DNA Transport and Delivery in Thermal Gradients near Optofluidic Resonators

Heat generation and its impact on DNA transport in the vicinity of an optofluidic silicon photonic crystal resonator are studied theoretically and experimentally. The temperature rise is measured to be as high as 57 K for 10 mW of input power. The resulting optical trapping and biomolecular sensing properties of these devices are shown to be strongly affected by the combination of buoyancy driven flow and thermophoresis. Specifically, the region around the electromagnetic hot spot is depleted in biomolecules because of a high free energy barrier.

Figure 1

Scale bars: 500 nm (a),(b), $15\mu \mathrm{m}$ (c),(d). (a) Modulus of Ey in a PC resonator with a central hole. The light is coupled from the bottom waveguide. (b) Numerical estimation of the temperature increase of a PC resonator with a central hole. The maximum temperature is 350 K. (c) Numerical estimation of the temperature $2\mu \mathrm{m}$ above the resonator. For 1.7 mW of power input, the maximum temperature reached is 4 K. (d) Fluorescently measured temperature increases for 1.7 mW of estimated power input, $2\mu \mathrm{m}$ above the surface of the resonator. The maximum temperature increase is 4.8 K after correction for bleaching and thermophoresis of the rhodamine $B$.

Figure 2

Times steps showing $\lambda$ DNA transport near the optical resonator (bright central light). The white arrow represents the direction of the flow. The flow rate is $12500\mu {\mathrm{m}}^3/\mathrm{s}$. One molecule contours the photonic crystal (yellow online), while one is thermally trapped (red online). Images taken from video in Supplemental Material (rotated $90°$) [16]. Scale: $50\mu \mathrm{m}$.

Figure 3

(a) Numerical (b) and experimental concentration profile in the vicinity of a PC resonator with a central hole. The power input is $10\pm 1\mathrm{m}\mathrm{W}$, and the flow is oriented top down at $12500\mu {\mathrm{m}}^3/\mathrm{s}$. The red spot corresponds to the thermophoretic trap due to opposed thermal and convective flows. Black lines: feeding waveguides. Black arrow represents the direction of the flow. Scale bars: $25\mu \mathrm{m}$.

Figure 4

(a) Sketch of the superposition of the free energy resulting from the thermodiffusion and the electromagnetic well. (b)–(d) Numerical estimations along the flow direction ($Y$ direction, horizontal scale: $-50\mu \mathrm{m}$ to $50\mu \mathrm{m}$, volumetric flow rate $12500\mu {\mathrm{m}}^3/\mathrm{s}$) for 10 mW of power input. The legend in (b) applies to (c),(d) as well. (b) Free energy diagram in $k_{B}T$ units. At the resonator, the electromagnetic potential well is added to the free energy. The EM potential well is much deeper than the free energy barrier but spans a smaller region. The potential barrier is about $12k_{B}T$. The arrow represents the flow direction. The gray area represents the region where the local equilibrium criteria is not met; hence, the free energy expansion [Eq. (6)] is less accurate (Supplemental Material [16]). (c) Concentration profile. Even with no superimposed flow, we notice a small accumulation in the vicinity of the resonator. This is the result of the buoyancy induced convective flow (Supplemental Material [16, 22]). (d) Diffusion rate estimated from the energy barrier through (7). At the resonator, the rate is $1/3000000$ times the average diffusion time.