**2. Photonic crystal waveguide sensor design and sensing principle**

Planar PCWs are one of the preferred photonic structures for the development of biosensing devices because of their reduced size and the high confinement of the optical field in the linear defect region. In this text, we will consider planar SOI PCWs, due to the compatibility of this technological platform with CMOS fabrication techniques.

When designing a PCW for biosensing there are several factors to be taken into account. We will focus on five of them:


Label-Free Biosensing Using Photonic Crystal Waveguides 241

and detected using an optical powermeter after passing through a free-space polarizer configured for TE polarization. Since the fabricated PCWs are designed for biosensing applications, and these require the use of the sensors in a wet environment, the design was optimized for these working conditions. Fig. 5 thus shows the transmission spectrum of one of the fabricated PCWs when deionized water (DIW, *n* = 1.3173) is used as upper cladding. Sharp peaks can be observed at the edge of the guided band (located around 1563 nm).

0.3 0.35 0.4 0.45 0.5

wavevector (2/a)

Fig. 3. Band diagram for TE modes of the SOI W1-PCW with a silicon thickness of 250 nm, a hole radius of 110 nm and a lattice constant of 390 nm. Dark and light shaded areas depict

Fig. 4. SEM image of the SOI photonic crystal waveguide used for the sensing, with close-up

Fringes appearing near the band edge of the transmission spectrum of the PCW are Fabry-Perot (FP) fringes of the cavity defined by the interface between the PCW and the access waveguides (García et al., 2006), as schematically depicted in Fig. 6. A good power coupling between modes in the access waveguides and the PCW is achieved for wavelengths in the transmission band, making the FP cavity effect almost negligible. However, mode mismatching increases between the two waveguides as we get closer to the edge of the

modes going into the bulk photonic crystal and the silicon oxide lower cladding,

1300

view of the sensor area and photonic crystal holes (insets)

1400

1500

wavelength (nm)

respectively.

1600

1700

 Finally, the interface between the PCW and the access waveguide is also something to be taken into account. As previously commented, the shift of the guided band's edge is used in PCW to perform the sensing. Therefore, it is important to have a PCW with a sharp band edge in order to be able to accurately determine its position.

PCWs are designed by means of simulations to determine their optimal parameters and match the previously commented criteria. The most widely used simulation techniques for the design of photonic crystals are FDTD (Finite-Differences Time-Domain), which is used to calculate the propagation of the electromagnetic wave through the structure, and the plane-wave expansion (PWE) method, which is used to determine the band diagram of the perfect infinite photonic crystal structure.

Now the design and experimental characterization of a PCW sample for biosensing will be described. We will consider a PCW in a holes-on-dielectric photonic crystal fabricated on a SOI wafer with a 250nm-thick silicon layer on a 3μm-thick buried oxide layer. The PCW will be a W1-type, where one row of holes is removed in the Γ-K direction to create the waveguide. The PCW was designed to have a working wavelength located around λ = 1550 nm.

By PWE simulations, the lattice constant and the hole radius which will yield a guided band's edge located around 1550 nm can be determined. In case we decide to have the upper edge (in terms of wavelength) of the guided band around this wavelength, these parameters must be 390 nm and 110 nm, respectively. Fig. 3 shows the band diagram for TEmodes calculated for the holes-on-silicon W1-PCW using the PWE method, where the fundamental mode of the PCW with its upper edge located around 1550 nm can be seen.

The next step is the fabrication of the PCW on a SOI substrate. For the fabrication of holeson-dielectric photonic crystal structures, the lithographic process is usually carried out using a positive resist such as PMMA, where the holes area and the trenches defining the structure need to be exposed by e-beam or DUV lithography. After developing the resist, the pattern is transferred to the silicon layer by an etching process such as inductively coupled plasma (ICP) etching.

Fig. 4 shows a scanning electron microscopy (SEM) picture of a W1-PCW fabricated to be used for biosensing. The structural parameters of this PCW were determined by the theoretical simulations, and its length is 20 μm (≈ 52 periods), which provide enough periods for achieving a strong photonic bandgap effect while keeping the structure size as compact as possible. For coupling, 450nm-wide single-mode access waveguides are used to couple/collect light to/from the PCW. The interface between the PCW and the single-mode access waveguides is the one shown in Fig. 4, where the structure ends next to the inner row of holes of the PCW. This interface presents a sharper band edge than other interfaces.

For the optical characterization of the PCW, which is essentially determined by its transmission spectrum, light from an external source must be coupled to the chip. The two main coupling mechanisms used for chip's characterization are butt coupling, where light from a lensed fiber is laterally coupled to the chip, and grating couplers, where light is vertically coupled to the chip using grated structures. For the characterization of these PCW sensors, light from a tunable laser is TE-polarized using a polarization controller and buttcoupled into the PCW using a lensed fiber. Output light is then collected using an objective

 Finally, the interface between the PCW and the access waveguide is also something to be taken into account. As previously commented, the shift of the guided band's edge is used in PCW to perform the sensing. Therefore, it is important to have a PCW with a

PCWs are designed by means of simulations to determine their optimal parameters and match the previously commented criteria. The most widely used simulation techniques for the design of photonic crystals are FDTD (Finite-Differences Time-Domain), which is used to calculate the propagation of the electromagnetic wave through the structure, and the plane-wave expansion (PWE) method, which is used to determine the band diagram of the

Now the design and experimental characterization of a PCW sample for biosensing will be described. We will consider a PCW in a holes-on-dielectric photonic crystal fabricated on a SOI wafer with a 250nm-thick silicon layer on a 3μm-thick buried oxide layer. The PCW will be a W1-type, where one row of holes is removed in the Γ-K direction to create the waveguide. The PCW was designed to have a working wavelength located around

By PWE simulations, the lattice constant and the hole radius which will yield a guided band's edge located around 1550 nm can be determined. In case we decide to have the upper edge (in terms of wavelength) of the guided band around this wavelength, these parameters must be 390 nm and 110 nm, respectively. Fig. 3 shows the band diagram for TEmodes calculated for the holes-on-silicon W1-PCW using the PWE method, where the fundamental mode of the PCW with its upper edge located around 1550 nm can be seen.

The next step is the fabrication of the PCW on a SOI substrate. For the fabrication of holeson-dielectric photonic crystal structures, the lithographic process is usually carried out using a positive resist such as PMMA, where the holes area and the trenches defining the structure need to be exposed by e-beam or DUV lithography. After developing the resist, the pattern is transferred to the silicon layer by an etching process such as inductively coupled plasma

Fig. 4 shows a scanning electron microscopy (SEM) picture of a W1-PCW fabricated to be used for biosensing. The structural parameters of this PCW were determined by the theoretical simulations, and its length is 20 μm (≈ 52 periods), which provide enough periods for achieving a strong photonic bandgap effect while keeping the structure size as compact as possible. For coupling, 450nm-wide single-mode access waveguides are used to couple/collect light to/from the PCW. The interface between the PCW and the single-mode access waveguides is the one shown in Fig. 4, where the structure ends next to the inner row of holes of the PCW. This interface presents a sharper band edge than other interfaces.

For the optical characterization of the PCW, which is essentially determined by its transmission spectrum, light from an external source must be coupled to the chip. The two main coupling mechanisms used for chip's characterization are butt coupling, where light from a lensed fiber is laterally coupled to the chip, and grating couplers, where light is vertically coupled to the chip using grated structures. For the characterization of these PCW sensors, light from a tunable laser is TE-polarized using a polarization controller and buttcoupled into the PCW using a lensed fiber. Output light is then collected using an objective

sharp band edge in order to be able to accurately determine its position.

perfect infinite photonic crystal structure.

λ = 1550 nm.

(ICP) etching.

and detected using an optical powermeter after passing through a free-space polarizer configured for TE polarization. Since the fabricated PCWs are designed for biosensing applications, and these require the use of the sensors in a wet environment, the design was optimized for these working conditions. Fig. 5 thus shows the transmission spectrum of one of the fabricated PCWs when deionized water (DIW, *n* = 1.3173) is used as upper cladding. Sharp peaks can be observed at the edge of the guided band (located around 1563 nm).

Fig. 3. Band diagram for TE modes of the SOI W1-PCW with a silicon thickness of 250 nm, a hole radius of 110 nm and a lattice constant of 390 nm. Dark and light shaded areas depict modes going into the bulk photonic crystal and the silicon oxide lower cladding, respectively.

Fig. 4. SEM image of the SOI photonic crystal waveguide used for the sensing, with close-up view of the sensor area and photonic crystal holes (insets)

Fringes appearing near the band edge of the transmission spectrum of the PCW are Fabry-Perot (FP) fringes of the cavity defined by the interface between the PCW and the access waveguides (García et al., 2006), as schematically depicted in Fig. 6. A good power coupling between modes in the access waveguides and the PCW is achieved for wavelengths in the transmission band, making the FP cavity effect almost negligible. However, mode mismatching increases between the two waveguides as we get closer to the edge of the

Label-Free Biosensing Using Photonic Crystal Waveguides 243

and closer between them. This reduction in the group velocity will also provoke a higher

*<sup>a</sup>* **<sup>2</sup>***<sup>r</sup>*

*L*

*t***<sup>23</sup> ,** *r***<sup>23</sup>**

Fig. 6. (a) Schematic picture of the PCW with its access waveguides. The interface with the access waveguides is that of the fabricated PCW. The structural parameters of the PCW (i.e.,

coefficients at each interface (*tij*, *rij*) are depicted. (b) All signal contributions generated in the PCW because of the reflections at the interfaces with the access waveguides are combined at the output, being responsible of the appearance of FP oscillations in the transmission spectrum. Media 1 and 3 represent the access waveguides and medium 2 represents the

When these three parameters are combined using the expression shown in Fig. 6.(b), the transmission response shown in Fig. 7.(b) for a 20μm-long 2D-PCW is obtained. One can see how FP resonances appear because of the cavity created inside the PCW, and how these FP fringes get stronger and narrower as we approach the edge of the guided band because of

To corroborate the appearance of these FP fringes in the edge of the guided mode of the PCW and analyze the potential for using them for biosensing purposes, 3D-FDTD simulations of the PCW with the parameters of the fabricated structure and two different

lattice constant, hole radius and PCW length), and the transmission and reflection

the increase of the reflection coefficient and the decrease of the group velocity.

*t***<sup>23</sup> ,** *r***<sup>23</sup>**

*<sup>j</sup> <sup>L</sup> E E t t e*

<sup>2</sup> <sup>0</sup> <sup>12</sup> <sup>23</sup> <sup>23</sup> <sup>21</sup> ( ) *<sup>j</sup> <sup>L</sup> E E t t r r e*

<sup>3</sup> <sup>0</sup> <sup>12</sup> <sup>23</sup> <sup>23</sup> <sup>21</sup> ( )

*<sup>n</sup> E E t t r r e*

<sup>0</sup> <sup>12</sup> <sup>23</sup> <sup>23</sup> <sup>21</sup> ( )

*<sup>T</sup> r r e <sup>t</sup> <sup>t</sup> <sup>e</sup> <sup>E</sup> <sup>E</sup>*

<sup>1</sup> <sup>0</sup> <sup>12</sup> <sup>23</sup> *<sup>j</sup> <sup>L</sup> E E t t r r e*<sup>3</sup>

(b)

(a)

*n n j L*

1 (2 1) 

*j L j L*

2 23 21 12 23 0 <sup>1</sup>

2 5 

interaction of the optical field with the target analytes.

*t***<sup>12</sup> ,** *r***<sup>12</sup>** *t***<sup>21</sup> ,** *r***<sup>21</sup>**

**123**

*L*

*t***<sup>12</sup> ,** *r***<sup>12</sup>** *t***<sup>21</sup> ,** *r***<sup>21</sup>**

*E*0

PCW.

guided band, thus reducing the coupling efficiency and increasing the reflected power, so higher amplitude FP fringes begin to appear. Not only is there an increase of the reflection coefficient at the interfaces (and thus a reduction of the transmission coefficient), but also a reduction of the group velocity of the guided mode of the PCW as we get closer to the edge of the Brillouin zone. The reduction of the group velocity makes the optical length of the FP cavity longer, thus increasing the frequency of the FP fringes of the transmission spectrum in the region of the band edge. The main point of using these fringes to perform the biosensing is that we are working in the slow-light regime of the PCW, so we will have a higher interaction of the electromagnetic field with the target analyte.

Fig. 5. Spectrum of the PCW in the region of the band edge when having DIW as upper cladding. Transmission fringes at the band edge are marked with dashed red line and enlarged in the inset.

From expressions shown in Fig. 6.(b), it can be seen that the transmission spectrum is dependent on both the transmission and reflection coefficients at the interfaces and the propagation constant of the guided mode in the PCW, which determines the optical length of the structure. Fig. 7.(a) shows these three parameters (transmission and reflection coefficients between the access waveguides and the PCW, and propagation constant of the PCW guided mode) obtained using the numerical tool CAMFR, which is based in the eigenmode expansion (EME) method, for the PCW with interface with the access waveguides as shown in Fig. 6.(a). Note that only the reflection coefficient for the incidence from the PCW to the access waveguide (*r*21, *r*23) is needed for the calculations and that the transmission coefficient is the same for the incidence from the PCW to the access waveguide and vice versa due to reciprocity properties (*t*ij = *t*ji). Although this software does not allow 3D calculations, a generic 2D modelling (i.e., infinite height of the structure) using an effective refractive index of 2.8 for the silicon slab and 1.33 for the cladding surrounding the structure is useful to realistically predict the appearance of FP fringes in the transmission spectrum. It can be seen that the transmission coefficient decreases to zero as we get closer to the band edge (the opposite is true for the reflection coefficient, which tends to one), thus the amount of power coupled into the PCW decreases and a stronger cavity effect is created. Concerning the propagation constant, it can be seen that it gets flatter as the edge of the guided band is approached, which means a reduction on the group velocity (which tends to zero) and makes the fringes narrower

guided band, thus reducing the coupling efficiency and increasing the reflected power, so higher amplitude FP fringes begin to appear. Not only is there an increase of the reflection coefficient at the interfaces (and thus a reduction of the transmission coefficient), but also a reduction of the group velocity of the guided mode of the PCW as we get closer to the edge of the Brillouin zone. The reduction of the group velocity makes the optical length of the FP cavity longer, thus increasing the frequency of the FP fringes of the transmission spectrum in the region of the band edge. The main point of using these fringes to perform the biosensing is that we are working in the slow-light regime of the PCW, so we will have a

1540 1550 1560 1570

<sup>1561</sup> <sup>1562</sup> <sup>1563</sup> <sup>1564</sup> -50

wavelength (nm)

From expressions shown in Fig. 6.(b), it can be seen that the transmission spectrum is dependent on both the transmission and reflection coefficients at the interfaces and the propagation constant of the guided mode in the PCW, which determines the optical length of the structure. Fig. 7.(a) shows these three parameters (transmission and reflection coefficients between the access waveguides and the PCW, and propagation constant of the PCW guided mode) obtained using the numerical tool CAMFR, which is based in the eigenmode expansion (EME) method, for the PCW with interface with the access waveguides as shown in Fig. 6.(a). Note that only the reflection coefficient for the incidence from the PCW to the access waveguide (*r*21, *r*23) is needed for the calculations and that the transmission coefficient is the same for the incidence from the PCW to the access waveguide and vice versa due to reciprocity properties (*t*ij = *t*ji). Although this software does not allow 3D calculations, a generic 2D modelling (i.e., infinite height of the structure) using an effective refractive index of 2.8 for the silicon slab and 1.33 for the cladding surrounding the structure is useful to realistically predict the appearance of FP fringes in the transmission spectrum. It can be seen that the transmission coefficient decreases to zero as we get closer to the band edge (the opposite is true for the reflection coefficient, which tends to one), thus the amount of power coupled into the PCW decreases and a stronger cavity effect is created. Concerning the propagation constant, it can be seen that it gets flatter as the edge of the guided band is approached, which means a reduction on the group velocity (which tends to zero) and makes the fringes narrower

Fig. 5. Spectrum of the PCW in the region of the band edge when having DIW as upper cladding. Transmission fringes at the band edge are marked with dashed red line and

higher interaction of the electromagnetic field with the target analyte.






power (dBm)

enlarged in the inset.



Fig. 6. (a) Schematic picture of the PCW with its access waveguides. The interface with the access waveguides is that of the fabricated PCW. The structural parameters of the PCW (i.e., lattice constant, hole radius and PCW length), and the transmission and reflection coefficients at each interface (*tij*, *rij*) are depicted. (b) All signal contributions generated in the PCW because of the reflections at the interfaces with the access waveguides are combined at the output, being responsible of the appearance of FP oscillations in the transmission spectrum. Media 1 and 3 represent the access waveguides and medium 2 represents the PCW.

When these three parameters are combined using the expression shown in Fig. 6.(b), the transmission response shown in Fig. 7.(b) for a 20μm-long 2D-PCW is obtained. One can see how FP resonances appear because of the cavity created inside the PCW, and how these FP fringes get stronger and narrower as we approach the edge of the guided band because of the increase of the reflection coefficient and the decrease of the group velocity.

To corroborate the appearance of these FP fringes in the edge of the guided mode of the PCW and analyze the potential for using them for biosensing purposes, 3D-FDTD simulations of the PCW with the parameters of the fabricated structure and two different

Label-Free Biosensing Using Photonic Crystal Waveguides 245

A straight-forward way to to test the possibility of using these band edge fringes to perform biosensing, is to carry out a simple refractive index sensing experiment, for instance using several dilutions of ethanol in DIW. Dilution concentrations are (in mass %): pure DIW, ethanol 2% in DIW, and ethanol 4% in DIW, whose refractive indices at λ ≈ 1550 nm and

For carrying out the RI sensing experiments, a flow cell is required in order to flow the target substances over the chip. In this case, a 2-port flow cell with a fluidic cavity of size 5.5mm x 2mm x 0.5mm (length x width x depth) is placed on the top of the chip. For pumping the liquid passing through the flow cell, an automatic syringe pump in withdrawal mode connected to one of the ports of the flow cell using silicone tubing is used. The liquid is flowed at a rate of 15 μl/min. Tubing from the second port of the flow cell is placed into a vial with the liquid to be flowed over the chip. This configuration is used in order to avoid having to replace the syringe to change the liquid to be flowed: with this configuration, the liquid is drawn from vials, enabling an easier handling of the tubes when manual changing between them is performed. The TE transmission spectrum of the PCW in the vicinity of the guided band edge (shown in Fig. 5) is continuously acquired using a tunable laser with a sweep resolution of 10 pm, and a cubic interpolation is used to increase the wavelength accuracy on the determination of the position of the peak's maximum. Fig. 9 shows the temporal evolution of the position of the maximum of the FP peak located around

0 20 40 60 80 100

time (min)

DIW DIW DIW DIW DIW

Fig. 9. Temporal evolution of the FP peak for the different ethanol-DIW dilutions flowed.

4%eth

2%eth

4%eth

2%eth

**Fringe #** 1 2 3 4 5 6 **Wavelength shift (nm)** 0.1543 0.1865 0.192 0.2002 0.2039 0.2125 **Sensitivity (nm/RIU)** 57.15 69.07 71.11 74.15 75.52 78.70 Table 1. Wavelength shift and sensitivity for each FP fringe near the guided band edge for

**3. Refractive index sensing using photonic crystal waveguides** 

T = 25ºC are 1.3173, 1.3186, and 1.3200, respectively (García-Rupérez et al., 2010).

1563.3 nm for the different ethanol-DIW dilutions flowed.

2%eth

1563.1 1563.2 1563.3 1563.4 1563.5 1563.6 1563.7 1563.8

peak wavelength (nm)

the 3D-FDTD simulations.

upper claddings (*n*1 = 1.3173 and *n*2 = 1.3200; corresponding to the refractive indices of DIW and a ethanol-DIW 4% dilution) can be performed (in this case, RSoft's FullWAVE software was used). Simulation results for each upper cladding are shown in Fig. 8, where the FP fringes at the band edge are observed again and where the position of the guided band is dependent of the refractive index of the upper cladding. Table 1 shows the wavelength shift and the calculated sensitivity in terms of refractive index units (RIU) for each fringe near the band edge. As predicted from the previous theoretical modeling, an increase in the sensitivity is obtained as we get closer to the guided band edge because of the reduction in the group velocity of the guided mode, obtaining a sensitivity ~40% higher for the fringe closest to the band edge compared to the first of the selected fringes (78.70 nm/RIU vs. 57.15 nm/RIU).

Fig. 7. (a) Theoretical transmission (blue dotted line) and reflection coefficients (blue solid line), and propagation constant of the PCW (green solid line) calculated with CAMFR. (b) Transmission response of the 20μm-long PCW when the created FP cavity is considered (blue solid line). The transmission response when no cavity is considered (only the direct contribution propagating into the PCW) is also depicted (red dashed line). The inset shows a detail of the transmission band edge.

Fig. 8. 3D-FDTD simulations of the transmission spectrum of the 20μm-long PCW for two different upper claddings: *n1* = 1.3173 (red line) and *n2* = 1.3200 (blue line). FP fringes near the band edge have been labeled from 1 to 6. The band edge fringes are slightly smoothed because of the stop time used to make the duration of the simulation reasonable.

upper claddings (*n*1 = 1.3173 and *n*2 = 1.3200; corresponding to the refractive indices of DIW and a ethanol-DIW 4% dilution) can be performed (in this case, RSoft's FullWAVE software was used). Simulation results for each upper cladding are shown in Fig. 8, where the FP fringes at the band edge are observed again and where the position of the guided band is dependent of the refractive index of the upper cladding. Table 1 shows the wavelength shift and the calculated sensitivity in terms of refractive index units (RIU) for each fringe near the band edge. As predicted from the previous theoretical modeling, an increase in the sensitivity is obtained as we get closer to the guided band edge because of the reduction in the group velocity of the guided mode, obtaining a sensitivity ~40% higher for the fringe closest to the band edge compared to the first of the selected fringes (78.70 nm/RIU vs. 57.15

nm/RIU).

0

detail of the transmission band edge.

0.5

coeficient value

1

1530 1540 1550

0.3

**<sup>1</sup> <sup>2</sup>**

0.4

propagation constant (2/a)

Fig. 7. (a) Theoretical transmission (blue dotted line) and reflection coefficients (blue solid line), and propagation constant of the PCW (green solid line) calculated with CAMFR. (b) Transmission response of the 20μm-long PCW when the created FP cavity is considered (blue solid line). The transmission response when no cavity is considered (only the direct contribution propagating into the PCW) is also depicted (red dashed line). The inset shows a

<sup>1575</sup> <sup>1580</sup> <sup>1585</sup> <sup>1590</sup> -30

wavelength (nm)

Fig. 8. 3D-FDTD simulations of the transmission spectrum of the 20μm-long PCW for two different upper claddings: *n1* = 1.3173 (red line) and *n2* = 1.3200 (blue line). FP fringes near the band edge have been labeled from 1 to 6. The band edge fringes are slightly smoothed

because of the stop time used to make the duration of the simulation reasonable.


**<sup>3</sup> <sup>4</sup> <sup>5</sup> <sup>6</sup>**



transmittance (dB)

(a) (b)


0

1530 1540 1550

<sup>1546</sup> <sup>1548</sup> <sup>1550</sup> -15

wavelength (nm)

0.5

wavelength (nm)


transmittance (dB)


Table 1. Wavelength shift and sensitivity for each FP fringe near the guided band edge for the 3D-FDTD simulations.
