spatial resolution and cannot exert enough force [25–31]. However, recent numerical calculations by different research groups have shown that a graphene-on-metal surface plasmon resonance (SPR) biosensor can be more sensitive than the conventional metal film-based biosensors [32, 33]. In this paper, an optimized combination of graphene and metal is used to investigate the enhancement of the optical pressure on a planar sample.
Graphene is the thinnest film in the universe and one of the strongest known materials which has a unique series of extraordinary structural, mechanical and electrical properties such as transparency, conductivity and bendability [34–39]. Graphene can be successfully placed on top of various substrates such as dielectrics and metals [40, 41]. A number of graphene layers can be coated on suitable surface in a controlled manner. Because of the existence of Van der Waals forces between two graphene layers, a multilayer graphene system is quite stable [42]. Single and multi (few) layer graphene have been shown to have numerous scientific and technological advancement with novel nanodevice applications [43]. Furthermore, experiments have verified the excitation of plasmons [44–46] using optical methods and plasmonic effects in graphene [47–54]. This is a great motivation for investigating graphene in the context of optical and plasmonic applications.
In this study a graphene based resonance structure is proposed to theoretically investigate the enhanced optical pressure on a planar sample. An optimized combination of MgF2, graphene and metal is used to enhance the optical pressure on a sample. Three different metals (silver, gold and copper) were considered. It was realized that an optimized metal thickness and the number of graphene layers can lead to a five order of magnitude enhancement in the optical pressure compared to the highest value which was reported in the literature [24]. To the best of our knowledge this is the highest ever reported optical pressure of the surface plasmon-coupled evanescent waves. The pressure arising from the enhanced evanescent fields can be useful for particle trapping, effective movement of micromechanical elements [55], to selectively manipulate planar structures and to design nanomechnical devices [56–59]. More importantly it can be employed to stimulate biological cells and perturb cell-substrate contacts at interfaces. Furthermore, it can be employed to visualize induced changes using a total internal reflection microscopy.
Simulations were carried out for the three different metals of gold, silver and copper. It is worth mentioning that silver and copper susceptibility to oxidation may decrease the magnitude of optical pressure. However, if their surfaces are coated with graphene, oxidation of the substrates can be prevented [32]. The dependency of optical pressure upon variation of the involved parameters including number of graphene layers (N), type of metals, thicknesses of MgF2 and metal films, and the refractive index of the sample were investigated. The thickness of these layers and the number of graphene layers were carefully optimized to obtain the highest optical pressure.
1. Theory
For simulation a prism base was coated with MgF2 layer. A metal film (Ag, Au or Cu) and graphene were further coated on MgF2. A medium containing the sample was placed in contact to graphene layers. Altogether, the resonance system consists of seven layers: prism, MgF2, metal, graphene, a narrow gap of ethanol between graphene and the sample, sample and the medium (that contains the sample; ethanol) above the sample. The sample is a planar dielectric layer. A gap of medium separates the sample from the graphene surface. Figure 1 illustrates the resonance structure and the sample. Here, ni and ti (i = 1-7) show the refractive index and thickness of various layers, respectively. ηi (i = 1-7) is the incident angle of the light for various layers. It is supposed that all the layers are homogeneous and isotropic. We modeled the sample as a planar dielectric layer in our study for simplicity and also to be able to compare our results with the highest reported value for the optical pressure in Ref. 24. To excite surface plasmons in the resonance structure, p-polarized monochromatic light is incident through the prism at an angle greater than the critical angle [24].
Fig. 1 Schematic of a resonance structure, based on a graphene-on-metal substrate to enhance the optical pressure on a dielectric sample. An MgF2 film (t2) is deposited on a prism substrate. Graphene layers (t4) are coated on the metal film (t3). Sample (t6) are modeled as a homogeneous layer with an initial refractive index of 1.515 in an aqueous medium (ethanol) of refractive index 1.36. A gap of aqueous medium (t5) separates the sample from the graphene. The center of the coordinate (x; y; z) is located at n1-n2 interface. η1, η5 and η7 are the incident angles of the wave in prism and media five and seven, respectively.
2. Optical pressure on the sample
To determine the optical force on the sample, the Maxwell stress tensor (MST) is used. The stress tensor T is given as, where e and h denote the electric and magnetic field vectors and the indices i, j are counted over the three field components. To obtain the electric and magnetic fields, transfer-matrix method (TMM) is used [60]:
where e1 and h1 are the components of electric and magnetic fields, respectively, at the boundary between the prism and MgF2 film, and eN−1 and hN−1 are the fields at the boundary of Nth layer. Here M is the characteristic matrix of the structure which is given by:
where The optical force can be calculated by computing the time average of the surface integral of the MST aswhere the bracket denotes the time average over one optical period and shows the outward normal vector. For any cross-section of the sample, the optical force is given by the outline integral in the following relation [61]:The exerted force per surface area is the optical pressure () [24].3. Result and discussion
In the present study there are several design parameters of the resonance structure that may affect the optical pressure on the sample. We thoroughly investigated the involved parameter effects. However, we emphasized some critical parameters such as metal type, the thicknesses of MgF2, metal, graphene and refractive indices of the sample. It is worth mentioning that the wavelength of the light source and refractive indices of prism, sample and medium which the sample is immersed in can also affect the magnitude of the optical pressure or its sign.
To numerically obtain the optical pressure on the sample, a p-polarized wave at wavelength 633nm and intensity 1w/m2 which propagates in the prism were considered. Using Eq. (5), the optical pressure () on the sample as a function of η1 for silver (Ag), gold (Au) and copper (Cu) were obtained. The number of graphene layers and thicknesses of MgF2 and metals were optimized to achieve the highest value for both positive (repulsive force) and negative (attractive force) optical pressure on the sample. Figure 2 shows the curves of the positive optical pressure as a function of η1 for Ag, Au and Cu. The optimized number of graphene layers, MgF2 (t2) and metal thickness along with the metal type are noted in this figure. In this section, we chose n1 = 1.515 for the prism. The refractive index of MgF2 is n2 = 1.38 and its thickness (t2) was optimized for various metals. The thickness of a single layer of graphene is considered to be 0.335nm and for a multilayer t4 = 0.335*N, where N is the number of graphene layers and n4 = 3.0-i1.4 [60, 62]. The thickness of the sample with refractive index of n6 = 1.515 was t6 = 0.5λ and its distance from the graphene surface was fixed at t5 = 0.5λ. The refractive index of metals are n3 = 0.066 + i4.045 (Ag), n3 = 0.1726 + i3.42 (Au), n3 = 0.14 + i3.15 (Cu) [63]. The sample was immersed in ethanol with a refractive index of 1.36. The optimized parameters depend on the metal type. As illustrated in Fig. 2, the optimized metal thicknesses (number of graphene layers, N) for silver, gold and cooper are 31nm (N = 6), 29nm (N = 10), and 43nm (N = 5), respectively. The optimized thickness of MgF2 film for Ag and Cu are equal to 700nm whereas for Au is 650nm. Two incidence angles exist, with positive and negative peak pressures, for all the three metals. Since we optimized the thicknesses and also the number of graphene layers to achieve the highest positive pressure, the magnitude of the positive peak is larger than that of the negative ones. The obtained maximum positive optical pressure along with the attractive force on the sample is listed in Table 1. This data shows that the highest value of the positive optical pressure for Au is (P = 1.70 × 10−3) which is about 105 times higher than data reported in literature [24]. Both the positive and negative optical pressures for Ag and Au are on the same order of magnitude and are higher by one order of magnitude than Cu. The optimized parameter values along with the maximum positive and negative optical pressure are summarized in Table 1. It is worth mentioning that the sample thickness and distance from the graphene surface was fixed to those values reported in Ref. 24. In this way, we are able to compare our results with the highest value which reported in the literature for the optical pressure. If we decrease the sample thickness and its distance from the graphene surface the optical pressure increases more.
Fig. 2 .Curves of the optical pressure, P, acting on a sample with thickness t6 = 0.5λ, at wavelength λ = 633nm for different metals Ag, Au, Cu as a function of the incident angle η1. The refractive index of metals are n3 = 0.066 + i4.045 (Ag), n3 = 0.1726 + i3.42 (Au), n3 = 0.14 + i3.15 (Cu). The figure subset shows the negative optical pressure (attractive force). The optimized thicknesses of MgF2 (t2) and metals along with the optimum number of graphene layers and to achieve the maximum optical pressure (P>0, repulsive force) have been listed inside the figure. We let n1 = 1.515, n2 = 1.38, n5 = n7 = 1.36, t5 = 0.5λ.
Table 1. Optimized values of thicknesses of MgF2, metal and the number of graphene layers for silver, gold and copper to achieve the highest positive optical pressure with corresponding positive and negative optical pressures for 633 nm wavelength.
Simulations, similar to the above, were also carried out to optimize t2, t3 and N in order to achieve the highest negative optical pressure or attractive force on the sample (Fig. 3). The other involved parameters are the same as those used in calculations of the positive pressure in the last section. Table 2 shows the optimized parameters and maximum values for negative pressures.
Fig. 3 .Curves of the optical pressure, P, acting on a sample with thickness t5 = 0.5λ, at wavelength λ = 633nm for different metals Ag, Au, Cu as a function of the incident angle η1. The optimized thicknesses of MgF2 (t2) and metals along with the optimum number of graphene layers to achieve the maximum optical pressure (P<0, attractive force) have been listed inside the figure.
Table 2. Optimized values of thicknesses of MgF2, metal and the number of graphene layers for silver, gold and cooper to achieve the highest negative optical pressure with corresponding positive and negative optical pressures for 633nm wavelength.
As can be seen in the Table 2, the optimized MgF2 and metal thicknesses and the coated graphene layers over the metals, for silver, gold and copper are 38nm (N = 9), 42nm (N = 10), and 34nm (N = 11), respectively. A comparison between data in Table 1 and 2 reveals that the number of graphene layers coating Ag and Cu and the thickness of Ag and Au increased for P<0. MgF2 film thickness which is coated on the prism changed for both Au and Cu. Since we optimized the parameters to achieve the highest negative pressure, the magnitude of the negative peak was larger than that of the positive one. It can be seen that the highest value of the negative optical pressure for Cu is (P = - 1.43 × 10−4) which is about 104 higher than data reported in literature [24]. The peak of the negative pressure for Ag is one order of magnitude smaller than Cu but greater than Au. It is also obvious that the positive optical pressure for Ag and Cu are on the same order of magnitude, but higher than Au.
In order to be able to compare the effect of the presence of the graphene on the optical pressure simulations are carried out in the absent of graphene. Figure 4 shows the optical pressure as a function of the incident angle η1, for different metals, Ag, Au and Cu when no graphene sheet is employed. The optimum thicknesses of metals and thicknesses of MgF2 were calculated. We have also chosen the parameters n1 = n6 = 1.515, n2 = 1.38, n5 = n7 = 1.36, t4 = 0 and t5 = t6 = 0.5λ (λ = 633nm). A comparison between Figs. 2, 3 and 4 reveals that the number of graphene layers coating on metals can increase the optical pressure by more than five orders of magnitude compared to the structure where no graphene sheets are employed. The refractive index of graphene, which contains both real (nr) and imaginary (ni) parts, affects the optical pressure. A comparison between graphene and metals refractive indices shows that the real (imaginary) part of the graphene’s refractive index is much higher (smaller) than those of metals. A higher real part enhances the electric field in graphene and a smaller imaginary part decreases the loss in the graphene. However, more investigations need to be done to find out why the graphene/metal interface leads to such a massive change in magnitude of the optical pressure.
Fig. 4 Plot of the optical pressure as a function of the incident angle η1, for different metal, Ag, Au and Cu. The optimum thicknesses of metal and thicknesses of MgF2 were calculated. We have also chosen the parameters n1 = n6 = 1.515, n2 = 1.38, n5 = n7 = 1.36, t4 = 0 and t5 = t6 = 0.5λ (λ = 633nm).
Another parameter that has an interesting effect on the optical pressure is the refractive index of the sample. We noticed that when the refractive index of the prism and sample are equal, both positive and negative peaks of the pressure exist. However, when the refractive index of the prism is less (more) than that of the sample, the optical pressure on the sample is negative (positive) and there is an attractive (repulsive) force between the sample and the resonance structure, Fig. 5. Figure 6 shows the curves of the reflectance (R) from the prism base in a multilayer system with different refractive indices of the sample. The optimum thicknesses of metal and thicknesses of MgF2 are the same as those in Fig. 5. We observe in Figs. 5 and 6 that the optical pressure, is enhanced substantially at the angle of minimum reflectance and that the peak pressure increases proportionally as the peak reflectance decreases.
Fig. 5 Plot of the optical pressure as a function of the incident angle η1, for different the refractive indices of the sample film, n6 = 1.45, 1.515 and 1.65. The optimum thicknesses of silver and the number of layers of graphene were calculated.
Fig. 6 Plot of the reflectance as a function of the incident angle η1, for different the refractive indices of the sample film, n6 = 1.45, 1.515 and 1.65. The optimum thicknesses of metal and thicknesses of MgF2 were calculated. The refractive indices and thicknesses of the layers are the same as those in Fig. 4.
4. Conclusion
We theoretically investigated an enhanced optical pressure on a dielectric film in a metal-graphene coated multilayer system when a p-polarized plane electromagnetic wave is incident at an angle above a critical angle. We appraised numerically the optical pressure for a sample film located in a graphene on metal coated multilayer system for different metals. Our numerical results show that the optical pressure increased by more than five orders of magnitude compared to the conventional metal-film-base resonance structure. Furthermore, we showed that when the refractive index of the prism and sample are equal, both positive and negative peaks of the pressure exist. However, when the refractive index of the prism was less (more) than that of the sample, the optical pressure on the sample was negative (positive) and there was an attractive (repulsive) force between the sample and the resonance structure. The curves of reflectance as a function of the incident angle showed that the optical pressure, was enhanced substantially at the angle of minimum reflectance and that the peak pressure increased proportionally as the peak reflectance decreased. The results presented in this paper will be useful in subwavelength-scale technologies, nanomechnical devices such as nano and micromotores, optical tweezers, optical force microscopy, surface plasmon based sensing and imaging techniques.
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