Abstract

A digital optical sensor based on two cascaded rings with different free spectral ranges (FSRs) is proposed. Because of their different FSRs, the major peak of the spectral response from the output port shifts digitally when the effective refractive index of ring #1 changes. And the shift of the major peak is equal to multiple FSRs of ring #2. Since it is easy to design a ring with a FSR of nanometers, the present digital optical sensor shows an ultra-high sensitivity (at the order of 105 nm/RIU) which is over two orders higher than that of a regular single-ring sensor. By using the present digital optical sensor, it becomes convenient to use an integrated optical micro-spectrometer (even with a low resolution) to monitor the peak shift of the spectral response. Therefore, it is promising to realize a low-cost and portable highly-sensitive optical sensor system on a single chip.

©2009 Optical Society of America

1. Introduction

Recently the demands of low-cost, highly sensitive and ultra-compact optical sensors increase rapidly for many areas such as biological, environmental and chemical detections [17]. People have developed various integrated optical sensors based on different structures and mechanisms, e.g., Mach-Zehnder interferometers (MZI) [1], surface plasmon sensors [2], microcavities [37], etc. Among them, a high-Q optical microcavity (including microring/microdisk [37]) is becoming one of the most attractive candidates because of the ultra-compact size, high-sensitivity, and easy realization of a sensor array.

For a microring sensor, when the concentration of the target material covering on the surface changes, the effective refractive index of the microring waveguide will change and consequently the resonant wavelength of the microring will shift. In order to monitor the change of the refractive index (or the concentration), one simple way for sensing is to measure the intensity change for a fixed wavelength. In this way, it is possible to have a high detect limit by using a high-Q ring resonator, which is usually obtained by minimizing the intrinsic loss and choosing a small coupling coefficient. However, the measurement range is very small because the response approaches zeros very fast as the index-changes. An alternative way for sensing is to measure the shift of the resonance wavelength [4]. In order to measure a small wavelength shift, a regular way is using the combination of a photodetector and a high-precision tunable laser, which is usually very expensive. It is possible to reduce the cost by using a low-cost DFB telecom laser that can be tuned with high resolution using the gain input. However, the tunability range is limited usually. An alternative way to measure the spectral response is using an optical spectrum analyzer (OSA) with a very high resolution. For example, in order to monitor a small refractive index-change of 1 × 10−5, the OSA should have a resolution as high as about 5 pm. Currently it is still not easy to achieve such a high-solution OSA. Besides, a high-solution OSA is very expensive and cumbersome. It is not convenient for the situation when a low-cost and portable highly-sensitive optical sensing system is required.

In this paper, we propose a digital optical sensor based on two cascaded rings with different free spectral ranges (FSRs). One of the two rings is covered by an up-cladding, and the up-cladding on the other ring is removed to form a sample reservoir. Due to their different FSRs, the output port will have a spectral response with a major peak and some minor peaks. When the refractive index increases, the major peak shifts discretely (or digitally) and the shift of the major peak is equal to multiple FSRs of the ring with the up-cladding. This is so-called vernier effect, which has been used for realizing tunable filter [8], lasers [9], etc. In this way, we could have an optical sensing with an ultra-high sensitivity which is many times higher than that of a single-ring sensor. Furthermore, since the FSR is usually at the order of nanometer, the present digital optical sensor makes it convenient to use an integrated-type optical micro-spectrometer (even with a low resolution at the order of nm) to monitor the major-peak shift of the spectral response. For example, one could use the micro-spectrometer based on an arrayed-waveguide grating (AWG) [10] combining with a photodetector array. Therefore, it becomes promising to realize a low-cost and portable optical sensor system with a highly-sensitivity on a single chip.

2. Structure and principle

Figure 1 shows the schematic configuration of the present digital optical sensor, which includes two cascaded rings, i.e., ring #1 and ring #2. These two rings have a common bus waveguide, which cascades these two rings. These two rings have different FSRs, which could be realized by choosing different radii (R 1 and R 2) for ring #1 and ring #2. In the present optical sensor, we choose R 1<R 2 and consequently one has ∆λFSR1>∆λFSR2. Because of their different FSRs, the output port will have a spectral response with major peaks locating at the common resonant wavelengths of these two cascaded rings.

 figure: Fig. 1

Fig. 1 The schematic configuration of the present digital optical sensor based on cascaded rings; (a) the top view; (b) the 3D view [in order to see the structure clearly, we separate the cladding from the substrate only for the view].

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The whole structure is covered by using an up-cladding except the region of ring #2, where the up-cladding is removed to form a sample reservoir. When the refractive index of the sample in the reservoir changes, the resonant wavelength of ring #2 changes accordingly, i.e., Δλ 2 = λ 2n eff/n eff), where n eff is the effective index of the fundamental modes in ring #2, Δn eff is the change of the effective index n eff, Δλ 2 is the shift of the resonant wavelength λ 2 correspondingly. Because ring #1 is covered by the up-cladding, the resonant wavelengths are unchanged.

In order to describe the principle of the present digital optical sensor, we show the frequency responses of ring #1 and ring #2 in Fig. 2(a) and 2(b), respectively. Both ring #1 and ring #2 have a series of resonant wavelengths λ1( i ) and λ2( j ). When the i-th resonance wavelength λ1( i ) of ring #1 is coincided with the j-th resonance wavelength λ2( i ) of ring #2, one has a common resonance wavelength λc( i ) as shown in Fig. 2(c). At these common resonance wavelengths λc( i ), one has a major peak which has a maximal amplitude. And the separation between the adjacent common resonance wavelengths is determined by the difference between the FSRs of ring #1 and ring #2.

 figure: Fig. 2

Fig. 2 The schematic spectral responses for the cascaded-rings.

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When the refractive index of the sample changes slightly (∆n>0), the resonant wavelength of ring #2 shifts and the resonant wavelengths λ1( i ) and λ2( j ) become separated while the adjacent resonance wavelengths λ1( i +1) and λ2( j +1) become close. Therefore, the amplitude of the major peak at around λ = λ1( i ) decreases while the amplitude of the adjacent minor peak at around λ1( i +1) = λ1( i ) + ∆λFSR1 increases. The maximal peak of the output response still locates at the position of λ = λ1( i ) when the index-change ∆n eff<∆n eff0/2, where

Δneff0=neff(ΔλFSR1ΔλFSR2)/λ1(i).

When the refractive index of the sample increases further, i.e., ∆n eff>∆n eff0/2, the major peak moves to the position of λ = λ1( i +1). When the change of the effective index ∆n eff = ∆n eff0, the adjacent resonant wavelengths λ1( i +1) and λ2( j +1) become coincided and the common resonant wavelength jumps to the wavelength λ1( i +1). Consequently the amplitude of the major peak is close to 1, as shown by the dotted curve in Fig. 2(c). When the refractive index of the sample increases further, the major peak will jump to the next resonant wavelength of ring #1. Therefore, as the refractive index increases, the wavelength λmax corresponding to the major peak shifts discretely (or digitally). In such a digital way, the shift of the wavelength λmax is equal to multiple FSRs of ring #1, i.e., ∆λmax = i∆λFSR1, as the refractive index increases.

In this way, the optical sensor has an ultra-high sensitivity S which is given by

S=ΔλFSR1/Δneff0=(λ1(i)/neff)[ΔλFSR1/(ΔλFSR1ΔλFSR2)]=S0M.
where M≡∆λFSR1/(∆λFSR1–∆λFSR2) and S 0≡∆λ/∆n eff = λ1( i )/n eff (here S 0 is actually the sensitivity of a single ring). From this equation, one sees the sensitivity of the present optical sensor based on cascaded-rings is M times higher than that of a single-ring sensor. And the detect limit (i.e., the minimal measurable index-change) of the present optical sensor is ∆n eff0 given by Eq. (1). When a higher detect limit is desired, one should choose a small difference ∆λFSR1–∆λFSR2 between the FSRs of the two rings. The difference ∆λFSR1–∆λFSR2 also determines the FSR of the cascaded-ring by
ΔλFSR=(M1)ΔλFSR1.
The measurement range of the present sensor is then given by ∆n max = ∆λFSR/S.

Furthermore, the FSR-difference ∆λFSR1–∆λFSR2 should be also chosen appropriately according to the resonance linewidth (i.e., the Q-value). Otherwise, there may be no measurable output signal for some refractive index values when the resonance peaks of these two rings do not overlap. For this sake, the FSR-difference ∆λFSR1–∆λFSR2 should be small enough. For example, when one chooses ∆λFSR1–∆λFSR2 = ∆λ3dB (here ∆λ3dB is the 3dB bandwidth of a single ring), the major peak will range from ~0.5 to 1.0 as the refractive index-changes. Consequently, one could always have a measurable output signal. It is possible have a stronger signal (with a peak larger than 0.5) by choosing a smaller FSR-difference (i.e., ∆λFSR1–∆λFSR2<∆λ3dB) if necessary. When concerning the fabrication, it is important to control the dimensions (the core width, and the radius) of the cascaded rings in order to have a suitable FSR-difference ∆λFSR1–∆λFSR2 (which should be close to ∆λ3dB as discussed above).

3. Design and result

In the following part we give a design with the present digital optical sensor based on a popular SOI (silicon-on-insulator) wafer, which has a 220nm Si layer (n Si = 3.445) on a 2μm SiO2 insulator layer (n SiO2 = 1.445). The core width of the SOI nanowire is w co = 500nm and the wavelength range is from 1500nm to 1600nm. Here we consider the TM polarization, which is preferred for a high sensitivity on the change of the ambient refractive index [1]. The effective refractive index is n = 1.848371 and 1.896591 for the SOI nanowire with a water- and SiO2 cladding, respectively. The group index n g is given by n g = n c, where λ c is the central wavelength and the dispersion coefficients are D = –1.4224μm–1 and –1.3542μm–1 for the SOI nanowire with a water- and SiO2 cladding, respectively. For ring #1, we choose the order m = 300 at the wavelength λ c of 1500nm and the corresponding bending radius R 1 is about 38.7475μm (which guarantees a very low bending loss). Ring #2 has a slightly different bending radius from ring #1 to have a smaller FSR. In the present example, we choose m = 312 and the bending radius R 2 = 39.2728μm. For ring #2, one could choose a slot waveguide to have an enhanced sensitivity when necessary [5]. Here we kept the radius value to four places of decimals in order to get the resonance wavelength at 1500nm as an example. For the fabrication, one should control the core width and the radius, to have a suitable FSR-difference ∆λFSR1–∆λFSR2 which should be close to the 3dB-bandwidth ∆λ3dB as discussed above. For the present example, the FSRs for ring #1 and ring #2 are ∆λFSR1 = 2.331nm and ∆λFSR2 = 2.325nm, respectively. The FSR-difference (~6pm) is a little smaller than the resonance linewidth of a single ring (∆λ3dB = 7.4pm). With such a design, one could always have a measurable output signal (with a peak larger than 0.5) as the refractive index-changes, which will be seen in Fig. 3(b) below. When there are fabrication errors, the resonance wavelength, and the FSR-difference ∆λFSR1–∆λFSR will deviate from the designed value. If the FSR-difference ∆λFSR1–∆λFSR2 is much smaller than the 3dB-bandwidth ∆λ3dB, the extinction ratio between the major peak and the minor peak becomes small, which makes it not easy to distinguish the major peak. On the other hand, if the FSR-difference ∆λFSR1–∆λFSR2 is much larger than the 3dB-bandwidth ∆λ3dB, there will be no measurable output signal because the overlapping between the resonance peaks of these two rings is too small. Therefore, when concerning to have a relatively larger fabrication tolerance, it is preferred to use the rings with relatively low Q-values (e.g., a relatively large 3dB-bandwidth).

 figure: Fig. 3

Fig. 3 (a) The response of at the output port of the cascaded rings in the broad band (the inset shows the enlarged view for the major peak); (b) the response at the output port of the cascaded rings when ∆n eff ranges from 0 to 20 × 10−6.

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Figure 3(a) shows the spectral response at the output port of the cascaded rings when ∆n eff = 0. One sees that there is only one major peak (which has the maximal amplitude) in a very broad wavelength range [here we only show a part from 1500nm to 1600nm in Fig. 3(a)]. This large band makes it allowed to realize a broad measurement range for the refractive index-change. The inset in Fig. 3(a) shows the enlarged view of the major peak, which has a 3dB bandwidth of about 4.8pm (the corresponding Q-value is 3.1 × 105). And there are also a series of minor peaks with small amplitudes. For the two adjacent minor peaks (at 1497.679nm and 1502.328nm), the amplitudes are about 0.4, which is much smaller than the major peak (~1.0).

In order to see how the major peak shifts, Fig. 3(b) shows the spectral responses at the output port of the cascaded rings as the index-change ∆n eff increases with a step of 4 × 10−6. When ∆n eff = 0, the major peak locates at λmax 1500nm and the two adjacent minor peaks locate at 1497.679nm and 1502.328nm. When the refractive index increases, the major peak decreases and one of the adjacent minor peak increases accordingly because the resonance wavelength of ring #2 shifts. For the present example, the major peak and one of the adjacent minor peak become similar when ∆n eff = 8 × 10−6. When the index-change increases further, e.g., ∆n eff = 12 × 10−6, the peak at 1502.328nm becomes the major one while the peak at 1500nm becomes the minor one. As the index-change ∆n eff further increases from 12 × 10−6, the major peak at 1502.328nm is further enhanced. From Fig. 3(b), one clearly sees how the wavelength λmax (where the major peak locates) switches as the refractive index-changes.

In Fig. 4(a) , we show the amplitudes of all the peaks (locating at different resonance wavelengths λ1( i )) as the index-change ∆n eff increases. In the present example, the resonance wavelength λ1(1) = 1500nm, and the separation between λ1( i ) and λ1( i +1) is around 2.33nm. From Fig. 4(a), one sees that the amplitude for any one peak has a Gaussian-like shape as the index-change ∆n eff increases. For any given index-change ∆n eff, one will find a major peak which has a larger amplitude than the other peaks (i.e., minor peaks). As the index-change ∆n eff increases, the major peak will be switched. When the amplitude of the major peak becomes maximal, the adjacent minor peaks have minimal amplitude. Consequently one obtains a maximal contrast between the major peak and the minor peaks, which makes it easy to distinguish the major peak. The major peak may have almost the same amplitude as the adjacent minor peak at a certain index-change ∆n eff [see Fig. 3(b)]. In this case, the small contrast makes it not easy to distinguish the major peak. Fortunately, one can easily distinguish these two similar peaks (locating at e.g. λ1( i ) and λ1( i +1)) from the other minor peaks. According to the position of these two similar peaks, it is easy to determine the index-change, which is approximately equal to (∆n eff( i ) + ∆n eff( i +1))/2, where ∆n eff( i ) is the index-change corresponding to the case with a major peak locating at λ1( i ).

 figure: Fig. 4

Fig. 4 As the index-change ∆n eff increases, (a) the amplitude of all the peaks locating at different resonance wavelengths λ1( i ); (b) the wavelength λ max corresponding to the major peak.

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Figure 4(b) shows the wavelength λ max corresponding to the major peak as the index-change ∆n eff increases. One sees that the wavelength λmax changes discretely (which is like a staircase). The wavelength λmax shifts 2.33nm when there is a refractive index-change of ∆n eff = 0.8 × 10−5. This gives an ultra-high sensitivity of about 2.91 × 105 nm/RIU, which is several hundreds times higher than the sensitivity of a single-ring-based sensor. We note that the major peak shift may be not sensitive to the refractive index-change when the index-change is smaller than ∆n eff0 [given by Eq. (1)]. On the other hand, as long as the index-change is larger than ∆n eff0, one will observe a significant wavelength shift of the major peak. Therefore, the detection limit is determined by ∆n eff0. The detect limit of the present digital optical sensor is ∆n eff0 = 0.8 × 10−5, which could be enhanced further by reducing the difference between the FSRs of these two rings according to Eq. (1). The present cascaded-ring not only has an ultra-high sensitivity but also a large measurement range because of the ultra-wide FSR. For the present example, the ∆λFSR of the cascaded-ring is about several hundreds nanometers estimated by Eq. (3). In this case the measurement range actually might be limited by the bandwidth of the light source. When using a broad-band light source with a bandwidth of ∆λ = 100nm, a measurement range is about 0.00034 (estimated by ∆n max = ∆λ/S). Thus, it is important to have a broadband light-source when a larger measurement range is desirable. When using a light-source with a limited bandwidth, it is also possible to have a larger measurement range by choosing smaller FSR for the cascaded rings.

Since the wavelength shift of the major peak of the spectral response is at the order of several nanometers when using the present digital optical sensor, it is very convenient to monitor the major peak switching even by using a low resolution integrated micro-spectrometer based on an AWG [10] combining with a photodetector array. The AWG micro-spectrometer used here should have a channel spacing equal to the FSR of the ring with the up-cladding. In this way, it is promising to realize a low-cost and portable highly-sensitive optical sensor system on a single chip.

4. Conclusion

In summary, we have proposed a digital optical sensor based on cascaded rings. One of the two rings is covered by an up-cladding and the up-cladding on the other ring is removed to form a sample reservoir. The two cascaded rings have different FSRs and consequently the output port will have a spectral response with a major peak and some minor peaks. The proposed optical sensor operates in a digital way, i.e., the wavelength of the major peak switches by a step equal to multiple FSRs of the ring with the up-cladding as the refractive index increases. Therefore, one has an ultra-high sensitivity which is M times higher than that of a single ring. With the present digital optical sensor, one does not need to use a high-resolution spectrometer to monitor the peak switching of the spectral response. It is allowed to use a low-resolution integrated optical micro-spectrometer (e.g., based on an AWG [10]) combining with a photodetector array. Consequently it provides a promising way to realize a low-cost and portable highly-sensitive optical sensor system on a single chip.

Acknowledgement

This project was supported Zhejiang Provincial Natural Science Foundation (No. J20081048).

References and links

1. A. Densmore, D.-X. Xu, P. Waldron, S. Janz, P. Cheben, J. Lapointe, A. Delge, B. Lamontagne, J. H. Schmid, and E. Post, “A silicon-on-insulator photonic wire based evanescent field sensor,” IEEE Photon. Technol. Lett. 18(23), 2520–2522 (2006). [CrossRef]  

2. G. Nemova and R. Kashyap, “Theoretical model of a planar integrated refractive index sensor based on surface plasmon-polariton excitation with a long period grating,” J. Opt. Soc. Am. B 24(10), 2696 (2007). [CrossRef]  

3. S.-Y. Cho and N. M. Jokerst, “A polymer microdisk photonic sensor integrated onto silicon,” IEEE Photon. Technol. Lett. 18(20), 2096–2098 (2006). [CrossRef]  

4. C.-Y. Chao and L. J. Guo, “Biochemical sensors based on polymer microrings with sharp asymmetrical resonance,” Appl. Phys. Lett. 83(8), 1527 (2003). [CrossRef]  

5. Q. F. Xu, V. R. Almeida, R. R. Panepucci, and M. Lipson, “Experimental demonstration of guiding and confining light in nanometer-size low-refractive-index material,” Opt. Lett. 29(14), 1626–1628 (2004). [CrossRef]   [PubMed]  

6. D.-X. Xu, A. Densmore, A. Delâge, P. Waldron, R. McKinnon, S. Janz, J. Lapointe, G. Lopinski, T. Mischki, E. Post, P. Cheben, and J. H. Schmid, “Folded cavity SOI microring sensors for high sensitivity and real time measurement of biomolecular binding,” Opt. Express 16(19), 15137–15148 (2008). [CrossRef]   [PubMed]  

7. 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]  

8. P. Rabiei and W. H. Steier, “Tunable polymer double micro-ring filters,” IEEE Photon. Technol. Lett. 15(9), 1255–1257 (2003). [CrossRef]  

9. B. Liu, A. Shakouri, and J. E. Bowers, “Wide tunable double ring resonator coupled lasers,” IEEE Photon. Technol. Lett. 14(5), 600–602 (2002). [CrossRef]  

10. P. Cheben, J. H. Schmid, A. Delâge, A. Densmore, S. Janz, B. Lamontagne, J. Lapointe, E. Post, P. Waldron, and D.-X. Xu, “A high-resolution silicon-on-insulator arrayed waveguide grating microspectrometer with sub-micrometer aperture waveguides,” Opt. Express 15(5), 2299–2306 (2007). [CrossRef]   [PubMed]  

References

  • View by:

  1. A. Densmore, D.-X. Xu, P. Waldron, S. Janz, P. Cheben, J. Lapointe, A. Delge, B. Lamontagne, J. H. Schmid, and E. Post, “A silicon-on-insulator photonic wire based evanescent field sensor,” IEEE Photon. Technol. Lett. 18(23), 2520–2522 (2006).
    [Crossref]
  2. G. Nemova and R. Kashyap, “Theoretical model of a planar integrated refractive index sensor based on surface plasmon-polariton excitation with a long period grating,” J. Opt. Soc. Am. B 24(10), 2696 (2007).
    [Crossref]
  3. S.-Y. Cho and N. M. Jokerst, “A polymer microdisk photonic sensor integrated onto silicon,” IEEE Photon. Technol. Lett. 18(20), 2096–2098 (2006).
    [Crossref]
  4. C.-Y. Chao and L. J. Guo, “Biochemical sensors based on polymer microrings with sharp asymmetrical resonance,” Appl. Phys. Lett. 83(8), 1527 (2003).
    [Crossref]
  5. Q. F. Xu, V. R. Almeida, R. R. Panepucci, and M. Lipson, “Experimental demonstration of guiding and confining light in nanometer-size low-refractive-index material,” Opt. Lett. 29(14), 1626–1628 (2004).
    [Crossref] [PubMed]
  6. D.-X. Xu, A. Densmore, A. Delâge, P. Waldron, R. McKinnon, S. Janz, J. Lapointe, G. Lopinski, T. Mischki, E. Post, P. Cheben, and J. H. Schmid, “Folded cavity SOI microring sensors for high sensitivity and real time measurement of biomolecular binding,” Opt. Express 16(19), 15137–15148 (2008).
    [Crossref] [PubMed]
  7. 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]
  8. P. Rabiei and W. H. Steier, “Tunable polymer double micro-ring filters,” IEEE Photon. Technol. Lett. 15(9), 1255–1257 (2003).
    [Crossref]
  9. B. Liu, A. Shakouri, and J. E. Bowers, “Wide tunable double ring resonator coupled lasers,” IEEE Photon. Technol. Lett. 14(5), 600–602 (2002).
    [Crossref]
  10. P. Cheben, J. H. Schmid, A. Delâge, A. Densmore, S. Janz, B. Lamontagne, J. Lapointe, E. Post, P. Waldron, and D.-X. Xu, “A high-resolution silicon-on-insulator arrayed waveguide grating microspectrometer with sub-micrometer aperture waveguides,” Opt. Express 15(5), 2299–2306 (2007).
    [Crossref] [PubMed]

2008 (1)

2007 (3)

2006 (2)

S.-Y. Cho and N. M. Jokerst, “A polymer microdisk photonic sensor integrated onto silicon,” IEEE Photon. Technol. Lett. 18(20), 2096–2098 (2006).
[Crossref]

A. Densmore, D.-X. Xu, P. Waldron, S. Janz, P. Cheben, J. Lapointe, A. Delge, B. Lamontagne, J. H. Schmid, and E. Post, “A silicon-on-insulator photonic wire based evanescent field sensor,” IEEE Photon. Technol. Lett. 18(23), 2520–2522 (2006).
[Crossref]

2004 (1)

2003 (2)

C.-Y. Chao and L. J. Guo, “Biochemical sensors based on polymer microrings with sharp asymmetrical resonance,” Appl. Phys. Lett. 83(8), 1527 (2003).
[Crossref]

P. Rabiei and W. H. Steier, “Tunable polymer double micro-ring filters,” IEEE Photon. Technol. Lett. 15(9), 1255–1257 (2003).
[Crossref]

2002 (1)

B. Liu, A. Shakouri, and J. E. Bowers, “Wide tunable double ring resonator coupled lasers,” IEEE Photon. Technol. Lett. 14(5), 600–602 (2002).
[Crossref]

Almeida, V. R.

Armani, A. M.

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]

Bowers, J. E.

B. Liu, A. Shakouri, and J. E. Bowers, “Wide tunable double ring resonator coupled lasers,” IEEE Photon. Technol. Lett. 14(5), 600–602 (2002).
[Crossref]

Chao, C.-Y.

C.-Y. Chao and L. J. Guo, “Biochemical sensors based on polymer microrings with sharp asymmetrical resonance,” Appl. Phys. Lett. 83(8), 1527 (2003).
[Crossref]

Cheben, P.

Cho, S.-Y.

S.-Y. Cho and N. M. Jokerst, “A polymer microdisk photonic sensor integrated onto silicon,” IEEE Photon. Technol. Lett. 18(20), 2096–2098 (2006).
[Crossref]

Delâge, A.

Delge, A.

A. Densmore, D.-X. Xu, P. Waldron, S. Janz, P. Cheben, J. Lapointe, A. Delge, B. Lamontagne, J. H. Schmid, and E. Post, “A silicon-on-insulator photonic wire based evanescent field sensor,” IEEE Photon. Technol. Lett. 18(23), 2520–2522 (2006).
[Crossref]

Densmore, A.

Flagan, R. C.

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]

Fraser, S. E.

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]

Guo, L. J.

C.-Y. Chao and L. J. Guo, “Biochemical sensors based on polymer microrings with sharp asymmetrical resonance,” Appl. Phys. Lett. 83(8), 1527 (2003).
[Crossref]

Janz, S.

Jokerst, N. M.

S.-Y. Cho and N. M. Jokerst, “A polymer microdisk photonic sensor integrated onto silicon,” IEEE Photon. Technol. Lett. 18(20), 2096–2098 (2006).
[Crossref]

Kashyap, R.

Kulkarni, R. P.

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]

Lamontagne, B.

P. Cheben, J. H. Schmid, A. Delâge, A. Densmore, S. Janz, B. Lamontagne, J. Lapointe, E. Post, P. Waldron, and D.-X. Xu, “A high-resolution silicon-on-insulator arrayed waveguide grating microspectrometer with sub-micrometer aperture waveguides,” Opt. Express 15(5), 2299–2306 (2007).
[Crossref] [PubMed]

A. Densmore, D.-X. Xu, P. Waldron, S. Janz, P. Cheben, J. Lapointe, A. Delge, B. Lamontagne, J. H. Schmid, and E. Post, “A silicon-on-insulator photonic wire based evanescent field sensor,” IEEE Photon. Technol. Lett. 18(23), 2520–2522 (2006).
[Crossref]

Lapointe, J.

Lipson, M.

Liu, B.

B. Liu, A. Shakouri, and J. E. Bowers, “Wide tunable double ring resonator coupled lasers,” IEEE Photon. Technol. Lett. 14(5), 600–602 (2002).
[Crossref]

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[Crossref]

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[Crossref]

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P. Rabiei and W. H. Steier, “Tunable polymer double micro-ring filters,” IEEE Photon. Technol. Lett. 15(9), 1255–1257 (2003).
[Crossref]

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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).
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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

J. Opt. Soc. Am. B (1)

Opt. Express (2)

Opt. Lett. (1)

Science (1)

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]

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Figures (4)

Fig. 1
Fig. 1 The schematic configuration of the present digital optical sensor based on cascaded rings; (a) the top view; (b) the 3D view [in order to see the structure clearly, we separate the cladding from the substrate only for the view].
Fig. 2
Fig. 2 The schematic spectral responses for the cascaded-rings.
Fig. 3
Fig. 3 (a) The response of at the output port of the cascaded rings in the broad band (the inset shows the enlarged view for the major peak); (b) the response at the output port of the cascaded rings when ∆n eff ranges from 0 to 20 × 10−6.
Fig. 4
Fig. 4 As the index-change ∆n eff increases, (a) the amplitude of all the peaks locating at different resonance wavelengths λ1( i ); (b) the wavelength λ max corresponding to the major peak.

Equations (3)

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Δ n eff0 = n eff ( Δ λ FSR 1 Δ λ FSR 2 ) / λ 1 ( i ) .
S = Δ λ FSR 1 / Δ n eff0 = ( λ 1 ( i ) / n eff ) [ Δ λ FSR 1 / ( Δ λ FSR 1 Δ λ FSR 2 ) ] = S 0 M .
Δ λ FSR = ( M 1 ) Δ λ FSR 1 .

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