We report on the behaviour of singly optically trapped nanospheres inside a hollow, resonant photonic crystal cavity and measure experimentally the trapping constant using back-focal plane interferometry. We observe two trapping regimes arising from the back-action effect on the motion of the nanosphere in the optical cavity. The specific force profiles from these trapping regimes is measured.

Since their demonstration by Ashkin,1 optical tweezers have been of great assistance for applications requiring non-invasive manipulation of micro- and nanometer-scale, delicate particles. They have found applications in the field of biology where they are routinely used to trap cells and allow measurements of mechanical characteristics of biomolecules or organelles.2,3 Optical trapping has been extensively used in other scientific fields, such as in atomic physics where it is used to confine or trap atoms or ions.4 Nevertheless, optical trapping is limited in its applications due to the spot size of the focused laser beam used for trapping and the size of the optical setup that is required. Recent publications have shown efforts by several groups for integrating optical trapping in a lab-on-a-chip platform and overcoming the diffraction limit to control smaller nanoparticles with lower optical power. In order to achieve this goal, different approaches were investigated such as plasmonics,5 optical waveguides,6 photonic crystal cavities and waveguides.7 Trapping in photonic crystal cavities has already been demonstrated by several groups. The trapped objects were ranging from bacteria7 to dielectric spheres8 using three holes defect (L3) cavity, nanobeams,9 and other designs.10–13 The most efficient trapping configuration comes from cavities where the resonant optical mode has a large overlap with the trapped particle. This is demonstrated in Ref. 13, where gold nanoparticles are trapped by the resonant mode of a slot photonics crystal cavity. Although in this case, the 100 nm slot is very limiting in size and prevents trapping of larger objects.

Recently, hollow photonic crystal cavities were successfully used to trap larger dielectric spheres.14,15 The cavity used is a circular hollow defect in the photonics crystal lattice, with a diameter of 700 nm (Fig. 1). The interaction between the particle and the optical mode of the hollow cavity induces a large frequency shift of the cavity resonance. This is in turn at the origin of the back-action effect16 where the displacement of the particle in the cavity retroactively modulates the power coupled to the cavity and hence the trap stiffness. The trapping optical mode of the resonant cavity is excited by a single mode laser at a wavelength around 1550 nm. As depicted in the SEM picture of the device (Fig. 1(a)), the excitation laser is guided in the W1 waveguide and evanescently coupled to the cavity. Changing the distance between the W1 waveguide and the cavity alters the Q-factor of the cavity by reducing the amount of losses from the cavity to the waveguide.

FIG. 1.

(a) Scanning electron micrograph of the photonic crystal cavity and W1 access waveguide at a coupling distance of 4 rows. In the inset, finite-element modeling (FEM) simulation of the norm of the electric field along the photonic crystal plane. The blue circle indicates the size of the hollow cavity. (b) Side view of the cavity with a 500 nm particle at the trapping position. (c) Schematic of the back-focal plane interferometry (BFPI) detection setup.

FIG. 1.

(a) Scanning electron micrograph of the photonic crystal cavity and W1 access waveguide at a coupling distance of 4 rows. In the inset, finite-element modeling (FEM) simulation of the norm of the electric field along the photonic crystal plane. The blue circle indicates the size of the hollow cavity. (b) Side view of the cavity with a 500 nm particle at the trapping position. (c) Schematic of the back-focal plane interferometry (BFPI) detection setup.

Close modal

The back-action mechanism leads to different trapping regimes where the forces acting on the particle have specific profiles. Both of these regimes can occur in the same cavity. They are selected by the choice of the excitation wavelength with respect of the empty resonance frequency. The first trapping regime is referred to “cage trapping regime,” based on a self-induced back-action (SIBA) phenomenon. In this regime, the cavity is excited at the empty resonance wavelength λ0. The coupling of the excitation laser to the cavity is highest when no object is overlapping with the optical mode. A particle in Brownian motion, moving randomly in the vicinity of the cavity, is pulled toward the center of the trap, inside the cavity. The refractive index modification induces a shift of the mode resonance, which modulates the coupling from the W1 to the resonant mode. The particle is kept in a dynamical minimum of the optical field, which reduces its exposure to strong optical powers. The particle escaping from the center of the trap couples back power to the optical mode from the W1 waveguide. This mechanism is at the origin of a highly non-harmonic potential trap that pulls a particle to the center of the cavity. The second trapping regime resembles a “classical trapping regime.” This regime is enforced by exciting the cavity at a shifted wavelength (λ0 + δλobj.) to account for the future presence of the trapped object shifting the resonance by δλobj. Coupling from the W1 waveguide to the cavity is then maximized when the object is at the center of the trap, and falls quickly as soon as the particle moves away. Looking at the force profile of this regime shows a behavior very similar to that of the classical evanescent optical tweezers, with an optical force linearly dependent on the small motion of the particle. More details about the two regimes can be found in Ref. 14.

Investigation of the position fluctuations of singly trapped colloidal particles is an excellent tool for characterizing the forces exerted by the cavity on the particle. The objective of this work is to study the motion of trapped single spheres inside a hollow photonic crystal cavity. For this purpose, we fabricate the photonic crystal samples and use them to trap 500 nm polystyrene spheres. The motion is recorded using back-focal plane interferometry (BFPI),17,19 from which we compute the power spectrum density (PSD) of the position of the particle. The use of Boltzmann's distribution function gives access to the potential energy and force profile, leading to the estimation of the stiffness of such an integrated trap.

The trapping chip consists of a silicon 2D photonic crystal membrane and a microfluidic layer. The photonic crystal is etched on a Silicon-On-Insulator wafer, with a silicon membrane thickness of 220 nm. The total thickness of the wafer is 250 μm. The lattice consists of a triangular array of holes, with a lattice constant of 420 nm, and the size of the lattice holes is 250 nm in diameter to create a bandgap for the TE-polarized light, for operation around 1550 nm. The design of the photonic crystal cavity is adapted from Ref. 20, as seen in Fig. 1(a), with a cavity of 700 nm in diameter for a simulated Q-factor of 8800 in air, and a Q-factor of 3300 in water (FDTD). The pattern is transferred on ZEP 50% photoresist using e-beam lithography. The holes are then etched by ICP. The liberation of the membrane is performed with a buffered hydrofluoric acid bath. Coupling to the hollow cavity is done by positioning a W1 photonic crystal waveguide close to the cavity. The distance between the W1 waveguide and the cavity allows for tuning the Q-factor of the cavity from 1000 up to 3000 measured in water. The excitation laser is injected by end-fire coupling after passing through a TE polarizer. The trapped objects are fluorescent polystyrene spheres with a diameter of 500 nm. They are trapped inside the 700 nm diameter cavity. As the spheres are slightly smaller than the cavity, the motion along the plane of the photonic crystal is mechanically confined. Moreover, the friction coefficient cannot be estimated in a straight-forward manner because of the wall effects arising from the proximity to the cavity wall. On the other hand, the motion of the sphere along a perpendicular axis (z) from the photonic crystal plane is not limited by the cavity wall. The force generated by the trap can then be estimated by looking at the Brownian motion of the spheres along the z-axis.

We use BFPI in order to monitor the motion of the trapped sphere.21 In this implementation (Fig. 1(c)), we use two distinct laser sources with different wavelengths. The first laser, coupled to the optical cavity resonance, is set around 1550 nm +/− 50 nm. This is effectively the laser used to trap the sphere. A second laser, referred to as the detection laser, is used for the BFPI. Its wavelength is set at 1300 nm precisely to help separate both wavelengths with a filter. The detection laser is focused with a 100× oil-immersion objective (Leica PL APO, with a NA of 1.4), creating a spot size of 1.1 μm in diameter. This spot overlaps with the cavity diameter of 0.7 μm, with the waist of the beam at the same position as the cavity surface. The power of the detection laser is constant and set to minimize its parasitic effect on the motion of the particle, while keeping a good signal-to-noise ratio. A long working distance objective (Leica PL FLuotar 100×, with a NA of 0.7) then collects the detection laser going through the sample. The collected beam is focused on an InGaAs Hammamatsu (G6849) quadrant photodiode (QPD), whose detection area is 2 mm in diameter. The beam spot from the detection laser on the QPD is adjusted around 1 mm in diameter. The signal from the QPD is recorded with a high bandwidth data acquisition setup. The sampling frequency of the acquisition is 50 kHz, which is at least one order of magnitude above the cut-off frequency from the cavity trapping. Calibration of the detection laser is done by trapping a 500 nm polystyrene sphere far away from the silicon surface. Since the power of the detection laser is kept constant during all the experiments, we can find the proportionality coefficient (beta) of the photonic-force microscope to convert the voltage output of the QPD to nanometers. After calibration, the detection laser is focused on the cavity used for optical trapping. Finally, we measure the viscosity of the water surrounding the particle in the optical cavity using the PSD measurements done far from the surface and inside the optical cavity. The detection laser also creates a weak optical trap which can be easily identified in the low frequency (<30 Hz) of the power density measurements.

A single 500 nm sphere is trapped inside a hollow photonic crystal cavity. The excitation wavelength is fixed in order to be in the “classical trapping regime,” at λ0 + δλmax, where the force profile is expected to be linear with small displacements of the trapped sphere. Fig. 2 describes the power spectrum density of the position of the trapped sphere for different excitation powers. The PSD exhibits a clear cut-off which is dependent on the estimated power coupled to the cavity. Higher power coupled to the cavity leads to higher cut-off frequency, which is related to a larger trap stiffness. More information can be retrieved by plotting the cut-off frequency as a function of the excitation wavelength (Fig. 3). The cavity investigated has a resonance line-width of 0.9 nm and the detuning induced by the polystyrene sphere is δλmax = 1 nm. Two maxima represented by the arrows R-1 and R-2 can be observed. They correspond to the two trapping regimes, R-1 being the “cage trapping regime” and R-2 the “classical trapping regime.” This extends the results presented in Ref. 15, namely, in Fig. 4. The impact of the Q-factor and δλmax on the back-action is discussed in the supplementary material.

FIG. 2.

(a) Power spectrum density of the position of the trapped nanoparticle for different power coupled to the cavity. (b) Time traces of the position (0 is relative) of trapped nanoparticles for 90 and 260 μW.

FIG. 2.

(a) Power spectrum density of the position of the trapped nanoparticle for different power coupled to the cavity. (b) Time traces of the position (0 is relative) of trapped nanoparticles for 90 and 260 μW.

Close modal
FIG. 3.

Evolution of the cutoff frequency of the PSD for a singly 500 nm polystyrene trapped sphere. (a) Data points and curve acting as a guide to the eye for an estimated power of 260 μW. (b) Data points and guide for the eye curve for an estimated power of 90 μW. (c) Comparison between the different guided powers. The first trapping regime is represented by R-1, the second trapping regime is represented by R-2.

FIG. 3.

Evolution of the cutoff frequency of the PSD for a singly 500 nm polystyrene trapped sphere. (a) Data points and curve acting as a guide to the eye for an estimated power of 260 μW. (b) Data points and guide for the eye curve for an estimated power of 90 μW. (c) Comparison between the different guided powers. The first trapping regime is represented by R-1, the second trapping regime is represented by R-2.

Close modal
FIG. 4.

Potential energy and the corresponding force profile for 260 μW, 170 μW, and 90 μW of guided power (a) in the “cage trapping regime” and (b) in the “classical trapping regime.”

FIG. 4.

Potential energy and the corresponding force profile for 260 μW, 170 μW, and 90 μW of guided power (a) in the “cage trapping regime” and (b) in the “classical trapping regime.”

Close modal

The trapping potential (Fig. 4) can be extracted from the analysis of the position of the trapped sphere, from the Boltzmann distribution of the position in a potential well following the procedure detailed in Refs. 22–25. In Fig. 4(a), we can see that the potential is not symmetric. This can come from the sample itself being non-symmetric in the z-direction, therefore favoring an escape. The notable feature in the plot is the plateau for 20 nm during which the optical forces are the weakest. The force peaks when the particle is further away, as explained in the introduction. In the second trapping regime, around R-2 (Fig. 4(b)), the potential energy and the force are symmetrical. For small displacements of the particle, the force is linear and scales linearly with guided power as seen in Fig. 5, which is expected from a classical trap of a harmonic potential. In the second regime, we use the theory for harmonic potentials to compute the force exerted on the particle from this information and find the stiffness of the trap in the second regime. We find kexp = 300 pN/μm/mW, which is more than one order of magnitude larger than the classical optical trapping techniques for similar objects.26–29 For comparison, we can calculate the trapping force created by a classical optical trap on a similar particle using the formula (8) from Ref. 18, which gives a theoretical trap stiffness of 85 pN/μm/mW.

FIG. 5.

Stiffness of the trap versus the guided laser power close to the cavity when operating in the “classical trapping regime” (δλ = 0.9 nm). The inset shows a linear fit (black line) used to obtain the slope of the force profile leading to kexp = 300 pN/μm/mW.

FIG. 5.

Stiffness of the trap versus the guided laser power close to the cavity when operating in the “classical trapping regime” (δλ = 0.9 nm). The inset shows a linear fit (black line) used to obtain the slope of the force profile leading to kexp = 300 pN/μm/mW.

Close modal

To summarize, we have demonstrated the use of back-focal plane interferometry for the comparison of the forces felt by a trapped sphere moving inside a hollow photonic crystal cavity. The presence of two trapping regimes is observable, which is in agreement with the previous observations.14 This approach can be implemented for capturing the Brownian motion of particles in a non-harmonic potential. Applications range from active cooling of dielectric spheres to the trapping of biological samples, such as small organelles, viruses, and small bacteria. Trapping with the back-action approach is very unique since the object can be trapped at a dynamic minimal of intensity inside the cavity, which can reduce the amount of damage produced by the strong light intensity and heating that often occurs in classical traps. This device can potentially be used for trapping single biological samples and perform Raman spectroscopy inside a chip. The back-action effect could be exploited to perform the refractive index sensing, to measure the size of the trapped nanoparticles. It enables sorting schemes to differentiate between particles in size, refractive index, and shape. Finally, such experimental set-up can be exploited for actively cooling a trapped particle in vacuum.

See supplementary material for an analysis of the dependence of the Q-factor of the cavity on the back-action trapping on single particles; PSD of the trapped nanoparticles in the plane of the photonic crystal and PSD of 250 nm particles in the plane of the photonic crystal.

The authors would like to acknowledge funding from the Swiss National Science Foundation through Project Nos. 200020_153538, 200021_143703, and R'Equip 206021_121396.

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Supplementary Material