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Optical microcavity sensors using intensity detection open up the possibility to realize fully integrated high-performance sensing devices, which are significant for both fundamental study of molecular interaction and rapid disease diagnosis. Although the performance of microresonator-based sensors has been studied focusing on the resonance-tracking method, the situation can be much different for intensity-detection sensors. Here we conducted a systematically investigation on the noises sources in intensity detection scheme and their influences on key performance parameters, e.g., signal-to-noise ratio (SNR), limit-of-detection (LOD), and detection range, for various sensors configurations. Especially, the trade-off between SNR and LOD is identified and theoretically analyzed. With experiment noises taken into consideration, our work aims to provide design guidelines for integrated microresonator sensors with optimized performance.
© 2016 Optical Society of America
1. Introduction
Over the past decades, optical sensors based on microcavities have emerged as promising candidates in the chemical and biological information acquisition arena, enabling label-free detection without complex fluorescence tagging process and providing real-time quantification of the analyte. Together with high quality (Q) factors and miniaturized sizes, micro-resonator sensors have demonstrated significantly reduced limit of detection (LOD) down to small molecules [1–9], such as protein [3–6], DNA/microRNA [6–8], and virus [9]. Naturally, optical sensors with excellent sensitivity are continuously pursued to improve system LOD, which in turn renders the sensors susceptible to various noise sources, requiring better signal-to-noise ratio (SNR) of a sensing system. Tremendous research efforts have been devoted to achieving a higher device sensitivity, but the importance to identify and suppress system noises is often overlooked.
Signal acquisition method by tracking the resonance shift has been vastly utilized, which offers a large dynamic range and rich sensing information with a tunable frequency sweeping laser and a subsequent spectral data processing subsystem [2, 10]. Nevertheless, practically portable, on-site, and agile biochemical monitoring poses a challenge to developing a sensing system with reduced complexity and device size. In this sense, intensity-based detection requiring optical signal at a fixed wavelength in the sensing process greatly simplifies the sensing system [2, 10]. Along with the blooming development of on-chip semiconductor lasers and photodiodes as well as microfluidics, it is promising to realize a fully integrated sensing system using intensity-based detection [10]. Moreover, as compared to the resonance-tracking method, the intensity-detection scheme potentially shows a lower LOD [3], requiring more stringent noise control. However, previous discussions on sensor performance are mostly focused on the resonance-shift method [11–14], and there are few reports on performance analysis of intensity-detection-based sensors.
In this work, we systematically analyze the performance of microresonator-based sensors using intensity detection, with an emphasis on fully integrated sensing system. First, we modify the definitions of key parameters, i.e., sensitivity, LOD, and detection range, to specifically quantify the performance of an intensity-detection sensor. We then analyze the noise mechanisms in the whole system, and thermal noise control is of great significance in intensity-based sensing. Interestingly, there exists a trade-off between important figure-of-merits, SNR, and LOD, and the influence of noises on system SNR, LOD, and detection range are investigated for different microcavity configurations. We found that intensity noise is the dominant noise source for a low-Q cavity, while the performance of high-Q resonators is mainly limited by the thermal and spectral noises. Also, LOD begins to saturate for extremely high-Q cavities, and SNR continuously degrades. There is an optimal Q factor for a sensor with given configurations and system noises. Based on these analyses, guidelines for effective noise suppression and optical microcavity sensor design are provided.
2. Sensitivity, LOD, and detection dynamic range
The sensing system is schematically illustrated in Fig. 1(a). To be general, the optical sensor consists of a single microcavity immersed in a homogenous environment, without surface adsorption. The refractive index change in the sample (nsam) caused by the concentration variation changes the effective refractive index (neff) in the optical mode of the sensor, leading to a shift in its transmitivity spectrum (∆λ), as shown in Fig. 1. By fixing the input laser wavelength (λ0) and monitoring intensity variation (∆I) at the sensor output, changes in nsam could be quantified. The sensitivity (S) of the sensor by probing the intensity variation is thus defined as S = ∆I/∆nsam [15, 16]. Note that due to the Lorentzian lineshape of the resonance, the sensitivity should be considered as a function of wavelength, i.e., S(λ) = ∂I(λ)/∂nsam. The sensitivity can be decomposed into three parts as [17, 18]:
where S1 = ∂I/∂λ is equivalent to the slope, ∂t/∂λ, of intensity spectral response in Fig. 1(b) if normalized by input power, and t is resonator transmitivity. Significantly enhanced S1 can be obtained using high Q resonators or physical effects in coupled resonators, such as electromagnetically-induced-transparency or Fano effects [18–20]. S2 represents the resonance shift caused by the neff change. It is almost a constant for a narrow bandwidth in intensity-detection scheme. S3 quantifies the influence of sample refractive index on the effective mode index of the optical mode. This parameter is closely related to the waveguide materials and structures [21–23]. Normally, microcavity structures with more light extended to the sample have a larger S3. Various cross-section structures and optimization methods have been investigated to improve S3 [21–23]. In the sensing process, both S2 and S3 stay constant, so the nonlinear response of the sensor stems from the wavelength dependence of S1. In this work, we thereby mainly focus on the sensitivity characteristics contributed from S1. This feature is unique for intensity-detection sensing, since the sensitivity in the wavelength-tracking method is calculated as S2·S3.
Fig. 1 (a) Schematic of an optical microcavity sensing system using intensity detection. (b) Principle of refractive-index sensing by monitoring the intensity change at a fixed wavelength (λ0). (c) Zoom-in view of the effective spectral range (∆λDR) around the maximum device sensitivity point (S1max) used for sensing.
Quantifying the minimal analyte variation that could be reliably detected by the sensor, the LOD of a sensor originates from the signal uncertainty from both device components and the environment and is expressed as:
where σ is the noise-induced intensity variation in the intensity-tracking detection scheme. Here we consider σ to be the intensity uncertainty normalized to the light input, i.e., σ = δI/Iin = 1/SNR. Note that the SNR here is generalized, including not only conventional intensity noise in lasers and detectors but also equivalent intensity uncertainty converted from the spectral and thermal noises, as detailed later in Section 3.Another important performance metric for a sensor is the detection range (DR), which determines unsaturated response range of the sensor to the variation in the analyte. As mentioned earlier, S1 is a function of wavelength, which has a maximum (S1max) at a specific wavelength (λmax), as shown in Fig. 1(c). It is desirable to operate the optical sensor near λmax. Accordingly, one can define the effective working range of the sensor with S1 > η∙S1max, where η ∈ (0, 1), and here η = 0.5 in Fig. 1(c). The corresponding wavelength range (∆λDR) is related to the DR of the sensor in RIU as follows
Note that in intensity-detection scheme, there exists a strong trade-off between the DR and sensitivity, more precisely, S1, since increasing the slope of transmitivity spectrum leads to a reduced transmitivity linewidth.
3. Noise analysis
Imperfection of each system component may contribute to the overall noise, including (1) relative intensity noise (RIN), finite linewidth, and frequency fluctuation in the laser; (2) dark current noise, shot noise, and Johnson noise in the photodetector; (3) thermal-optical shift; (4) fiber vibration at the coupling region in the case of micro-sphere/disk/toroid in the sensor device; and (5) contact noise in the optical connections. These noise sources are mainly classified into three noise mechanisms, i.e., intensity, spectral, and thermal noises. It is straightforward that the intensity noise affects the reliably detected intensity signal, whereas the spectral and thermal noises can be converted to equivalent intensity noises. Note that, if considering a fully integrated sensing system, one can ignore noise sources (4) and (5).
3.1 Intensity noise
For intensity-based sensing using integrated laser and detector, the intensity noise mainly consists of the laser RIN and the dark current noise, shot noise, and Johnson noise in the detector. The instability of laser power is described by the RIN, , where SRIN(λ) is the normalized power spectral density and ∆f is the bandwidth of the sensor system usually limited by the detector bandwidth. The SRIN peaks at the oscillation relaxation frequency of the laser, far from which it is nearly frequency-independent. The oscillation relaxation peak of the RIN for a semiconductor laser is normally at high frequencies (in GHz), and in lower frequency region SRIN typically ranges from −110 to −160 dB/Hz [24, 25].
In a detector, the shot noise is caused by the statistical uncertainty in the photon arrival rate, and the dark current noise results from the random generation of carriers in the photodetector with no light input. The dark current noise is typically much smaller compared to the shot noise and can be neglected. The intensity uncertainty resulting from shot noise is dependent on the optical power received at the photodetector (Pdet) and is calculated from the shot noise current (ishot) [26] and responsivity of the detector (R) as , where e is the electronic charge and ∆f is the detector bandwidth. The Johnson noise [26], the thermal noise in the load resistance of the detector (RL), can be converted to the optical intensity uncertainty as , where kB is the Boltzmann constant and T is the absolute temperature in Kelvin. The Johnson noise also depends on the light power received at the photodetector.
Here we neglect noise sources (4) and (5), and only consider the optical losses due to connections between on-chip devices. The power measured at the optical detector is Pdet = αPout = α2tPlas, where α is the transmission coefficient from the laser to the cavity as well as from the cavity to the detector, and t is the transmitivity of the resonator.
The intensity uncertainty (σint) is therein calculated as
Since all three intensity noise components depend on the detector bandwidth, it would be beneficial to use a detector with relatively small bandwidth, i.e., a low-speed detector, to suppress the noise. Fortunately, optical sensing based on intensity monitoring has no stringent requirement on the response speed of the detector, and the usage of detectors with bandwidth < GHz also avoids the RIN peak at the laser source. The detector bandwidth can be reduced by using a larger RL, which helps suppress the Johnson noise as well.The dependence of intensity noise on the power received at the detector is analyzed in Fig. 2, with laser and detector parameters listed in the figure caption considered. As shown in Fig. 2, the noise components, i.e., RIN, shot noise, and Johnson noise, vary with the Pdet at different rates in a logarithmic scale, which leads to varied intensity uncertainty features. As an example, when SRIN is large (SRIN = −110 dB/Hz), the intensity noise is dominated by the RIN and thus power independent, as shown in Fig. 2(a). In contrast, if the laser SRIN is reduced to −160 dB/Hz, the intensity noise becomes power-dependent, which is dominated by the Johnson noise, shot noise, and RIN at low, middle, and high power levels, respectively, as shown in Fig. 2(b). The intensity noise for SRIN = −160 dB/Hz is also much lower than that for SRIN = −110 dB/Hz with parameters considered here.
Fig. 2 The influence of optical power on the intensity uncertainty (σint) and its components. Pdet is the power received at the detector. (a) σint is dominated by RIN and becomes power-independent for SRIN = −110 dB/Hz. (b) For SRIN = −160 dB/Hz, σint is dominated by different noise sources, depending on Pdet. Other parameters are RL = 1 kΩ, T = 300 K, R = 0.9 (Si photodetector at the wavelength of 1.55 µm), and ∆f = 100 MHz.
3.2 Spectral noise
In an intensity-detection sensor, the finite linewidth and frequency instability in a real laser lead to a spectral uncertainty in the working wavelength, thus resulting in an uncertainty in the detected intensity signal. Integrated hybrid microdisk laser has demonstrated linewidth of several MHz [27], and linewidth narrowing technique promises to reduce the semiconductor laser linewidth to the order of kHz [28], making the laser linewidth noise negligible compared to its frequency fluctuation (typically ranging from 1 fm to tens of fm [12]). Note that the spectral noise is quite small in the intensity-detection sensing, in contrast with the wavelength-tracking scheme, which needs a tunable laser with frequency inaccuracy of 20 pm typically [2, 6, 13]. The intensity uncertainty (σspec) caused by spectral noise (δλ) is
3.3 Thermal noise
Temperature fluctuation leads to an unwanted spectrum shift through the thermo-optic effect of optical materials, resulting in a false-active signal at the photodetector. The thermally induced equivalent intensity uncertainty is calculated as
where β is the thermo-optic coefficient of the waveguide material and δT is the temperature uncertainty.Thermal noise can severely deteriorate the system SNR even in a microcavity with moderate Q factor for intensity-detection sensing. Here we consider commonly used microcavity configurations, e.g., Si and Si3N4 microrings and SiO2 microtoroids, to examine the impact of thermal noise. Table 1 lists the waveguide structure parameters and analysis results. S2 is calculated from S2 = λ/neff, with λ = 1.55 μm and neff for each structure obtained from the Wave Optics Module in COMSOL Multiphysics®, a finite-element method solver. S1 is obtained from transfer spectrum of a critically coupled microcavity using coupled mode theory. From Equ. 6, σther and SNRther can be obtained.
Table 1. Microcavity configurations and SNR limited by thermal noise (SNRther).
From Table 1, the SNR of a sensing system with uncontrolled thermal noise is very poor for all three waveguide configurations even with a small Q factor. The SNR further degrades, if with a higher Q factor or a temperature fluctuation of > 1 K. Therefore, the thermal noise should be carefully suppressed. One direct way is to actively control the temperature fluctuation in the sensing system at the expense of increased system complexity. Demonstrated heat pump can assure a 10 mK thermal drift [31], which improves the SNRs in Table 1 by two orders. Another commonly adopted method is to utilize a dummy reference sensor together with the active sensor and differentiate the signals [7, 13]. The effectiveness of this solution is degraded by the common-mode signal inconsistency between the active and the reference sensors caused by unavoidable fabrication errors. The thermally induced uncertainty can also be almost eliminated through athermal device design [4, 17, 32], where materials of opposite thermo-optic coefficients are exploited to achieve thermal balance, i.e., the effective thermo-optic coefficient of an optical mode in the proximity of zero. This method promises to reduce the effective thermo-optic coefficient by more than 2 orders without adding much fabrication difficulty or device complexity [17]. In practice, different suppression methods for the thermal noise can be employed simultaneously to achieve further enhanced sensing performance.
4. SNR and LOD analysis
The performance of an optical sensor system is evaluated by both the SNR and the LOD. In general, a high-performance optical sensor should have a low LOD and a reasonably large SNR. Seemingly, they can be simultaneously met, according to Eq. (2), i.e., LOD = 1/(SNR∙S). However, this holds only if the sensitivity of the sensor is a constant. In fact, the connection between the LOD and the SNR is not very intuitive, since they both are dependent on the sensor sensitivity. Here we discuss the trade-off between SNR and LOD and the influence of cavity configurations on the sensor performance.
4.1 The trade-off between SNR and LOD
We first discuss the SNR (or the overall uncertainty, σ) and LOD in the full detection range of a single-cavity sensor. From Eqs. (4)-(6), the overall uncertainty of the microcavity-based sensing system is
Since S1 varies within ∆λDR, σspec and σther also become wavelength-dependent and reach their maxima at S1max. As discussed in Section 3.1, σint can be either power dependent or independent, determined by the laser RIN. If σint is power independent, it is also wavelength independent, and the overall σ is largest at S1max. Otherwise, the maximum of overall σ appears near S1max, on the low-transmitivity side, due to the power dependence of σint. The system SNR = 1/σ is worst at that point. In other words, operating the laser at a wavelength around the largest S1 point typically means a reduced SNR (One should make sure to produce acceptable SNR when reaching S1max).Then, to evaluate LOD, one needs to plug in the sensor sensitivity as well.
where LODint, LODspec, and LODther are LOD components resulting from intensity noise, spectral noise, and thermal noise. Since both LODspec and LODther are wavelength independent, the optical sensor reaches its smallest LOD around S1max, corresponding to the minimum of LODint, although σ (or SNR) is worst at that point. Therefore, the reduced SNR around S1max does not mean a degraded LOD.LODint for two optical microcavity sensors with different Q factors is analyzed in Fig. 3. Both microcavities are set to be critically coupled, and the maximum sensitivity can be thus expressed using cavity Q, , where λr is the resonance wavelength. Here we use the left part of the spectral lineshape around S1max point for optical sensing, as shown by the solid lines in Fig. 3(a).
Fig. 3 (a) Transmitivity spectra for optical microcavity with Q = 105 and 106. The effective parts of spectra used for sensing are indicated by the solid lines. (b) Corresponding LODint in a full spectral detection region, where λmax is the wavelength corresponding to S1max. LODint is obtained in two situations, where intensity noises are independent (SRIN = −110 dB/Hz) and dependent (SRIN = −160 dB/Hz) on the transmitted power, respectively. The minima of the LODint are indicated by the solid dotes. Plas = 4 mW and α = 3 dB are considered.
As shown in Fig. 3(b), LODint in the cavity with Q = 106 is about one order lower than that with Q = 105 for both power independent (SRIN = −110 dB/Hz) and dependent (SRIN = −160 dB/Hz) cases, respectively. However, the spectral detection range for a high-Q cavity is also reduced, compared to a low-Q cavity as a cost of LOD improvement. When intensity noise is power independent (SRIN = −110 dB/Hz), as labeled in Fig. 3(b), the LODint has a minimum at S1max. For intensity noise with SRIN = −160 dB/Hz, LODint becomes power dependent, and the minima shift to a shorter wavelength, where the transmitivity is larger than that at S1max. In this case, the LODint becomes better at the shorter wavelength edge of detection region due to the increased power. Therefore, when the intensity noise is power dependent, it is more desirable to use the high-transmitivity spectral region away from λmax for a lower LODint and thus the lower overall LOD.
4.2 The role of cavity Q factor in different microcavities
The configuration of microcavity has a significant influence on the system SNR and LOD, due to the difference in materials, structures, and Q factors. In this section, we analyze and compare the commonly used optical microcavities, e.g., Si and Si3N4 microrings and SiO2 microtoroids, with increasingly higher cavity Q-factors. For simplicity without losing generality, the microcavities are set critically coupled only to correlate S1max with Q [33].
Note that, as the Q factor of the cavity increases, the optical nonlinear effect becomes more significant because of the large on-resonance power enhancement. The nonlinear Kerr effect gives rise to a red-shift of the transmitivity spectrum, resulting in a determinate error in the intensity signal. The predictable nonlinear error is intrinsically different from the uncertainty caused by random noises discussed earlier. In Fig. 4, we analyze the nonlinearity-induced normalized intensity change (ΔINL) and corresponding ambient refractive index change (ΔRINL), together with SNR and LOD caused by random noises.
Fig. 4 (a) 1/SNR or intensity uncertainty (σ) and (b) LOD for Si3N4 microrings with varied cavity Q factors.
First, we consider a critically coupled Si3N4 microring cavity with a moderate cavity Q-factor and other parameters shown in Table 1. From the analysis above, the main limiting factors of sensor performance are intensity noise, thermal noise and spectral noise, and depending on the device choices in practice, we evaluate the following specific cases:
- • Case 1: intensity noise consisting of SRIN = −110 dB/Hz, thermal noise of δT = 0.1 K, and spectral noise of δλ = 8 fm
- • Case 2: intensity noise consisting of SRIN = −110 dB/Hz, thermal noise of δT = 0.01K, and spectral noise of δλ = 8 fm
- • Case 3: intensity noise consisting of SRIN = −160 dB/Hz, thermal noise of δT = 0.01K, and spectral noise of δλ = 8 fm
Note that in the cases above we already use a designed athermal structure with a reduced thermo-optic coefficient of β = 4 × 10−7 RIU/K [17, 29], which is 2-order smaller than that of the Si3N4 material. Laser output power and cavity’s insertion loss are set to be Plas = 4 mW and α = 3 dB. The nonlinear shift in the Si3N4 microring is calculated, with a nonlinear index n2 = 2.4 × 10−19 m2/W [34] and the effective mode area obtained from COMSOL Multiphysics®. The equivalent intensity change ΔINL and ambient refractive index change ΔRINL are also shown in Fig. 4.
As shown in Fig. 4(a), σ in Case 1 stays almost invariant at 10−2 (SNR = 20 dB) for Q < 2 × 105, limited by the intensity noise. σ begins to degrade for higher Q factors and is restricted by the thermal noise. For an optical cavity with high Q-factor of 107, σ reaches 0.33, corresponding to a poor SNR of 4.8 dB. For Case 2 (red line), σ is the same as in Case 1 for low-Q cavities, and then starts to increase from Q = 106. Because of the better thermal control of δT = 0.01 K, σ is reduced by 4.5 times compared to Case 1 in the high-Q region, and spectral noise becomes the dominant noise sources instead. When the intensity noise is suppressed to SRIN = −160 dB/Hz in Case 3 (yellow line), σ in the low-Q region is reduced to 3 × 10−4, and spectral noise quickly becomes dominant for Q > 8 × 104.
On the other hand, there is a linear improvement in LOD as the Q factor increases for Case 1 (blue line), as shown in Fig. 4(b), because the LOD in low-Q regions is dominated by the intensity noise, which is inversely proportional to the cavity Q or sensitivity. The LOD becomes saturated and limited to 1.9 × 10−7 RIU when the Q factor continues increasing, dominated by the thermal noise for Q > 106. With improved thermal control in Case 2 (red line), the saturated LOD becomes 4.2 × 10−8 RIU, which is 4.5 times enhancement to that in Case 1, and the LOD begins to be limited by the spectral noise instead from a higher cavity Q. For Case 3 (yellow line), LOD in the low-Q region is significantly reduced by more than two orders as compared to Cases 1 and 2 due to smaller intensity noise. Also, the LOD is quickly saturated by the spectral noise with increasing Q factor for Q > 2 × 105. In all three cases, the saturated LODs with noise conditions considered here are among the best results achieved theoretically or experimentally [3, 5, 17–19]. It is important to note that, although exhibiting a low LOD, the extremely high-Q optical sensor shows a poor SNR.
DR is another important evaluator of on-chip sensors, especially for the ones with a high Q factor. From Eqs. (2) and (3), one can find
where ∆IDR = ∆λDRS1 is the transmitivity variation in the DR, and it is a constant determined by η in Fig. 1. Here it is close to unity with η = 0.5 for critically coupled microcavities. In fact, SNR relates DR to LOD. The poor SNR ≈1 for a sensor with Q = 1 × 107 corresponds to a situation that the LOD becomes comparable with the DR in Fig. 4(b). In this sense, for given experiment conditions with certain system noises, one has to wisely choose a proper cavity Q factor to make DR sufficiently larger than LOD.Although predictable, both ΔINL and ΔRINL increase severely with cavity Q. In the low-Q region, the nonlinear errors are small compared to the random noises, while they become comparable or larger than the random noises for high-Q cavities. These large false-active errors cannot be diminished through repeated measurements. ΔINL and ΔRINL increase to be larger than unity and even exceed the DR for a cavity of Q ~107, respectively, making the sensor useless. Thus, the nonlinear errors should be taken seriously when high-Q cavities are used. Besides using microcavities with a smaller Q factor, one can reduce nonlinear errors by lowering the input laser power.
Other commonly used cavities include the Si microrings and SiO2 microtoroids. Because of the large material loss, Si microrings usually have a smaller Q factor than Si3N4 resonators. On the other hand, silica microtoroids can have an ultra-high Q factor of > 107 [4, 35]. In Fig. 5, Si rings and SiO2 microtoroids with configurations detailed in Table 1 are analyzed. The microcavity cross-sections are supposed to be designed athermal with reduced thermo-optic coefficients of β = 1.8 × 10−6 RIU/K and 1 × 10−7 RIU/K for Si and SiO2 microcavities, respectively, which are two orders smaller than the corresponding material thermo-optic coefficients [30]. The nonlinear Kerr index of Si material (n2 = 2.4 × 10−18 m2/W) is one order larger than Si3N4 and two orders larger than SiO2 (n2 = 3 × 10−20 m2/W) [36, 37]. The noise parameters considered here are similar to those in Fig. 4.
Fig. 5 1/SNR or intensity signal uncertainty (σ) and LOD for optical microcavities with varied cavity Q factors. (a) and (b) are for Si microrings, while (c) and (d) are for SiO2 microtoroids. The dash lines mark two cavity configurations used in Fig. 6 for laser power tuning illustrations.
Since the Q factors of Si rings are usually < 105, the performance of Si-based optical sensors is mainly limited by the intensity noises, as shown in Figs. 5(a) and 5(b). Compared with Si3N4 microrings, the nonlinear errors in Si microrings are much larger and easily become dominant, resulting from both a larger material nonlinear coefficient and a smaller effective mode area of the Si waveguide. Lowering Plas helps suppress ΔRINL at the expense of increased LOD, if the intensity noise is power dependent, e.g., in the case of LOD3 with SRIN = −160 dB/Hz, as shown in Fig. 6(a). In contrast, LOD1 and LOD2 dominated by the power-independent RIN (SRIN = −110 dB/Hz) are not affected by Plas.
Fig. 6 The sensor performance can be optimized through balancing the LOD and RINL by tuning the laser output power (Plas). Two examples are presented: (a) Si microring cavity with Q factor of 5 × 104 and (b) SiO2 microtoroid cavity with Q factor of 5 × 107. Plas values used in Fig. 5 are labeled by the dash lines.
For high-Q SiO2 microtoroid cavities, the SNR and LOD are limited by the spectral or thermal noise [Figs. 5(c) and 5(d)]. The LOD becomes saturated with Q factors increasing, while the SNR continuously degrades. Thus, it should be noted that high-Q microtoroids are advantageous only with well-controlled spectral and thermal noises. The small material nonlinear coefficient of SiO2 and large effective mode area of microtoroid cross-section lead to a reduced nonlinear error by about one order as compared to Si3N4 microring with similar Q factors, which means that the microtoroid-based sensors can work with less concern about nonlinearity when operated in the high-Q region. Nevertheless, the nonlinear error can still become problematic for extremely high-Q microtoroids, e.g., 107~108 in this study, where ΔINL is around unity [Fig. 5(c)] and ΔRINL becomes comparable or even larger than the sensor DR [Fig. 5(d)]. Again, the nonlinear noise can be suppressed through reducing Plas, as shown in Fig. 6(b). Unlike the case in Fig. 6(a), all the LOD1, LOD2, and LOD3 stay invariant with Plas, because the dominant noise sources for high-Q microtoroids are power-independent spectral or thermal noise.
Summarizing results obtained from Figs. 4-6, we note that the SNR and LOD are generally limited by the intensity noise for low-Q cavities, such as most Si microrings and some Si3N4 microrings, and by the spectral or thermal noise for high-Q ones like the SiO2 microtoroids. Identification of dominant noise sources provides the guidelines for sensor performance enhancement. For example, by lowering intensity noises, both the SNR and the LOD of sensors are enhanced for low-Q cavities. On the other hand, these results also offer insight for cavity Q selection to maximize the sensor performance for given noise conditions. It is obvious that poor LOD is obtained in low-Q cavities, but using extremely high-Q cavity can result in poor SNR, small DR, and unacceptable nonlinear errors. Therefore, the desirable cavity Q factors are typically the ones in-between, i.e., those before LOD starts to saturate, such as Q = 2 × 106 for silica microtoroid configuration 1 in Figs. 5(c) and 5(d). The exact Q factors are dependent on the cavity configurations and noise values. These cavities offer similar sensing LOD but maximized SNR and smaller nonlinearity error as compared to extremely high-Q cavities. In addition, tuning the input power offers a simple but effective method to optimize the sensor performance through balancing the nonlinear error and random noises.
5. Conclusion
In this work, we present a comprehensive study on the sensor performance of optical microcavity sensors in intensity detection scheme. Main noise mechanisms in the sensing system are analyzed, and their influences on the sensor performance, such as SNR, LOD and DR, are investigated. We found that low-Q cavities are mainly limited by the intensity noise, while high-Q ones by spectral or thermal noise for high-Q cavities. The nonlinearity error of the optical microcavity is also considered and compared with random noises. Finally, design principles for the sensing system concerning input laser power, microcavity structure, and cavity Q factor are provided for optimized sensor performances.
Funding
National High Technology Research and Development Program of China (863 Program) (2015AA042603); the 111 Project (B07014).
References and links
1. F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: Label-free detection down to single molecules,” Nat. Methods 5(7), 591–596 (2008). [CrossRef] [PubMed]
2. M. S. Luchansky and R. C. Bailey, “High-Q optical sensors for chemical and biological analysis,” Anal. Chem. 84(2), 793–821 (2012). [CrossRef] [PubMed]
3. C.-Y. Chao, W. Fung, and L. J. Guo, “Polymer microring resonators for biochemical sensing applications,” IEEE J. Sel. Top. Quantum Electron. 12(1), 134–142 (2006). [CrossRef]
4. A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317(5839), 783–787 (2007). [CrossRef] [PubMed]
5. C. A. Barrios, M. J. Bañuls, V. González-Pedro, K. B. Gylfason, B. Sánchez, A. Griol, A. Maquieira, H. Sohlström, M. Holgado, and R. Casquel, “Label-free optical biosensing with slot-waveguides,” Opt. Lett. 33(7), 708–710 (2008). [CrossRef] [PubMed]
6. M. Iqbal, M. A. Gleeson, B. Spaugh, F. Tybor, W. G. Gunn, M. Hochberg, T. Baehr-Jones, R. C. Bailey, and L. C. Gunn, “Label-free biosensor arrays based on silicon ring resonators and high-speed optical scanning instrumentation,” IEEE J. Sel. Top. Quantum Electron. 16(3), 654–661 (2010). [CrossRef]
7. A. Ramachandran, S. Wang, J. Clarke, S. J. Ja, D. Goad, L. Wald, E. M. Flood, E. Knobbe, J. V. Hryniewicz, S. T. Chu, D. Gill, W. Chen, O. King, and B. E. Little, “A universal biosensing platform based on optical micro-ring resonators,” Biosens. Bioelectron. 23(7), 939–944 (2008). [CrossRef] [PubMed]
8. M. D. Baaske, M. R. Foreman, and F. Vollmer, “Single-molecule nucleic acid interactions monitored on a label-free microcavity biosensor platform,” Nat. Nanotechnol. 9(11), 933–939 (2014). [CrossRef] [PubMed]
9. L. He, Ş. K. Özdemir, J. Zhu, W. Kim, and L. Yang, “Detecting single viruses and nanoparticles using whispering gallery microlasers,” Nat. Nanotechnol. 6(7), 428–432 (2011). [CrossRef] [PubMed]
10. N. Jokerst, M. Royal, S. Palit, L. Luan, S. Dhar, and T. Tyler, “Chip scale integrated microresonator sensing systems,” J. Biophotonics 2(4), 212–226 (2009). [CrossRef] [PubMed]
11. I. M. White and X. Fan, “On the performance quantification of resonant refractive index sensors,” Opt. Express 16(2), 1020–1028 (2008). [CrossRef] [PubMed]
12. M. I. Cheema, C. Shi, A. M. Armani, and A. G. Kirk, “Optimizing the signal to noise ratio of microcavity sensors,” IEEE Photonics Technol. Lett. 26(20), 2023–2026 (2014). [CrossRef]
13. F. Ghasemi, M. Chamanzar, A. A. Eftekhar, and A. Adibi, “An efficient technique for the reduction of wavelength noise in resonance-based integrated photonic sensors,” Analyst (Lond.) 139(22), 5901–5910 (2014). [CrossRef] [PubMed]
14. M. R. Foreman, W. L. Jin, and F. Vollmer, “Optimizing detection limits in whispering gallery mode biosensing,” Opt. Express 22(5), 5491–5511 (2014). [CrossRef] [PubMed]
15. C. Y. Chao and L. J. Guo, “Design and optimization of microring resonators in biochemical sensing applications,” J. Lightwave Technol. 24(3), 1395–1402 (2006). [CrossRef]
16. Z. Xia, Y. Chen, and Z. Zhou, “Dual waveguide coupled microring resonator sensor based on intensity detection,” IEEE J. Quantum Electron. 44(1), 100–107 (2008). [CrossRef]
17. X. Zhou, L. Zhang, A. M. Armani, D. Zhang, X. Duan, J. Liu, H. Zhang, and W. Pang, “On-chip biological and chemical sensing with reversed fano lineshape enabled by embedded microring resonators,” IEEE J. Sel. Top. Quantum Electron. 20(3), 35–44 (2014). [CrossRef]
18. X. Zhou, L. Zhang, A. M. Armani, J. Liu, X. Duan, D. Zhang, H. Zhang, and W. Pang, “An integrated photonic gas sensor enhanced by optimized Fano effects in coupled microring resonators with an athermal waveguide,” J. Lightwave Technol. 33(22), 4521–4530 (2015). [CrossRef]
19. H. Yi, D. S. Citrin, and Z. Zhou, “Highly sensitive silicon microring sensor with sharp asymmetrical resonance,” Opt. Express 18(3), 2967–2972 (2010). [CrossRef] [PubMed]
20. X. Zhou, L. Zhang, W. Pang, H. Zhang, Q. Yang, and D. Zhang, “Phase characteristics of an electromagnetically induced transparency analogue in coupled resonant systems,” New J. Phys. 15(10), 103033 (2013). [CrossRef]
21. A. Densmore, D. X. Xu, P. Waldron, S. Janz, P. Cheben, J. Lapointe, A. Delâge, B. Lamontagne, J. H. Schmid, and E. Post, “A silicon-on-insulator photonic wire based evanescent field sensor,” IEEE Photonics Technol. Lett. 18(23), 2520–2522 (2006). [CrossRef]
22. F. Dell’Olio and V. M. Passaro, “Optical sensing by optimized silicon slot waveguides,” Opt. Express 15(8), 4977–4993 (2007). [CrossRef] [PubMed]
23. Y. F. Xiao, C. L. Zou, B. B. Li, Y. Li, C. H. Dong, Z. F. Han, and Q. Gong, “High-Q exterior whispering-gallery modes in a metal-coated microresonator,” Phys. Rev. Lett. 105(15), 153902 (2010). [CrossRef] [PubMed]
24. C. F. Abari, A. T. Pedersen, and J. Mann, “An all-fiber image-reject homodyne coherent Doppler wind lidar,” Opt. Express 22(21), 25880–25894 (2014). [CrossRef] [PubMed]
25. G. Yabre, H. de Waardt, H. Van den Boom, and G. D. Khoe, “Noise characteristics of single-mode semiconductor lasers under external light injection,” IEEE J. Quantum Electron. 36(3), 385–393 (2000). [CrossRef]
26. B. E. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991).
27. G. Roelkens, L. Liu, D. Liang, R. Jones, A. Fang, B. Koch, and J. Bowers, “III-V/silicon photonics for on-chip and intra-chip optical interconnects,” Laser Photonics Rev. 4(6), 751–779 (2010). [CrossRef]
28. F. Aflatouni and H. Hashemi, “Wideband tunable laser phase noise reduction using single sideband modulation in an electro-optical feed-forward scheme,” Opt. Lett. 37(2), 196–198 (2012). [CrossRef] [PubMed]
29. F. Qiu, A. M. Spring, F. Yu, and S. Yokoyama, “Complementary metal–oxide–semiconductor compatible athermal silicon nitride/titanium dioxide hybrid micro-ring resonators,” Appl. Phys. Lett. 102(5), 051106 (2013). [CrossRef]
30. B. Guha, J. Cardenas, and M. Lipson, “Athermal silicon microring resonators with titanium oxide cladding,” Opt. Express 21(22), 26557–26563 (2013). [CrossRef] [PubMed]
31. C. Ciminelli, C. M. Campanella, F. Dell’Olio, C. E. Campanella, and M. N. Armenise, “Label-free optical resonant sensors for biochemical applications,” Prog. Quantum Electron. 37(2), 51–107 (2013). [CrossRef]
32. L. He, Y. F. Xiao, C. Dong, J. Zhu, V. Gaddam, and L. Yang, “Compensation of thermal refraction effect in high-Q toroidal microresonator by polydimethylsiloxane coating,” Appl. Phys. Lett. 93(20), 201102 (2008). [CrossRef]
33. M. Sumetsky, “Optimization of optical ring resonator devices for sensing applications,” Opt. Lett. 32(17), 2577–2579 (2007). [CrossRef] [PubMed]
34. K. Ikeda, R. E. Saperstein, N. Alic, and Y. Fainman, “Thermal and Kerr nonlinear properties of plasma-deposited silicon nitride/ silicon dioxide waveguides,” Opt. Express 16(17), 12987–12994 (2008). [CrossRef] [PubMed]
35. X. Zhang, H. S. Choi, and A. M. Armani, “Ultimate quality factor of silica microtoroid resonant cavities,” Appl. Phys. Lett. 96(15), 153304 (2010). [CrossRef]
36. Q. Lin, J. Zhang, G. Piredda, R. W. Boyd, P. M. Fauchet, and G. P. Agrawal, “Dispersion of silicon nonlinearities in the near infrared region,” Appl. Phys. Lett. 91(2), 21111 (2007). [CrossRef]
37. R. H. Stolen and C. Lin, “Self-phase-modulation in silica optical fibers,” Phys. Rev. A 17(4), 1448–1453 (1978). [CrossRef]
