1. Introduction

Nanophotonics has opened up novel possibilities for the spatial and spectral control of light [1,2]. Integrated photonic devices can break the diffraction barriers of conventional optics and confine light in sub-wavelength volumes [1–4]. The tightly-confined near fields of dielectric photonic devices have been extensively used for optical trapping of microscopic matter [5–8]. Parallel trapping of multiple objects can be achieved by using devices that support multiple, high-intensity spots in the near-field profile [9–11]. To develop tunable or reconfigurable traps, mechanisms for changing the spatial periodicities of the near field are desirable. Such a capability would allow real-time reconfiguration of “optical matter [12],” the pattern of objects trapped on the device.

Typical approaches for reconfiguring the near field of a photonic device, such as mechanical deformation, liquid infiltration, thermo-optic and nonlinear tuning [13–17], can pose practical challenges for implementation within optical trapping systems. A relatively straightforward route to reconfiguring the field is to design a device that supports different spatial profiles at different wavelengths and/or polarizations within the tuning range of the laser. In previous work, we have suggested this scheme theoretically for optical traps based on guided resonance modes [18] of photonic-crystal slabs [19]. However, our initial design required a laser tuning range much larger than is typical for lasers used in trapping experiments.

In this work, we propose, simulate, and demonstrate a method for designing closely-spaced guided resonance modes in photonic crystals. We break the symmetry of an underlying photonic-crystal lattice by introducing two sets of orthogonal slots. The slots create two modes with different spatial field periodicities and polarizations. We show that the wavelength separation between the modes can be made arbitrarily small by varying the lattice parameters, while the center wavelength is adjustable. We implement our design experimentally in a silicon photonic crystal near a wavelength of 1550nm. Our measurements demonstrate the ability to adjust center wavelength and wavelength separation for two modes excited with orthogonal linear polarizations. For optical trapping applications, our systematic design approach for dual, closely-spaced modes can be used to create different optical potential landscapes for reconfigurable trapping [19]. Our approach may also be useful for the development of differential-mode biosensors [20,21] and dual-band notch filters [22–26] in photonic crystals.

2. Dual-slot photonic crystal design

As a starting point for our design, we consider a photonic-crystal slab comprised of a square lattice of holes in silicon. This structure supports guided-resonance modes at the center of its first Brillouin zone ($\Gamma$ point) [18]. We set the lattice constant a = 642nm, the hole radius r = 90nm, the thickness of the Si photonic crystal slab to 250nm, and the refractive index to 3.45. The slab lies on top of a semi-infinite SiO₂ substrate with refractive index 1.44, and the surrounding medium is assumed to have an index of 1.33 (e.g. water). The structure was simulated using the 3D Finite-Difference Time Domain (FDTD) method in the Lumerical FDTD Solutions tool. Figure 1 shows the electromagnetic fields excited by normally-incident light for a resonance mode wavelength of 1695nm. The in-plane electric field (${\overline{E}}_{xy}$) and magnetic field component ($\left|H_z\right|$)at the center of the slab are shown for x- and y-polarized light in Figs. 1(a) and 1(b) respectively.

 

Fig. 1 a,b) In-plane electric field vector (arrows) and out-of-plane magnetic field component (color map) at the center of the photonic-crystal slab formed by a square lattice of holes in silicon for a) x- and b) y-polarized incident light, prior to the introduction of slots. c) Locations of center slots (red) and edge slots (green) introduced into the square lattice. d) The design parameters of the dual-slot photonic crystal. a and r are the lattice constant and hole radius of the original square lattice. The width and height of the center slots are represented by w_c, h_c, and the edge slots by w_e, h_e.

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We next introduce slots into the square lattice. Due to the boundary conditions on the electric field, a narrow slot in a dielectric will strongly enhance the electric field perpendicular to the slot [27]. As shown in our previous works [11,19,28], this principle can also be used to perturb guided-resonance modes. We introduce both horizontally and vertically-oriented slots in the locations indicated by the white dashed lines in Figs. 1(a) and 1(b). These positions are indicated schematically in Fig. 1(c). We call the slots oriented in the y direction (red symbols) “center slots,” since they are placed at the center of each unit cell in the original lattice. They form a square lattice with periodicity a. We call the slots oriented in the x- direction (green symbols) “edge slots,” since they are placed along the edges between holes of the original lattice. They also form a square lattice, but with a periodicity of $\sqrt{2} a$, and a rotation by 45°. By using different periodicities for the center and hole slots, we can obtain modes with different near-field periodicities, as will be seen below. The slot dimensions are labeled symbolically in Fig. 1(d).

Figure 2 shows the evolution of the guided-resonance mode in the square lattice as the slots are introduced. The slot widths were set to w_e = w_c = 250nm, while the slot height h = h_e = h_c = was varied from 0 to 80nm. The transmission spectrum is plotted in Fig. 2(a). The guided-resonance modes appear as dips in the spectrum. In the limit where the slots disappear (h = 0), the guided resonances are degenerate for both polarization states (top graph). Introduction of slots into the design breaks the degeneracy. As the slot height increases, both modes shift to lower wavelengths. For $h=80nm$, the x-polarized mode lies at λ₁ = 1535.30nm, and the y-polarized mode at λ₂ = 1566.3nm, with a difference Δλ of 31nm. We note that incident light with a linear polarization not aligned with the x- or y- axis will partially excite both modes, yielding two dips in the transmission spectrum.

 

Fig. 2 a) The transmission spectrum of the device for different slot heights. b-d) The magnetic (H_z) and electric field (|E|²) distribution at the center of the square lattice of holes for (b, d) x- and (c, e) y- polarized light. f-i) The magnetic (Hz) and electric field (|E|²) distribution at the center of the dual-slot photonic crystal for (f, h) x- and (g, i) y- polarized light.

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We compare the field distributions in the photonic crystal before and after the introduction of slots in Figs. 2(b)-2(i). From Figs. 2(d) and 2(h), it can be seen that the introduction of vertically-oriented (center) slots creates strong field confinement for the x-polarized mode. Likewise, the introduction of horizontally-oriented (edge) slots creates strong field confinement for the y-polarized mode (Figs. 2(e) and 2(i)). In addition, the x- and y-polarized modes have distinct intensity distributions. The intensity distribution in Fig. 2(h) peaks at the center of each center slot, while the intensity distribution in Fig. 2(i) peaks at the center of each edge slot. The peak near-field intensity values corresponding to x- and y- polarizations thus form square lattices with lattice constants of 642nm and 908nm, respectively.

The resonance wavelengths can be tuned by varying design parameters. This can be done by modifying the underlying square lattice or by perturbing the slot dimensions. Figure 3 shows the variation of x- and y- polarized modes as a function of the lattice constant a and hole radius r of the photonic crystal. The slot dimensions were kept constant at 80nm and 250nm.

 

Fig. 3 a) The resonant wavelength as a function of r and a for x- and y- polarizations. b) The difference in resonant wavelengths for y- polarized and x- polarized modes as a function of r and a.

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From Fig. 3(a), it is evident that both resonances are sensitive to the hole size and lattice constant. The resonances redshift with the increase in lattice constant and blue shift with the radius. The separation between the resonances varies with the radius and remains mostly unaffected by the lattice constant (Fig. 3(b)). This gives us a convenient tool for controlling the resonances. The relative locations of resonances can be controlled with the hole radii, and then their absolute locations can be shifted with the lattice constant. We also investigated the effect that the perturbation of slot dimensions has on the resonance wavelengths and quality factors. The results are shown in Fig. 4.

 

Fig. 4 The resonance wavelengths for x- and y- polarizations with a) width and b) height of edge slots, c) width and d) height of center slots.

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The lattice constant and hole radius are fixed at 620nm and 55nm so that both resonances are close to 1550nm. Both the resonances blue shift with increase in slot sizes w_e, h_e, w_c, and h_c, as is apparent from the negative slope in Figs. 4(b)-4(e). The changes in dimensions of the edge slots shift both the resonances equally (Figs. 4(b) and 4(c)), while the center slots change the relative locations of the resonances (Figs. 4(d) and 4(e)). The resonance wavelengths are more affected by the center slots (Figs. 4(d) and 4(e)) than the edge slots (Figs. 4(b) and 4(c)).

The quality factors of the resonances depend on the slot dimensions. The change in the quality factors of the resonances with slot perturbation is shown in Fig. 5. The x-polarized mode has orders of magnitude higher simulated quality factor than the y-polarized mode. The quality factor of the x-polarized resonance is greatly affected by both the slots, but in opposite directions. Increasing the width or height of the edge slots increases the quality factor of the x-polarized mode, while the effect is reversed for the center slots. The quality factor of the y-polarized resonance is marginally affected by the change in size of either of the slot types. Increasing the size of the central slots and/or decreasing the size of the edge slots will reduce the difference in quality factors of x- and y- polarized modes.

 

Fig. 5 The quality factor of resonances for x- and y polarizations with a) width and b) height of edge slots, c) width and d) height of center slots.

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From the simulation results, the slot dimensions can be used to change the quality factors of the resonances. By expanding the central slots and shrinking the edge slots, the quality factor of the two resonances can be made more similar. The corresponding change in locations of the resonances can be compensated by adjusting the lattice constant and hole dimension.

3. Fabrication and characterization

The photonic crystal devices are fabricated on a silicon-on-insulator wafer from SOITEC with a 250nm Si device layer, 3μm buried oxide layer, and a 4500μm Si handle layer. The patterns are transferred to the wafer using e-beam lithography (Vistec EBPG 5000 + ES, 100kV acceleration voltage) followed by ICP-reactive ion etching (Oxford) with ZEP 520A resist. A 200nm thick Si₃N₄ antireflection layer is coated on the backside of the polished wafer using plasma enhanced chemical vapor deposition (Oxford). The lattice constant a and the hole radius r of the devices were tuned from 644nm to 668nm and 65 nm to 101nm respectively, by keeping the slot dimensions constant. The slot dimensions w_e, h_e, w_c, h_c were chosen as 250nm, 80nm, 275nm and 100nm respectively. The central slots were chosen to be slightly larger than the edge slots to have comparable quality factors. The SEM image of one of the fabricated devices is shown in Fig. 6.

 

Fig. 6 SEM image of one of the devices. The scale bar represents 1µm.

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The transmission spectra of the devices were characterized at normal incidence in parallel polarization-mode. To achieve alignment, we attached each polarizer and the sample to separate rotation mounts inserted into an optical cage system. The polarizers were set to be parallel to one another, and oriented in either in the x- or y-directions, using the marked orientations. A Santec TSL-510 tunable laser (1500-1620nm) was used for the characterization. The power and polarization of the incident beam were controlled using an erbium-doped fiber amplifier combined with polarization-control optics. An aspherical lens (f = 11 mm and NA = 0.25, Thorlabs C220 TME-C) was used to launch the laser from a single-mode fiber (mode diameter 10.4 ± 0.8 μm) to free space. An achromatic doublet (f = 30 mm, Thorlabs AC254), mounted on a lens tube, was used to refocus the beam to the back side of the sample. A second lens was used to collect the transmission. The FWHM of the beam was measured to be 27μm using the knife edge method. The second lens was also used to form a visible image of the sample on a camera. The image was used to orient the x-axis of the sample parallel to the optical table, using alignment markers patterned on the sample.

Figure 7(a) shows the measured transmission spectra for x- and y- polarizations for varying lattice constants, for fixed hole radius of 65nm. Each polarization state selectively excites one of the guided modes. Both x and y polarized resonances red shift with the increase in lattice constant, while the separation between the resonances remains nearly constant. By varying the lattice constant, the resonances can be spectrally shifted to the left or right without affecting their separation. We also measured the samples at intermediate polarizations. As the polarization is rotated from x- to y-, one starts to see the excitation of both modes. The relative amplitude of the two transmission dips changes smoothly as a function of polarization angle.

 

Fig. 7 Transmission spectrum of dual-slot devices for a) different lattice constants and b) different hole radius.

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The measured transmission spectra for devices with varying hole radii is shown in Fig. 7(b), for fixed lattice constant of 644nm. The increase in hole size blue shifts both resonances. The x-polarized resonance shifts more strongly than the y-polarized one, reducing the separation between the individual resonances. For the largest radius used here, the two resonances nearly coincide.

Figure 8 shows the experimental quality factors of the measured devices and compares with simulation. The measured quality factors are lower than in simulations, a common effect of slight fabrication errors and/or surface roughness [28]. However, the x-polarized mode has higher Q than the y-polarized mode, as predicted by the simulation results.

 

Fig. 8 Quality factor of the fabricated devices as a function of the a) lattice constant and b) hole radii. Circles denote the measured Q; stars denote the value of Q from simulation.

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4. Conclusion

We have proposed and experimentally demonstrated an approach to designing photonic-crystal slabs that support closely-spaced guided-resonance modes with orthogonal linear polarizations. The use of slots to break the symmetry of the underlying photonic-crystal lattice produces both strong field confinement and modes with different spatial periodicities. The absolute and relative location of the modes can be tuned by varying the design parameters, which we verify via experiments in a silicon photonic-crystal slab at 1550nm. We envision that our design approach can be used for reconfigurable optical trapping of nanoparticles with different spatial separations and orientations [19], as well as in polarization-dependent filters and differential-mode sensors. More abstractly, a difference in the spatial field profiles of multiple, closely-spaced resonances of the same device could also prove useful in other applications that rely on intensity-dependent nonlinearities and/or phase transitions [29]. Future designs may benefit from the use of multiple sets of slots with different lattice constants and/or dimensions.