1. Introduction

The application of the thermo-optic (TO) and thermal expansion (TE) effects as a thermodynamic means for operating optical devices, such as switch [1], attenuator [2] and filter, is currently of great interest. On the other hand, the monitoring of temperature using the optical methods [3,4] has also been extensively explored due to many attractive advantages over the conventional electric sensors in the form of electric immunity and pollution free. In spite of the above advantages, the sensitivity of those optical temperature sensors is relatively low. For instance, the encoded wavelength shift in the FGB sensor [3] cannot evaluate the temperature change within 10 °C. This low temperature sensitivity does not guarantee the accurate implementation of high Q factor equipments, such as whispering-gallery mode resonators [5], and the exact measurement of material parameters, such as refractive index (RI) [6], because tiny thermal fluctuation could affect the characteristics of these devices. Possible solutions to increase sensitivity include drawing support from interferometry [7], filling alcohol into the photonic crystal fiber [8], and performing phase measurement of surface plasmon resonance (SPR) [9]. However, the desired sensitivity is achieved at the cost of introducing complex fabrication process or complicated measurement setup. Recent theoretical studies [10,11] indicated that the Goos-Hänchen (GH) shift exhibits a high sensitivity to the variation of temperature, but the experimental demonstration still remains an open question.

The GH effect, which refers to a lateral discrepancy between the reflected light position and its incident counterpart when a finite-size light is totally reflected by a dielectric interface, was first experimentally observed [12] in 1947 and subsequently interpreted by the stationary-phase theory [13]. Usually this discrepancy is extremely small, but several models have been proposed to enlarge its magnitude by using dispersive materials [14] or structural resonances [15]. Because of its intimate connection with the material and structure parameters, the GH shift can be modulated by the external stimuli, including nonlinear effect [16] and electro-optic effect, etc, and this tunable property has been employed to carry out sensing [17] and switching [18] function. Taking sensing as an example, a millimeter-scale GH shift in a symmetrical metal-cladding waveguide (SMCW) gives a RI resolution down to 2.2$\times$10⁻⁷ RIU [17]. Actually, the RI and the thickness of the guiding layer in the SMCW is strongly dependent on the temperature via the TO and TE effects, thus the temperature fluctuation will change the resonant condition of the ultrahigh-order modes [19] and lead to a dramatic variation of GH shift. Here, we present a high-sensitivity optical temperature sensor by measuring the enhanced GH shift in the SMCW. The experimental results demonstrate that our optical temperature sensor exhibits a good linearity and a high resolution of approximately 5$\times$10^{-3 o}C.

2. Structure and principle

The schematic structure of the optical temperature sensor based on the enhanced GH effect in the SMCW is illustrated in Fig. 1(a). The SMCW is composed of three segments: a 1 mm thick BK7 glass acts as the guiding layer; a 31 nm and a 300 nm thick gold films deposit on the top and bottom sides of BK7 glass and serve as the coupling layer and the substrate, respectively. Silica gel is adopted as the link layer between the SMCW and the metal heater due to its good thermal conductivity and adhesion ability. From top to bottom, the dielectric coefficient, the RI and the thickness of the SMCW are denoted by ${\epsilon }_j,n_j,h_j$ $(j=1,2,3)$, respectively. Owing to the millimeter scale thickness of the guiding layer, the dispersion equation of the $m$th ultrahigh-order mode ($m>1000$) can be simply approximated as [19]

 

Fig. 1 (a) Schematic diagram of the optical temperature sensor based on the enhanced GH effect in the SMCW, where the BK7 glass is employed as the guiding layer and sandwiched between two gold films (functioned as the cladding layers). (b) Calculated reflectivity spectrum of the ultrahigh-order modes with respect to the effective RI, the simulation parameters are given in the text.

Download Full Size | PDF

According to the stationary-phase approach [13], the GH shift is given by

 

Fig. 2 (a) L (dashed curve) and S₁ (solid curve) as functions of the effective RI for one selected ultrahigh-order mode (see dashed rectangular in Fig. 1(b)), simulated by stationary-phase method. The incident beam is TE polarized and 860 nm in wavelength. (b) Field distributions of the Gaussian incident and reflected light beams. The incident angle $\theta ={5.15}^{\text{o}}$, the waist radius is 800 $\mu m$, the TO coefficient $\xi =2.531\times {10}^{-6}\text{RIU}/{}^{\text{o}}C$, the TE coefficient $\alpha =0.55\times {10}^{-6}{/}^{\text{o}}C$. Vertical dashed lines represent the magnitudes of the GH shift.

Download Full Size | PDF

The ultrahigh-order mode-enhanced GH effect in the SMCW can also be understood in the framework of energy flux conversion [23]. When the incident light is introduced onto the SMCW, a portion of the incident energy is directly reflected from the top gold film; another portion of the incident energy is guided laterally in the form of an oscillating wavefield. While propagating laterally along the SMCW, this field radiates energy continuously back into the incident medium. The superposition of the leaky wavefield and the directly reflected field results in an actual reflected light that is laterally shifted with respect to the incident light position. We calculate the field distribution of the incident and reflected beams at different temperatures based on the Gaussian beam model [24]. As can be seen in Fig. 2(b), the shape of the light beam is distorted after the reflection, and the barycentric position of the reflected beam shifts to different positions from the center of the incident beam. In the proposed temperature sensor, as the temperature changes from $T=$50.0 °C to $T=$51.2 °C, the corresponding change in the GH shift reaches nearly 1 mm. In addition, the intensity of the reflected beam is reduced since the energy coupling from incident light into the ultrahigh-order mode.

3. Experimental results

The experimental arrangement for the proposed temperature sensor is shown in Fig. 3. A TE polarized light, enabled by a tunable laser (DL100, Topical Photonics) and followed by a polarizer, two apertures with diameters of 0.1 mm and a mirror to further collimate and adjust the light direction, incidents onto the top side of the SMCW, which is firmly mounted on a computer controlled $\theta /2\theta$ goniometer. The temperature of the metal heater is controlled by a temperature controller with a temperature range of 30-110 °C and a resolution of 0.1 °C. It is well known that the ultrahigh-order modes are excited at certain extremely small resonant angles. For the optical characterization, a homemade software allows us to rotate the goniometer and record serial attenuated total dips with the light intensity from a photodiode (PD). During our experiment, the room temperature is held constant at 18.4 °C and the temperature controller is firstly set to be 50.0 °C. The incident angle is fixed at the maximum of one selected resonant dip ($\theta ={5.15}^{\text{o}},N=0.0897$), where the GH shift is not remarkable due to the weak coupling condition. Since the magnitude of the GH shift is strongly dependent on the coupling efficiency between the incident light and the guide mode, it is reasonable to take this position of the reflected beam as the reference of the GH shift. With the experimental apparatus remains unchanged, a position sensitive detector (PSD) is placed in the optical path instead of the PD, so the reflected beam impinges perpendicularly onto the PSD at its central point. Subsequently, to obtain the maximal sensitivity, we tune the wavelength of the tunable laser and eventually settle the wavelength at the midpoint on the rising edge of a resonant peak, which corresponds to the GH shift monitored by the PSD as a function of the wavelength. Finally, the temperature increases from 50.0 °C to 51.2 °C and gradually reduces back to the initial temperature with a step of 0.2 °C.

 

Fig. 3 Experimental arrangement for the temperature sensing. PSD: position sensitive detector, PD: photodiode.

Download Full Size | PDF

The time evolution of the measured GH shift at different temperatures and the linear fit lines for temperature increasing (solid line) and temperature decreasing (dash-dotted line) are plotted in Fig. 4(a) and 4(b), respectively. The GH shift monotonically toward higher values with an increase of the temperature and the results show a good linear relationship ($R^2=0.991$ for temperature increasing and $R^2=0.998$ for temperature decreasing) between the GH shifts and the temperatures. The tiny nonlinearity at the higher temperatures is mainly caused by the GH shift around the resonance dip, which is a nonlinear function of the RI and thickness of the guiding layer. Note that the GH shift magnitudes of theory and experiment are not the same. The reason may be that the used parameters in numerical calculation are not equal to that of actual SMCW structure. Shown in the insets of Fig. 4(a) are three representative images of the spatial profile of the reflected light spot corresponding to the temperature at 50.0 °C, 50.6 °C and 51.2 °C. It confirms that the intensity of reflected light decreases gradually when the GH shift becomes large. Since the step change of 0.2 °C in temperature induces a GH shift change about 76 $\mu m$ and the smallest variation of GH shift that can be detected with our PSD is 2 $\mu m$, we deduce that the minimum detectable temperature variation is about 5$\times$10^{-3 o}C. By increasing the thickness of the guiding layer or selecting material with high TO and TE coefficients as the guiding layer, the slop of the GH shift becomes steeper and the sensitivity can be further enhanced.

 

Fig. 4 (a) Experimental results of the GH shift vs. the temperatures increasing from 50.0 °C to 51.2 °C and reducing back to the initial temperature, insets are three representative images of the spatial profile of the reflected beam spot corresponding to 50.0 °C, 50.6 °C and 51.2 °C, respectively. During the experiments, the GH shifts are only detected when the whole system is stable. (b) Linear fit lines for temperature increasing (solid line) and temperature decreasing (dash-dotted line).

Download Full Size | PDF

4. Conclusion

In conclusion, we have presented an SMCW structure which contains the BK7 glass in the guiding layer to achieve high-sensitivity temperature monitoring via thermally tuned GH effect. The millimeter-scale GH shift, which is enhanced by the excitation of the ultrahigh-order modes, linearly responds to the temperature variation and shows a high resolution of approximately 5$\times$10^{-3 o}C. Owing to its simple structure and high resolution, this device could have potential application in the future.