Abstract

A novel multimode waveguide based Mach-Zehnder interferometer (MZI) is demonstrated on an SOI platform with the properties of compact footprint and temperature-insensitive operation. The device can achieve a thermal dependence around 13pm/°C in a wavelength range of 40nm. Owing to the utilization of one single straight multimode waveguide, the device is naturally immune to local temperature distributions. The measured results exhibit transmissions with an extinction ratio better than 8dB and a minimum insertion loss lower than 0.31dB over the wavelength range of 1545nm-1585nm. Moreover, the proposed device is compatible with CMOS process.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Silicon photonic integrated circuits based on silicon-on-insulator (SOI) platform are very promising thanks to the compact footprint, high integration level, low cost of integrated photonic devices and compatibility with complementary metal-oxide-semiconductor (CMOS) process [1–4]. Nowadays, silicon photonic multiplexing schemes such as wavelength-division multiplexing (WDM) [5–7], mode-division multiplexing (MDM) [8–11] and the polarization-division multiplexing (PDM) [12,13] have been extensively investigated in pursuits of larger network capacity and higher bandwidth. WDM is widely adopted in modern fiber transmission systems. The key components are filters such as ring resonators, echelle diffraction gratings (EDGs) [14,15], arrayed-waveguide gratings (AWGs) [16–18], or cascaded Mach-Zehnder interferometers (MZIs) [19,20]. For cascaded MZI devices, they are widely studied due to their advances in insertion loss and flat-topped pass-bands. However, owing to the large thermo-optic (TO) coefficient of silicon material (~1.86 × 10−4 RIU/K) [21] the devices suffer from high temperature sensitivity. Several methods have been proposed to alleviate the wavelength shift caused by temperature change. One of the strategies tries to stabilize the temperature by using local heater with a feedback loop [22,23], which calls for additional energy consumption and space. Another strategy tries to lower the temperature sensitivity with special designed waveguides. One method utilizes materials with negative TO coefficient as the cladding layer [24,25], polymers for example, but they are not fully compatible with CMOS process and the reliability issue also concerns. Another approach involves a special design of interference arms, which cancel the temperature sensitivity by choosing the appropriate dimensions of the interfering waveguides. MZI interferometers consist of narrow and wide waveguides [26–28] are designed, because the TO coefficient depends directly upon the mode confinements in a silicon core. However, the path lengths of the two arms also require precise calculations to ensure that the temperature dependences of both arms cancel each other out within a specific temperature range [28], which increases the design complexity for functional filters with requirements of different free spectral ranges (FSRs). What’s more, the footprint or insertion loss of the device is considerably increased, and the extinction ratio may also be limited as the loss differences between two arms. Designs using different polarization [29], mode order [30] and material [31,32] of the two arms are also proposed in the literature. However, all these designs suffer from local temperature changes when the two arms have different temperature distribution [21].

In this paper, we demonstrated an athermal MZI consisting of two symmetrical mode-converters and one multimode waveguide. The input mode is converted into TE0 /TE1 hybrid modes with designed ratio by the first mode-converter and then propagate in the multi-mode waveguide. By choosing an appropriate multimode waveguide width, the temperature dependences of TE0 and TE1 meet each other, and thus achieve the device’s temperature sensitivity. At last, the second mode-converter convert the hybrid modes back to TE0 or TE1 mode. Compared with other approaches using polymer [24,25], local heater [22,23] or two different arms [26–32] reported in the previous literature, our device makes a good job in terms of simple structure, low insertion loss and compact footprint. Except for the global temperature changes, the use of one single multimode waveguide makes the device naturally immune to local temperature changes. What’s more, for an athermal MZI with two special-designed arms, both waveguide’s width and length are tailored in order to obtain a temperature-insensitive operation, resulting in complicated design of devices with different FSRs. The device is fabricated with CMOS compatible process and a spectra temperature shift less than 13pm/°C from 1545nm-1585nm and an insertion loss less than 0.31dB are demonstrated.

2. Design and simulation results of Mach-Zehnder interferometer

Figures 1(a) and 1(b) sketch the core structure and schematic of the Mach-Zehnder interferometer. The proposed device is composed of two mode converters and one multimode waveguide. The hybrid modes are excited after the mode converter when TE0 mode input. After propagating in the multimode waveguide, the two modes combine together with another mode converter and interfere with each other. The response of the device depends on the phase differences between two modes in the multimode waveguide. For in-phase and out-of-phase conditions, TE0 or TE1 mode is obtained at the output separately. Directional couplers could be added at the output to separate the two modes to different output waveguides, as shown in Fig. 1(b). The device works well for TE1 mode input also. To minimize temperature sensitivity, the width of multimode waveguide is carefully designed to achieve the same thermo-optic coefficient. Thus a compact temperature-insensitive multimode waveguide based MZI is constructed.

 figure: Fig. 1

Fig. 1 (a) Core structure of the Mach-Zehnder interferometer. The MZI consists of two symmetrical mode converters and a straight multimode waveguide (b) Schematic of the MZI. The mode converter can convert the TE0 mode into TE0/TE1 hybrid modes. The interference is achieved due to the different group index in different modes. When the TE0 mode input to the device, two interference curves can be obtained through TE0 mode output and TE1 mode output, respectively. Similar to the TE1 mode input to the device.

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2.1 Design of the mode converter

The structure of the mode converter is shown in Fig. 2, which is used to convert the input TE0 or TE1 mode into TE0/TE1 hybrid modes. The mode converter consists of three parts: two asymmetric tapers and a straight multimode waveguide. Taking TE1 mode input as an example, the wave fronts of the TE1 mode transmitted with different effective lengths due to the asymmetry of the device in the y direction. When the corresponding parameter satisfies the phase matching condition Δφ=2π×ΔLeffλ=π (here Δφ and ΔLeff are the effective path difference of the antiphase components in TE1 wavefront), the input TE1 mode is completely converted to the TE0 mode. What’s more, since the λ and ΔLeff are temperature independent, the mode converter is a temperature insensitive device. A more detailed discussion of the mode converter can be found in [33]. We use Eigen mode Expansion (EME) method to optimize the device and find the TE0-TE1 conversion efficiency over 99.9% with the parameters W1, W2, W3, L1, L2 and L3 of 1200nm, 1300nm, 500nm, 7600nm, 3600nm, and 5100nm, respectively. In order to obtain an arbitrary ratio between TE0 and TE1 modes through the mode converter, we scanned the parameter W2 while keeping other parameters fixed, the corresponding results are illustrated in Fig. 3. One can see that with a variation range from 1.30 to 2.15μm for W2, the mode converter can convert the TE0 mode into a hybrid mode composed by arbitrary ratios of TE0/TE1 with an insertion loss less than 0.13dB. In this paper, we take the value of W2 with 1.95μm (TE0:TE1 = 50:50) in following simulation.

 figure: Fig. 2

Fig. 2 Schematic of the mode converter in the MZI. The mode converter can convert the TE0 or TE1 mode into TE0/TE1 hybrid modes.

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 figure: Fig. 3

Fig. 3 Simulated results of transmission curves of TE0 -TE0 and TE0-TE1 via different width of W2 in mode converter.

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2.2 Temperature characteristic analysis

The temperature characteristics of the MZI is discussed in this section. As the device works with two modes in one single multimode waveguide, the waveguide length L is fixed and a group index difference Δng exits between the TE0 and TE1. The Free Spectral Range (FSR) is defined by the Eq. (1):

FSR=λ2ng(TE0)*Lng(TE1)*L

Here λ is the center wavelength. As wavelength dispersion is considered, the thermal sensitivity of MZI can be described by

dλdT=λ(dneff(TE0)dTdneff(TE1)dT)ng(TE0)ng(TE1)

In order to achieve the temperature insensitivity, the wavelength shift with temperature dλdT should be zero.

In the proposed device, the height of the waveguide is fixed at 220nm. Standard SiO2 cladding is used to meet the requirement of large scale integrations with other photonic devices. The parameters of TOCs are chosen as 0.08x10−4/°C for SiO2 top cladding and 1.86x10−4/°C for silicon, respectively [34]. And the refractive indices of Si and SiO2 are set as 3.455 and 1.445 in the simulation. The dneffdT of different widths of the waveguide are calculated by the commercial simulation software package (Lumerical Mode Solutions) and the results is sketched in Fig. 4. Here the change of dneffdT comes from the difference of propagation constant and optical confinement [28]. We can see two curves crossing at 646nm, dneffdT for both TE0 mode and TE1 mode are equal to 1.96x10−4/°C. According to the Eq. (2), temperature dependence can be eliminated in this case. Hence, the width of the multimode waveguide is set as 646nm.

 figure: Fig. 4

Fig. 4 Calculated temperature dependence of the effective index for the TE0 (black) and TE1 (red) modes on the waveguide width of the multimode waveguide with the height of 220nm.

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2.3 Simulation results

Finally, the properties of the whole device is calculated. Figures 5(a)-5(b) shows the simulated wavelength response of the whole MZI interferometer. The length of delay line is set at 1100μm. When TE0 mode launches into the left port of the waveguide, the mode converter first converts the mode into TE0/TE1 hybrid mode. Then the hybrid mode transmit in the straight multimode waveguide. At last, the TE0/TE1 hybrid modes are completely converted to TE0 mode or TE1 mode at different wavelengths by another mode converter. The light propagation is similar to the TE1 mode input to the device. The insertion loss of TE0-TE0, TE0-TE1, TE1-TE0, TE1-TE1 are 0.025dB, 0.25dB, 0.25dB and 0.15dB over the wavelength range from 1545nm-1585nm. The extinction ratio of better than −20dB are obtained near 1550nm. As can be seen from Fig. 5, TE0-TE1 and TE1-TE0 have the same transmission curve, which is due to the principle of optical reversibility.

 figure: Fig. 5

Fig. 5 Simulation results of (a) TE0 input-TE0/TE1 output (b) TE1 input-TE0/TE1 output MZI. The insertion loss of TE0-TE0, TE0-TE1, TE1-TE0, and TE1-TE1 are 0.025dB, 0.25dB, 0.25dB and 0.15dB over the wavelength range from 1545nm-1585nm. The extinction ratio of better than −20dB are obtained near 1550nm.

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The transmission spectra of the MZI are simulated at the temperatures of 20°C and 50°C in Fig. 6(b). It is noteworthy that a minor spectral shift with temperature is seen over a 40nm wavelength span from 1545 nm to 1585 nm. And the thermal sensitivity of the device is less than 13pm/°C over the 40nm wavelength range. The temperature dependence on the multimode-waveguide width is also simulated with a width variation of ± 5nm. From the results in Figs. 6(a)-6(c), it can be found the center wavelength with minimum temperature dependence shifts to a shorter one with increasing waveguide width. Instead, the minimum thermal sensitivity remains less than 13pm/°C

 figure: Fig. 6

Fig. 6 TE0-TE0 at 20°C (black) and 50°C (red) simulated with different multimode waveguide widths (a) 641nm (b) 646 nm (c) 651nm. The thermal sensitivity of the device is less than 13pm/°C over the 40nm wavelength range.

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3. Fabrication and measurements

The proposed device is fabricated on a SOI wafer with a top silicon thickness of 220nm and a buried oxide (BOX) layer of 3μm. Electron beam lithography (EBL) is used to define the waveguide pattern. Then the silicon waveguides are formed by inductively coupled plasma reactive ion etching (ICP-RIE). 70nm etched grooves are formed on silicon layer for light coupling. Finally, a 1-μm SiO2 layer was cladded on the wafer surface to protect the waveguides and achieve monolithic integration of active devices.

The fabricated device is tested on a temperature controlled mount which can precisely controls the temperature of device. And the temperature was raised from room temperature to high temperature with an interval of 10°C during the test. In order to ensure the temperature of controlled mount consistent with the device, it's necessary to keep the heating time long enough and use an infrared thermometer to test the chip temperature during the test. Light from a tunable laser is coupled into the waveguide through a standard single mode fiber. Polarization controller is also applied for TE0 input. And directional couplers are added at TE1 input and output at the ends of the devices for the conversion between TE0 mode and TE1 mode to realize a TE1 mode input. Finally, the light of the device is coupled out through another grating coupler and received by a powermeter.

Figures 7(a) and 7(b) depict the normalized measured transmission spectrum of the fabricated MZI at different ports. We can observe the clear interference patterns and the minimum insertion loss and extinction ratio around 1550nm of TE0 input- TE0 output/ TE1 input - TE1 output to be about 0.23dB and 8dB, while 0.31dB and 13dB for TE0 input-TE1 output / TE1 input-TE0 output, respectively. Compared with the Fig. 5, the experimental results are generally consistent with the simulation results except for the property of extinction ratio, which is reduced by 10dB in the test result of TE0-TE0. The fabrication tolerance analysis of the mode converter in [31] shows that with a width deviation of ± 50 nm and a top-Si thickness deviation of ± 20 nm, the variation of conversion efficiency within 0.2dB. However, the background TE0 mode comes from inefficient conversion of mode converter, it propagates through the whole devices, resulting in an extinction ratio reduction of 11 dB under the condition of 0.2 dB mode conversion loss. And it can also be found the extinction ratio is systematically better for TE0-TE1 than TE0-TE0, which caused by the filtering function of asymmetric directional coupler at the output end.

 figure: Fig. 7

Fig. 7 Measured transmission curves of (a) TE0 input –TE0 output(black)/ TE0 input –TE1 output(dark red) (b) TE1 input –TE0 output(blue)/ TE1 input –TE1 output(green) at 20°C. The measured results show the minimum insertion loss lower than 0.31dB with a minimum extinction ratio larger than 8dB for all channels from 1545nm to 1585nm.

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To verify the temperature characteristics of the device, we measured the performance of the device at different substrate temperatures. Figure 8 records the transmission spectrums measured from 20°C to 50°C with an interval of 10°C at each port, respectively. We can find the thermal sensitivity is less than 13pm/°C over the 1545-1585nm.The proposed device achieves a temperature sensitivity reduction of over 80% compared to 80pm/°C thermal sensitivity of conventional devices. For wavelength shift out of this band caused by temperature change, since the TO coefficients are the function of wavelength, the wavelength shift with the temperature dλdT defines in Eq. (2) is less than zero at shorter wavelengths and the interference pattern is red-shifted. While at longer wavelengths, dλdT is greater than zero and the spectrum is blue-shifted. The coefficient of dλdT is brought to zero at the center wavelength, thus enabling temperature insensitivity characteristics of the device. It is found in Fig. 8 that the extinction ratio changes with temperature increasing, especially for TE0 input - TE1 output, which is caused by the directional couplers added at the end output for TE1-TE0 mode conversion. The phase matching condition is no longer satisfied because the group index of the mode changes with temperature, resulting in the change of conversion efficiency. Figure 9 illustrates the approximate calculation of the extinction ratio as a function of the conversion efficiency. It can be seen from the calculation results that when the mode conversion efficiency of the directional coupler is less than 95%, the extinction ratio of the device is reduced more than 10 dB. This is the main reason for the extinction ratio are not good as expected and a fabrication tolerant coupler is used for further improvement.

 figure: Fig. 8

Fig. 8 Measured transmission curves of (a) TE0 input –TE0 output (b) TE0 input –TE1 output (c) TE1 input –TE0 output (d) TE1 input –TE1 output at 20°C (black)/30°C (purple)/40°C (blue)/50°C (orange). The thermal sensitivity of the device is less than 13 pm/°C over the 40nm wavelength range.

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 figure: Fig. 9

Fig. 9 Simulated results of extinction ratio vary with the conversion efficiency of directional coupler.

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4. Conclusion

In summary, a novel temperature-insensitive Mach-Zehnder interferometer based on one single multimode waveguide is demonstrated in this paper. Temperature independent operation is realized by carefully choosing the width of the multimode waveguide. The proposed device exhibits a thermal sensitivity less than 13pm/°C over a wavelength range of 40nm. The measured results show the minimum insertion loss are lower than 0.31dB with a minimum extinction ratio larger than 8dB for all channels from 1545nm to 1585nm. Using only one multimode waveguide in the device reduces the width of the device to 1.95μm. For further research, a functional athermal filter can be obtained by cascading the multimode waveguide based MZI. It can also be used in future WDM and MDM combined multiplexing communications systems.

Funding

National Key Research and Development Program of China (2017YFA0206403); National Natural Science Foundation of China (61475180); Science and Technology Commission of Shanghai Municipality (16ZR1442600); Strategic Priority Research Program of Chinese Academy of Sciences (XDB24020400); Shanghai Municipal Science and Technology Major Project (2017SHZDZX03); Shanghai Sailing Program (18YF1428100).

References

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6. L. Chen, C. R. Doerr, L. Buhl, Y. Baeyens, and R. A. Aroca, “Monolithically Integrated 40-Wavelength Demultiplexer and Photodetector Array on Silicon,” IEEE Photonic. Technol. Lett. 23(13), 869–871 (2011). [CrossRef]  

7. P. Dong, “Silicon Photonic Integrated Circuits for Wavelength-Division Multiplexing Applications,” IEEE J. Sel. Top. Quantum Electron. 22(6), 370–378 (2016). [CrossRef]  

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9. J. B. Driscoll, C. P. Chen, R. R. Grote, B. Souhan, J. I. Dadap, A. Stein, M. Lu, K. Bergman, and R. M. Osgood Jr., “A 60 Gb/s MDM-WDM Si photonic link with < 0.7 dB power penalty per channel,” Opt. Express 22(15), 18543–18555 (2014). [CrossRef]   [PubMed]  

10. N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013). [CrossRef]   [PubMed]  

11. M. Hayee, M. Cardakli, A. Sahin, and A. Willner, “Doubling of bandwidth utilization using two orthogonal polarizations and power unbalancing in a polarization-division-multiplexing scheme,” IEEE Photonic. Technol. Lett. 13(8), 881–883 (2001). [CrossRef]  

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13. J. Wang, S. He, and D. Dai, “On‐chip silicon 8‐channel hybrid (de) multiplexer enabling simultaneous mode‐and polarization‐division‐multiplexing,” Laser Photonics Rev. 8(2), L18–L22 (2014). [CrossRef]  

14. J. Brouckaert, W. Bogaerts, P. Dumon, D. Van Thourhout, and R. Baets, “Planar Concave Grating Demultiplexer Fabricated on a Nanophotonic Silicon-on-Insulator Platform,” J. Lightwave Technol. 25(5), 1269–1275 (2007). [CrossRef]  

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References

  • View by:

  1. G. T. Reed, “Device physics: the optical age of silicon,” Nature 427(6975), 595–596 (2004).
    [Crossref] [PubMed]
  2. R. Soref, “Silicon Photonics: A Review of Recent Literature,” Silicon 2(1), 1–6 (2010).
    [Crossref]
  3. T. Baehrjones, T. Pinguet, P. L. Guoqiang, S. Danziger, D. Prather, and M. Hochberg, “Myths and rumours of silicon photonics,” Nat. Photonics 6(4), 206–208 (2012).
    [Crossref]
  4. H. Li, H. Wang, L. You, P. Hu, W. Shen, W. Zhang, X. Yang, L. Zhang, H. Zhou, Z. Wang, and X. Xie, “Multispectral superconducting nanowire single photon detector,” Opt. Express 27(4), 4727–4733 (2019).
    [Crossref] [PubMed]
  5. C. A. Brackett, “Dense wavelength division multiplexing networks: Principle and applications,” IEEE J. Sel. Areas Comm. 8(6), 948–964 (1990).
    [Crossref]
  6. L. Chen, C. R. Doerr, L. Buhl, Y. Baeyens, and R. A. Aroca, “Monolithically Integrated 40-Wavelength Demultiplexer and Photodetector Array on Silicon,” IEEE Photonic. Technol. Lett. 23(13), 869–871 (2011).
    [Crossref]
  7. P. Dong, “Silicon Photonic Integrated Circuits for Wavelength-Division Multiplexing Applications,” IEEE J. Sel. Top. Quantum Electron. 22(6), 370–378 (2016).
    [Crossref]
  8. J. Wang, P. Chen, S. Chen, Y. Shi, and D. Dai, “Improved 8-channel silicon mode demultiplexer with grating polarizers,” Opt. Express 22(11), 12799–12807 (2014).
    [Crossref] [PubMed]
  9. J. B. Driscoll, C. P. Chen, R. R. Grote, B. Souhan, J. I. Dadap, A. Stein, M. Lu, K. Bergman, and R. M. Osgood, “A 60 Gb/s MDM-WDM Si photonic link with < 0.7 dB power penalty per channel,” Opt. Express 22(15), 18543–18555 (2014).
    [Crossref] [PubMed]
  10. N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
    [Crossref] [PubMed]
  11. M. Hayee, M. Cardakli, A. Sahin, and A. Willner, “Doubling of bandwidth utilization using two orthogonal polarizations and power unbalancing in a polarization-division-multiplexing scheme,” IEEE Photonic. Technol. Lett. 13(8), 881–883 (2001).
    [Crossref]
  12. P. Dong, C. Xie, L. Chen, L. L. Buhl, and Y.-K. Chen, “112-Gb/s monolithic PDM-QPSK modulator in silicon,” Opt. Express 20(26), B624–B629 (2012).
    [Crossref] [PubMed]
  13. J. Wang, S. He, and D. Dai, “On‐chip silicon 8‐channel hybrid (de) multiplexer enabling simultaneous mode‐and polarization‐division‐multiplexing,” Laser Photonics Rev. 8(2), L18–L22 (2014).
    [Crossref]
  14. J. Brouckaert, W. Bogaerts, P. Dumon, D. Van Thourhout, and R. Baets, “Planar Concave Grating Demultiplexer Fabricated on a Nanophotonic Silicon-on-Insulator Platform,” J. Lightwave Technol. 25(5), 1269–1275 (2007).
    [Crossref]
  15. D. Chowdhury, “Design of low-loss and polarization-insensitive reflection grating-based planar demultiplexers,” IEEE J. Sel. Top. Quantum. Electron. 6(2), 233–239 (2000).
    [Crossref]
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  18. J. Wang, Z. Sheng, L. Li, A. Pang, A. Wu, W. Li, X. Wang, S. Zou, M. Qi, and F. Gan, “Low-loss and low-crosstalk 8 × 8 silicon nanowire AWG routers fabricated with CMOS technology,” Opt. Express 22(8), 9395–9403 (2014).
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  22. C. Li, J. H. Song, J. Zhang, H. Zhang, S. Chen, M. Yu, and G. Q. Lo, “Silicon polarization independent microring resonator-based optical tunable filter circuit with fiber assembly,” Opt. Express 19(16), 15429–15437 (2011).
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2019 (1)

2017 (2)

2016 (3)

2015 (4)

D. Chen, X. Xiao, L. Wang, Y. Yu, W. Liu, and Q. Yang, “Low-loss and fabrication tolerant silicon mode-order converters based on novel compact tapers,” Opt. Express 23(9), 11152–11159 (2015).
[Crossref] [PubMed]

S. Dwivedi, H. D’Heer, and W. Bogaerts, “Maximizing Fabrication and Thermal Tolerances of All-Silicon FIR Wavelength Filters,” IEEE Photonic. Technol. Lett. 27(8), 871–874 (2015).
[Crossref]

P. Xing and J. Viegas, “Broadband CMOS-compatible SOI temperature insensitive Mach-Zehnder interferometer,” Opt. Express 23(19), 24098–24107 (2015).
[Crossref] [PubMed]

T. Hiraki, H. Fukuda, K. Yamada, and T. Yamamoto, “Small Sensitivity to Temperature Variations of Si-Photonic Mach–Zehnder Interferometer Using Si and SiN Waveguides,” Front. Mater. 2, 26 (2015).
[Crossref]

2014 (5)

2013 (2)

J. Zou, X. Jiang, X. Xiang, T. Lang, and J. J. He, “Ultra-Compact Birefringence-Compensated Arrayed Waveguide Grating Triplexer Based on Silicon-On-Insulator,” J. Lightwave Technol. 31(12), 1935–1940 (2013).
[Crossref]

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

2012 (2)

P. Dong, C. Xie, L. Chen, L. L. Buhl, and Y.-K. Chen, “112-Gb/s monolithic PDM-QPSK modulator in silicon,” Opt. Express 20(26), B624–B629 (2012).
[Crossref] [PubMed]

T. Baehrjones, T. Pinguet, P. L. Guoqiang, S. Danziger, D. Prather, and M. Hochberg, “Myths and rumours of silicon photonics,” Nat. Photonics 6(4), 206–208 (2012).
[Crossref]

2011 (2)

L. Chen, C. R. Doerr, L. Buhl, Y. Baeyens, and R. A. Aroca, “Monolithically Integrated 40-Wavelength Demultiplexer and Photodetector Array on Silicon,” IEEE Photonic. Technol. Lett. 23(13), 869–871 (2011).
[Crossref]

C. Li, J. H. Song, J. Zhang, H. Zhang, S. Chen, M. Yu, and G. Q. Lo, “Silicon polarization independent microring resonator-based optical tunable filter circuit with fiber assembly,” Opt. Express 19(16), 15429–15437 (2011).
[Crossref] [PubMed]

2010 (2)

2009 (2)

2007 (1)

2004 (1)

G. T. Reed, “Device physics: the optical age of silicon,” Nature 427(6975), 595–596 (2004).
[Crossref] [PubMed]

2001 (1)

M. Hayee, M. Cardakli, A. Sahin, and A. Willner, “Doubling of bandwidth utilization using two orthogonal polarizations and power unbalancing in a polarization-division-multiplexing scheme,” IEEE Photonic. Technol. Lett. 13(8), 881–883 (2001).
[Crossref]

2000 (1)

D. Chowdhury, “Design of low-loss and polarization-insensitive reflection grating-based planar demultiplexers,” IEEE J. Sel. Top. Quantum. Electron. 6(2), 233–239 (2000).
[Crossref]

1996 (1)

H. Tanobe, Y. Kondo, Y. Kadota, H. Yasaka, and Y. Yoshikuni, “A Temperature Insensitive InGaAsP/InP Wavelength Filter,” IEEE Photonic. Technol. Lett. 8(11), 1489–1491 (1996).
[Crossref]

1990 (1)

C. A. Brackett, “Dense wavelength division multiplexing networks: Principle and applications,” IEEE J. Sel. Areas Comm. 8(6), 948–964 (1990).
[Crossref]

Adibi, A.

P. Alipour, E. S. Hosseini, A. A. Eftekhar, B. Momeni, and A. Adibi, “Temperature-insensitive silicon microdisk resonators using polymeric cladding layers, ” in Lasers and Electro-Optics, 2009 and 2009 Conference on Quantum electronics and Laser Science Conference. CLEO/QELS 2009 (IEEE, 2009), pp. 1–2.
[Crossref]

Alipour, P.

P. Alipour, E. S. Hosseini, A. A. Eftekhar, B. Momeni, and A. Adibi, “Temperature-insensitive silicon microdisk resonators using polymeric cladding layers, ” in Lasers and Electro-Optics, 2009 and 2009 Conference on Quantum electronics and Laser Science Conference. CLEO/QELS 2009 (IEEE, 2009), pp. 1–2.
[Crossref]

Aroca, R. A.

L. Chen, C. R. Doerr, L. Buhl, Y. Baeyens, and R. A. Aroca, “Monolithically Integrated 40-Wavelength Demultiplexer and Photodetector Array on Silicon,” IEEE Photonic. Technol. Lett. 23(13), 869–871 (2011).
[Crossref]

Baehrjones, T.

T. Baehrjones, T. Pinguet, P. L. Guoqiang, S. Danziger, D. Prather, and M. Hochberg, “Myths and rumours of silicon photonics,” Nat. Photonics 6(4), 206–208 (2012).
[Crossref]

Baets, R.

Baeyens, Y.

L. Chen, C. R. Doerr, L. Buhl, Y. Baeyens, and R. A. Aroca, “Monolithically Integrated 40-Wavelength Demultiplexer and Photodetector Array on Silicon,” IEEE Photonic. Technol. Lett. 23(13), 869–871 (2011).
[Crossref]

Bergman, K.

Bogaerts, W.

Bozinovic, N.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

Brackett, C. A.

C. A. Brackett, “Dense wavelength division multiplexing networks: Principle and applications,” IEEE J. Sel. Areas Comm. 8(6), 948–964 (1990).
[Crossref]

Brouckaert, J.

Buhl, L.

L. Chen, C. R. Doerr, L. Buhl, Y. Baeyens, and R. A. Aroca, “Monolithically Integrated 40-Wavelength Demultiplexer and Photodetector Array on Silicon,” IEEE Photonic. Technol. Lett. 23(13), 869–871 (2011).
[Crossref]

Buhl, L. L.

Cardakli, M.

M. Hayee, M. Cardakli, A. Sahin, and A. Willner, “Doubling of bandwidth utilization using two orthogonal polarizations and power unbalancing in a polarization-division-multiplexing scheme,” IEEE Photonic. Technol. Lett. 13(8), 881–883 (2001).
[Crossref]

Chen, C. P.

Chen, D.

Chen, L.

P. Dong, C. Xie, L. Chen, L. L. Buhl, and Y.-K. Chen, “112-Gb/s monolithic PDM-QPSK modulator in silicon,” Opt. Express 20(26), B624–B629 (2012).
[Crossref] [PubMed]

L. Chen, C. R. Doerr, L. Buhl, Y. Baeyens, and R. A. Aroca, “Monolithically Integrated 40-Wavelength Demultiplexer and Photodetector Array on Silicon,” IEEE Photonic. Technol. Lett. 23(13), 869–871 (2011).
[Crossref]

Chen, P.

Chen, S.

Chen, Y.-K.

Chowdhury, D.

D. Chowdhury, “Design of low-loss and polarization-insensitive reflection grating-based planar demultiplexers,” IEEE J. Sel. Top. Quantum. Electron. 6(2), 233–239 (2000).
[Crossref]

Chu, T.

D’Heer, H.

S. Dwivedi, H. D’Heer, and W. Bogaerts, “Maximizing Fabrication and Thermal Tolerances of All-Silicon FIR Wavelength Filters,” IEEE Photonic. Technol. Lett. 27(8), 871–874 (2015).
[Crossref]

Dadap, J. I.

Dai, D.

J. Wang, P. Chen, S. Chen, Y. Shi, and D. Dai, “Improved 8-channel silicon mode demultiplexer with grating polarizers,” Opt. Express 22(11), 12799–12807 (2014).
[Crossref] [PubMed]

J. Wang, S. He, and D. Dai, “On‐chip silicon 8‐channel hybrid (de) multiplexer enabling simultaneous mode‐and polarization‐division‐multiplexing,” Laser Photonics Rev. 8(2), L18–L22 (2014).
[Crossref]

Danziger, S.

T. Baehrjones, T. Pinguet, P. L. Guoqiang, S. Danziger, D. Prather, and M. Hochberg, “Myths and rumours of silicon photonics,” Nat. Photonics 6(4), 206–208 (2012).
[Crossref]

Deng, Q.

DeRose, C. T.

C. T. DeRose, M. R. Watts, D. C. Trotter, and D. L. Luck, “Silicon microring modulator with integrated heater and temperature sensor for thermal control, ” in Conference on Lasers and Electro-optics (Optical Society of America, 2010), paper CThJ3.
[Crossref]

Doerr, C. R.

L. Chen, C. R. Doerr, L. Buhl, Y. Baeyens, and R. A. Aroca, “Monolithically Integrated 40-Wavelength Demultiplexer and Photodetector Array on Silicon,” IEEE Photonic. Technol. Lett. 23(13), 869–871 (2011).
[Crossref]

Dong, P.

P. Dong, “Silicon Photonic Integrated Circuits for Wavelength-Division Multiplexing Applications,” IEEE J. Sel. Top. Quantum Electron. 22(6), 370–378 (2016).
[Crossref]

P. Dong, C. Xie, L. Chen, L. L. Buhl, and Y.-K. Chen, “112-Gb/s monolithic PDM-QPSK modulator in silicon,” Opt. Express 20(26), B624–B629 (2012).
[Crossref] [PubMed]

Driscoll, J. B.

Dumon, P.

Dwivedi, S.

S. Dwivedi, H. D’Heer, and W. Bogaerts, “Maximizing Fabrication and Thermal Tolerances of All-Silicon FIR Wavelength Filters,” IEEE Photonic. Technol. Lett. 27(8), 871–874 (2015).
[Crossref]

Eftekhar, A. A.

P. Alipour, E. S. Hosseini, A. A. Eftekhar, B. Momeni, and A. Adibi, “Temperature-insensitive silicon microdisk resonators using polymeric cladding layers, ” in Lasers and Electro-Optics, 2009 and 2009 Conference on Quantum electronics and Laser Science Conference. CLEO/QELS 2009 (IEEE, 2009), pp. 1–2.
[Crossref]

Fournier, M.

Frandsen, L. H.

X. Guan and L. H. Frandsen, “All-silicon thermal independent Mach-Zehnder interferometer with multimode waveguides,” in IEEE 13th International Conference on Group IV Photonics (IEEE, 2016), pp. 8–9.
[Crossref]

Fu, Y.

Fukuda, H.

T. Hiraki, H. Fukuda, K. Yamada, and T. Yamamoto, “Small Sensitivity to Temperature Variations of Si-Photonic Mach–Zehnder Interferometer Using Si and SiN Waveguides,” Front. Mater. 2, 26 (2015).
[Crossref]

Gan, F.

Gao, G.

Gondarenko, A.

Grote, R. R.

Guan, X.

X. Guan and L. H. Frandsen, “All-silicon thermal independent Mach-Zehnder interferometer with multimode waveguides,” in IEEE 13th International Conference on Group IV Photonics (IEEE, 2016), pp. 8–9.
[Crossref]

Guha, B.

Guoqiang, P. L.

T. Baehrjones, T. Pinguet, P. L. Guoqiang, S. Danziger, D. Prather, and M. Hochberg, “Myths and rumours of silicon photonics,” Nat. Photonics 6(4), 206–208 (2012).
[Crossref]

Han, X.

Hayee, M.

M. Hayee, M. Cardakli, A. Sahin, and A. Willner, “Doubling of bandwidth utilization using two orthogonal polarizations and power unbalancing in a polarization-division-multiplexing scheme,” IEEE Photonic. Technol. Lett. 13(8), 881–883 (2001).
[Crossref]

He, J. J.

He, S.

H. Yang, J. Zhang, Y. Zhu, X. Zhou, S. He, and L. Liu, “Ultra-compact and temperature-insensitive Mach-Zehnder interferometer based on one multimode waveguide on silicon,” Opt. Lett. 42(3), 615–618 (2017).
[Crossref] [PubMed]

J. Wang, S. He, and D. Dai, “On‐chip silicon 8‐channel hybrid (de) multiplexer enabling simultaneous mode‐and polarization‐division‐multiplexing,” Laser Photonics Rev. 8(2), L18–L22 (2014).
[Crossref]

Hiraki, T.

T. Hiraki, H. Fukuda, K. Yamada, and T. Yamamoto, “Small Sensitivity to Temperature Variations of Si-Photonic Mach–Zehnder Interferometer Using Si and SiN Waveguides,” Front. Mater. 2, 26 (2015).
[Crossref]

Hochberg, M.

T. Baehrjones, T. Pinguet, P. L. Guoqiang, S. Danziger, D. Prather, and M. Hochberg, “Myths and rumours of silicon photonics,” Nat. Photonics 6(4), 206–208 (2012).
[Crossref]

Hosseini, E. S.

P. Alipour, E. S. Hosseini, A. A. Eftekhar, B. Momeni, and A. Adibi, “Temperature-insensitive silicon microdisk resonators using polymeric cladding layers, ” in Lasers and Electro-Optics, 2009 and 2009 Conference on Quantum electronics and Laser Science Conference. CLEO/QELS 2009 (IEEE, 2009), pp. 1–2.
[Crossref]

Hu, P.

Huang, H.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

Jian, X.

Jiang, X.

Kadota, Y.

H. Tanobe, Y. Kondo, Y. Kadota, H. Yasaka, and Y. Yoshikuni, “A Temperature Insensitive InGaAsP/InP Wavelength Filter,” IEEE Photonic. Technol. Lett. 8(11), 1489–1491 (1996).
[Crossref]

Kim, M.

Kondo, Y.

H. Tanobe, Y. Kondo, Y. Kadota, H. Yasaka, and Y. Yoshikuni, “A Temperature Insensitive InGaAsP/InP Wavelength Filter,” IEEE Photonic. Technol. Lett. 8(11), 1489–1491 (1996).
[Crossref]

Kristensen, P.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

Labeye, P.

Lang, T.

Lee, J.-M.

Li, C.

Li, H.

Li, L.

Li, W.

Li, X.

Lipson, M.

Liu, L.

Liu, W.

Lo, G. Q.

Lu, M.

Luck, D. L.

C. T. DeRose, M. R. Watts, D. C. Trotter, and D. L. Luck, “Silicon microring modulator with integrated heater and temperature sensor for thermal control, ” in Conference on Lasers and Electro-optics (Optical Society of America, 2010), paper CThJ3.
[Crossref]

Michel, J.

Momeni, B.

P. Alipour, E. S. Hosseini, A. A. Eftekhar, B. Momeni, and A. Adibi, “Temperature-insensitive silicon microdisk resonators using polymeric cladding layers, ” in Lasers and Electro-Optics, 2009 and 2009 Conference on Quantum electronics and Laser Science Conference. CLEO/QELS 2009 (IEEE, 2009), pp. 1–2.
[Crossref]

Moooka, T.

Morthier, G.

Osgood, R. M.

Oton, C. J.

Pang, A.

Pinguet, T.

T. Baehrjones, T. Pinguet, P. L. Guoqiang, S. Danziger, D. Prather, and M. Hochberg, “Myths and rumours of silicon photonics,” Nat. Photonics 6(4), 206–208 (2012).
[Crossref]

Prather, D.

T. Baehrjones, T. Pinguet, P. L. Guoqiang, S. Danziger, D. Prather, and M. Hochberg, “Myths and rumours of silicon photonics,” Nat. Photonics 6(4), 206–208 (2012).
[Crossref]

Qi, M.

Qiao, L.

Ramachandran, S.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

Reed, G. T.

G. T. Reed, “Device physics: the optical age of silicon,” Nature 427(6975), 595–596 (2004).
[Crossref] [PubMed]

Ren, Y.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

Sahin, A.

M. Hayee, M. Cardakli, A. Sahin, and A. Willner, “Doubling of bandwidth utilization using two orthogonal polarizations and power unbalancing in a polarization-division-multiplexing scheme,” IEEE Photonic. Technol. Lett. 13(8), 881–883 (2001).
[Crossref]

Shen, W.

Sheng, Z.

Shi, Y.

Song, J. H.

Soref, R.

R. Soref, “Silicon Photonics: A Review of Recent Literature,” Silicon 2(1), 1–6 (2010).
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Souhan, B.

Stein, A.

Tanobe, H.

H. Tanobe, Y. Kondo, Y. Kadota, H. Yasaka, and Y. Yoshikuni, “A Temperature Insensitive InGaAsP/InP Wavelength Filter,” IEEE Photonic. Technol. Lett. 8(11), 1489–1491 (1996).
[Crossref]

Tao, S.

Teng, J.

Testa, F.

Trotter, D. C.

C. T. DeRose, M. R. Watts, D. C. Trotter, and D. L. Luck, “Silicon microring modulator with integrated heater and temperature sensor for thermal control, ” in Conference on Lasers and Electro-optics (Optical Society of America, 2010), paper CThJ3.
[Crossref]

Tur, M.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

Uenuma, M.

Van Thourhout, D.

Viegas, J.

Wang, H.

Wang, J.

Wang, L.

Wang, X.

Wang, Z.

Watts, M. R.

C. T. DeRose, M. R. Watts, D. C. Trotter, and D. L. Luck, “Silicon microring modulator with integrated heater and temperature sensor for thermal control, ” in Conference on Lasers and Electro-optics (Optical Society of America, 2010), paper CThJ3.
[Crossref]

Willner, A.

M. Hayee, M. Cardakli, A. Sahin, and A. Willner, “Doubling of bandwidth utilization using two orthogonal polarizations and power unbalancing in a polarization-division-multiplexing scheme,” IEEE Photonic. Technol. Lett. 13(8), 881–883 (2001).
[Crossref]

Willner, A. E.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

Wu, A.

Xia, J.

Xiang, X.

Xiao, X.

Xie, C.

Xie, X.

Xing, P.

Yamada, K.

T. Hiraki, H. Fukuda, K. Yamada, and T. Yamamoto, “Small Sensitivity to Temperature Variations of Si-Photonic Mach–Zehnder Interferometer Using Si and SiN Waveguides,” Front. Mater. 2, 26 (2015).
[Crossref]

Yamamoto, T.

T. Hiraki, H. Fukuda, K. Yamada, and T. Yamamoto, “Small Sensitivity to Temperature Variations of Si-Photonic Mach–Zehnder Interferometer Using Si and SiN Waveguides,” Front. Mater. 2, 26 (2015).
[Crossref]

Yang, H.

Yang, Q.

Yang, X.

Yasaka, H.

H. Tanobe, Y. Kondo, Y. Kadota, H. Yasaka, and Y. Yoshikuni, “A Temperature Insensitive InGaAsP/InP Wavelength Filter,” IEEE Photonic. Technol. Lett. 8(11), 1489–1491 (1996).
[Crossref]

Ye, T.

Yoshikuni, Y.

H. Tanobe, Y. Kondo, Y. Kadota, H. Yasaka, and Y. Yoshikuni, “A Temperature Insensitive InGaAsP/InP Wavelength Filter,” IEEE Photonic. Technol. Lett. 8(11), 1489–1491 (1996).
[Crossref]

You, L.

Yu, M.

Yu, Y.

Yue, Y.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

Zhang, H.

Zhang, J.

Zhang, L.

Zhang, R.

Zhang, W.

Zhang, Y.

Zhao, M.

Zhou, H.

Zhou, X.

Zhou, Z.

Zhu, S.

Zhu, Y.

Zou, J.

Zou, S.

Front. Mater. (1)

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Figures (9)

Fig. 1
Fig. 1 (a) Core structure of the Mach-Zehnder interferometer. The MZI consists of two symmetrical mode converters and a straight multimode waveguide (b) Schematic of the MZI. The mode converter can convert the TE0 mode into TE0/TE1 hybrid modes. The interference is achieved due to the different group index in different modes. When the TE0 mode input to the device, two interference curves can be obtained through TE0 mode output and TE1 mode output, respectively. Similar to the TE1 mode input to the device.
Fig. 2
Fig. 2 Schematic of the mode converter in the MZI. The mode converter can convert the TE0 or TE1 mode into TE0/TE1 hybrid modes.
Fig. 3
Fig. 3 Simulated results of transmission curves of TE0 -TE0 and TE0-TE1 via different width of W2 in mode converter.
Fig. 4
Fig. 4 Calculated temperature dependence of the effective index for the TE0 (black) and TE1 (red) modes on the waveguide width of the multimode waveguide with the height of 220nm.
Fig. 5
Fig. 5 Simulation results of (a) TE0 input-TE0/TE1 output (b) TE1 input-TE0/TE1 output MZI. The insertion loss of TE0-TE0, TE0-TE1, TE1-TE0, and TE1-TE1 are 0.025dB, 0.25dB, 0.25dB and 0.15dB over the wavelength range from 1545nm-1585nm. The extinction ratio of better than −20dB are obtained near 1550nm.
Fig. 6
Fig. 6 TE0-TE0 at 20°C (black) and 50°C (red) simulated with different multimode waveguide widths (a) 641nm (b) 646 nm (c) 651nm. The thermal sensitivity of the device is less than 13pm/°C over the 40nm wavelength range.
Fig. 7
Fig. 7 Measured transmission curves of (a) TE0 input –TE0 output(black)/ TE0 input –TE1 output(dark red) (b) TE1 input –TE0 output(blue)/ TE1 input –TE1 output(green) at 20°C. The measured results show the minimum insertion loss lower than 0.31dB with a minimum extinction ratio larger than 8dB for all channels from 1545nm to 1585nm.
Fig. 8
Fig. 8 Measured transmission curves of (a) TE0 input –TE0 output (b) TE0 input –TE1 output (c) TE1 input –TE0 output (d) TE1 input –TE1 output at 20°C (black)/30°C (purple)/40°C (blue)/50°C (orange). The thermal sensitivity of the device is less than 13 pm/°C over the 40nm wavelength range.
Fig. 9
Fig. 9 Simulated results of extinction ratio vary with the conversion efficiency of directional coupler.

Equations (2)

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FSR= λ 2 n g (T E 0 )*L n g (T E 1 )*L
dλ dT = λ( d n eff (T E 0 ) dT d n eff (T E 1 ) dT ) n g (T E 0 ) n g (T E 1 )

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