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Abstract
A highly sensitive temperature sensor based on a long period grating (LPG) written metal clad ridge waveguide (MCRW) with poly-dimethylsiloxane (PDMS) surrounding is proposed and theoretically analyzed. We have exploited the coupling between the fundamental and a higher order quasi-TE mode via the long period grating written in the core of the MCRW. It is shown that owing to the differential enhancement of the two participating modes' evanescent fields in the PDMS surroundings due to the metal under cladding and the high thermo-optic coefficient of PDMS, the thermal dependence of the higher order mode is significantly enhanced as compared to the fundamental mode. In addition, a dispersion turn around behavior in the phase matching graph of the LPG is observed due to the metal under cladding. As a result, a temperature sensitivity as high as ∼100 nm/°C can be achieved by using the dual resonance near the dispersion turning point. Further, due to the highly lossy nature of the quasi-TM modes, no inline polarizer is required to be used with the proposed structure.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Long period fiber grating (LPFG) based devices have found numerous applications in the field of chemical and physical sensing [1–4] due to its various advantages such as ease of fabrication, availability of evanescent field to interact with the ambient medium, freedom they offer in tailoring output spectrum and also they can be operated in wavelength interrogation scheme thus free from the intensity fluctuations of sources. However, the temperature sensitivity of a conventional fiber gratings are found to be quite low because of the low thermo optic coefficient (TOC) of silica [5–9]. In order to enhance the sensitivity, researchers have used different techniques such as fibers having air holes filled with polymers [10], coating the fiber with different materials having high TOC [11–13] etc. Recently Qi Wang et.al have shown that using a high TOC polymer poly-dimethylsiloxane (PDMS) as the coating material, it is possible to significantly enhance the temperature sensitivity and reported a sensitivity of −255 pm/°C [13]. The temperature sensitivity in such cases can be enhanced further by etching the cladding of the fiber thus exposing the cladding mode to the PDMS region more. However, due to the etching we have to compromise the fiber's robustness. In this context an integrated optical waveguide geometry is a smart choice, as not only it provides freedom in choosing the geometry and material but also suitable for lab on chip applications. Utilizing these features, various waveguide grating structures have been proposed for the sensing purpose [14–20]. Recently we have reported that by using a metal layer in between the core and substrate of a ridge waveguide, the evanescent field of the guided modes can be enhanced significantly [21] and the enhancement is much more prominent for the higher order modes as compared to the fundamental mode [22]. Utilizing this differential enhancement, here we are proposing a highly sensitive temperature sensor where the high TOC polymer PDMS has been used as the surrounding medium to a long period grating (LPG) written metal clad ridge waveguide (MCRW). It is shown that because of the metal layer, it is possible to achieve the dispersion turning point (DTP) in the phase matching graph near which temperature sensitivity ∼100 nm/°C can be achieved by using the dual resonance. In addition, because of the very high differential loss of quasi-TE and TM modes no extra polarizer is required to be used with the device to separate them out at the input or output end, which gives the proposed device an edge over the temperature sensors based on SPP assisted LPWG [23] or polymer LPWGs [24].
2. Proposed structure and theoretical analysis
The schematic of the proposed structure is shown in Fig. 1. It consists of two identical single mode ridge waveguides (SMRWs) with a long period grating (LPG) written multimode metal clad ridge waveguide (MCRW) in between. The core and the substrate of the waveguides are considered to be made of 19.3% GeO2 doped SiO2 and fused silica respectively. A metal layer of silver having thickness 200 nm is considered to be underneath the core of the MCRW section. The entire structure is surrounded by the polymer PDMS. Light is launched through the input SMRW and detected through the output SMRW. The mode excitation coefficient from/to the SMRW to/from the (m,n)th mode of MCRW can be calculated by using [25],
where, $\Delta {n_{eff}} = n_{0,0}^r - n_{m,n}^r$ and the factor $\gamma$ can be shown to be,
3. Results and discussions
The core dimension of the MCRW is considered to be 3×4 µm supporting three quasi-TE modes (TE00, TE10 and TE01 modes) at wavelength λ=1.55 µm. For SMRW the core dimension is selected to be 3×4.3 µm such that it mainly excites the TE00 mode of the MCRW. In Fig. 2, we have shown the fraction of coupled power (|am,n|2) to the three modes of the MCRW which shows that almost 95% power is coupled to the TE00 mode whereas there is hardly any power coupled to the higher order modes. Here we like to mention that, as the dimension of the MCRW is slightly different from SMRW there will be a slight power leakage. As a result, the summation of the modal power coupled to all the modes of MCRW is found to be 95% instead of 100%. It should be noted that, out of the two higher order modes (TE10 and TE01) the coupling coefficient due to the LPG in between the TE00 and TE10 is zero, as in the x-direction the refractive index distribution as well as the field distribution of TE00 mode is symmetric while TE10 is an anti-symmetric mode. On the other hand, the coupling coefficient of the TE00 mode with TE01 mode has a significant value, as the refractive index distribution in the y-direction of the MCRW is asymmetric. As a result, in the proposed structure LPG is made to couple power between the TE00 and TE01 modes, whose field distributions are shown in Fig. 3. It can be seen from the figure that the TE00 mode is well confined within the core of the MCRW whereas TE01 mode has significant amount of fractional modal power (FMP) to interact with the PDMS surrounding which can be attributed to the metal under cladding. In order to make this point clear, we have compared the modal characteristics of the MCRW with that of a ridge waveguide having no metal layer (denoted as RW onwards). For the MCRW, due to the high reflectance of the metal layer, modal power cannot penetrate into the substrate. As a result, the modal cut-offs of the various modes are decided by the surrounding medium PDMS (RI = 1.4195 at λ=1.55 µm and T = 25°C) instead of the substrate (RI = 1.4440) as in the case of a RW. As a result, the modal effective index of the higher order modes approaches the RI of PDMS more closely as compared to the case of the RW. On the other hand, fundamental mode (TE00) is well confined within the core, and hence it is not affected much by the metal under cladding. As a consequence of these, the FMP in the PDMS surrounding is significantly enhanced due to the metal under cladding more prominently for the TE01 mode. This is clear from Fig. 4, where we have plotted the variation of FMP for TE00 and TE01 mode in the PDMS as a function of temperature for the MCRW as well as for the RW at λ = 1.55 µm. The dimension of RW is considered to be 3×6 µm so that it also supports three quasi-TE modes with TE01 being the highest order mode.
Fig. 2. Fraction of modal power coupled (|amn|2) to the various modes of MCRW (3×4 µm) from SMRW (3×4.3 µm) at λ=1.55 µm.
Figure 4 clearly shows that the FMP in the PDMS is enhanced due to the metal layer and the enhancement is much higher for the TE01 mode as compared to TE00 mode, due to which TE01 mode will be affected much more by any change in PDMS's property. Since, PDMS has a very high TOC as compared to the silica, the change of modal effective index with the temperature is much more prominent for the TE01 mode. This leads to a significant enhancement in the factor ${{\partial ({\Delta {n_{eff}}} )} / {\partial T}}$, to which the sensitivity is directly proportional Eq. (4). In Fig. 5, we have shown the variation of ${{\partial ({\Delta {n_{eff}}} )} / {\partial T}}$ with the temperature for MCRW and RW, which clearly shows the enhancement in ${{\partial ({\Delta {n_{eff}}} )} / {\partial T}}$. The behavior of the phase matching graph which shows the variation of resonance wavelength with the grating period also plays an important role in determining the sensitivity. In Fig. 6, we have plotted the phase matching graphs for the MCRW up to the cut-off points of the TE01 mode for different temperatures. The phase matching graphs (Fig. 6) show a turn around point for each temperature which is commonly known as dispersion turning point (DTP) at which ${{\partial {\lambda _R}} / {\partial \Lambda \to \infty }}$ resulting in $\gamma \to \infty$ to which the sensitivity is directly proportional Eq. (4) [7,36]. From Eq. (5) it is also clear that the DTP corresponds to the wavelength at which the group index difference of two participating modes becomes zero. Figure 6 shows that at different temperature the DTP occur at different values of grating period. Thus, extremely high sensitivity can be achieved at any temperature by appropriately selecting the grating period. Here we have selected the grating period to be 60.6 µm (represented by vertical line in Fig. 6) which is near the DTP of T = 20°C. In order to show that $\gamma$ increases as we approach DTP, In Fig. 7 we have plotted the variation of γ as a function of temperature, for the lower resonance wavelength (λR) corresponding to the selected grating period. Since, the selected grating period is near the DTP (Fig. 6) of the phase matching graph at 20°C, a very fast increase in γ is observed near 20°C. The important point to note is that, in the absence of metal layer no such dispersion turn around behavior is observed in the phase matching graph. In Fig. 8, we have presented the phase matching graphs for the RW up to the cut-off point of TE01 mode for different temperatures and for different core dimensions, which clearly shows the absence of any dispersion turn around behavior. Thus, the metal under cladding not only enhances the factor ${{\partial ({\Delta {n_{eff}}} )} / {\partial T}}$ but also help to achieve DTP which increases the factor γ leading to a further enhancement in temperature sensitivity. In Fig. 9, we have shown the output spectrum of the proposed structure for different temperatures. The grating period, length and strength are considered to be 60.6 µm, 3.64 mm and 1.1×10−3 respectively. The grating length is taken as one coupling length (${L_g} = {\pi / {({2{\kappa_{0,1}}} )}}$) in between TE00 and TE01 mode at T = 20°C and λ = 1.55 µm. In the above mentioned expression ${\kappa _{0,1}}$ is the coupling coefficient between the TE00 and TE01 mode which is defined in our earlier work [22]. It is to note that, the output spectrum corresponding to T = 20°C has dual dips (i.e. having dual resonance) as the selected grating period meets the phase matching graph twice for T = 20°C (inset of Fig. 6). On the other hand, the output spectrum corresponding to the higher temperatures have only one dip as the selected grating period meets the phase matching graph only once (Fig. 6). This is due to the fact that for higher temperatures, TE01 mode reached its modal cut off before the selected grating period can cut the phase matching graphs for second time. Here we like to mention that as the temperature increases, the phase matching point shifts towards lower wavelengths where the coupling length also decreases. Since we consider the grating length as the one coupling length at 20°C, the difference between the grating length and the coupling length increases as we move to higher temperature. As a result, the transmission is much smaller for the higher temperature than the lower temperature (Fig. 9). In Fig. 10, we have shown the variation of the sensitivity associated with the lower resonance wavelength (i.e. left dip), which shows that for the grating period 60.6 µm the sensitivity varies between −54 nm/°C to −1.97 nm/°C for a temperature range of 20 to 60°C. This figure also shows that the sensitivity increases very rapidly as we approach the DTP as discussed earlier. It is important to note that near 20°C the dual dips can be utilized to the further increment of temperature sensitivity. In case of dual resonance the two dips in the spectrum shifts in opposite direction with the change in temperatures, resulting in an overall sensitivity [37], ${S_{ove}} = |{{{({\Delta {\lambda_{{R_L}}} - \Delta {\lambda_{{R_R}}}} )} / {dT}}} |$, where $\Delta {\lambda _{{R_L}}}$ is the shift in the left dip and $\Delta {\lambda _{{R_R}}}$ is the shift in the right dip. In the proposed structure, the temperature sensitivity associated with the left dip is found to be −54 nm/°C whereas for right dip 59 nm/°C resulting in an overall sensitivity of 113 nm/°C. The variation of overall sensitivity with the temperature up to the temperature where dual resonance can occur for the selected grating period 60.6 µm is shown in Fig. 11. The temperature up to which the dual resonance can occur is found to be 23°C. The overall sensitivity is found to vary between 113 nm/°C to 28.9 nm/°C for a temperature range of 20 to 23°C.
Fig. 5. Variation of ${{\partial ({\Delta {n_{eff}}} )} / {\partial T}}$ with the temperature for MCRW and RW.
Fig. 9. Output spectrum of the LPG written MCRW for different temperatures for grating period 60.6 µm.
Fig. 10. Variation of sensitivity associated with lower resonance wavelength (left dip) with temperature for Λ = 60.6 µm.
Fig. 11. Variation of overall sensitivity with temperatures up to which the dual resonance can occur for Λ = 60.6 µm.
In Table 1, we have compared our proposed device's performance with the earlier reported sensors and observed that the sensitivity is much higher as compared to the other sensors. The proposed sensor can find application in the study of various chemical and biological processes such as growth, protein synthesis, and metabolism of animal cell culture, cardiac tissue engineering, ethanol fermentation etc, where a small variation in temperature has a significant impact [38–40].
It is to note that, since the major field component (Ey) of the quasi-TM modes is perpendicular to the metal layer, the quasi-TM modes are either pure or hybrid surface plasmon modes in nature [22,41,42]. As a result, the TM modes are highly lossy. For example, for the considered dimension of MCRW, three TM modes are guided, out of which TM00, TM10 are pure surface plasmon modes whereas TM01 is hybrid one in nature. The propagation lengths of these three modes are 0.28 mm, 0.32 mm and 1.42 mm respectively. On the other hand, the propagation lengths of the participating quasi-TE00 and TE01 modes are 67 mm to 24 mm respectively. Since the grating length of the proposed structure is 3.4 mm, at the output end of the waveguide, the power associated with the TM modes are negligibly small. As a result, no inline polarizer is required to be used with the structure to separate the TE and TM modes as in the cases of SPP assisted LPWG [23] or polymer LPWGs [24].
Table 1. Comparison of temperature sensitivity of the proposed sensor with earlier reported sensors
In order to fabricate the proposed device, sputtering process can be used to deposit the metal layer and the GeO2 doped silica. Electron beam lithography and dry etching should be used to form the ridge waveguide since a tight control in waveguide's width is required to operate the proposed structure near DTP. As reported by Barwicz et.al. this technique can provide an inaccuracy below ± 15 nm [43] in waveguide's width. The grating can be written by point by point writing technique by the UV-laser which can give us a ± 10 nm control on the grating period as reported in Ref. [44]. In order to see the effect of such an inaccuracy in the MCRW's width and grating period over the sensitivity near the DTP, we have plotted the phase matching graph for three different MCRW's widths in Fig. 12 and shown the overall sensitivity (${S_{ove}}$) values for three different grating periods. In the figure, graph ‘B’ corresponds to the phase matching graph for the considered MCRW's width 3 µm and graph ‘A’ and ‘C’ respectively represents the phase matching graphs for an inaccuracy of + 15 nm and −15 nm. The three vertical lines correspond to three grating periods where the middle one is the considered period 60.6 µm and the left and right ones are for an inaccuracy of −10 nm and + 10 nm. Values written adjacent to each graph represent the overall sensitivity (${S_{ove}}$) values for each width and period in unit of nm/°C. Figure 12 shows that for such an inaccuracies in width and period, the temperature sensitivity of the proposed structure varies in between 83 to 359 which shows that it is possible to have sensitivity ∼100 nm/°C even with simultaneous inaccuracies of ± 15 nm in width and ± 10 nm in grating period. This makes the proposed structure an excellent choice for the measurement of temperature with high sensitivity. The film of the polymer PDMS can be deposited by following the process depicted in Ref. [45]. Here we like to mention that as the contrast in waveguide's core and cladding (PDMS surrounding) is very small the scattering loss due to the sidewall roughness is very small (∼ 0.001 dB/cm) as reported in Ref. [46]. The proposed device can be integrated with a light source at the input end and a detector at the output end via two fiber lenses as shown in Ref. [47] for the practical uses. A tunable laser source [47] or a broadband light source (ASE) [13] having wavelength range 1.3 µm to 1.7 µm can be used as the light source whereas an optical spectrum analyzer with wavelength resolution of 20 pm [13] can be used as a detector to monitor the output spectrum. It is to note that due to higher loss of TM modes there is no need to use the polarization controller (PC) and the polarization maintaining fiber lenses (PMFL) as used in [47], which makes the proposed device more compact.
4. Conclusions
In summary, we have theoretically analyzed a highly sensitive temperature sensor based on long period grating written metal under clad ridge waveguide with PDMS as surrounding medium. Using the quasi-TE modes of the structure, it is shown that the proposed structure can give a sensitivity as high as ∼100 nm/°C due to the combined effect of metal under cladding and high thermo optic coefficient of PDMS. We have also discussed a possible way to fabricate the proposed structure and shown the effect of inaccuracies in waveguide's width and grating period over sensitivity. It is observed that a sensitivity ∼100 nm/°C is achievable even with a simultaneous inaccuracy of ± 15 nm in width and ± 10 nm in grating period. Further, it is observed that due to the highly lossy nature of the TM modes, no inline polarizer is required to use with structure.
Acknowledgment
Author Nabarun Saha gratefully acknowledges the Council of Scientific and Industrial Research (CSIR), India, for providing Senior Research Fellowship.
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