Broadband CMOS-compatible SOI temperature insensitive Mach-Zehnder interferometer

Peng Xing; Jaime Viegas

doi:10.1364/OE.23.024098

1. Introduction

Silicon has been considered as a promising platform for photonic integrated circuits. The high refractive index of silicon enables the high confinement of light in the waveguides and leads to the reduction of the footprint of the silicon-based photonic devices [1,2]. Also, mature complementary metal-oxide-semiconductor (CMOS) fabrication technology opens the possibility of mass-produced photonic circuits with low cost and high reliability. However, the high thermo-optic (TO) coefficient of silicon which is around 1.86 × 10⁻⁴/K [3] and the high confinement of light in the waveguide core leads to high temperature sensitivity of the silicon photonic devices.

To overcome this limitation for silicon photonics, several solutions have been proposed. One of the solutions is to counteract the positive TO coefficient of silicon by covering the devices with some materials like polymers which have negative TO coefficient [4–7]. However, these polymers cannot undergo high temperature processes and thus are not compatible with modern CMOS processes. Another solution is to stabilize the operational temperature of the devices by heating it dynamically [8–10]. The active heating in this approach consumes extra energy and increases the energy consumption of the silicon photonic circuits. Moreover, the device footprint and fabrication complexity is increased.

Recently, some research groups [11,12] propose an approach to design CMOS compatible passively compensated temperature insensitive Mach-Zehnder interferometer (MZI) in which narrow and wide waveguides with carefully chosen lengths are combined in different arms to make both arms have the same optical path change with temperature to achieve zero spectral shift with temperature. However, as shown in the work from [13], the fabricated device has a temperature sensitivity of 8 pm/K over a narrow spectral range of 30nm. So there is a need to extend the operation spectral range with minimal temperature sensitivity for the MZIs.

In this paper, we propose a design approach for achieving an athermal MZI with near-zero temperature sensitivity over a wide temperature and spectral range by carefully optimizing waveguide width and length. We demonstrate that spectral shift with temperature of the device designed following our improved design approach and fabricated using CMOS-compatible fabrication technology can be reduced to 2.5 pm/K over a 40K temperature range and more than 60 nm spectral range.

2. Design approach and simulation results

2.1 Design approach

In a MZI, assuming that the effective index and length of two arms are $n_{1}$ , $L_{1}$ and $n_{2}$ , $L_{2}$ respectively at temperature $T$ , then the phase condition for destructive interference at wavelength $λ_{0}$ can be expressed as:

m λ_{0} = n_{1} \cdot L_{1} - n_{2} \cdot L_{2}

Here m is a half integer for the destructive interference. If the temperature changes by

Δ T

and the consequential spectral shift is

Δ λ

, the effective index at temperature

T + Δ T

and wavelength

λ_{0} + Δ λ

is

n + \partial n / \partial T \cdot Δ T + \partial n / \partial λ \cdot Δ λ

. Then Eq. (1) can be expressed as:

m (λ_{0} + Δ λ) = (n_{1} + \frac{\partial n_{1}}{\partial T} Δ T + \frac{\partial n_{1}}{\partial λ} Δ λ) L_{1} - (n_{2} + \frac{\partial n_{2}}{\partial T} Δ T + \frac{\partial n_{2}}{\partial λ} Δ λ) L_{2}

The MZI’s spectral shift with temperature at wavelength

λ_{0}

can be derived by combining Eq. (1) and Eq. (2) as shown in Eq. (3) in which

n_{g, 1}

and

n_{g, 2}

correspond to the group index of two arms respectively.

\frac{Δ λ}{Δ T} = \frac{\frac{\partial n_{1}}{\partial T} \cdot L_{1} - \frac{\partial n_{2}}{\partial T} \cdot L_{2}}{n_{g, 1} \cdot L_{1} - n_{g, 2} \cdot L_{2}} \cdot λ_{0} \Rightarrow 0

To make the MZI temperature insensitive, the spectral shift with temperature should be zero. Then the first requirement for athermal operation as proposed by [11,12] can be derived as Eq. (4). However, the behavior of the MZI designed following the first requirement has a great dependence on the wavelength which means that the spectral shift with temperature at

λ_{0}

is zero and increases very fast when the wavelength diverges from

λ_{0}

.

\frac{\partial n_{1}}{\partial T} \cdot L_{1} - \frac{\partial n_{2}}{\partial T} \cdot L_{2} = 0

Two approaches are deployed to derive the second requirement for designing a broadband athermal MZI. The first one is described in Eq. (5). The Free Spectral Range (FSR) of the MZI is expressed in Eq. (6). If the spectral shift with temperature at spectral minima

λ_{0}

is zero as a result of the first requirement – Eq. (5) and the FSR change with temperature is set to zero, the spectral shift at the spectral minima

λ_{0} \pm F S R

should be also zero. By this way, zero spectral shift with temperature can be achieved over a wide spectral range.

\frac{\partial F S R}{\partial T} = 0

F S R = \frac{λ^{2}}{n_{g, 1} \cdot L_{1} - n_{g, 2} \cdot L_{2}}

Another approach to derive the second requirement for athermal operation is to solve Eq. (7) in which the dependence of temperature sensitivity on wavelength is brought to zero. Both these two approaches described in Eq. (5) and Eq. (7) give the same result shown in Eq. (8) which is called the second requirement for athermal operation.

\frac{\partial (Δ λ / Δ T)}{\partial λ} = 0

\frac{\partial^{2} n_{1}}{\partial T \partial λ} \cdot L_{1} - \frac{\partial^{2} n_{2}}{\partial T \partial λ} \cdot L_{2} = 0

In the design of an integrated MZI, the first step is to set its waveguide profiles which include the material and the geometry. Because this work is aiming at addressing the problem induced by the high TO coefficient of silicon, the material of the waveguide core must be silicon. In this work, we choose the most commonly used SOI waveguides shown in Fig. 1(a) as the constituent elements of the MZI. In silicon-on-insulator based waveguides, it is usually hard to change the height of the waveguide due to process constraints. So the only easily changeable dimension of the waveguides is the waveguide width. For our design, the first step is simplified as setting the waveguide width. We start with a simple design that the waveguide in the first arm of MZI has width w₁, length

L_{1}

and the second arm has w₂,

L_{2}

, assuming light mode is TE₀. To make it temperature insensitive and broadband, the length

L_{1}

and

L_{2}

must fulfil the design constraints including FSR requirement in Eq. (6) and two requirements for athermal operation in Eq. (4) and Eq. (8) in which

\partial n_{e f f} / \partial T

,

\partial^{2} n_{e f f} / \partial λ \partial T

and group index can be computed with a numerical method. If two arms in the MZI have the same waveguide w₁ = w₂, Eq. (4) and Eq. (8) will give the solution that

L_{1} = L_{2}

which means that the two arms are identical and this cannot meet the FSR requirement. Thus the waveguide width in two arms should be different w₁ ≠ w₂. When the waveguides are different, the two requirements for athermal operation, Eq. (4) and (8), will give one set of solution (

L_{1}

,

L_{2}

) resulting in that the MZI will have a fixed FSR. However, in some applications, the control over the FSR of the MZI in the design is necessary. To enable independent FSR tuning while maintaining athermal operation, another waveguide (width w₃ and length L₃) is introduced in the second arm. Then the two requirements for athermal operation become the first two equations in Eq. (9). There are infinite number of solutions (

L_{1}

,

L_{2}

,

L_{3}

) for these two equations. Therefore the FSR in Eq. (9) could be set to any number by changing

L_{1}

,

L_{2}

, and

L_{3}

.

{\begin{cases} \frac{\partial n_{1}}{\partial T} \cdot L_{1} - \frac{\partial n_{2}}{\partial T} \cdot L_{2} - \frac{\partial n_{3}}{\partial T} \cdot L_{3} = 0 \\ \frac{\partial^{2} n_{1}}{\partial T \partial λ} \cdot L_{1} - \frac{\partial^{2} n_{2}}{\partial T \partial λ} \cdot L_{2} - \frac{\partial^{2} n_{3}}{\partial T \partial λ} \cdot L_{3} = 0 \\ F S R = \frac{λ^{2}}{n_{g, 1} \cdot L_{1} - n_{g, 2} \cdot L_{2} - n_{g, 2} \cdot L_{3}} \end{cases}

In summary, the design process could be described as following. i) Choose the waveguide widths (w₁, w₂, w₃) which are different from each other. ii) Set the FSR. iii) Calculate

\partial n_{e f f} / \partial T

,

\partial^{2} n_{e f f} / \partial λ \partial T

and group index for three waveguides with a numerical method. iv) Find the solution (

L_{1}

,

L_{2}

,

L_{3}

) for Eq. (9).

Fig. 1 (a) Schematic of the silicon-on-insulator waveguide. (b) Thermo-optic coefficient of TE₀, TM₀, and TE₁ mode of the waveguide as a function of the waveguide width. (c) Group index of TE₀, TM₀, and TE₁ mode of the waveguide as a function of the waveguide width. (d) Dependence of thermo-optic coefficient on wavelength of TE₀, TM₀, and TE₁ mode of the waveguide as a function of the waveguide width.

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2.2 Simulation results

Theoretically, for any combination of (w₁, w₂, w₃₎, there is a solution ( $L_{1}$ , $L_{2}$ , $L_{3}$ ). Different combinations of w₁, w₂, w₃ will give different $L_{1}$ , $L_{2}$ , $L_{3}$ , resulting in different device footprint. To find the design with the smallest device footprint, we need to find the solutions for various combinations of w₁, w₂, w₃. Also, different propagating modes in the same waveguide have different waveguide properties ( $\partial n_{e f f} / \partial T$ , $\partial^{2} n_{e f f} / \partial λ \partial T$ and group index). Changing the mode will also lead to different waveguide lengths ( $L_{1}$ , $L_{2}$ , $L_{3}$ )and thus different device size. So waveguide properties needed in Eq. (9) for quasi TE₀, TM₀, and TE₁ mode of 0.2-1.0µm wide waveguides are computed.

The schematic of the SOI waveguides used in our simulation is shown in Fig. 1(a). The waveguide height is fixed as 220nm with 2µm buried silicon oxide. The waveguides are covered by 2µm silicon oxide. The effective index of the TE₀, TM₀, and TE₁ mode for 0.2-1.0µm wide waveguide is calculated using a full vector Finite Element Method solver for temperatures ranging from 20°C to 40°C and wavelengths from 1.50µm to 1.60µm. The refractive index of silicon and silica at different wavelengths and temperatures are from [14,15].The effective index of the TE₀, TM₀, and TE₁ mode are assumed to be linearly dependent on both temperature and wavelength. From the result, we can see that the linearity of the dependence of the waveguide’s effective index on temperature is very good. However, the waveguide’s effective index has a quadratic dependence on wavelength. This will cause the thermal sensitivity to have a small quadratic dependence on wavelength which will be discussed in section 4. By fitting the computed effective index to temperature and wavelength, $\partial n_{e f f} / \partial T$ , $\partial^{2} n_{e f f} / \partial λ \partial T$ , and group index can be derived. All the results are plotted in Figs. 1(b)-1(d).

3. Design and fabrication

The schematic of the designed device is shown in Fig. 2. Because the symmetry of our SOI waveguides as shown in Fig. 1(a) in both the horizontal and vertical direction is maintained, we cannot use the easily fabricated polarization rotator, for example, the one proposed in [16]. Therefore only the TE₀ and TE₁ mode are considered in the design.

Fig. 2 The schematic of the designed MZI and the TE mode profile in each interferometer arm.

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As shown in Fig. 2, two different TE modes are used in two arms to reduce the footprint of the device which is similar to the idea in [13]. The arm with waveguide width w₁ supports a TE₁ mode while the other arm with waveguides width w₂ and w₃ supports a TE₀ mode; w₂ is set to be 400 nm because the TO coefficient sensitivity with width, for the 400 nm waveguide, is as small as 7.18 × 10⁻⁸(K∙nm)⁻¹, as it can be seen from the slope of the TE₀ (blue) curve in Fig. 1(b). With a fabrication linewidth variation of 10 nm, the TO coefficient of the 400 nm waveguide will only change by 0.38%, allowing for a very stable performance of the designed device. This will increase the device’s fabrication error tolerance. We find that the smaller w₃ is, the more compact the device will be. To balance the propagation loss and the footprint of the device, w₃ is set to be 270 nm. These two waveguides are connected with a 3 μm long adiabatic taper whose effect on the thermal sensitivity is also taken into account and eliminated in the design. w₁ is 600 nm which meets the matching condition for the directional coupler. Another advantage of this design is its high fabrication error tolerance. The TO coefficient sensitivity with width variation for waveguide w₁ and w₃ is 9.1340 × 10⁻⁷(K∙nm)⁻¹ and 1.598 × 10⁻⁶(K∙nm)⁻¹. Assuming the fabrication error is proportional to the waveguide width and is 5%, the spectral shift with temperature in Eq. (3) for a device with such fabrication error is 0.13 pm/K where the device is still temperature insensitive. The FSR of the device is set to be 10 nm. The length of the waveguides satisfying Eq. (9) are listed in Table 1 together with other design parameters. The proposed device is designed to have zero spectral shift with temperature near the vacuum wavelength of 1.55µm.

Table 1. Waveguide length of two arms of the designed MZI

View Table

In the device, the equal split of the light from the input to two arms as well as the mode change from the input TE₀ to TE₁ is realized by a directional coupler which consists of two waveguides with different widths as shown in Fig. 3(a) [17]. While the matching condition is met, the TE₀ mode light can be coupled into the wide waveguide from the narrow waveguide and become TE₁ mode. In our case, as shown in Fig. 3(b), the matching condition means that the effective index of TE₀ mode of the 270 nm wide waveguide equals the effective index of the TE₁ mode of the 600 nm waveguide. To split the light into two arms equally, the coupling length is 10 µm when the gap between two waveguides is 400 nm, as found from three dimensional FDTD simulations.

Fig. 3 (a) Schematic of the directional coupler. (b) Phase matching condition.

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The devices are fabricated on a commercial silicon photonics foundry (IME, Singapore), based on 248 nm deep UV lithography SOI platform (220 nm Si device layer, 2 µm buried oxide, and 2 µm undoped silicon oxide cladding), with all designed devices in accordance with the platform design rules. The details of the fabrication process and design rules can be found in [18]. An array of devices with different dimensions is fabricated. Figure 4 is a micrograph of three fabricated devices. Due to the fabrication error, the waveguide width w₁ in TE₁ arm is measured to be 620 nm and the widths w₂ and w₃ in TE₀ arm are 415 nm and 280 nm respectively, well within our design tolerance of 5%. Also, the error in waveguide length is on the order of a few tens of nanometers. Compared to the length of the arms, which is on the order of hundred micrometers, the error in waveguide length is very small. Assuming that the error in waveguide length is 50 nm for all the three waveguides, the temperature sensitivity of our designed devices will only change by 0.046 pm/K calculated from Eq. (3). Therefore, we can assume that the thermal sensitivity change induced by the fabrication error in waveguide length is negligible.

Fig. 4 Optical micrograph of the fabricated devices.

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4. Measurements

Figure 5 depicts the setup used to characterize the fabricated devices. Light from a tunable laser (Agilent 81800B) is coupled into the waveguide through a lensed fiber. The TE polarized input is achieved using a polarization controller. The devices under test are placed on a thermoelectric cooler which is used to control the temperature of the devices. The light coupled out of the devices is received by a power meter (Agilent 81636B). A laptop is used to communicate with Agilent 8164B in which the tunable laser and power meter are built.

Fig. 5 (a) Sketch of the characterization setup. (b) Setup image.

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The measured spectra at different temperatures ranging from 20°C to 60°C over the spectral range from 1.5 µm to 1.6 µm are shown in Fig. 6(a). The transmission in Fig. 6(a) is normalized to the transmission of waveguides which have the same length and width as the waveguides used to connect the device under test and the fibers. Then, the transmission loss includes the propagation losses of the arms and the excess loss of the two directional couplers.

Fig. 6 (a) Measured spectra of the fabricated device at different temperature. (b) Fitted spectra of the fabricated device at different temperature. (c) Simulated spectral shift with temperature of the designed device, and simulated and measured spectral shift with temperature of the fabricated device.

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Due to fabrication error, the gap between two waveguides in the directional coupler changes from 400 nm to 365 nm. The 3D FDTD simulation of the as-fabricated directional coupler shows that 60% of the light is coupled into the TE₁ arm. The extinction ratio of the MZI is reduced by the power imbalance of the directional coupler.

The losses of the three waveguides (w₁, w₂, w₃) are estimated based on our measurements on test waveguides with a width of 450nm, for which a 2.7 dB/cm propagation loss was obtained from the cutback method, and an analytical model [19] which can be expressed as:

α = \frac{4 σ^{2} h^{3}}{β (w + 2 / p)}

where α is the propagation loss per unit length, σ is waveguide interface roughness, β is the modal propagation constant, w is the waveguide width, h and p is the transverse propagation constants in the waveguide core and cladding. The propagation losses per unit length of the three waveguides (w₁, w₂, w₃) are then 6.94 dB/cm, 3.49 dB/cm, and 9.49 dB/cm, respectively. The propagation losses of the waveguides in the TE₁ arm and the TE₀ arm are 0.2dB and 0.36dB. Additionally, the bends and tapers in the TE₀ arm will increase its propagation loss. So the propagation loss of the TE₀ arm is higher than that of the TE₁ arm. This will further degrade the extinction ratio due to power imbalance. Another important fact is the temperature dependence of the extinction ratio of the transmission spectra caused by the temperature dependence of the directional coupler. When the temperature changes, the effective index of the waveguides will also vary. The resulting change of the coupling efficiency will affect the splitting of the light between two arms and thus the extinction ratio. Nevertheless, the temperature dependence of the extinction ratio is still quite small as seen from Fig. 6(a) and will not affect the thermal sensitivity of the devices.

Due to the very small temperature sensitivity (<5 pm/K), it is very hard to measure the spectral shift from the original spectra. So we get the fitted spectra which is Fig. 6(b). By comparing Figs. 6(a) and 6(b), we find that the fitted spectra represent the original spectra very well. The spectral shift at different wavelength in Fig. 6(c) is measured from the fitted spectra. As shown in Fig. 6(c), the measurement results of the fabricated device match very well with the simulated results. Over the spectral range from 1.54 µm to 1.60 µm, the spectral shift with temperature is less than 2.5 pm/K. In either the designed device or the fabricated device, the dependence of the thermal sensitivity on wavelength is not reduced to zero while the second requirement [Eq. (8)] is satisfied. This is due to the inaccuracy of the approximation in Eq. (2) that the effective index of the waveguides is linearly dependent on the wavelength. In reality, the waveguide’s effective index has quadratic dependence on wavelength as discussed before. This is why the spectral shift with wavelength is parabolic. However, the dependence of the spectral shift on wavelength is brought to a very small number using the second requirement. So near zero temperature sensitivity could be achieved over a wide spectral range.

Also, even with the present of fabrication error, the thermal sensitivity of the fabricated device doesn’t differ largely from the designed device. This is another advantage of this design as discussed in section 3. If we could extend the spectral range of our test light source to 1.62 µm, we believe that the spectral shift with temperature will still be smaller than 2.5pm/K.

5. Conclusion and discussion

An improved approach to design a broadband temperature insensitive all-silicon Mach-Zehnder interferometer is proposed. Following this approach, a device is designed, fabricated and characterized. The dependence of the temperature sensitivity on wavelength is largely reduced. The measured results show that the device has a near-zero (2.5 pm/K) over more than 60 nm spectral range near 1550 nm which is much wider than the previous works reported in the literature. The measurement result matches very well with our simulation result. Also, the athermal spectral range can be extended to 80 nm. The proposed approach is also applicable for the MZIs working on other wavelengths and made of other materials and waveguide geometry.

Acknowledgments

This work is part of the Twinlab 3D stacked chips projects supported by Mubadala Technology, Abu Dhabi, United Arab Emirates. The authors acknowledge IME Singapore for the fabrication of the prototype devices. The authors would like to thank Dr. Marcus Dahlem and Hayk Gevorgyan for their help with the characterization of the fabricated devices.

References and links

1. R. Soref, “The past, present, and future of silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1678–1687 (2006). [CrossRef]

2. V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431(7012), 1081–1084 (2004). [CrossRef] [PubMed]

3. Y. P. Varshni, “Temperature dependence of the energy gap in semiconductors,” Physica 34(1), 149–154 (1967). [CrossRef]

4. M. Han and A. Wang, “Temperature compensation of optical microresonators using a surface layer with negative thermo-optic coefficient,” Opt. Lett. 32(13), 1800–1802 (2007). [CrossRef] [PubMed]

5. M. Ibrahim, J. H. Schmid, A. Aleali, P. Cheben, J. Lapointe, S. Janz, P. J. Bock, A. Densmore, B. Lamontagne, R. Ma, D.-X. Xu, and W. N. Ye, “Athermal silicon waveguides with bridged subwavelength gratings for TE and TM polarizations,” Opt. Express 20(16), 18356–18361 (2012). [CrossRef] [PubMed]

6. J. Teng, P. Dumon, W. Bogaerts, H. Zhang, X. Jian, X. Han, M. Zhao, G. Morthier, and R. Baets, “Athermal Silicon-on-insulator ring resonators by overlaying a polymer cladding on narrowed waveguides,” Opt. Express 17(17), 14627–14633 (2009). [CrossRef] [PubMed]

7. X. Wang, S. Xiao, W. Zheng, F. Wang, Y. Hao, X. Jiang, M. Wang, and J. Yang, “Athermal silicon arrayed waveguide grating with polymer-filled slot structure,” in 2008 5th IEEE International Conference on Group IV Photonics, 2008, pp. 253–255. [CrossRef]

8. S. Manipatruni, R. K. Dokania, B. Schmidt, N. Sherwood-Droz, C. B. Poitras, A. B. Apsel, and M. Lipson, “Wide temperature range operation of micrometer-scale silicon electro-optic modulators,” Opt. Lett. 33(19), 2185–2187 (2008). [CrossRef] [PubMed]

9. M. R. Watts, W. A. Zortman, D. C. Trotter, G. N. Nielson, D. L. Luck, and R. W. Young, “Adiabatic resonant microrings (ARMs) with directlyintegrated thermal microphotonics,” in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference, 2009, paper CPDB10. [CrossRef]

10. R. Amatya, C. W. Holzwarth, F. Gan, H. I. Smith, F. Kärtner, R. J. Ram, and M. A. Popovic, “Low power thermal tuning of second-order microring resonators,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, 2007, p. CFQ5. [CrossRef]

11. M. Uenuma and T. Moooka, “Temperature-independent silicon waveguide optical filter,” Opt. Lett. 34(5), 599–601 (2009). [CrossRef] [PubMed]

12. B. Guha, A. Gondarenko, and M. Lipson, “Minimizing temperature sensitivity of silicon Mach-Zehnder interferometers,” Opt. Express 18(3), 1879–1887 (2010). [CrossRef] [PubMed]

13. S. Dwivedi, H. D’heer, and W. Bogaerts, “A compact all-silicon temperature insensitive filter for WDM and bio-sensing applications,” IEEE Photonics Technol. Lett. 25(22), 2167–2170 (2013). [CrossRef]

14. B. J. Frey, D. B. Leviton, and T. J. Madison, “Temperature dependent refractive index of silicon and germanium,” arXiv:physics/0606168, 62732J (2006).

15. D. B. Leviton and B. J. Frey, “Temperature-dependent absolute refractive index measurements of synthetic fused silica,” ArXiv08050091 (2008).

16. L. Liu, Y. Ding, K. Yvind, and J. M. Hvam, “Efficient and compact TE-TM polarization converter built on silicon-on-insulator platform with a simple fabrication process,” Opt. Lett. 36(7), 1059–1061 (2011). [CrossRef] [PubMed]

17. D. Dai and J. E. Bowers, “Novel concept for ultracompact polarization splitter-rotator based on silicon nanowires,” Opt. Express 19(11), 10940–10949 (2011). [CrossRef] [PubMed]

18. Institute of Microelectronics, “Design rules for silicon photonics prototyping,” https://www.a-star.edu.sg/Portals/30/IME_Research/NanoPhotonicsProgramme/IME_design%20rules%20for%20silicon%20photonics%20prototyping%20V1_2008.pdf.

19. P. K. Tien, “Light waves in thin films and integrated optics,” Appl. Opt. 10(11), 2395–2413 (1971). [CrossRef] [PubMed]

Arm	Mode	Waveguide width (nm)	Waveguide length (µm)
1	TE₁	600	294.6
2	TE₀	400	25.8
2	TE₀	270	374.6

Broadband CMOS-compatible SOI temperature insensitive Mach-Zehnder interferometer

Abstract

1. Introduction

2. Design approach and simulation results

2.1 Design approach

2.2 Simulation results

3. Design and fabrication

4. Measurements

5. Conclusion and discussion

Acknowledgments

References and links

Cited By

Figures (6)

Tables (1)

Equations (10)

Optics Express