## Long-range surface plasmon triple-output Mach-Zehnder interferometers |

Optics Express, Vol. 22, Issue 4, pp. 4006-4020 (2014)

http://dx.doi.org/10.1364/OE.22.004006

Acrobat PDF (1202 KB)

### Abstract

A triple-output Mach-Zehnder interferometer (MZI) operating with long-range surface plasmon-polariton waves, consisting of a MZI in cascade with a triple coupler, is demonstrated at a wavelength of ~1370 nm, using the thermo-optic effect to produce phase shifting. A theoretical model for three-waveguide coupling is also proposed and was applied to compute the transfer characteristic of various designs. Dimensions for the device were selected to optimize performance, experiments were performed, and the results were compared to theory. The outputs were sinusoidally related to the thermally-induced phase shift and separated by ~2π/3 rad, as expected theoretically. Four detection schemes that take advantage of the 3 times larger dynamic range and suppress time-varying common perturbations are proposed and analyzed in order to improve the detection limit of the device. A minimum detectable phase shift ~2/3 that of a single output was obtained from a power difference scheme and a normalization scheme. The smallest minimum detectable phase shift was 7.3 mrad. The device is promising for sensing applications, including (bio)chemical sensing.

© 2014 Optical Society of America

## 1. Introduction

3. P. Berini, “Long-range surface plasmon polaritons,” Adv. Opt. Photon. **1**(3), 484–588 (2009). [CrossRef]

4. R. Charbonneau, C. Scales, I. Breukelaar, S. Fafard, N. Lahoud, G. Mattiussi, and P. Berini, “Passive integrated optics elements based on long-range surface plasmon-polaritons,” J. Lightwave Technol. **24**(1), 477–494 (2006). [CrossRef]

5. P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of symmetric structures,” Phys. Rev. B **61**(15), 10484–10503 (2000). [CrossRef]

*T*is the temperature, and

*dn/dT*is the thermo-optic coefficient (TOC) - the ratio of the change of the refractive index of a material over that of the temperature. The linear model for the thermo-optic effect is assumed to hold over a small temperature range for constant pressure and operating wavelength. Thermo-optic modulation devices that have been designed and investigated includes straight variable optical attenuators (VOAs) based on thermally-induced anti-guiding [6

6. K. Leosson, T. Nikolajsen, A. Boltasseva, and S. I. Bozhevolnyi, “Long-range surface plasmon polariton nanowire waveguides for device applications,” Opt. Express **14**(1), 314–319 (2006). [CrossRef] [PubMed]

7. G. Gagnon, N. Lahoud, G. A. Mattiussi, and P. Berini, “Thermally activated variable attenuation of long-range surface plasmon-polariton waves,” J. Lightwave Technol. **24**(11), 4391–4402 (2006). [CrossRef]

8. I. Breukelaar, R. Charbonneau, and P. Berini, “Long-range surface plasmon-polariton mode cutoff and radiation in embedded strip waveguides,” J. Appl. Phys. **100**(4), 043104 (2006). [CrossRef]

9. H. Fan and P. Berini, “Thermo-optic characterization of long-range surface-plasmon devices in Cytop,” Appl. Opt. **52**(2), 162–170 (2013). [CrossRef] [PubMed]

10. T. Nikolajsen, K. Leosson, and S. I. Bozhevolnyi, “Surface plasmon-polariton based modulators and switches operating at telecom wavelengths,” Appl. Phys. Lett. **85**(24), 5833–5835 (2004). [CrossRef]

11. J. Gosciniak, S. I. Bozhevolnyi, T. B. Andersen, V. S. Volkov, J. Kjelstrup-Hansen, L. Markey, and A. Dereux, “Thermo-optic control of dielectric-loaded plasmonic waveguide components,” Opt. Express **18**(2), 1207–1216 (2010). [CrossRef] [PubMed]

12. S. Kaya, J.-C. Weeber, F. Zacharatos, K. Hassan, T. Bernardin, B. Cluzel, J. Fatome, and C. Finot, “Photo-thermal modulation of surface plasmon polariton propagation at telecommunication wavelengths,” Opt. Express **21**(19), 22269–22284 (2013). [CrossRef] [PubMed]

13. S. Y. Wu, H. P. Ho, W. C. Law, C. Lin, and S. K. Kong, “Highly sensitive differential phase-sensitive surface plasmon resonance biosensor based on the Mach-Zehnder configuration,” Opt. Lett. **29**(20), 2378–2380 (2004). [CrossRef] [PubMed]

14. J. Ptasinski, L. Pang, P. C. Sun, B. Slutsky, and Y. Fainman, “Differential detection for nanoplasmonic resonance sensors,” IEEE Sens. J. **12**(2), 384–388 (2012). [CrossRef]

15. R. G. Heideman and P. V. Lambeck, “Remote opto-chemical sensing with extreme sensitivity: Design, fabrication and performance of a pigtailed integrated optical phase-modulated Mach–Zehnder interferometer system,” Sens. Actuators B Chem. **61**(1), 100–127 (1999). [CrossRef]

16. A. Khan, O. Krupin, E. Lisicka-Skrzek, and P. Berini, “Mach-Zehnder refractometric sensor using long-range surface plasmon waveguides,” Appl. Phys. Lett. **103**(11), 111108 (2013). [CrossRef]

18. K. C. Vernon, D. E. Gómez, and T. J. Davis, “A compact interferometric sensor design using three waveguide coupling,” J. Appl. Phys. **106**(10), 104306 (2009). [CrossRef]

17. B. J. Luff, J. S. Wilkinson, J. Piehler, U. Hollenbach, J. Ingenhoff, and N. Fabricius, “Integrated optical Mach-Zehnder biosensor,” J. Lightwave Technol. **16**(4), 583–592 (1998). [CrossRef]

20. S. K. Sheem, “Optical fiber interferometers with [3x3] directional couplers: Analysis,” J. Appl. Phys. **52**(6), 3865 (1981). [CrossRef]

21. K. P. Koo, A. B. Tveten, and A. Dandridge, “Passive stabilization scheme for fiber interferometers using (3x3) fiber directional couplers,” Appl. Phys. Lett. **41**(7), 616 (1982). [CrossRef]

22. P. Hua, B. Jonathan Luff, G. R. Quigley, J. S. Wilkinson, and K. Kawaguchi, “Integrated optical dual Mach-Zehnder interferometer sensor,” Sens. Actuators B Chem. **87**(2), 250–257 (2002). [CrossRef]

23. H. Fan and P. Berini, “Noise cancellation in long-range surface plasmon dual-output Mach-Zehnder interferometers,” J. Lightwave Technol. **31**(15), 2606–2612 (2013). [CrossRef]

18. K. C. Vernon, D. E. Gómez, and T. J. Davis, “A compact interferometric sensor design using three waveguide coupling,” J. Appl. Phys. **106**(10), 104306 (2009). [CrossRef]

25. S. L. Chuang, “Application of the strongly coupled-mode theory to integrated optical devices,” IEEE J. Quantum Electron. **23**(5), 499–509 (1987). [CrossRef]

26. S. L. Chuang, “A coupled-mode theory for multiwaveguide systems satisfying the reciprocity theorem and power conservation,” J. Lightwave Technol. **5**(1), 174–183 (1987). [CrossRef]

## 2. Theoretical

### 2.1 Structure

*ss*[5

_{b}^{0}5. P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of symmetric structures,” Phys. Rev. B **61**(15), 10484–10503 (2000). [CrossRef]

*λ*~1310 nm). The MZI has a Y-junction splitter with a 1 μm inner waveguide separation at the split and a separation of 140 μm between its two arms at the widest point. All curved sections have the same radius of curvature of 5.5 mm. The dimensions for these elements were selected based on the modelling and design results summarised in [4

_{0}4. R. Charbonneau, C. Scales, I. Breukelaar, S. Fafard, N. Lahoud, G. Mattiussi, and P. Berini, “Passive integrated optics elements based on long-range surface plasmon-polaritons,” J. Lightwave Technol. **24**(1), 477–494 (2006). [CrossRef]

27. H. Fan, R. Buckley, and P. Berini, “Passive long-range surface plasmon-polariton devices in Cytop,” Appl. Opt. **51**(10), 1459–1467 (2012). [CrossRef] [PubMed]

### 2.2 Coupling model

4. R. Charbonneau, C. Scales, I. Breukelaar, S. Fafard, N. Lahoud, G. Mattiussi, and P. Berini, “Passive integrated optics elements based on long-range surface plasmon-polaritons,” J. Lightwave Technol. **24**(1), 477–494 (2006). [CrossRef]

8. I. Breukelaar, R. Charbonneau, and P. Berini, “Long-range surface plasmon-polariton mode cutoff and radiation in embedded strip waveguides,” J. Appl. Phys. **100**(4), 043104 (2006). [CrossRef]

17. B. J. Luff, J. S. Wilkinson, J. Piehler, U. Hollenbach, J. Ingenhoff, and N. Fabricius, “Integrated optical Mach-Zehnder biosensor,” J. Lightwave Technol. **16**(4), 583–592 (1998). [CrossRef]

25. S. L. Chuang, “Application of the strongly coupled-mode theory to integrated optical devices,” IEEE J. Quantum Electron. **23**(5), 499–509 (1987). [CrossRef]

*z*= 0), the input field distribution is taken as the fundamental LRSPP mode supported by a single waveguide (

*ss*) centered on one of the outside waveguides of the coupler, superimposing the same mode field distribution centered on the other outside waveguide of the coupler multiplied by a factor

_{b}^{0}*e*representing the thermally induced phase shift, as expressed as follows:

^{jϕ}*s*is the coupler separation and

*E*is the mode field of the

_{y,s}*ss*mode supported by a single waveguide, as shown in Fig. 2(a). As the input field enters the triple coupler, it redistributes among the three supermodes supported by the coupler, namely mode (1 1 1), mode (−1 0 1), and mode (1 −1 1), for which the field distributions are shown in Figs. 2(b)–2(d), respectively, and forward propagating radiative modes. The latter are neglected (but could be included by discretizing the continuum of radiative modes into a finite set of box modes, following [8

_{b}^{0}8. I. Breukelaar, R. Charbonneau, and P. Berini, “Long-range surface plasmon-polariton mode cutoff and radiation in embedded strip waveguides,” J. Appl. Phys. **100**(4), 043104 (2006). [CrossRef]

*C*into each supermode at the input of the coupler are given as follows [8

_{i}**100**(4), 043104 (2006). [CrossRef]

28. P. Berini, R. Charbonneau, N. Lahoud, and G. Mattiussi, “Characterization of long-range surface plasmon-polariton waveguides,” J. Appl. Phys. **98**(4), 043109 (2005). [CrossRef]

*A*is the area of the entire computational domain at the transverse plane where the modes meet, and

_{∞}*E*is the field of one of the three super modes supported by the coupler (with

_{y,i}*i*= (1 1 1), (−1 0 1), or (1 −1 1)). It was checked that

*z = L*), the super modes superimpose to yield the output field distribution as:

*L*is the coupler length. The

*α*and

_{i}*β*of each supermode must be used as they are different. The output field redistributes again among the single modes centered on the individual waveguides connected to the output of the coupler, and the output overlap factors

_{i}*C*are calculated similarly as in Eq.(2.2):

_{m}*C*relates to the middle waveguide while

_{2}*C*and

_{1}*C*to the outside two. The normalized optical powers in the individual output waveguides are then calculated as

_{3}*P*= |

_{m}*C*|

_{m}^{2}with

*m*= 1, 2, or 3. We neglect the effects of the s-bends before and after the coupler on the mode field distribution of a single waveguide

*E*as the radii of curvature are large [27

_{y,s}27. H. Fan, R. Buckley, and P. Berini, “Passive long-range surface plasmon-polariton devices in Cytop,” Appl. Opt. **51**(10), 1459–1467 (2012). [CrossRef] [PubMed]

### 2.3 Validation

17. B. J. Luff, J. S. Wilkinson, J. Piehler, U. Hollenbach, J. Ingenhoff, and N. Fabricius, “Integrated optical Mach-Zehnder biosensor,” J. Lightwave Technol. **16**(4), 583–592 (1998). [CrossRef]

*s*= 1 μm and coupler length

*L*= 0.75

*L*.

_{c}*L*is defined as the coupling length where maximum power is transferred from a single input at one outside waveguide to the other outside waveguide. The dielectric coupler has claddings of refractive index of 1.6 and cores of refractive index 1.646, operating at a free-space wavelength of 786 nm, and the core width was 1 μm. The modeling work was conducted using the Finite Element Method (FEM) and COMSOL. As shown in Fig. 3, the results coincide very well, providing verification of our theoretical model.

_{c}### 2.4 Design

*ϕ*) for coupler separations

*s*= 1, 2 and 3μm, respectively. All three normalized powers are sinusoidal with the phase shift. The corresponding coupler lengths

*L*were chosen as 457 μm, 828.57 μm and 1530 μm in order that the individual sinusoidal responses separate to ~2π/3 rad from each other. The wider the separation the longer the required coupler length. The total output power is also plotted and is observed to be approximately constant with

*ϕ*in all cases, justifying our neglect of the forward propagating radiative modes. Comparing Figs. 5(a), 5(b) and 5(c), the total output power becomes increasingly constant as the separation increases, but at the expense of a decrease in the dynamic range, so there is a trade-off between these two quantities. Another consideration is that a shorter device is more compact and profits integration. The devices used in the experiments are designed to have a coupler separation of

*s*= 2 μm and coupler length

*L*= 828.57 μm, providing a flatter total output power response, with good dynamic range, and an adequate device length.

## 3. Experimental

### 3.1 Device and setup

32. C. Chiu, E. Lisicka-Shrzek, R. N. Tait, and P. Berini, “Fabrication of surface plasmon waveguides and devices in Cytop with integrated microfluidic channels,” J. Vac. Sci. Technol. B **28**(4), 729–735 (2010). [CrossRef]

27. H. Fan, R. Buckley, and P. Berini, “Passive long-range surface plasmon-polariton devices in Cytop,” Appl. Opt. **51**(10), 1459–1467 (2012). [CrossRef] [PubMed]

### 3.2 Results

**51**(10), 1459–1467 (2012). [CrossRef] [PubMed]

9. H. Fan and P. Berini, “Thermo-optic characterization of long-range surface-plasmon devices in Cytop,” Appl. Opt. **52**(2), 162–170 (2013). [CrossRef] [PubMed]

23. H. Fan and P. Berini, “Noise cancellation in long-range surface plasmon dual-output Mach-Zehnder interferometers,” J. Lightwave Technol. **31**(15), 2606–2612 (2013). [CrossRef]

## 4. Discussion

### 4.1 Operation with maximum sensitivity

### 4.2 Dynamic range

*e.g.*, Fig. 5(c)), the three outputs can be combined appropriately to obtain a response having a dynamic range three times larger than that of a single output, without significantly increasing the time-varying perturbations. Ideally, the dynamic range of the three individual outputs are nearly equal, the phase separation between them is very close to ~2π/3, and the total power can be taken as constant. Thus the three sinusoidal outputs

*P*,

_{1}*P*and

_{2}*P*can be modeled mathematically using the following equations in terms of the induced phase shift

_{3}*ϕ*and the input optical power

*P*, with time-varying common perturbation terms (

_{in}*p*,

_{i}*p*) included:

_{o}*a*is the amplitude and

*b*,

_{1}*b*and

_{2}*b*are the constant offsets of the sinusoidal curves.

_{3}*p*represents a perturbation on the input side, such as a drift in the input optical power or input coupling conditions, and

_{i}*p*represents a perturbation received on the output side, for instance, due to background light. We define three power difference terms based on the individual powers:

_{o}*D*, where

_{i}= 2P_{i}- P_{j}-P_{k}*i*is one of 1, 2, 3 while

*j*and

*k*are the other two. In the case of

*D*for example, by multiplying Eq. (4.1.b) by 2 and subtracting Eqs. (4.1.a) and (4.1.b), the following expression is obtained:

_{2}*P*, the input common perturbation

_{2}*p*of

_{i}*D*remains the same whereas the output common perturbation

_{2}*p*is cancelled and the amplitude of the sinusoidal term triples. It is easy to calculate

_{o}*D*and

_{1}*D*and observe that they behave the same way as

_{3}*D*. Thus the difference terms provide a signal with 3 times larger dynamic range compared to the individual ones without increasing the level of any time-varying perturbations. Figure 9 shows

_{2}*D*,

_{1}*D*and

_{2}*D*obtained from the measurements of Fig. 8(a). It is observed that they have 3 times larger dynamic ranges, in agreement with Eq. (4.2).

_{3}### 4.3 Suppression of common perturbations

*p*, then the input perturbation

_{o}*p*can be removed by normalization. Take the normalized

_{i}*P*for instance; it has the following expression as obtained from Eqs. (4.1.a)-(4.1.c):

_{2}*p*= 0) the above simplifies to:

_{o}*p*is removed. If the output perturbation

_{i}*p*exists, the term

_{o}*P*cannot be completely cancelled but normalization can at least suppress to some extent the time-varying perturbation.

_{in}+ p_{i}*p*. Figure 10(b) shows the same measurements but normalised, revealing significant suppression of the time-varying perturbations.

_{i}*D*is calculated as:

_{2}*p*= 0 into the above, yielding:

_{o}*i.e. P*), a power difference (

_{2}*i.e. D*), a normalized individual power (

_{2}*i.e. P*(

_{2}/*P*)), and a normalized power difference (

_{1}+ P_{2}+ P_{3}*i.e. D*(

_{2}/*P*)). A statistical comparison between the four detection schemes is necessary. One way of doing this is to conduct a time tracing experiment where the applied voltage (dissipated electrical power, phase difference between arms) is kept constant and the output optical power is recorded over time. The standard deviation

_{1}+ P_{2}+ P_{3}*σ*of each scheme is then calculated, however, those of the normalized group cannot be directly compared to those of the unnormalized group (the units are different). Therefore the minimum detectable phase shift Δ

*ϕ*is introduced and used to compare all schemes directly; it is defined as [23

_{min}23. H. Fan and P. Berini, “Noise cancellation in long-range surface plasmon dual-output Mach-Zehnder interferometers,” J. Lightwave Technol. **31**(15), 2606–2612 (2013). [CrossRef]

*P*is taken as the corresponding

_{min}*σ*times a factor

*k*, say

*k*= 2. Rewriting Eq. (4.1.b) by removing all the perturbation terms, we obtain:from which ∂

*P*/∂

_{2}*ϕ*is obtained as:substituting Eq. (4.9) into Eq. (4.7) yields the minimum detectable phase shift based on

*P*:

_{2}*ϕ*for the other individual powers

_{min}*P*and

_{1}*P*are obtained, and so are those for the power differences, the normalized individual powers and the normalized power differences:

_{3}*ϕ*term in Eq. (4.8) is very close to 0, so sin

*ϕ*~1. Substituting this and

*k*= 2 into Eqs. (4.10)-(4.13), with our experimental value for

*P*and the standard deviations obtained from a time-tracing experiment, the minimum detectable phase shifts of the four schemes can be calculated and compared directly to determine which scheme provides the best performance. Table 1 gives the

_{in}*σ*and the Δ

*ϕ*for three time-tracing experiments (nominally M 1, M 2 and M 3 in Table 1), each taken on the same triple-output MZI device with

_{min}*P*= 0.7 mW (the absolute power was determined by calibration), and each with a different voltage applied so that a different output operates in the linear region (

_{in}*i.e.*, M 1 has

*P*in the linear region, M 2 has

_{1}*P*in the linear region and M3 has

_{2}*P*in the linear region). The parameters

_{3}*a*= 0.22 and

*b*= 1.01 are chosen by best fitting with the transfer characteristic.

_{1}+ b_{2}+ b_{3}*P*and

_{i}*D*for all three measurements in Table 1, suggests that there was very little time-varying output perturbation (

_{i}*p*, see Eqs. (4.1.a)-(4.1.c)) in the experiments to be cancelled using the power difference scheme, because all power differences have ~2 times larger standard deviation than the individual powers. However, comparing their corresponding Δ

_{o}*ϕ*it is observed that the power difference scheme provides an reduction of ~3/2 which originates from the 3 times larger dynamic range and the 2 times worse standard deviation (compare Eq. (4.10) with Eq. (4.11)). If the standard deviation of the power difference scheme remains comparable to that of a single power then Δ

_{min}*ϕ*would be reduced by a factor of 3.

_{min}*D*,

_{i}*D*/(

_{i}*P*+

_{1}*P*+

_{2}*P*) can be expressed as 3[

_{3}*P*/(

_{i}*P*+

_{1}*P*+

_{2}*P*)]-1 and thus always has a 3 times larger standard deviation than

_{3}*P*/(

_{i}*P*+

_{1}*P*+

_{2}*P*). Substituting this relation into Eqs. (4.12) and (4.13) it is observed that the 3 times larger dynamic range of

_{3}*D*/(

_{i}*P*+

_{1}*P*+

_{2}*P*) is cancelled and the Δ

_{3}*ϕ*remains the same. Therefore the normalized individual power and the normalized power difference can actually be regarded as the same scheme. This is verified experimentally by comparing Δ

_{min}*ϕ*of

_{min}*P*/(

_{i}*P*+

_{1}*P*+

_{2}*P*) and

_{3}*D*/(

_{i}*P*+

_{1}*P*+

_{2}*P*) in Table 1.

_{3}*ϕ*of the power difference scheme and the normalized schemes reveals very similar values though not exactly equal, However, both are smaller compared to the individual power scheme, thus both are good schemes. The smallest value of Δ

_{min}*ϕ*obtained in these experiments was 7.3 mrad compared to 3.1 mrad in the dual-output case [23

_{min}**31**(15), 2606–2612 (2013). [CrossRef]

*ϕ*in the triple-output case. Considering that the two cases were tested under different experimental conditions, and the perturbation levels were neither controllable nor comparable, the larger detection limit in the triple-output case is attributed to larger perturbations that were not as easily suppressed. Relative to the dual-output, the triple-output eliminates the sensitivity fading and directional ambiguity in the former (there is always one output in a linear region).

_{min}## 5. Conclusions

## Acknowledgments

## References and links

1. | A. D. Boardman, ed., |

2. | H. Raether, |

3. | P. Berini, “Long-range surface plasmon polaritons,” Adv. Opt. Photon. |

4. | R. Charbonneau, C. Scales, I. Breukelaar, S. Fafard, N. Lahoud, G. Mattiussi, and P. Berini, “Passive integrated optics elements based on long-range surface plasmon-polaritons,” J. Lightwave Technol. |

5. | P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of symmetric structures,” Phys. Rev. B |

6. | K. Leosson, T. Nikolajsen, A. Boltasseva, and S. I. Bozhevolnyi, “Long-range surface plasmon polariton nanowire waveguides for device applications,” Opt. Express |

7. | G. Gagnon, N. Lahoud, G. A. Mattiussi, and P. Berini, “Thermally activated variable attenuation of long-range surface plasmon-polariton waves,” J. Lightwave Technol. |

8. | I. Breukelaar, R. Charbonneau, and P. Berini, “Long-range surface plasmon-polariton mode cutoff and radiation in embedded strip waveguides,” J. Appl. Phys. |

9. | H. Fan and P. Berini, “Thermo-optic characterization of long-range surface-plasmon devices in Cytop,” Appl. Opt. |

10. | T. Nikolajsen, K. Leosson, and S. I. Bozhevolnyi, “Surface plasmon-polariton based modulators and switches operating at telecom wavelengths,” Appl. Phys. Lett. |

11. | J. Gosciniak, S. I. Bozhevolnyi, T. B. Andersen, V. S. Volkov, J. Kjelstrup-Hansen, L. Markey, and A. Dereux, “Thermo-optic control of dielectric-loaded plasmonic waveguide components,” Opt. Express |

12. | S. Kaya, J.-C. Weeber, F. Zacharatos, K. Hassan, T. Bernardin, B. Cluzel, J. Fatome, and C. Finot, “Photo-thermal modulation of surface plasmon polariton propagation at telecommunication wavelengths,” Opt. Express |

13. | S. Y. Wu, H. P. Ho, W. C. Law, C. Lin, and S. K. Kong, “Highly sensitive differential phase-sensitive surface plasmon resonance biosensor based on the Mach-Zehnder configuration,” Opt. Lett. |

14. | J. Ptasinski, L. Pang, P. C. Sun, B. Slutsky, and Y. Fainman, “Differential detection for nanoplasmonic resonance sensors,” IEEE Sens. J. |

15. | R. G. Heideman and P. V. Lambeck, “Remote opto-chemical sensing with extreme sensitivity: Design, fabrication and performance of a pigtailed integrated optical phase-modulated Mach–Zehnder interferometer system,” Sens. Actuators B Chem. |

16. | A. Khan, O. Krupin, E. Lisicka-Skrzek, and P. Berini, “Mach-Zehnder refractometric sensor using long-range surface plasmon waveguides,” Appl. Phys. Lett. |

17. | B. J. Luff, J. S. Wilkinson, J. Piehler, U. Hollenbach, J. Ingenhoff, and N. Fabricius, “Integrated optical Mach-Zehnder biosensor,” J. Lightwave Technol. |

18. | K. C. Vernon, D. E. Gómez, and T. J. Davis, “A compact interferometric sensor design using three waveguide coupling,” J. Appl. Phys. |

19. | A. B. Buckman, |

20. | S. K. Sheem, “Optical fiber interferometers with [3x3] directional couplers: Analysis,” J. Appl. Phys. |

21. | K. P. Koo, A. B. Tveten, and A. Dandridge, “Passive stabilization scheme for fiber interferometers using (3x3) fiber directional couplers,” Appl. Phys. Lett. |

22. | P. Hua, B. Jonathan Luff, G. R. Quigley, J. S. Wilkinson, and K. Kawaguchi, “Integrated optical dual Mach-Zehnder interferometer sensor,” Sens. Actuators B Chem. |

23. | H. Fan and P. Berini, “Noise cancellation in long-range surface plasmon dual-output Mach-Zehnder interferometers,” J. Lightwave Technol. |

24. | A. Yariv, |

25. | S. L. Chuang, “Application of the strongly coupled-mode theory to integrated optical devices,” IEEE J. Quantum Electron. |

26. | S. L. Chuang, “A coupled-mode theory for multiwaveguide systems satisfying the reciprocity theorem and power conservation,” J. Lightwave Technol. |

27. | H. Fan, R. Buckley, and P. Berini, “Passive long-range surface plasmon-polariton devices in Cytop,” Appl. Opt. |

28. | P. Berini, R. Charbonneau, N. Lahoud, and G. Mattiussi, “Characterization of long-range surface plasmon-polariton waveguides,” J. Appl. Phys. |

29. | Asahi Glass Co, Ltd., Japan, “Amorphous fluoropolymer CYTOP,” Jan. 2009 [Online]. Available: http://www.agc-cytop.com. |

30. | E. D. Palik and G. Ghosh, |

31. | H. Asiri, “Fabrication of surface plasmon biosensors in CYTOP,” Master’s thesis, Dep. Chem. Biol. Eng., Univ. Ottawa, Ottawa, Canada, 2012. |

32. | C. Chiu, E. Lisicka-Shrzek, R. N. Tait, and P. Berini, “Fabrication of surface plasmon waveguides and devices in Cytop with integrated microfluidic channels,” J. Vac. Sci. Technol. B |

**OCIS Codes**

(230.3120) Optical devices : Integrated optics devices

(240.6680) Optics at surfaces : Surface plasmons

**ToC Category:**

Plasmonics

**History**

Original Manuscript: November 15, 2013

Revised Manuscript: February 3, 2014

Manuscript Accepted: February 3, 2014

Published: February 13, 2014

**Virtual Issues**

Vol. 9, Iss. 4 *Virtual Journal for Biomedical Optics*

**Citation**

Hui Fan, Robert Charbonneau, and Pierre Berini, "Long-range surface plasmon triple-output Mach-Zehnder interferometers," Opt. Express **22**, 4006-4020 (2014)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-22-4-4006

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### References

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