Goos-Hanchen effect is experimentally studied when the Bloch surface wave is excited in the forbidden band of a one-dimensional photonic band-gap structure. By tuning the refractive index of the cladding covering the truncated photonic crystal structure, either a guided or a surface mode can be excited. In the latter case, strong enhancement of the Goos-Hanchen shift induced by the Bloch-surface-wave results in sub-millimeter shifts of the reflected beam position. Such giant Goos-Hanchen shift, ~750 times of the wavelength, could enable many intriguing applications that had been less than feasible to implement before.
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Goos-Hanchen (GH) effect is one of the most studied nonspecular reflection phenomena, where a bounded light beam reflected from an interface between different materials is laterally shifted from its ideal position. Though some argued that the phenomenon had been predicted as early as by Isaac Newton, the evasively small Goos-Hanchen shift had not been experimentally observed until 1940s . Through a clever experimental setup that ‘magnified’ the magnitude of the shift through multiple total internal reflections, up to more than a hundred times, Goos and Hanchen managed to demonstrate its existence. Since then, this interesting phenomenon and its potential applications have inspired many research works [2–12], especially in the past decade.
One of the most intensively investigated issues among these studies is the scheme to enhance the Goos-Hanchen effect. Since the Goos-Hanchen shift under a conventional total internal reflection (TIR) configuration is only on the order of the wavelength or less, achieving a much larger Goos-Hanchen shift is critical for the proposed applications in sensing , switching  and ‘rainbow’ trapping of light . Numerous novel materials and structures have been explored, though mostly by theoretical studies. In the early reports, absorbing media are found to be able to enhance the Goos-Hanchen shift by several folds [15, 16]. Structures based on unconventional optical materials, such as the left-hand metamaterials [7, 8, 17], have been theoretically studied, but with no experimental demonstrations yet. It’s noted that the Goos-Hanchen shift sometimes is deemed to be related to the ‘depth of penetration’, as the incident beam propagates in the form of a guided or surface wave at the interface. Thus, the Goos-Hanchen effect could be enhanced by coupling to a guided mode , or by exciting a preferably low-loss, surface electromagnetic wave. In the past few years, optical phenomena associated with the surface electromagnetic waves, such as surface plasmon polariton, have become one of hottest studied areas in photonics with a wide range of applications from label-free sensing, nanophotonic integrations, to subwavelength imaging and more [18, 19]. While strong field confinement and enhancement at the interface has been leveraged in these applications, there are far less studies on the related Goos-Hanchen effect. Theoretical study and experimental demonstration of the enhanced Goos-Hanchen effect under the surface plasmon resonance condition at the metal/dielectric surface had been carried out [10-11, 20]. The measured Goos-Hanchen shift was boosted to a maximal ~100 times of the wavelength, when the surface plasmon wave was excited . Yet, the huge Ohmic loss of the metal poses serious limitations to any applications based on the Goos-Hanchen effect.
On the other hand, it’s been shown that surface electromagnetic waves could also exist at the interface of a truncated stack of periodically alternating dielectric layers (e.g. the photonic band-gap (PBG) structure) [21, 22]. Also known as the Bloch surface wave (BSW), it can be excited when the supported mode falls within the forbidden band of the PBG structure. In contrast to its surface plasmon counterpart, by properly designing the photonic band-gap structure, Bloch surface wave could be excited at either polarization and over a much wider range of wavelengths. Its propagation loss can be significantly reduced, due to the all-dielectric structure. As a promising alternative to the plasmonic devices, fluorescence enhancement, sensing based on reflectivity measurements, and nano-waveguides had been demonstrated based on the BSW phenomenon very recently [23–25]. Though the Goos-Hanchen effect could occur by directly illuminating a one-dimensional photonic crystal slab near the angle of its band edge  or its defect mode  due to the abrupt, angular-dependent reflectance and phase jumps, only limited (several to tens of times) enhancement is theoretically predicted. An alternative approach based on exciting Bloch surface wave of the truncated photonic crystal structures could be a more effective way to generate much larger GH shifts. Recently, under a prism-based configuration, the enhanced GH shift as large as ~50 times of the wavelength in the presence of surface wave was first detected at the surface of the photonic crystal using a microscope , showing the potential to generate GH effect similar to the SPR-enhanced ones [11, 20]. Under a similar geometry, yet by exciting a guided mode with the optical field confined within a PBG structure under the TIR configuration, GH shifts as large as a couple of hundreds of microns was observed .
Here, we experimentally demonstrate that giant GH shifts as large as nearly 3 orders of magnitude of wavelength could be realized by exciting Bloch surface wave at the dielectric interface between a truncated photonic crystal and the cladding medium. Through changing the refractive index of the cladding, either a BSW mode or a guided mode can be excited. The experimental results show that the former leads to far larger GH shift enhancement than the latter. This sub-millimeter Bloch-surface-wave-Induced Giant Goos-Hanchen (BIGG) shift could enable many important applications. The field enhancement feature of the BSW at the surface could also be advantageous for potential sensing applications over the enhanced GH schemes where the field is mostly confined within the device structures [9, 27, 29].
2. Experimental setup
As shown in Fig. 1 , the PBG device consists of 10 periods of alternating TiO2 (n=2.30) and SiO2 (n=1.434) layers on a ZF10 glass slide (n=1.668), terminated with a TiO2 buffer layer. The thickness of the TiO2 and SiO2 layers in the photonic crystal and the buffer layer are estimated as 163nm, 391nm, and 23nm, respectively, based on the fabrication conditions and the measured photonic band-gap structures. A fiber-pigtailed Fabry–Perot 980nm laser is used as the light source. The device is illuminated by the p-polarized Gaussian beam through a high index ZF3 glass prism (n=1.695) under the Kretschmann configuration. Its optical properties for the p-polarized input are shown to be very different from those for the s-polarized input as in , though the devices are similar. The collimated Gaussian beam is spatially filtered and has a waist of ~750 μm. Its state of the polarization is controlled by a λ/2 waveplate followed by a Glan-Taylor prism. The incident angle is set by a motorized rotation stage, on which the prism is mounted. A CCD camera (Toshiba, IK-SX1) captures the reflected beam intensity profile, based on which the GH shift is calculated. A separate photodiode connected to a lock-in amplifier (SRS, SR530) is used to more accurately measure the reflectance.
To compare the Goos-Hanchen effect when the BSW is excited with that under the guided mode, we’d like to find a way to excite different kinds of optical modes with the same device under test. Though that could be done by changing the thickness of the buffer layer  or the coupling gap under the Otto configuration , a simple and effective scheme we use here is to change the refractive index of the external medium, i.e. the cladding, in contact with the truncated photonic band-gap structure. A change in the cladding results in a change in the critical angle, which in turn can significantly vary the phase delay induced by the total internal reflection at the interface between the device and the cladding. This variation effectively tunes the resonant condition for the mode, and the modal properties of the supported mode are modified accordingly. To realize this scheme, a Polydimethylsiloxane (PDMS) flow-cell is attached to the buffer-layer-side of the device to facilitate the injection of different aqueous solution or air to the surface of the device, as shown in Fig. 1.
3. Results and discussions
Based on the device structure, the angular-dependent reflectance of the device can be calculated using the Fresnel equations . The results are compared with the experimental data in Fig. 2 , where reasonably good agreements are shown for both states of polarization. All angles discussed here are defined as the internal angles in the ZF10 substrate. Using the theoretical model of an infinite photonic crystal stack based on our device parameters, the rising edge of the main band-gap for the s-and p-polarizations are at ~45.4 o and 52.2 o, respectively. Thus, when the cladding is air, the main band-gap of the PBG is well beyond the critical angle for either state of polarization, and the reflectance curves are nearly constant beyond that angle. The small dips in the measured reflectance near the above corresponding bandedges show the coupling to some guided modes supported by the PBG and TIR effect . The modal loss is due to the scattering loss from the interfacial roughness and the intrinsic material loss. To match the experimental results, the extinction coefficient of TiO2 is set at 2*10−4 in the simulation to roughly account for both losses.
When the cladding is switched to water, the critical angle is changed to 52.9°. For the s-polarization, the reflectance rises to nearly unity near the edge of the calculated main band-gap after several sidelobes that correspond to some sidebands of the PBG structure. For the p-polarization, the situation is rather different, though. The band-edge (52.2 o) is very close to, but slightly smaller than, the critical angle. While the reflectance rises to its maximum near that angle, another reflection dip appears at a larger angle, which indicates the existence of another mode. This mode’s propagation constant is significantly different from those of the others and its loss is expected to be higher. Figure 3 further illustrates the dispersion diagram of frequency versus wave vector for the p-polarized modes under different claddings. The band structure of an ideally periodic, infinite photonic crystal is also calculated based on ref . The grey region is the allowed band of the perfect photonic crystal, and the white region is its forbidden band, i.e. band-gap. The above measured modal constants are shown along with the corresponding light lines under different cladding media. As seen in Fig. 3, when the index of the cladding increases, the supported mode moves from slightly out of the band-gap to the inside of the band-gap. These two cases correspond to two types of modes [22, 31]. One is a guided mode, similar to that in , and the other is a surface mode. The normalized distributions of the magnitude of E field are calculated by the transfer matrix method and shown in Fig. 3. For the guided mode, the field is mostly confined within the multilayer stack. For the surface mode, i.e. the Bloch surface wave mode, it is tightly bound at the interface and exponentially decays into the neighboring media, similar to the surface plasmon polariton.
Angular-dependent Goos-Hanchen shifts are also measured under different claddings. Since negligible Goos-Hanchen shift of the s-polarized input is expected in the angular range of interest (50~54°), the Goos-Hanchen shift of the p-polarized beam is obtained by measuring the difference in the position of the p- and s-polarized spots. For either polarization, the centroids of the horizontal intensity distribution along the direction of the beam are recorded as the positions of the beam. The intensity is averaged within a horizontal stripe with a height of 30% of the 1/e intensity radius around the vertical center of the captured image of the beam. The simulated values in Fig. 4 are obtained by numerically calculating the centroid of the reflected field distribution of a Gaussian beam .
As shown in Fig. 4, both Goos-Hanchen shift curves show a peak when an optical mode is excited by the incident beam (see Fig. 3). For the guided mode with the air cladding, the measured peak GH shift is ~90 μm, i.e. ~92 times of the wavelength. In contrast, in presence of BSW, the corresponding Goos-Hanchen shift is boosted by nearly an order of magnitude, to a peak value of ~740 μm (i.e. ~750 times of the wavelength), as in Fig. 4(b). The extremely large Goos-Hanchen effect can be clearly seen by naked eyes using an infrared viewer, as shown by the pictures in Fig. 4(b). The splitting of the beam profile under the gigantic Goos-Hanchen effect is typical for extremely large Goos-Hanchen shifts, caused by the very steep angular phase response variations . We also note that, as shown in Fig. 2(b), the optical reflection loss at the maximal GH shift is significantly lower when compared to the case leveraging the surface plasmon resonance [11, 20], while the maximal Goos-Hanchen shift in our study is improved by nearly an order of magnitude. The reduced optical loss could be very helpful for applications like switching , data storage , and sensing .
Goos-Hanchen effect induced by the Bloch surface wave is also expected to be very sensitive to the surface properties, such as the refractive index of the cladding, considering the similarity of BSW to surface plasmon waves. That is also experimentally demonstrated by measuring the Goos-Hanchen shifts for sodium chloride solutions of different concentrations instead of pure water. The results are shown in Fig. 5 , where the neighboring curves have a concentration difference of 0.1% (i.e. an estimated refractive index change of 1.76*10−4 RIU ). The curves show significant shifts under such small index changes, and such Goos-Hanchen devices could be very useful for high-sensitivity sensing applications.
Giant Goos-Hanchen shifts are demonstrated by exciting the Bloch surface wave at the surface of a relatively simple, truncated photonic band-gap structure. The sub-millimeter Goos-Hanchen shift is shown to be very sensitive to the surface properties. Even larger Goos-Hanchen response could be realized by further optimizing the photonic crystal structure and the fabrication procedures. Many previously envisioned applications, especially high-sensitivity sensing, could be enabled by such huge Goos-Hanchen shifts.
This work was supported by 973 Program (2009CB930701), NSFC (61077064 /60921001), and the Innovation Foundation of BUAA for PhD Graduates.
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