**2. In-plane coupling of photonic crystal waveguides**

W1 PhC can be obtained by introducing a line defect within the periodic lattice, usually realized through a triangular lattice layout of air holes etched into the substrate. This configuration is compatible with standard planar-semiconductor processing technology. A way to couple efficiently in-plane the light is the use of tapered waveguides. The best geometrical configurations of the tapered profiles are found by performing a good electromagnetic field confinement and low losses. In order to define the frequency response and the electromagnetic coupling of the tapered waveguides, we consider two numerical approach: the finite difference time domain (FDTD) method, and finite element method (FEM). The first one defines accurately the scattered light and the field coupled inside the device, and the second one analyzes the peak frequency resonance and provides the frequency shift versus different taper lengths. This section is organized as follows:


We design integrated tapered waveguides coupled in-plane with an external source (0=1.31 m) and able to focus the energy in a small waveguide region (ridge of the waveguide).

According with the technological limits (technology resolution) we fix the optical and the geometrical parameters indicated in Fig. 2 (a) and (b) as: D=2m, d=1.2m, s=0.3m, *n*(GaAs)=3.408, *n*(AlGaAs)=3.042, w=0.5m, Ls=16.77 m. We analyze the bandpass behaviour around the working *<sup>0</sup>*=1.31 m, and evaluate the energy density at the output of the two coupled tapered waveguides. This procedure allows to calculate the best optimum length L of the tapered profile. The inset of Fig. 3 reports a schematic representation of the employed transmission experimental set-up. In this set-up a light probe beam (tungsten broad band lamp) is launched from a tapered fibre and directly injected into the ridge waveguide. The light exiting the waveguide is collected and collimated by a microscope objective with high numerical aperture. The real image of the output facet of the waveguide is then formed on the common focal plane of a telescopic system, where a horizontal slit is placed. This allows us to separate the light coming from the ridge waveguide from the

Photonic Crystal Waveguides and Bio-Sensors 117

waveguides with L=200 m and helps to discriminate the part of energy irradiated by the

Fig. 2. a) 3D Coupled tapered waveguides; b) top view of coupled tapered waveguide; c) W1 PhC and tapered waveguides. (d) SEM image of the W1 PhC coupled to the input and

Fig. 3. Central wavelength: comparison between experimental, 2D FDTD and 3D FEM method. Inset: Experimental setup which measures the optical transmittivity of the coupled

photonic crystal from the part irradiated by the tapered profile.

output by tapered waveguides.

tapered waveguides of Fig. 1 (a).

radiation freely propagating in the air and through the substrate. The transmitted light is collected by a multimode fibre with its free end lying on the focal plane of a lens (end-fire coupling) and brought to an N-cooled InGaAs OMA (optical multichannel analyzer).

As reported in Fig. 4 (2D FDTD simulation) and in Fig. 5 (3D FEM simulation) we have predicted the measured shift of the central wavelength. In our analysis, we have considered four lengths L of the tapered profile (in particular L=25 m, L=50 m, L=100 m, L=200 m): the central wavelength decreases for the cases L=25 m to L=50 m and increases from L=50 m to L=200 m. As reported in the 3D FEM results of Fig. 4 and in the 2D FDTD results of Fig. 5, the case of L=50 m is characterized by a central wavelength far from the working wavelength. Moreover, we observe in the same figures other peaks due to backscattering interference phenomena of the slanted profile. In Fig. 6 we show the comparison between measured, 2D FDTD and 3D FEM spectra by considering L=100 m: a low error about the central wavelength is observed (the different band amplitudes are due to different kind of light sources). By evaluating the coupled energy at the output of both tapered waveguides, we observe that the cases of L=100 m and L=200 m represent the best coupling condition (see Fig. 7 where the energy is defined by the subtended area of the electric field density). in these cases, the losses due to the radiation in the external space are low and, consecutively, the light coupling inside the guiding region is strong (compromise between high transmittivity and low losses at the working frequency). The integral used to evaluate the electric field density of Fig. 7 is:

$$S(t) = \int\_{V} \varepsilon(\mathbf{r}) \left| \mathbf{E}(t) \right|^2 dV \tag{1}$$

Where *E* is the electric field, is the spatial dependent permittivity index, and *V* is the volume of calculus.

We use for the calculus of (1) as source a carrier modulated by an exponential signal expressed by

$$\Psi\_{source} = \exp(-(t \cdot dt \,/\, T\_0)^2) \cdot \cos(a\_0 \cdot t \cdot dt) \tag{2}$$

where *<sup>0</sup>* is the angular frequency at *λ0*=1.31 m,*T0* is a constant, and *dt* is the time step.

We note from numerical results that the 3D FEM results provide better the accuracy of the frequency shift according with the experimental spectra.

We conclude that good choices of tapered waveguides working at 0 =1.31 m are the profiles with L=100 m and L=200 m. The field losses can be estimated by introducing a PhC waveguide between the two tapered waveguides as the W1 PhC illustrated in Fig. 8 (a), where the input is coupled through the tapered waveguide with the defect region, and, the signal is coupled with a cavity (as shown by the simulations of Fig. 8 (b) and Fig. 9 (a) illustrating different perspectives of the *Ey* field component). We analyze as filter a triangular lattice structure characterized by a lattice constant of 0.95 m and air hole radius of 0.399 m. In order to confine better the electromagnetic field inside the cavity, the radius of the holes near the cavity are reduced to 0.304 m (optimization process). In Fig. 9 (b) are illustrated the radiation losses of the whole device using L=100 m. Moreover the comparison between Fig. 9 (c) and Fig. 9 (d) shows the losses distribution for tapered

radiation freely propagating in the air and through the substrate. The transmitted light is collected by a multimode fibre with its free end lying on the focal plane of a lens (end-fire

As reported in Fig. 4 (2D FDTD simulation) and in Fig. 5 (3D FEM simulation) we have predicted the measured shift of the central wavelength. In our analysis, we have considered four lengths L of the tapered profile (in particular L=25 m, L=50 m, L=100 m, L=200 m): the central wavelength decreases for the cases L=25 m to L=50 m and increases from L=50 m to L=200 m. As reported in the 3D FEM results of Fig. 4 and in the 2D FDTD results of Fig. 5, the case of L=50 m is characterized by a central wavelength far from the working wavelength. Moreover, we observe in the same figures other peaks due to backscattering interference phenomena of the slanted profile. In Fig. 6 we show the comparison between measured, 2D FDTD and 3D FEM spectra by considering L=100 m: a low error about the central wavelength is observed (the different band amplitudes are due to different kind of light sources). By evaluating the coupled energy at the output of both tapered waveguides, we observe that the cases of L=100 m and L=200 m represent the best coupling condition (see Fig. 7 where the energy is defined by the subtended area of the electric field density). in these cases, the losses due to the radiation in the external space are low and, consecutively, the light coupling inside the guiding region is strong (compromise between high transmittivity and low losses at the working frequency). The integral used to evaluate the

> <sup>2</sup> () () () *V S t t dV*

We use for the calculus of (1) as source a carrier modulated by an exponential signal

2 0 0 exp( ( / ) ) cos( ) *source t dt T*

*<sup>0</sup>* is the angular frequency at *λ0*=1.31 m,*T0* is a constant, and *dt* is the time step. We note from numerical results that the 3D FEM results provide better the accuracy of the

We conclude that good choices of tapered waveguides working at 0 =1.31 m are the profiles with L=100 m and L=200 m. The field losses can be estimated by introducing a PhC waveguide between the two tapered waveguides as the W1 PhC illustrated in Fig. 8 (a), where the input is coupled through the tapered waveguide with the defect region, and, the signal is coupled with a cavity (as shown by the simulations of Fig. 8 (b) and Fig. 9 (a) illustrating different perspectives of the *Ey* field component). We analyze as filter a triangular lattice structure characterized by a lattice constant of 0.95 m and air hole radius of 0.399 m. In order to confine better the electromagnetic field inside the cavity, the radius of the holes near the cavity are reduced to 0.304 m (optimization process). In Fig. 9 (b) are illustrated the radiation losses of the whole device using L=100 m. Moreover the comparison between Fig. 9 (c) and Fig. 9 (d) shows the losses distribution for tapered

frequency shift according with the experimental spectra.

**r E** (1)

*t dt* (2)

is the spatial dependent permittivity index, and *V* is the

coupling) and brought to an N-cooled InGaAs OMA (optical multichannel analyzer).

electric field density of Fig. 7 is:

Where *E* is the electric field,

volume of calculus.

expressed by

where  waveguides with L=200 m and helps to discriminate the part of energy irradiated by the photonic crystal from the part irradiated by the tapered profile.

Fig. 2. a) 3D Coupled tapered waveguides; b) top view of coupled tapered waveguide; c) W1 PhC and tapered waveguides. (d) SEM image of the W1 PhC coupled to the input and output by tapered waveguides.

Fig. 3. Central wavelength: comparison between experimental, 2D FDTD and 3D FEM method. Inset: Experimental setup which measures the optical transmittivity of the coupled tapered waveguides of Fig. 1 (a).

Photonic Crystal Waveguides and Bio-Sensors 119

Fig. 7. Density of energy for different taper lengths L at 0=1.31m.

Fig. 8. (a) SEM image of the simulated add drop filter. (b) 2D FDTD simulation of the

Fig. 9. (a) FDTD simulation: *Ey* component along the W1 region and into the cavity defect. (b) Top view of *Ey* distribution for tapered waveguides with L=100 m. (c) Top view of *Ey* distribution for tapered waveguides with L=200 m. (d) Top view of *Ey* distribution for

photonic crystal by using a continuous wave at 0=1.31 m as source.

L=200 m and Ls= 16.77 m.

Fig. 4. Wavelength shift: 3D-FEM transmittivity for different lengths L.

Fig. 5. 2D FDTD spectra comparison.

Fig. 6. Comparison between measured, 2D FDTD and 3D FEM spectra of tapered waveguides with L=100 m.

Fig. 4. Wavelength shift: 3D-FEM transmittivity for different lengths L.

Fig. 6. Comparison between measured, 2D FDTD and 3D FEM spectra of tapered

Fig. 5. 2D FDTD spectra comparison.

waveguides with L=100 m.

Fig. 7. Density of energy for different taper lengths L at 0=1.31m.

Fig. 8. (a) SEM image of the simulated add drop filter. (b) 2D FDTD simulation of the photonic crystal by using a continuous wave at 0=1.31 m as source.

Fig. 9. (a) FDTD simulation: *Ey* component along the W1 region and into the cavity defect. (b) Top view of *Ey* distribution for tapered waveguides with L=100 m. (c) Top view of *Ey* distribution for tapered waveguides with L=200 m. (d) Top view of *Ey* distribution for L=200 m and Ls= 16.77 m.

Photonic Crystal Waveguides and Bio-Sensors 121

Our optical signal detecting device featuring high sensitivity and multiplexing detection is composed of an array of PhC resonators with specific probes (e.g. single-stranded DNA (ssDNA) sequences, antibodies, receptors, aptamers, etc…) for analytes (e.g. DNA, proteins, ligands, etc.) attached on them. Analytes are trapped with high spatial precision through chemical, physical, electrostatic techniques, and so on (Fig. 10). The target analytes can be directly (e.g. through syntesis) or indirectly marked by conjugation with one or more fluorophores. The basic schemes for a detection of biomolecules (proteins, ligands, etc.) and nucleic acids are shown in Figs. 11 (a) and (b), respectively. To eliminate background noise caused by scattering of excitation light, excitation light can be selectively provided to readout regions via PhC waveguides. The proposed system is based on a unique optical detection scheme. The detection is performed through the collection of the emission spectrum coming from the whole bio-recognition area of the chip. As previously discussed, by applying a suitable matrix composed by PhC resonators possessing different resonant wavelengths, each bio-recognition element of the device is unambiguously associated to a different resonance peak. By detecting resonant peak emissions at certain wavelengths, it is therefore possible to detect the presence of specific target (bio) molecules contained in the analyzed sample. Thus, it is possible to collect signals from several resonators in a single analysis, increasing the signal collection speed. Moreover, the PhC strongly inhibits the excitation radiation that is diffused or reflected towards the detection direction. Elimination of radiation of excitation light together with the increase in the intensity of the emission signal increases significantly the overall signal-to-noise ratio. This feature helps to reduce reading errors, allowing operators skip the step of complex post-processing to correct readout errors. Photonic crystals can control the light propagation by introducing a 1D, 2D or 3D periodicity in materials having high optical transparency in the frequency range of interest. Light can be trapped, for instance, by introducing a defect in the periodicity. Summarizing, photonic crystals technology could, therefore, be applied to biochip technology in order to

a. controllability of the resonant wavelength of each resonator in the matrix through the accurate material and geometry design. Specifically, it becomes possible to enhance the emission spectrum of the fluorophore conjugated to an analyte. This allows us to perform an optical detection not only on the basis of a spatial discrimination of the different contributions but also on the basis of a spectral discrimination, since each pixel

b. increase of the fluorophore emission efficiency in specific spectral bands through the Purcell effect (e.g. micro resonators with high quality factor (Q-factor) and small modal

c. possibility to selectively excite light-emitting marker via waveguides or a resonance of a certain optical mode of photonic crystal to suppress diffused, reflected or diffracted excitation light from the substrate. This can be achieved by controlling the angle of emission or excitation by properly engineering a photonic crystal. This property can be

exploited to spatially separate the excitation radiation and the emission band. d. Regarding point (a), an external excitation light sent towards the matrix at a proper angle will excite the marker bound to the captured analyte, which will emit its typical broad signal. Then, the broad emission is peculiarly amplified in specific spectral bands by the underlying pixel with a photonic crystal resonator (Fig. 12 (a)). The variation from pixel to pixel (that is, from analyte to analyte), of the frequencies contemporarily

contains a specific optical resonator working at a different frequency.

volume), thus increasing the signal-to-noise ratio.

provide the following advantages:
