1. Introduction

Mesoscopic Photonic Crystals (MPhCs) support the Mesoscopic Self-Collimation (MSC) phenomenon, which ensures ‘guideless’ waveguiding in linear media. As in traditional Self-Collimation (SC) [1], this behaviour can be reached by engineering the angular anisotropy [2] of the crystal. This is a change of paradigm as light guiding occurs without any need for alignment with a guiding structure. In fact, a MPhC is a 1D-periodic superstructure that can be fabricated by cascading slabs of different materials (or metamaterials) exhibiting opposite spatial dispersion, such as slab of PhCs in the self-focussing regime and slabs of bulk materials. From the spatial dispersion engineering point of view, for a specific direction, MSC is obtained when the focusing properties of the PhC slabs compensate the natural defocusing of the bulk material slabs [2–9]. This ‘guideless’ waveguiding paves the way for the conception of structures showing lateral translational invariance. A key advantage of MSC as compared to SC, is that several optical properties can be achieved simultaneously, thanks to higher degrees of freedom: input facet impedance perfect matching [3], stable Fabry-Pérot-like microcavities having flat parallel mirrors with an improved reflectivity able to reflect even non-paraxial beams, as curved mirrors do [4, 5], slow light waveguides [2, 7] compensation of time and space dispersion to achieve linear solitons [7].

One original application of MPhCs is the design of high sensitivity and high Q-factor microcavities [4–6,8,9] on thin membranes. However, these theoretical predictions are based on 2D calculations that ignore vertical losses due to out-of-plane diffraction. As MSC occurs well above the light line (due to large meso-period as compared to the wavelength), these losses are potentially high and might be detrimental to the predicted high-Q confinement.

In this paper, we report on 3D-FDTD simulations and experimental demonstration of a fabricated MPhC Fabry-Pérot microcavity exhibiting high-Q, 3D-light confinement.

2. 3D modelling

Figure 1 depicts a sketch of the MPhC microcavity numerically investigated with 3D-FDTD (Lumerical FDTD Solutions), comprised of two MPhC mirrors (MM) on each side of a homogeneous defect. The geometry of the microcavity is based on the 2D numerical analysis reported in [4]. Each MM is obtained by interleaving focusing slabs, constituted by 13 rows of holes of a 45°-tilted square-lattice PhC (with lattice constant a = 350 nm, hole radius r = 0.25 × a = 87.5 nm and an overall width d_c = 9.192 × a), and defocusing slabs, constituted by bulk material with a refractive index n_b and a width d_b = 2.612 × a (a sketch of the MPhC unitary cell is shown in Fig. 1(b)). The cavity defect width is W = 5.32 × a. We modelled the device by considering a 276-nm-thick GaAs membrane (n_b = 3.31 at 1550 nm), fully surrounded by air having refractive index n = 1.

 

Fig. 1 (a) Sketch of the fabricated MPhC microcavity. The highlighted green and yellow area is reported in (b), where the yellow one represents the elementary cell of the MPhC. The highlighted light blue strip represents the portion of the structure that is actually calculated in the 3D-FDTD simulation. (b) Sketch of the MPhC elementary cell. (c) Sketch of the FDTD calculation region. The red region bordering the cell along the x- and z-directions represent the PML boundary conditions. The two black vertical arrows indicate the xz-planes where the PBCs enclose the computational region along the y-direction. The orange strip, parallel to the xy-plane, represents the monitor where collect the scattered power is collected.

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Since the structure is periodic along the y-direction, showing a period $\sqrt{2}$ × a (see Fig. 1(c)), we have imposed periodic boundary conditions (PBCs) to the computational cell boundaries perpendicular to this direction. PMLs are imposed at the boundaries perpendicular to the remaining directions (x- and z-directions). The structure is excited in by injecting a broadband source (1460 nm < λ < 1580 nm) having a spatial distribution matching that of the fundamental TE mode (with the x-component of the electric field E_x = 0) of the membrane (at λ = 1520 nm).

Figure 2 shows the simulated spectrum of the vertically scattered light above the cavity. In good agreement with 2D-FDTD simulations reported in [4], despite the vertical losses, a long-lived mode showing a high-Q spectral peak around 1480 nm is observed with a Q-factor of about 4773 (≈half of the corresponding 2D one). Another weaker peak, with a lower Q factor is also observed around 1551 nm (Q-factor equal to about 889) and which was observed in [4].

 

Fig. 2 FDTD vertically scattered light spectrum (normalized to the input power). The two peaks suggesting the formation of an optical mode inside the cavities are highlighted by two markers: one at 1480 nm and one at 1551 nm.

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In order to investigate the nature of both the modes, a second set of 3D-FDTD simulations were carried out where the total electric field and the z-component of the Poynting vector were recorded. Results are shown on Fig. 3: total electric field at 1480 nm (a) and at 1551 nm (b) and z-component of the Poynting vector at 1480 nm (c) and 1551 nm (d). To highlight the vertically scattered light above the cavity, self-normalized Poynting vector depicted in Figs. 3(c) and 3(d) is plotted using a logarithmic scale.

 

Fig. 3 Self-normalised magnitude of the total electric field (a-b) and (c-d) z-component of the logarithm of the self-normalised Poynting vector at 1480 nm and 1551 nm, respectively.

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From these simulations, we conclude that both the spectral peaks correspond to modes that are fully localized: in xy-plane (2D) by the MSC cavity, and in the vertical direction by the membrane with partial leaking out of the membrane.

3. Sample fabrication and characterization

Several samples with the geometry described in Fig. 1 were fabricated on suspended GaAs membranes in a three-step process described in [10]. Firstly, e-beam lithography was used to define the pattern in an electronic resist and form a mask that, in a second step, was used to etch the PhC holes using dry etching (ICP - RIE). In a last step, the samples were immersed into a hydrofluoric acid bath to remove a 1.5µm-thick AlGaAs sacrificial layer.

Figures 4(a) and 4(b) shows a scanning electron microscope (SEM) in-plane image of the micro-cavity (with an overall length along x and y of 41.3 µm and 92.5 µm, respectively).

 

Fig. 4 (a) In-plane SEM image of a fabricated MPhC based microcavity having a lattice constant a = 350 nm and a hole radius r = 0.25 × a = 87.5 nm. The white arrows on the right indicate the position of the beginning and the end of the cavity and the defect position. The red stripe with a superimposed white arrow indicates the incident light direction. (b) Close-up of (a) inside a PhC slab. (c) Sketch of the optical characterization set-up of the sample.

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Figure 4(c) shows the optical characterization set-up of the sample: the beam of a tunable laser (spanning 1460 – 1580 nm) is focused on the sample facet using two aspherical lenses; a polarizer, placed in between the two lenses, controls the input light polarization. A microscope system, composed by a microscope objective and a VIS-IR vidicon camera, collects the scattered light and displays it on a monitor. Finally, the video signal is acquired by a commercial acquisition card and numerically processed.

An image of the scattered light is acquired for each wavelength, forming an hyperspectral cube A(p_x,p_y,λ_p), where λ_p is a given wavelength, p_x and p_y are the pixel indices along the x and y directions, respectively.

In Fig. 4(a) the alignment position of the first and last row of the matrix of pixels (p_x = 1 and p_x = p_x,cav corresponding to the beginning and end of the cavity, respectively) are superimposed on the SEM image.

In order to calculate the experimental vertically scattered light, we define a pseudospectral map M(p_x,λ_p) as the sum of the pixel intensities A along the transverse direction of the cavity (y-direction):

 

Fig. 5 (a) Measured pseudospectral map of the fabricated microcavity with a = 350 nm. The superimposed horizontal white dotted line indicates the pixel labelled p_x,cav. (b) Experimental pseudospectrum (blue curve) and the simulated self-normalized scattering spectrum (red curve), which corresponds to the result shown on Fig. 2. The green squared mark and the green star mark indicate the resonant peaks wavelengths λ₀ = 1482.2 nm and λ₃ = 1547 nm, respectively. The green triangle marks denote the wavelengths λ₁ = 1545 nm, λ₂ = 1546 nm and λ₄ = 1548 nm, corresponding to the subfigures shown in Fig. 6.

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Figure 5(b) shows the final experimental pseudospectrum (blue curve) that is compared with the simulated normalized vertically scattered light spectrum calculated previously (red curve). This simulated spectrum is normalized to its maximum (as the pseudospectrum). The experimental results show a good agreement with the numerical ones. Specifically, in the experimental pseudospectrum the resonant peaks within the bandgaps, corresponding to the formation of a stable cavity mode, are at λ₀ = 1482.2 nm (green square mark) and λ₃ = 1547 nm (green star mark) allowing for a Q factor equal to 1720 and 1170, respectively. The differences between simulated and measured Q factors are attributed to the fact that the experimental beam is laterally confined, while in the simulation, an infinitely large beam was used.

To experimentally investigate the localization of the mode, we concentrate on the λ₃ = 1547 nm mode. We choose this mode as it exhibits a higher signal to noise ratio on the camera signal as compared to the λ₀ = 1482.2 nm mode. Figure 6 depicts the collected scattered light images at λ₁ = 1545 nm, λ₂ = 1546 nm, λ₃ = 1547 nm and λ₄ = 1548 nm. In particular, Fig. 6(c) illustrates the formation of a stable mode at λ₃. At the same time, the region beyond the output facet in Fig. 6(c) is dark due to absence of scatterers (PhC holes and PhC/bulk interfaces).

 

Fig. 6 Collected scattered light at wavelengths (a) λ₁, (b) λ₂, (c) λ₃ and (d) λ₄. The p_y-axis and the superimposed white dotted line indicate the input facet (p_x = 1) and the output facet (p_x = p_x,cav) of the cavity, respectively.

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4. Conclusion

In conclusion, we demonstrated experimentally that MPhC microcavities can confine light in 3D using a Fabry-Pérot-like 2D cavity on a slab. Despite being well above the light cone and thus being well coupled to the vertical axis, the confined mode exhibits experimental Q factor in excess of 1700. These experimental results are in agreement with the 3D numerical findings in terms of resonant wavelength and Q-factors.

These results pave the way for a new class of devices showing translational invariance and strong near-field localization, together with a strong coupling with surroundings. Those features could be extremely valuable for optical devices devoted to biochemical sensing, optical tweezing and nanoparticle manipulation and for the design of innovative tweeze-and-sense micro- and nano-object systems that could be integrated in microfluidic systems and labs-on-chip.