# Effect of Excitation Beam Divergence on the Goos-Hanchen Shift Enhanced by Bloch Surface Waves
## 4 Experiment and Result  
The experimental setup is based on a typical Kretschmann-Raether prism-coupled configuration. As shown in Figure 5, the 1D PBG device is attached to a high-index SF10 prism (n = 1.704), and a flow cell made of polydimethylsiloxane (PDMS) is attached to the buffer layer side of the device. A 980 nm fiber-pigtailed Fabry-Perot laser is used as the light source, whose output is collimated by a lens (f = 12 mm) and set to TM polarization using a Polarization Beam Splitter (PBS). The collimated beam has a waist of \(\sim\)800 \(\upmu\)m. The Bloch surface wave is then excited by the incident light when water is injected into the flow cell and clads the buffer layer of the device [19]. As the Block surface wave can strongly enhance the GH shift to sub-millimeter magnitude, the resulting lateral shift is detected by the Position Sensitive Detector (PSD) (Hamamatsu Photonics, S3979).  
The PSD converts the position of a beam incident to the detector into an output voltage, where the readout voltage linearly corresponds to the beam position. So before using the PSD for experiments, the calibration is carried out first, where the incident light is fixed, and the PSD is mounted on a linear translation stage. The center of the PSD is found by monitoring the zero output voltage while moving the position of the PSD horizontally. Once the central position of PSD is found, it is moved to the left for 500 \(\upmu\)m and then scanned backwards to the right for a total distance of 1 mm with an interval of 100 \(\upmu\)m. During the interrogation, the voltage readout for each position is recorded as shown in Figure 6, where a linear relationship is obtained with a slope of 161 \(\upmu\)m/V.  
Figure 4: (**a**) GH shift vs. incident angle (**b**) The max GH shift distribution for different waist radiuses of incident beam.  
Figure 5: Schematic diagram of the experimental setup.  
During the experiment, the prism and the Block surface wave device are placed on a motorized rotation stage, which is controlled by a stepper motor to change the incident angle. Total internal reflection occurs when the incident angle is greater than the critical angle. The incident angle is continuously changed from 53.4 deg to 53.9 deg by rotating the motorized rotation stage, among which the Bloch surface wave is excited, and the PSD is used to record the shift of the reflected beam. As the said 1D PDG device is only designed to excite the Block surface wave for TM polarization in this angular range, TE polarization could be used as the reference for GH shift measurement. Therefore, that the GH shift could be retrieved by subtracting the PSD readout for TM polarization from that for TE polarization. As shown in Figure 7, the maximum of the GH shift is obtained when incident angle equals to 53.69 deg, where the Block surface wave is excited.  
As shown in Figure 7, the blue curve is obtained for an incident beam with a waist radius of ~800 \(\upmu\)m and the red curve for a waist radius of ~1100 \(\upmu\)m. For a larger incident beam, the obtained maximum of the GH shift is larger, and the corresponding full width at half maximum is narrower. For an incident beam with a waist radius of ~1100 \(\upmu\)m, the Block surface wave enhanced GH shift is as large as 326 \(\upmu\)m, which agrees well with the simulation result in Figure 4.