# Silicon Integrated Dual-Mode Interferometer with Differential Outputs

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Designs of Dual-Mode Interferometers

## 3. Operating Principle of the Dual-Mode Interferometer with Differential Outputs

_{bulk}is defined as the change of the phase difference Δφ over the change of the refractive index of the cladding, and can be expressed by

_{sens}. The effective refractive indices of the fundamental and second-order modes are n

_{m1}and n

_{m2}, respectively. The phase difference between the two modes changes with the refractive index of the cladding due to different modal sensitivities resulting from their modal profiles. This fundamental behavior is also the same for other DMIs [5], and the sensitivity of a waveguide cross-section can be characterized by the intrinsic bulk sensitivity to changes in the cladding layer η

_{bulk}, which can be larger than 50%. However, depending on the requested Δφ, the optical signals in the dual-mode waveguide of a type 7 DMI can be coupled to output 1 or output 2 (see Figure 1b).

_{3})

_{2}in water (see Appendix A). The transmission minimum moves towards a longer wavelength due to the phase shift induced by the increased concentration of Pb(II) ions. At the same time, the spectrum is shifted upwards to higher transmitted power levels, i.e., the total losses also depend on the concentration of Pb(II) ions. With a measurement of the transmitted power at only a single wavelength there is neither the possibility to distinguish between phase shift induced change in transmission and loss dependent change in transmission nor the possibility of perceiving input power fluctuations.

_{1}and P

_{2}by

_{1}at 1530 nm to maximum P

_{1}at 1541 nm, where the phase relation ∆φ ranges from 180° to 0°. The well-known problem of estimating a phase shift larger than π can be circumvented [13] by either using a transmission measurement versus time or else by placing several interferometers with different sensing lengths in parallel, which can be done very easily with DMIs.

## 4. Performance of Type 7 Dual-Mode Interferometers

_{1}/P

_{2}at the combiner [12]. Due to different mode profiles in the sensing region, usually the mode losses differ, which consequently decreases the ER (see Figure 5a). This effect is clearly visible in the measured transmission spectra of two MZIs with different arm length differences (see Figure 5b). The additional waveguide loss in one MZI arm decreases the ER.

_{2}layer. Utilizing measurements in the same technology resulting from the cut-back method for a width W of 400 nm and for the fundamental TE mode results in ${\mathsf{\alpha}}_{m1}$ is equal to 3.3 dB/cm at 1550 nm. As a consequence, ${\mathsf{\alpha}}_{m2}$ for W = 420 nm can be estimated to be smaller than 14 dB/cm in the analyzed wavelength range. Taking the smallest loss difference into account and assuming ${\mathsf{\alpha}}_{m2}>\text{}{\mathsf{\alpha}}_{m1}$ results in ${\mathsf{\alpha}}_{m2}$ ≈ 4.5 dB/cm. The variation of the additional loss over wavelength may be closely associated with the influence of stitching errors caused by the e-beam lithography fabrication step. In addition, the wavelength dependency of the mode-to-mode coupling strength should be investigated in further works. In addition to the IL and ER, the thermal dependency is an important characteristic for sensor applications. For type 7 DMIs, the thermal dependency is mainly caused by the phase relation of both modes in the dual-mode waveguide, and can be minimized with a proper waveguide geometry as discussed in [12].

## 5. Comparison between DMI and MZI

_{sens}for each interferometer type, a determination of the additional loss caused by only the sensing region becomes possible. An increased sensor region length leads to a larger sensitivity of the device, although usually there is a compromise between loss and sensitivity of a designed interferometer. The decrease in loss given in dB and gain in sensitivity increase linearly with the sensor region length. Therefore, the product of the sensitivity and the reciprocal additional loss is calculated to make the comparison as fair as possible, and length-independent. The resulting figure of merit (FOM) is the bulk sensitivity per loss, which can be expressed by

_{sens}is the difference of the sensor region waveguide length and ΔIL is the difference in IL of the two interferometers. This parameter and the other results are listed in Table 2 for DMIs and MZIs.

## 6. Discussion and Conclusions

^{−1}in the sensor region of dual-mode interferometers is more than twice as high as in MZIs. This makes the DMI attractive especially when very long sensing waveguides are required.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Appendix A

**Figure A1.**Fabrication of a P(VPS-co-EBA) particle covered dual-mode waveguide. (

**a**) Fabrication steps; (

**b**) Resulting layer stack.

**Figure A2.**Measurement of the resulting phase condition with fixed fibers resulting from a particle-covered DMI and a not-covered DMI by varying concentration of Pb(II) ions in water. The evaluation of the phase condition is done using the minima in the transmission spectra close to 1540 nm. The temperature influence is reduced by recording the solution temperature and using a temperature coefficient of 0.1249 rad/K for the resulting corrected phase shift. The temperature coefficient can be decreased with an optimized waveguide geometry, as shown in [12].

## References

- Dhakal, A.; Wuytens, P.; Peyskens, F.; Jans, K.; Le Thomas, N.; Baets, R. Nanophotonic Waveguide Enhanced Raman Spectroscopy of Biological Submonolayers. ACS Photonics
**2016**, 3, 2141–2149. [Google Scholar] [CrossRef] - Makarona, E.; Petrou, P.; Kakabakos, S.; Misiakos, K.; Raptis, I. Point-of-Need bioanalytics based on planar optical interferometry. Biotechnol. Adv.
**2016**, 34, 209–233. [Google Scholar] [CrossRef] [PubMed] - Duval, D.; González-Guerrero, A.; Dante, S.; Osmond, J.; Monge, R.; Fernández, L.; Zinoviev, K.; Domínguez, C.; Lechuga, M. Nanophotonic lab-on-a-chip platforms including novel bimodal interferometers, microfluidics and grating couplers. Lab Chip
**2012**, 12, 1987–1994. [Google Scholar] [CrossRef] [PubMed] - Hoppe, N.; Diersing, P.; Föhn, T.; Kaschel, M.; Polder, T.; Vogel, W.; Rathgeber, L.; Félix Rosa, M.; Berroth, M. Integrated Dual-Mode Interferometer with Differential Single-Mode Outputs. In Proceedings of the European Conference on Integrated Optics (ECIO), Eindhoven, The Netherlands, 3–5 April 2017. [Google Scholar]
- Ramirez, J.; Lechuga, L.; Gabrielli, L.; Hernandez-Figueroa, H. Study of a low-cost trimodal polymer waveguide for interferometric optical biosensors. Opt. Express
**2015**, 23, 11985–11994. [Google Scholar] [CrossRef] [PubMed] - Chao, T.; Davis, S.; Rommel, S.; Farca, G.; Luey, B.; Martin, A.; Anderson, M. Compact Liquid Crystal Waveguide Based Fourier Transform Spectrometer for In-Situ and Remote Gas and Chemical Sensing. Proc. SPIE
**2008**, 6977, 69770P. [Google Scholar] [CrossRef] - Levy, R.; Ruschin, S. Design of a Single-Channel Modal Interferometer Waveguide Sensor. IEEE Sens. J.
**2009**, 9, 146–153. [Google Scholar] [CrossRef] - Zinoviev, K.; González-Guerrero, A.; Domínguez, C.; Lechuga, M. Integrated Bimodal Waveguide Interferometric Biosensor for Label-Free Analysis. J. Light. Technol.
**2011**, 29, 1926–1930. [Google Scholar] [CrossRef] - Liu, Q.; Kim, K.; Gu, Z.; Kee, J.; Park, M. Single-channel Mach-Zehnder interferometric biochemical sensor based on two-lateral-mode spiral waveguide. Opt. Express
**2014**, 22, 27910–27920. [Google Scholar] [CrossRef] [PubMed] - Bruck, R.; Hainberger, R. Sensitivity and design of grating-assisted bimodal interferometers for integrated optical biosensing. Opt. Express
**2014**, 22, 32344–32352. [Google Scholar] [CrossRef] [PubMed] - Hoppe, N.; Föhn, T.; Félix Rosa, M.P.; Vogel, W.; Sfar Zaoui, W.; Kaschel, M.; Butschke, J.; Letzkus, F.; Berroth, M. Integrated Dual-Mode Waveguide Interferometer. NUSOD
**2015**, 155–156. [Google Scholar] [CrossRef] - Hoppe, N.; Föhn, T.; Diersing, P.; Scheck, P.; Vogel, W.; Félix Rosa, M.; Kaschel, M.; Bach, M.; Berroth, M. Design of an Integrated Dual-Mode Interferometer on 250 nm Silicon-on-Insulator. IEEE J. Sel. Top. Quantum Electron.
**2017**, 23, 444–451. [Google Scholar] [CrossRef] - Dante, S.; Duval, D.; Sepúlveda, B.; González-Guerrero, A.; Sendra, J.; Lechuga, M. All-optical phase modulation for integrated interferometric biosensors. Opt. Express
**2012**, 20, 7195–7205. [Google Scholar] [CrossRef] [PubMed] - Zhang, Z.; Hu, X.; Wang, J. On-chip optical mode exchange using tapered directional coupler. Sci. Rep.
**2015**, 5, 1–7. [Google Scholar] [CrossRef] [PubMed] - Niedergall, K.; Kopp, D.; Besch, S.; Schiestel, T. Mixed-Matrix Membrane Adsorbers for the Selective Binding of Metal Ions from Diluted Solutions. Chem. Ing. Tech.
**2016**, 88, 437–446. [Google Scholar] [CrossRef]

**Figure 1.**Buildup of the DMI with two differential DMI outputs (type 7). The schematic view (

**a**) and the field profiles (

**b**) of the combiner section are shown.

**Figure 2.**Measurements of a type 5 DMI with two different concentrations of Pb(II) ions in water. The optical input power is 0 dBm.

**Figure 3.**(

**a**) Transmission spectra of two differential DMI outputs (type 7) and the corresponding sum. The dual-mode waveguide length and width are 200 μm and 625 nm, respectively; (

**b**) Resulting phase relation.

**Figure 4.**Transmission spectra of two differential DMI outputs (type 7) with straight output tapers and the transmission spectrum of the reference. The dual-mode waveguide length and width are 200 μm and 625 nm, respectively. The transmission of a reference structure is shown, which is used for the determination of the IL.

**Figure 5.**(

**a**) Extinction ratio versus signal loss difference Δα for a 1 mm long DMI; (

**b**) Transmission spectra of two exemplary MZIs with corresponding arm length differences. The decreased extinction ratio can be used for the calculation of the waveguide loss.

**Figure 6.**Loss difference versus wavelength for two fabricated DMIs with a waveguide width of 420 nm and 575 nm.

**Table 1.**A comparison of different TE dual-mode interferometer designs is shown: The schematic buildups of the designs are depicted on the left. Corresponding assets and drawbacks of the design are shown on the right. Notes: 0 indicates large additional space requirements; + indicates minor additional space requirements; ++ indicates large on-chip arrays possible; * indicates theoretical values for balanced mode excitation.

Reference/Year | DMI Array | Excess Loss of Mode Conversion | Single Wavelength Operation | ||
---|---|---|---|---|---|

Type 1(side view) | [7]/2009 | ++ | 0.5 dB * | ✕ | |

Type 2(side view) | [8]/2011 | + | unknown | ✓ | |

Type 3(top view) | [9]/2014 | ++ | 0.5 dB * | ✕ | |

Type 4(side view) | [10]/2014 | ++ | < 0.22 dB * | ✕ | |

Type 5(top view) | [11]/2015 | 0 | < 4.2 dB | ✕ | |

Type 6(top view) | [12]/2016 | ++ | 0.25 dB * < 0.5 dB | ✕ | |

Type 7(top view) | [4]/2017 this work | ++ | 0.55 dB * < 2 dB | ✓ |

**Table 2.**Resulting performance values for DMIs and MZIs close to 1550 nm. The intrinsic bulk sensitivity is simulated with the FIMMWAVE finite difference waveguide mode solver for a refractive index change of 0.01 and for the DMI as difference of the two intrinsic mode sensitivities.

Device | Waveguide Width | Sensor Region Length | Measured IL | Intrinsic Bulk Sensitivity | Measured ER | Bulk Sensitivity per Loss |
---|---|---|---|---|---|---|

MZI | 250 nm | 500 µm | 1 dB | 79% | >30 dB | 1441 dB^{−1} |

5000 µm | 11 dB | >25 dB | ||||

DMI | 575 nm | 500 µm | 2.5 dB | 44% | ≈20 dB | 3237 dB^{−1} |

6400 µm | 5.2 dB | ≈10 dB |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Hoppe, N.; Scheck, P.; Sweidan, R.; Diersing, P.; Rathgeber, L.; Vogel, W.; Riegger, B.; Southan, A.; Berroth, M.
Silicon Integrated Dual-Mode Interferometer with Differential Outputs. *Biosensors* **2017**, *7*, 37.
https://doi.org/10.3390/bios7030037

**AMA Style**

Hoppe N, Scheck P, Sweidan R, Diersing P, Rathgeber L, Vogel W, Riegger B, Southan A, Berroth M.
Silicon Integrated Dual-Mode Interferometer with Differential Outputs. *Biosensors*. 2017; 7(3):37.
https://doi.org/10.3390/bios7030037

**Chicago/Turabian Style**

Hoppe, Niklas, Pascal Scheck, Rami Sweidan, Philipp Diersing, Lotte Rathgeber, Wolfgang Vogel, Benjamin Riegger, Alexander Southan, and Manfred Berroth.
2017. "Silicon Integrated Dual-Mode Interferometer with Differential Outputs" *Biosensors* 7, no. 3: 37.
https://doi.org/10.3390/bios7030037