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Sensors based on whispering gallery modes have been extensively investigated with respect to their possible application as physical or biological sensors. Instead of using a single resonator, we use an all polymer resonator array as sensing element. A tunable narrowband laser is coupled into a PMMA plate serving as an optical wave guide. PMMA spheres are placed in the evanescent field on the surface of the plate. Due to small size variations, some spheres are in resonance at a given wavelength while others are not. We show that this device is well suited for the determination of an unknown wavelength or for temperature measurements. Moreover, we discuss several general aspects of the sensor concept such as the number and size of sensing elements which are necessary for a correct measurement result, or the maximum acceptable linewidth of the laser.
© 2016 Optical Society of America
1. Introduction
When excited with an electromagnetic wave, spherical objects show sharp optical resonances at specific wavelengths, called whispering gallery modes (WGMs). They correspond to light waves circling around the cavity, relying on continuous total internal reflection at the cavity surface. After one roundtrip, the light waves return to the same point with the same phase, hence interfere constructively with themselves and standing waves arise. So the resonance wavelengths of such micro-resonators depend on the radius and the refractive index of the sphere as well as the surrounding refractive index [1]. All physical quantities which change one of these parameters can be well detected and quantified with such resonators, because they cause a resonance wavelength shift, resonance line broadening or mode splitting [2, 3, 4]. Such WGM sensors can have a high sensitivity due to the sharpness of the resonances and the high quality factor (also called Q-factor) of the spheres. In materials in which the light can circulate nearly without losses, Q-factors in the range of 107 [5, 6] to 109 [7] have been observed. Therefore such resonators were extensively investigated [8, 9] with respect to their possible application as physical or biological sensors [3]. Besides the possibility to determine quantities like temperature [10], pressure [11] or the use of the WGMs as biosensors [12], they can also be employed for high resolution wavelength measurement [13]. In many technical applications such as the wavelength control of single frequency lasers, an accurate determination of the wavelength is crucial. The most frequently applied techniques to determine the wavelength utilize interferometric principles, for example Michelson- or Fabry-Perot-interferometers [14], which are often large and very expensive.
To overcome these limitations Schweiger et al. built a small and less expensive system based on WGMs. It consists of an array of PMMA micro-spheres on a microscope slide [13] or on a fused silica prism [15]. A laser is coupled into the prism or the microscope slide, respectively, and generates an evanescent field at the surface. The micro-spheres are placed in close proximity to this field. In a calibration process, the wavelength of the laser is scanned and images of the array are taken at each wavelength step. Due to small variations in the size of the spheres, some spheres are in resonance at a given wavelength while others are not. By comparing the intensity distribution of the array at an unknown wavelength with the reference data, the actual wavelength can be determined. The acceptable linewidth of the unknown light source, the sensitivity and the reliability of such a WGM array sensor depend on several factors. These factors are, among others, the number of micro-spheres [15], their size [16] and material [17] as well as their position with respect to each other [18, 19]. Both the free spectral range (FSR) c/(2πnR) between two neighboring WGMs and the shift ΔR/Rλ of the resonance wavelength λ scale with 1/R where R is the radius and n is the refractive index of the resonator [2]. A reduction of the size simplifies the detection of the resonance wavelength shift, which supports sensing applications. On the other hand in order to achieve high resolution in spectral applications, resonators with high Q-factors are desirable. High Q-factors and, thus, sharp optical resonances occur in spheres with extremely smooth resonator surfaces [1, 3]. Reducing the size of the resonator causes a bandwidth broadening of the resonance due to the higher curvature of smaller resonators and this leads to a lower Q-factor. The Q-factor is reduced further by using PMMA spheres instead of glass spheres due to higher losses caused by larger internal scattering [17]. Therefore, it is crucial to choose the best resonator size as a compromise between these competing effects [16]. Schweiger et al. showed, that the disadvantage of the lower resonance quality of PMMA spheres can be partly compensated by using an array of resonators instead of a single one [13]. At least 16 spheres are necessary to reliably determine an unknown wavelength in their setup [15]. However, the influence of the resonator size was not considered.
In this work, we use an array of polymer WGMs to study the influence of the resonator size on the optical detection of temperature. In contrast to the work reported by other groups before we realized an all-polymer system consisting of PMMA spheres of three different sizes on a 2 mm thick PMMA plate.We demonstrate that the sensor approach can be used for sensitive detection of temperature and wavelength.
2. Experimental setup
The experimental setup is shown in Fig. 1. A tunable narrow-band laser (TLB-6700, Newport Spectra-Physics GmbH, Darmstadt, Germany) with a tuning speed of 5 nms−1, a linewidth of ≤200 kHz and a resolution of 0.01 nm is collimated and coupled under 45° in a PMMA plate with dimensions 50 mm × 50 mm × 2 mm. Due to total internal reflection, the plate acts as a light guide. At the surface of the plate, an evanescent field is present. In this field, commercially available PMMA spheres (Bangs Laboratories, Indiana, USA) are placed with random distribution and positions. To investigate the influence of the resonator size, three arrays of PMMA spheres with different mean diameters are employed. As specified by the manufacturer, the mean diameter of the spheres is 14.74 μm (with a deviation of ±1.26 μm), 74.44 μm (all spheres smaller than 90 μm), and 165 μm (diameters between 150 μm–180 μm) for the three arrays, respectively. In Fig. 2 the different arrays are shown. Since the sphere diameters vary in each array, only some of the spheres are in resonance at a particular wavelength and the intensity pattern generated changes with the wavelength. Therefore the light distribution in the array directly correlates with the incident wavelength. The light distribution is captured by a CMOS camera (DCC1645C, Thorlabs, Newton, USA) equipped with a microscope objective (M-10X, Newport Spectra-Physics GmbH, Darmstadt, Germany). To reduce the influence of fluctuations in the laser intensity on the measurement, ten percent of the light is detected with a photodiode (PDA36A-EC, Thorlabs, Newton, USA) and used for intensity normalization of each picture. The wavelength of the laser is determined by an optical spectrum analyzer (OSA201, Thorlabs, Newton, USA).
Fig. 1 Experimental setup: The intensity of the tunable laser is split with a ratio of 90 : 10 (C: coupler, OF: optical fiber). Ten percent of the laser intensity is either detected with an optical spectrum analyzer (OSA) or with a photodiode for calibration purposes. The remaining ninety percent of the laser intensity is collimated (CO: collimation optic) and coupled under 45° in a PMMA plate and guided based on total internal reflection. The WGMs are placed in the evanscent field present at the plate surface. The light distribution is captured by a CMOS camera equipped with a microscope objective.
Fig. 2 Images of the three different arrays used in this work. The spheres lying in the evanescent field generated by a red laser with a wavelength of 635 nm are excited. Additionally the arrays are illuminated from above for better visibility. The magnification of the optical imaging system is 10X. Mean diameter: Left: 14.74 μm. Middle: 74.44 μm. Right: 165 μm.
3. Calibration and measurement procedure
Before an array can be used to measure the wavelength of an unknown light source, the array needs to be calibrated once. To do so, the tunable laser is scanned from 635 nm to 637 nm with a scanning speed of 0.01 nms−1 in steps of 0.01 nm. At each wavelength, an image of the intensity distribution of the array is captured with the CMOS camera, see Fig. 1. Simultaneously the photodiode records the laser intensity. In a first step, the spheres that show the strongest intensity changes are identified and the associated CMOS camera pixel values are integrated over the sphere area. The integrated intensity values of all spheres in one single image i.e. for one particular wavelength, are saved as one dataset. To eliminate uncertainties due to the laser intensity variation, the sphere intensities are divided by the laser intensity value recorded from the photodiode. Following this, all datasets for different wavelengths are stored together in a database. Fig. 3 shows the wavelength dependence of one single sphere, see Fig. 3(a), and the database for a whole array consisting of 18 spheres with a mean diameter of 74.44 μm, see Fig. 3(b). Thus far, the wavelength that is connected to each frame is the wavelength value displayed by the laser unit. To ensure that each frame is assigned to the correct wavelength, in a second calibration step, the wavelength value of the display of the tunable laser is compared to the value measured with the optical spectrum analyzer which is calibrated by the manufacturer. Fig. 4(a) shows the wavelength measured with the OSA against the values displayed by the laser unit. A linear regression results in an offset of 0.226 nm. The achievable theoretical accuracy is limited by the spectral resolution of the optical spectrum analyzer of approximately 0.01 nm. As the readout of the OSA is slow, the laser has to be scanned stepwise for this comparison. It is obvious that the laser is not scanned continuously but in small steps corresponding to the resolution of the digitizer card in the scanning unit, as shown in Fig. 4(b). The database generated this way is suitable to determine the wavelength of an unknown laser source. The intensity distribution of the array at the unknown wavelength is captured and compared to the database via the correlation function r(λ) [15, 20]:
is the intensity of the j-th sphere in the calibration database and Ij the intensity of this sphere at the unknown wavelength. The minimum of the correlation function marks the unknown wavelength. Fig. 5 shows the correlation function for an array of N = 18 spheres with a mean diameter of 74.44 μm at a wavelength of 636 nm.Fig. 3 (a) Resonance spectrum for one exemplary sphere (mean diameter 74.44 μm), (b) intensities of all spheres (here: 18 spheres with a mean diameter of 74.44 μm), as stored in the database.
Fig. 4 Wavelength calibration with the optical spectrum analyzer: (a) wavelength measured with the OSA compared to the values displayed by the laser unit. (b) Enlargement of the graph in (a) for the range between 635.5 nm–635.8 nm shows that the laser is in fact not scanned continuously but in small discrete steps with minimal size determined by the digitizer card of the scanning unit.
Fig. 5 Correlation function r(λ) for 18 spheres with a mean diameter of 74.44 μm. At the true wavelength of 636 nm the correlation function has a pronounced minimum.
The same micro-resonator array can also be used for temperature measurement [21]. In this case, the system can be calibrated either by a wavelength scan as discussed above or by tuning the temperature while keeping the wavelength of the laser fixed [21]. To show, that our all-polymer sensor is suitable for temperature measurements, a Peltier element (193550, Conrad Electronic SE, Hirschau, Germany) and a temperature sensor (QC-PC-CC-12, Quick-Ohm Küpper & Co. GmbH, Wuppertal, Germany) are placed on the plate with an array of 74.44 μm-spheres. The temperature was controlled with a PID temperature controller (QC-PC-CC-12, Quick-Ohm Küpper & Co. GmbH, Wuppertal, Germany). The intensity distribution of the array for different temperatures is recorded with the CMOS camera.
4. Results
As shown in [15, 20], the accuracy of the wavelength determination depends on the number of spheres used to build the database on the one hand and on the linewidth of the irradiating laser light on the other hand. Moreover, the size of the spheres influences the number of spheres required and the maximum acceptable linewidth of the light source.
4.1. Dependence on the number of spheres
To investigate the dependence on the number of spheres, the following procedure was carried out: Three arrays each equipped with spheres of a different mean diameter (14.74 μm, 74.44 μm and 165 μm, respectively) were build. For each array, the wavelength was scanned twice. With the first scan, the database for each array was created. The frames recorded during the second scan were used to evaluate how many spheres of a given size are necessary to determine an unknown wavelength. To achieve this, the frames of the second scan were compared with the database at each specific wavelength. This was done several times for each array changing the numbers of spheres which were compared. Fig. 6 shows the results for the three arrays and in each case for three different numbers of spheres and Table 1 gives the corresponding standard deviation indicating the uncertainty of the wavelength determination for the different systems. In the left column in Fig. 6, 6(a), 6(d) and 6(g), respectively, only one sphere was considered and obviously the accuracy of the wavelength is limited due to large scatter of the data. However, using the sphere array with a mean diameter of 74.44 μm, a considerable number of evaluated wavelength values are already correct. Therefore, including five spheres already leads to a notable improvement of the accuracy, see Fig. 6(e) and Table 1. Inclusion of additional spheres into the analysis only increases redundancy, see Fig. 6(f) and Table 1. For a sphere array with a mean diameter of 165 μm ten instead of five spheres are necessary for an acceptable accuracy, see Figs. 6(h) and 6(i) and Table 1. However utilizing the array with the smallest spheres, not even 20 spheres are sufficient to determine an unknown wavelength reliably, see Fig. 6(b) and 6(c) and Table 1. The sensitivity of the sensor is defined as the minimal shift in the mode position of the spheres in response to changes in their ambient which can still be detected. The better the detection of mode shifts the better is the sensitivity. Large FSR and small FWHM facilitate mode separation and therefore the detection of the mode shifts. This is the reason why on the one side small diameters can improve the sensitivity, as they lead to a large FSR (scaling with 1/R). On the other side, small PMMA spheres usually have a low Q-factor, i.e. resonances with a large full-width-half-maximum (FWHM), thus reducing the sensitivity. For the sphere array with a mean diameter of 74.44 μm these competitive effects balance each other. Using the larger sphere array (mean diameter of 165 μm), the positive effect caused by resonances with a small FWHM and, thus, a higher Q-factor is dominated by a the negative effect originating from the small FSR. In case of the smaller sphere array (mean diameter of 14.74 μm), it is the other way around. Due to a higher radius of the spheres, the FWHM of the resonances broadens and the Q-factor decreases. Moreover, the dynamic range of the recorded intensity is considerably smaller for the 14.74 μm spheres compared to the other two cases, because the sphere area over which the intensity is integrated in the calibration process is smaller.
Fig. 6 Dependence of the wavelength measurement on the number of spheres for different sphere diameters: (a)–(c) 14.74 μm, (d)–(f) 74.44 μm and (g)–(i) 165 μm.
These results show, that a suitable choice of the number and size of the spheres is crucial for achieving high accuracy of the micro-sphere array as a spectral measurement system. We also found that our all-polymer system is competitive concerning reliability and required number of spheres to systems reported in previous works [15]. In the 74.44 μm-setup our all-polymer system needs only 5 spheres to achieve a good reliability instead of 16 spheres with a diameter around 120 μm [15] indicating that such a system can be used for optical sensing applications.
Table 1. Standard deviation of the wavelength determination [nm].
4.2. Dependence on the linewidth
Beside the number of spheres, also the spectral width of the light source influences the accuracy of the wavelength determination [15, 20]. Therefore, the largest acceptable linewidth is an essential parameter of the system. To examine the influence of the linewidth on the measurement result and to verify, if the largest acceptable linewidth depends on the sphere diameter, the linewidth needs to be changed. As this was not possible experimentally, a numerical simulation of this effect was performed [15, 20]. A new database was generated by weighting the original intensity of the spheres with a Gaussian function:
with g0 as a normalization coefficient and Δλ denoting the linewidth of the laser: After weighting the original mode spectra of the spheres with a Gaussian function, the intensities for all wavelengths were integrated: is the intensity of the j-th sphere in the original database at the wavelength λ and is the intensity of the j-th sphere in the new database. We assume, that the result represents the intensity of a sphere array generated by a laser with the linewidth used in the Gaussian function. This method was applied to the original databases which were calculated for the calibration for each sphere size (see Sec. 3). This was done multiple times for each sphere size, using a different linewidth in the Gaussian function every time and resulting in a set of new databases for each sphere size. Afterwards, the correlation function was calculated with these new databases. Fig. 7 and 8 show the correlation function for different linewidths and sphere diameters. Again, λ0 = 636nm was used for excitation in these datasets so, as described above, the correlation function has a minimum at the real wavelength λ0 = 636nm for our case, compare Fig. 5 in Sec. 3. In Fig. 7(a) the correlation functions for the 14.74 μm-spheres using the original database and the new databases and are plotted. Even the correlation function using the original database does not have its minimum at the true wavelength λ0, see the solid line in Fig. 7(a). This confirms the result of the Sec. 4.1, that 20 spheres are not sufficient to obtain a satisfying accuracy for this sphere size and laser linewidth. Further increase of the linewidth, , dotted line in Fig. 7(a), and , dashed line in Fig. 7(a), lead to more local minima at wrong wavelength values. In Fig. 7(b) the correlation functions for the 165 μm-spheres using the databases , and are shown. In this case, up to a linewidth of Δλ = 0.0136nm the correlation functions have their minimum at the correct wavelength λ0 = 636nm. Hence the maximum acceptable linewidth is larger than the one for the 14.74 μm-spheres. In Fig. 8 the correlation functions for the 74.44 μm-spheres using the databases , and are plotted. Up to a linewidth of Δλ = 0.018nm, the correlation functions have their minimum at the correct wavelength of λ0 = 636nm.Fig. 7 Correlation function r(λ) around the true wavelength λ0 = 636nm for different linewidths. Sphere diameter: (a) 14.74 μm and (b) 165 μm.
Fig. 8 Correlation function r(λ) around the true wavelength λ0 = 636nm for different linewidths. Sphere diameter 74.44 μm
These results, thus, also show that the 74.44 μm-spheres are most suited for wavelength measurements, because the competitive effects of a low Q-factor and a large FSR balance each other (see Sec. 4.1). Moreover, using our all-polymer setup, the largest acceptable linewidth of Δλ = 0.018nm is larger than the one reported in previous works using a glass prism instead of a PMMA plate (Δλ = 0.008nm) [15]. Additionally, for all sphere sizes, the minimum at λ0 broadens with increasing linewidth, see Fig. 8. Hence it is possible to use the array not only to determine the wavelength but also to measure the linewidth.
4.3. Temperature Measurement
The micro-resonator array described is not only suited to determine an unknown wavelength but also for temperature measurement, see also [21]. The conventional method to measure the temperature with WGMs is to record the resonance shift of a single sphere resonator [22]. For such a measurement, an expensive narrow-linewidth tunable laser system with high accuracy and a high resolution optical spectrum analyzer are necessary. One advantage of the micro-sphere array sensor presented here is that such an expensive laser system is not required, because the system can be calibrated either by tuning the parameter to be measured later on while keeping the wavelength fixed, i.e. changing the temperature, or by a wavelength scan as shown above [21]. If a temperature scan is chosen for calibration, a fixed-wavelength inexpensive light source can be used. In order to show that our all-polymer sensor is suitable for temperature measurements, we used the 74.44 μm-sphere array and increased the temperature from 25 °C to 35.8 °C. Fig. 9 shows the resulting wavelength dependence of one single sphere of this array. In contrast to the glass array used in [21] a blue-shift instead of a red-shift is observed. From our data, the sensitivity can be calculated to 0.001 nmK−1. This is two times better than the one of the glass array (0.0005 nmK−1) [21]. Theoretically the relative resonance shift Δλ/λ depends linearly on the change of the temperature ΔT as:
where α is the thermal expansion coefficient and β the thermo-optic coefficient. As opposed to silica, α and β have different signs for PMMA. As a result, using PMMA as resonator material, the possible sensitivity achievable and whether a red- or a blue-shift occurs strongly depend on the composition of the PMMA material which allows for even higher sensitivities [23]. In general, using the all-polymer micro-resonator array sensor described, a simple to fabricate and robust temperature sensor can be realized and, as a consequence, an interesting alternative to glass sensors is possible.Fig. 9 Wavelength dependence of one single sphere from the array with spheres of a mean diameter of 74.44 μm at different temperatures.
5. Conclusion
In summary, we present a small and completely polymer based spectral measurement device on the basis of the evaluation of optical resonances in micro-spheres. Using PMMA instead of glass, ensures that the device is inexpensive and easy to manufacture. Additionally we found, that the device is well suited for the determination of an unknown wavelength or for temperature measurements suitable calibration provided. An array consisting of 18 spheres with a mean diameter of 74.44 μm was used to realize a wavelength and temperature sensor with an accuracy of Δλ = 0.01nm and a sensitivity of 0.001 nmK−1, respectively. Numerical experiments show, that the unknown light source can be relatively broad band with a linewidth up to Δλ = 0.018nm and the width itself can be evaluated by the width of the correlation function r(λ). The accuracy of the determination of an unknown wavelength and the acceptable maximum linewidth depend not only on the resonator Q-factor, which influences the coupling efficiency, but also on the number and mean size of the resonators in the array. We showed that the performance of the PMMA sensor system is comparable or better than similar systems based on glass. With our system, the best results can be achieved with 74.44 μm-spheres which is the best compromise between two competing aspects: the requirement for a large free spectral range of the WGMs to achieve high detection sensitivity which favours small sphere diameters on the one side and a large quality factor Q and, thus, narrow WGM resonance linewidths, again to achieve high sensitivity, which demands for larger spheres with better surface quality. In our case the accuracy was limited by the uncertainty in the wavelength reading of the laser and the spectral resolution is limited by the wavelength steps of the tunable laser used for the calibration process. Currently, the scanning range restricts the possible wavelength region of the unknown source to be measured. Nevertheless, the method is simple, the requirements on the spheres concerning resonator quality are relatively moderate and the measurement principle is not only suitable for wavelength and temperature sensing as addressed in this work but also for other physical quantities, for example, for biosensing in the life sciences. In the future, we aim at an appropriate functionalization of the WGM sensor system to detect biological substances with high sensitivity and specificity.
Acknowledgments
The authors gratefully acknowledge the financial support by Deutsche Forschungsgesellschaft (DFG) within the Collaborative Research Center Transregio 123 - Planar Optronic Systems.
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