Analysis of ring resonators for chemical vapor sensor development

Yuze Sun; Xudong Fan

doi:10.1364/OE.16.010254

1. Introduction

Highly sensitive chemical vapor detection is very important in many applications ranging from environmental monitoring, personal health and safety, to homeland security. The desirable characteristics of a chemical vapor sensor include ultra-high sensitivity, specific and rapid response to a certain vapor molecule, as well as the ability of the on-the-spot chemical analyses, which usually requires the sensor to be small, portable, and reusable. Towards this end, various sensing techniques have been studied extensively, including microcantilever based sensors [1], surface acoustic wave sensors [2], fiber optic/waveguide sensors [3–6], interferometers [7], and surface plasmon resonance sensors [8].

Recently, chemical vapor sensors based on microring resonators have been proposed and investigated [9–13]. In a ring resonator, the light propagates in the form of whispering gallery modes or circulating waveguide modes (WGMs) [14]. Although the ring resonator is only a few tens to a few hundreds of micrometers in size, the effective detection length can significantly be enhanced due to the high Q-factors of the WGMs. Therefore, the ring resonator technology enables large density of sensor arrays for portable devices with multiplexed detection capability. Like many other optical chemical vapor sensors, the ring resonator vapor sensor relies on the polymer to provide selectivity towards the analytes. In the presence of vapor molecules, the polymer undergoes RI and/or thickness change [8,9], resulting in a WGM spectral shift. Therefore, by directly or indirectly monitoring the WGM spectral position in the real time, both quantitative and kinetic information regarding the interaction between vapor molecules and polymer can be extracted.

In general, there are four basic ring resonator configurations that can potentially be used as a vapor sensor: (1) chip based planar ring resonator made of solid dielectric materials such as SiON and coated with a vapor sensitive polymer as the cladding [9,10]; (2) chip based polymer ring resonator, in which polymer is used as the building block of the ring resonator and also as the sensing material [11], (3) free-standing microsphere or cylinder whose exterior surface is coated with a layer of polymer (Fig. 1(A)); and (4) optofluidic ring resonator (OFRR) whose interior surface is coated with a layer of polymer (Fig. 1(B)) [12,13]. The first two planar ring resonator vapor sensor configurations have been experimentally or theoretically investigated, showing a detection limit (DL) on the order of tens of ppm for alcohol [9,11] and 0.4% for ammonia [10]. While the third configuration, to our best knowledge, has not been explored for vapor sensing, it has strong potential to be a promising vapor sensing platform due to its high Q-factors, ease to fabricate, and convenience to use. The fourth configuration utilizes a thin-walled glass capillary as a microfluidic channel to conduct samples and as a ring resonator to detect the analyte passing through the capillary. Because of this unique structure, this type of ring resonator is called optofluidic ring resonator (OFRR). The OFRR bears several distinctive advantages in comparison with the other three types of ring resonator based vapor sensors. Since the OFRR achieves dual use of the capillary as a fluidic channel and a sensing head, it requires only a few µL sample volume, in contrast to a typical level of a few liters used in planar ring resonator based vapor sensors that usually requires a chamber and extra delivery channels [13]. Additionally, the sensing events take place on the inner surface of the capillary. The circular nature of the capillary ensures the most efficient interactions between the vapor molecules and the polymer layer. Consequently, rapid detection becomes possible [12,13]. Moreover, the OFRR is highly compatible with well-developed GC technology, which can be adopted for OFRR vapor sensor development.

In earlier investigations, we showed that the OFRR based chemical-vapor sensors are capable of discriminatively detecting ethanol and hexane vapors with sub-second response and recovery time [13]. We also demonstrated a micro-GC system based on the OFRR with on-column detection and rapid analyte separation capability, and nano-gram DL [12, 13]. With these successful initial demonstrations, it is now crucial to systematically analyze the WGM behavior in the OFRR vapor sensing system. This will elucidate how the WGM responds to the interaction between the polymer and vapor molecules, thus enabling the optimization of the OFRR sensing performance from the optical point of view. Although our main interest will be to study the OFRR with the polymer coating on its interior surface due to its excellent fluidics, it would also be constructive to study another case where the polymer is coated on the exterior surface of the ring resonator, which will not only further help understand the role of the polymer layer in WGM guiding and vapor sensing, but also provide an insight into microsphere and solid cylinder based vapor sensor systems (the third configuration mentioned previously).

Fig. 1. Ring resonator chemical vapor sensor configurations, in which a polymer layer is coated on the exterior (A) or interior (B) surface of the ring resonator. OD: ring resonator outer diameter. t: polymer thickness. d: ring resonator wall thickness. n₁, n₂, n₃, and n₄ are the refractive indices for the medium inside (air), silica ring resonator, polymer, and medium outside (air), respectively.

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In this article, we will use a hollow cylindrical ring resonator as a model system when its exterior or interior surface is coated with a layer of polymer (see Figs. 1(A) and 1(B)). Both configurations will be treated uniformly under the framework of a four-layer Mie model. The RI sensitivity and thickness sensitivity will be studied as a function of the polymer coating RI and thickness, and the ring resonator size and wall thickness, as well as the mode order and polarization. Similarities and differences between these two configurations will be discussed. Finally, we will apply the simulation results to an actual OFRR vapor sensor system to estimate its DL.

2. Model

The four-layer Mie model used in the simulation is illustrated in Fig. 1, where a fused silica cylindrical ring resonator (n₂=1.45) of a given outer diameter (OD) is coated with a polymer layer of thickness, t, on its exterior or interior surface. The ring resonator contains an air core and is surrounded by air. The behavior of a given WGM can be conveniently analyzed using the analog of a quantum mechanical potential well, V(r), defined as [15]:

V (r) = k^{2} [1 - n^{2} (r)] + \frac{m^{2}}{r^{2}},

where the total energy is given by k² (k=2π/λ, λ is the WGM wavelength in vacuum). n is the RI and m is the angular momentum. The radial distribution of the WGM of the ring resonator shown in Fig. 1(A) can be described by Mie theory [16]:

E_{m, l} (r) = {\begin{matrix} \begin{matrix} A J_{m} (k n_{1} r) & (r \leq \frac{O D}{2 - d}) \end{matrix} \\ \begin{matrix} B J_{m} (k n_{2} r) + C H_{m}^{(1)} (k n_{2} r) & (\frac{O D}{2 - d} \leq r \leq \frac{O D}{2}), \end{matrix} \\ \begin{matrix} D J_{m} (k n_{3} r) + E H_{m}^{(1)} (k n_{3} r) & (\frac{O D}{2} \leq r \leq \frac{O D}{2 + t}) \end{matrix} \\ \begin{matrix} F H_{m}^{(1)} (k n_{4} r) & (r \geq \frac{O D}{2 + t}) \end{matrix} \end{matrix}

where J_m and H_m⁽¹⁾ are the mth Bessel function and the m ^th Hankel function of the first kind, respectively. The RI of the core, the ring resonator wall, the polymer, and the surrounding medium are described by n₁, n₂, n₃, and n₄. Likewise, the equation for the configuration shown in Fig. 1(B) can be written similarly. The WGMs have two polarizations, a-mode and b-mode, with the magnetic field and the electric field being along the cylinder longitudinal direction, respectively.

When interacting with vapor molecules, the polymer undergoes RI change and/or thickness change [7–11,13,17,18], which results in a spectral shift in the WGM. This effect can be described by the ring resonator sensitivity, S:

S = \frac{d λ}{d ρ} = \frac{\partial λ}{\partial t} \cdot \frac{\partial t}{\partial ρ} + \frac{\partial λ}{\partial n_{3}} \cdot \frac{\partial n_{3}}{\partial t} \cdot \frac{\partial t}{\partial ρ} + \frac{\partial λ}{\partial n_{3}} \cdot \frac{\partial n_{3}}{\partial ρ},

where dλ/dρ is the WGM spectral shift due to the change of the vapor molecule density in the polymer matrix, $ρ . \frac{\partial λ}{\partial t}$ and $\frac{\partial λ}{\partial n_{3}}$ refer to the WGM thickness sensitivity (S_t) and RI sensitivity (S_RI), respectively, which are the intrinsic properties associated with the optical modes of the coated ring resonator. $\frac{\partial t}{\partial ρ}$ and $\frac{\partial n_{3}}{\partial ρ}$ are the polymer swelling/shrinkage and the RI change due to the vapor molecule absorption, which depend on the polymer-analyte interaction. $\frac{\partial n_{3}}{\partial t}$ represents the polymer RI change when the polymer swells/shrinks. Note that the RI change can be caused by either the polymer volume change induced by vapor molecules, or the doping effect due to the presence of the vapor molecules in the polymer matrix [8], as described respectively by the second and the third term on the right-hand-side of Eq. (3). In this article, we will focus on S_t and S_RI as a function of the polymer coating RI and thickness, the ring resonator size and wall thickness, and the mode order and polarization.

3. Results

3.1. Case I: polymer is coated on the outer surface of the ring resonator

As the WGM on the exterior surface of a bare ring resonator has been well studied, we will first investigate the case where the polymer is coated on the exterior surface of a hollow cylindrical ring resonator (Fig. 1(A)), which will also provide a foundation for the analysis of the interior coating case in the next section (Section 3.2). Teraoka et al. and Gaathon et al. have recently carried out similar investigations on sensitivity enhancement using a polymer coated microsphere [19–21]. In their work, the evanescent field outside the coated polymer layer is studied for biosensing applications. In contrast, for vapor sensing applications, our focus is on the electric field confined within the polymer layer. This is one of the major differences between the chemical vapor sensing and biosensing, which we will emphasize throughout the paper.

Polymers of various RI have been used in chemical vapor sensors, such as PDMS (n=1.41) [4], syndiotactic polystyrene [6], Poly(vinyl pyrrolidone) (n=1.53) [7], Teflon (n=1.31) [8], ethyl cellulose (n=1.45) [9], PMMA (n=1.48) [10], PHTES:MTES:TEOS prepared by a sol-gel method (n=1.48) [11], Carbowax (n=1.46) [12,13], and poly (3-octylthiophene) (n=1.7) [22]. As the optical characteristics of the WGMs may be different for different the polymer RI, we categorize our simulation into two situations: low RI polymer and high RI polymer relative to the RI of the OFRR wall.

3.1.1. Low-index polymer

Figure 2 shows the two potential wells for a ring resonator with an OD of 95 µm and a wall thickness of 3 µm when the polymer has a RI lower than that of the wall. When the polymer layer is sufficiently thin (Fig. 2 (A)), it does not support any WGMs and the field in it can be regarded as the evanescent field of the mode supported by the ring resonator wall (wall mode). As the polymer thickness increases, the mode in the polymer layer (polymer mode) starts to emerge and interacts with the wall mode to form new bonding and anti-bonding modes [23,24], as illustrated in Figs. 2(B) and 2(C). With a larger polymer thickness, the wall mode and the polymer mode eventually become de-coupled, at which point, nearly all the light of the polymer mode is confined within the polymer layer (Fig. 2(D)). Figure 3 plots the dispersion curves for the first three WGMs where the bonding and anti-bonding crossings can easily be identified.

Fig. 2. The WGM radial distribution (left axis) and the potential well and k² (right axis) of the 2^nd order mode for various polymer thicknesses (A): 0.5 µm. (B) 2 µm. (C) 2.5 µm. and (D) 5 µm. Vertical lines indicate the boundaries of the ring resonator wall and the polymer layer. The relevant parameters are: OD=95 µm. d=3 µm. n₁=1. n₂=1.45. n₃=1.40. n₄=1. m=257. b-mode.

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Fig. 3. k² as a function of polymer thickness for the first three WGMs. The relevant parameters are the same as in Fig. 2. Arrows indicate the polymer thickness used in Fig. 2.

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The RI sensitivity for the polymer RI change, S_RI, is related to the fraction of light in the polymer, η, by [25–27]:

S_{R I} = \frac{\partial λ}{\partial n_{3}} = \frac{λ}{n_{eff}} η,

where n_eff=mλ/2πR (R: ring resonator radius) is the WGM effective RI. Figure 4 plots S_RI for various polymer thicknesses. When the polymer coating is thin, the majority of the light is confined within the ring resonator wall and the higher order modes have a higher fraction of light in the polymer and hence higher RI sensitivity, which is the same as in a typical ring resonator biosensor where the evanescent field outside the ring resonator is utilized for sensing [28,29]. When the polymer becomes thicker, all modes are pulled into the polymer layer and start to be de-coupled from the wall mode. While the 2^nd and 3^rd order mode still have a significant portion of light in the ring resonator wall, the predominant amount of light of the 1^st order mode is localized in the polymer, resulting in a much higher RI sensitivity than the other two modes. When the polymer thickness is larger than 6 µm, all modes are confined within the polymer layer, equivalent to creating a new polymer-based ring resonator. At this point, all modes reach nearly the same sensitivity, which is 1300 nm/RIU, in good agreement with the estimation from Eq. (4). Note that although the RI sensitivity of the 1^st order mode increases monotonically with the increased polymer thickness, oscillatory S_RI is observed for the other two modes when the energy splitting occurs. This behavior becomes obvious when we compare Figs. 2(B) and 2(C), which are located on the opposite side of the energy splitting region plotted in Fig. 3. Figure 4 also shows the polarization dependence of the RI sensitivity. The b-mode has a slightly higher sensitivity than a-mode, which is opposite to the ring resonator biosensors where the evanescent field outside the ring resonator is used for sensing.

Fig. 4. RI sensitivity as a function of polymer thickness for the first three WGMs. The simulation parameters are the same as in Fig. 2. The RI sensitivity for the first order WGM of different polarization (a-mode) is also plotted.

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The thickness sensitivity for the polymer thickness change, $S_{t} = \frac{\partial λ}{\partial t}$ , can be deduced from Fig. 3 by taking the first order derivative of the dispersion curve. Generally, S_t is positive, meaning that the WGM shifts to a longer wavelength when the polymer swells. However, for a certain coating thicknesses, S_t is virtually zero and the ring resonator becomes insensitive to the polymer thickness change. This somewhat unintuitive behavior is due solely to the strong interaction between the wall mode the polymer mode. When the polymer is sufficiently thick (e.g., when t>6 µm in Fig. 3), the WGM shift becomes linear with respect to the polymer thickness increase, which is simply caused by the increase in the overall ring resonator radius.

3.1.2. High-index polymer

Now we study the situation when the polymer RI is higher than that of the ring resonator wall. The overall behavior of S_RI and S_t are similar to the low-RI polymer case discussed previously. Since the potential well for the polymer is deeper, the polymer modes start to de-couple with the wall modes at a thinner polymer layer, as exemplified by S_RI which is plotted in Fig. 5. Same as in Fig. 4, the b-mode has a slightly higher sensitivity than a-mode. Note that in the above simulations, the ring resonator wall thickness is chosen to be 3 µm. The results, however, do not change qualitatively when the wall becomes thicker or thinner. Therefore, the results obtained for both low and high RI polymer are also applicable to microspheres and solid cylinders without major modifications.

Fig. 5. RI sensitivity as a function of polymer thickness for the first three WGMs. The simulation parameters are the same as in Fig. 2, except that the polymer RI, n₃, is 1.7. The RI sensitivity for the first order WGM of different polarization (a-mode) is also plotted.

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3.2. Case II: polymer is coated on the inner surface of the ring resonator

3.2.1. Low-index polymer

We now move to the case where the polymer is coated on the inner surface of the OFRR (Fig. 1(B)). When the polymer RI is smaller than or close to that of the ring resonator, the polymer layer can be regarded as the extension of the ring resonator wall, regardless of the polymer thickness. Initially, when the polymer layer is thin, only the evanescent field exists in the polymer layer and the RI sensitivity is low. With the increased polymer thickness, higher order modes start to move inward, resulting in a higher RI sensitivity for those modes while the lower order modes are not affected much. This behavior is shown in Fig. 6(A) and its insets. Since there is no energy splitting arising in the dispersion curve in Fig. 6(A), the RI sensitivity plotted in Fig. 6(B) increases monotonically with the increased polymer thickness and no oscillatory characteristics are expected. The maximum of S_RI depends highly on the mode order. For example, S_RI can reach approximately 600 nm/RIU for the 3^rd order mode, whereas it is nearly zero for the 1^st order mode, which is different from the outside coating case where all modes have a very similar maximal S_RI value (see Fig. 4). Note that since the light tends to localize near the outer rim of the polymer layer (see, for example, the 3^rd order mode in Inset (B) of Fig. 6(A)), excessively thick polymer may not be beneficial in vapor sensing, as vapor molecules have to travel an additional distance to reach the maximal interaction with the light in the polymer. Polarization dependent S_RI is also given in Fig. 6(B), showing that the b-mode has a slightly higher sensitivity than the a-mode, which is in agreement with the outside coating case, but opposite to the OFRR biosensors where the evanescent field in the core is used for sensing [30].

For the OFRR based vapor sensor, the ring resonator wall thickness has a significant impact on the sensor performance. Since the polymer layer is treated as the extension of the ring resonator, the relative thickness between the wall and the polymer determines the distribution of the WGMs. As a result, the fraction of light and hence the RI sensitivity is lower with a thicker ring resonator wall, as shown in Fig. 7. Eventually, the RI sensitivity drops to zero when the wall is sufficiently thick, in which case, the WGM is predominantly confined within the wall. The thickness sensitivity, S_t, is still positive. However, with the increased polymer thickness, S_t drops gradually to zero, opposite to Case I where the WGM spectral position increases with the increased polymer thickness.

Fig. 6. k² as a function of polymer thickness for the first three WGMs. The relevant parameters are: OD=95 µm. d=3 µm. n₁=1. n₂=1.45. n₃=1.47. n₄=1. m=257. b-mode. Inset: Intensity radial distribution for the first three modes when the polymer thickness is 0.5 µm (A) and 2.9 µm (B). Vertical lines indicate the boundaries of the ring resonator and the polymer layer. (B) The corresponding RI sensitivity. The RI sensitivity for the third order WGM of different polarization (a-mode) is also plotted.

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3.2.2. High-index polymer

When a polymer of sufficiently high RI is used as a coating, the WGMs exhibit completely different behavior. Initially, the light is confined within the ring resonator wall as a wall mode. With the increased polymer thickness, a polymer potential well starts to support a new set of WGMs that interact with the wall modes. Figure 8(A) shows the dispersion for the three lowest modes in such a polymer coated ring resonator. The energy splitting occurs when the 1^st order wall mode (shown as the dashed line in Fig. 8(A)) intersects the polymer modes.

Fig. 7. RI sensitivity as a function of the ring resonator wall thickness for the first three WGMs. The polymer thickness is fixed at 1 µm. Other parameters are the same as in Fig. 6.

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Fig. 8. (A) k² as a function of polymer thickness for the first three WGMs. Dashed line indicates the k² position for the 1^st order ring resonator wall mode in the absence of the polymer layer. The simulation parameters are the same as in Fig. 6, except that the polymer RI, n₃, is 1.7. (B) The WGM radial distribution (left axis) and the potential well (right axis) of the 2_nd order mode for various polymer thicknesses indicated by the arrows in (A). Vertical lines indicate the boundaries of the ring resonator wall and the polymer layer.

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Eventually, when the polymer is sufficiently thick, polymer modes and wall modes are decoupled. This is equivalent to creating a new polymer ring resonator in a capillary and the glass capillary simply acts as the physical substrate. Figure 8(B) shows such a transition for the 2^nd order mode.

Fig. 9. RI sensitivity as a function of polymer thickness for the first three WGMs. The polymer is coated on the inner surface of the ring resonator. The simulation parameters are the same as in Fig. 6, except that the polymer RI, n₃, is 1.7.

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The RI sensitivity of the above sensor structure is given in Fig. 9. Whereas the sensitivity for the 1^st order mode increases monotonically with the increased wall thickness, the sensitivity for the 2^nd and 3^rd order modes oscillates significantly. In particular, the sensitivity becomes nearly zero at certain regions that correspond to the plateaus in Fig. 8(A), where the mode possesses the dominant characteristic of the wall mode (e.g., the mode in the second figure of Fig. 8(B)). After the de-coupling process, all modes approach their respective maximal sensitivity.

The RI sensitivity also depends on the mode order with the behavior similar to that in Case I (but different from Case II with a low RI polymer). The effect of the ring resonator wall thickness on S_RI is shown in Fig. 10. Initially, the 1^st order mode consists dominantly of the polymer mode, which has very high sensitivity. After the polymer mode intersects with the wall mode, the sensitivity drops to nearly zero, as at this time, the 1^st order mode is of the characteristic of the wall mode, which has negligible presence in the polymer. Meanwhile, polymer mode becomes the 2^nd order mode, which again has a high sensitivity. The thickness sensitivity is still positive. However, at those plateau regions, S_t becomes zero. Furthermore, S_t gradually decreases to zero with the increased polymer thickness.

Fig. 10. k² vs. ring resonator wall thickness for a fixed polymer thickness (A) and (C), and the corresponding RI sensitivity (B) and (D). Other parameters are the same as in Fig. 9.

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4. Discussion

4.1. Sensitivity

As shown by Eq. (3), the overall sensing sensitivity, e.g., the WGM spectral shift versus vapor molecule density change (S), has two sources of contribution, polymer thickness change $(\frac{\partial t}{\partial ρ})$ and the polymer RI change $(\frac{\partial n_{3}}{\partial ρ})$ . The polymer RI change can be induced by the polymer thickness change or by doping effect. While the thickness change and the thickness-induced RI change may have to be determined experimentally [7,17,18], the RI change due to the doping effect can be modeled by Lorentz-Lorenz equation [8]:

{δ n}_{3} = \frac{{({n_{3}}^{2} + 2)}^{2}}{6 n_{3}} \frac{1}{3 ε_{0}} (δ ρ) α,

where α is the vapor molecule polarizability. Generally, these effects may not work additively to shift the WGM to a longer wavelength when the polymer interacts with the vapor molecules. For example, while the doping induced polymer RI change is always positive, its thickness-related RI decreases when polymer swells. As a result, depending on the ring resonator sensor configuration and the target vapor analyte, a negative sensitivity may occur, which causes the WGM to shift to a shorter wavelength upon detecting chemical vapors. This phenomenon was also experimentally observed in OFRR vapor sensor previously [12], which provides an additional chemical differentiation capability [4,12].

4.2. Detection limit

The DL of the ring resonator vapor sensor is determined by its sensitivity and its minimally resolvable spectral shift (δλ)_m, i.e.:

D L = \frac{δ λ_{m}}{S} .

(δλ)_m is usually chosen to be 1/20–1/50 of the WGM resonance linewidth [29], which inversely proportional to the ring resonator’s Q-factor given by [31]:

Q = \frac{2 π n}{λ σ η},

where σ is the polymer optical attenuation coefficient. It should be emphasized that although a thicker polymer layer may result in a higher sensitivity (e.g., a larger S_RI), it does not necessarily lead to a better DL, as polymers typically have a much larger attenuation coefficient than fused silica wall. Excessive exposure of the WGM in the polymer layer may significantly degrade the WGM Q-factor and hence the DL. Therefore, for those polymer ring resonators formed on a chip (the second configuration) and those formed by coating the exterior surface of a microsphere/cylinder with a thick polymer layer (the third configuration), their DL may not be optimal.

We now apply our simulation results to analyze the performance of the OFRR based vapor sensor, assuming that the doping effect is dominant. Considering that a 1 µm thick polymer layer with RI of 1.47 is coated on the OFRR inner surface and using the parameters given in Fig. 6(B), a RI sensitivity of approximately 400 nm/RIU for the 3^rd order WGM can be obtained. Further assuming that the polymer absorption loss is 1 dB/cm, which is equivalent to an attenuation coefficient σ=0.23 cm^-1, and using Eq. (7), we achieve Q=5×10⁵, at λ=1550 nm, n=1.45, and η=50%. Although practically the Q-factor of the ring resonator could be degraded due to the roughness of the coating, a relatively high Q-factor can still be obtained. In fact, a Q-factor over 10⁶ has been demonstrated with a 1.5 µm thick polymer coating on the inner surface of a ring resonator [32]. Assuming that we are able to resolve 1/50 of the resonance linewidth [33] and that the temperature induced WGM spectral fluctuation can be controlled below 0.1 pm at 1550 nm, we arrive at a sensor spectral resolution of 0.1 pm, which has also been experimentally demonstrated recently [13]. As a result, the sensor DL is estimated to be 2.5×10^-7 RIU.

Equation (5) relates the RI change in the polymer layer to the vapor molecule density in the polymer matrix, which is further related to the vapor concentration in free space, ρ₀, by K=ρ/ρ ₀, where K is the partition coefficient ranging from a thousand to hundreds of thousand [34,35]. Using K=1000 and N_Aα/(3ε₀)=30 cm³/mol (N_A is the Avogadro’s number), which are typical for many types of vapor molecules [8], we have δ(n₃)=2.4×10^-6 RIU/ppm at room temperature and the atmospheric pressure. This result is close to the experimental data [8,13]. Using the DL of 2.5×10^-7 RIU for RI, we obtain a concentration DL of 0.1 ppm for chemical vapors.

For the polymer thickness induced WGM shift, we use the same parameters as in the previous discussion (i.e., t=1 µm and the 3^rd WGM) and assume that the thickness swelling coefficient is 10^-6/ppm [17,18], which results in a 0.03 pm/ppm in the WGM shift based on the simulation in Fig. 6. Further using the 0.1 pm spectral resolution, we arrive at a DL of 3.3 ppm for chemical vapors. Note that in practice, both polymer swelling and the RI change may co-exist and their relative contribution to the WGM shift may vary, depending on the polymer and its interaction with the analyte. However, the derivation discussed above should still be valid.

4.3. Sensor response time

In the previous section, the sensitivity and the DL are deduced based on the assumption that the vapor molecules is fully adsorbed by the whole polymer layer and reaches equilibrium with the polymer. However, for rapid vapor detection and gas chromatography, the diffusion time for vapor molecules to reach the location in the polymer with the highest light intensity need to be taken into account in sensor development. Typically, the diffusion constant for vapor molecules is on the order of 10^-10–10^-12 cm² s^-1 [8,33]. Therefore, it takes tens of seconds for the detection signal to achieve its saturation value [8]. Sensitivity may have to be compromised for quick detection. For example, when the polymer thickness is reduced to 0.5 µm from 1 µm, the diffusion time will be shortened by 4 times, but in the meantime, the RI sensitivity presented in the previous section will drop to 200 nm/RIU (see Fig. 6(B)). This problem could be mitigated by using a high RI polymer. With the same 0.5 µm thickness, a RI sensitivity of nearly 600 nm/RIU is achieved (Fig. 9), provided that the diffusion constant remains unchanged. A polymer with a high partition coefficient may also be used for a higher vapor density in the polymer matrix.

4.4. Comparison of different ring resonator chemical vapor sensors

After discussing the simulation results for both exterior and interior coated ring resonators, it is worthwhile to evaluate the sensing performance of various ring resonator sensor configurations. The OFRR provides excellent fluidics for rapid gas detection while maintaining high Q-factors for sensitive detection [12,13]. It requires very low sample volume and quantity. In particular, the OFRR is highly compatible with GC technology with on-column detection capability [12]. However, a thin wall is needed for the low RI polymer coating, which may add difficulties in OFRR fabrication. Although the polymer ring resonator has the best RI sensitivity as the light is predominantly confined within the polymer, it may not have the optimal performance in terms of the DL due to the relatively low Q-factor, or in terms of the response time due to slow diffusion of molecules into the thick polymer layer, as discussed earlier. Bare microspheres and solid cylinders have very high Q-factors (>10⁶) and are easy to fabricate. Therefore, they provide a unique platform that allows us to adjust the sensor’s Q-factor, sensitivity, and response time for optimal sensing performance by varying the polymer coating thickness and RI.

5. Summary

We have performed detailed analysis of the chemical vapor sensing performance of two important ring resonator configurations where a vapor sensitive polymer layer is coated on the exterior or interior surface of the ring resonator. The main important findings are summarized as follows:

(1) In the outside coating case, the polymer layer of both low and high RI supports a potential well and when the polymer is sufficiently thick, a new polymer ring resonator forms. However, when the polymer is coated on the ring resonator inner surface, the sensing behavior is qualitatively different. The polymer mode can form only with the high RI polymer and it has a very high RI sensitivity when the polymer layer is sufficiently thick.

(2) The RI sensitivity depends on the mode order. For the outside coating case and the inside high RI coating case, the higher order mode has a higher RI sensitivity when the polymer is thin. The lower order mode takes over gradually when the polymer becomes thicker. Eventually, all modes reach their maximal sensitivities, which are nearly equal. Furthermore, oscillatory RI sensitivity is observed. In particular, the RI sensitivity can be nearly zero for the high RI inner coating case. In contrast, when the inner surface is coated with the low RI polymer, the higher order mode always has a higher RI sensitivity.

(3) While in the outside coating case, the sensitivity does not depend heavily on the ring resonator wall thickness, the ring resonator wall plays an important role in the inner coating case. For the inside low RI coating case, the RI sensitivity drops to zero when the wall is thick. For the inside high RI coating case, the RI sensitivity drops slightly when the wall thickness increases. However, when the wall becomes sufficiently thick, the wall mode and polymer mode become completely de-coupled. At this point, a new polymer ring resonator forms and has a high RI sensitivity. Note that although for inside high RI coating case, a very thick wall is preferred so that the polymer mode is not affected by the existence of the wall mode, the excessively thick wall may prevent the polymer mode from being excited through a tapered fiber or a waveguide in contact with the ring resonator outer surface [24]. How to efficiently excite the polymer mode will be an important topic for the future research.

(4) Polarization studies show that the b-mode has a slightly higher sensitivity than the a-mode. This is opposite to biosensors where the evanescent field outside the polymer is used for sensing.

(5) Thickness sensitivity studies show that the WGM shifts to a longer wavelength when the polymer layer expands. However, at certain regions the sensor becomes insensitive to the polymer thickness change, which results from the formation of bonding and anti-bonding states through the strong interaction between the polymer mode and the wall mode [23,24].

(6) Using the simulation results and the typical values for many vapor molecules, we have found that the ring resonator chemical vapor sensor is capable of detecting a RI change down to 10^-7 RIU, which corresponds to a vapor concentration on the order of 0.1 ppm. Additionally, analysis of polymer thickness change has resulted in a DL of chemical vapor on the order of 1 ppm.

The results listed above will provide an insight into the WGM interaction with vapor molecules and enable sensor optimization for various applications. Finally, our work will also have important applications in ring resonator based photonic molecules, which form via the polymer/wall mode interaction [23,24].

Acknowledgments

This work is sponsored by the National Science Foundation under Grant No. ECCS-0729903.

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Analysis of ring resonators for chemical vapor sensor development

Abstract

1. Introduction

2. Model

3. Results

3.1. Case I: polymer is coated on the outer surface of the ring resonator

3.1.1. Low-index polymer

3.1.2. High-index polymer

3.2. Case II: polymer is coated on the inner surface of the ring resonator

3.2.1. Low-index polymer

3.2.2. High-index polymer

4. Discussion

4.1. Sensitivity

4.2. Detection limit

4.3. Sensor response time

4.4. Comparison of different ring resonator chemical vapor sensors

5. Summary

Acknowledgments

References and links

Cited By

Figures (10)

Equations (7)

Optics Express