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Fourier-transform spectrometer chip covering visible band on silica planar waveguide Xiao Ma a , Jun Zou b , Qiongchan Shao a , Mingyu Li c , Jian-Jun He a ,∗ a

College of Optical Science and Engineering, Zhejiang University, Hangzhou 310027, China College of Science, Zhejiang University of Technology, Hangzhou 310023, China c School of Electro-Optical Engineering, Changchun University of Science and Technology, Changchun 130022, China b

ARTICLE

INFO

Keywords: Integrated optics devices Spectrometer chips Fourier-transform algorithm Visible light spectrum

ABSTRACT To minimise a spectrometer maximally, using a micro-electro-mechanical system or planar waveguide chip, has aroused interest in both academia and industry. This is because a portable and inexpensive spectral analysis tool has tremendous potential in various applications including scientific exploration, industrial inspection, and environmental protection. Here, we design, fabricate, and characterise a Fourier-transform spectrometer (FTS) chip consisting of 101 Mach–Zehnder interferometers (MZIs) with gradually varying optical path differences on a silica planar waveguide platform, aiming to cover the entire visible band. To ensure a wide-band operation while simultaneously compressing the size of the chip, wide-bending arm waveguides that can support highorder modes in a short wavelength range are employed in the design of the MZI array. The experimental result of our FTS chip shows its ability to analyse the visible spectrum with a minimum resolution of better than 10 nm and to reproduce the original spectrum with an accuracy of less than 0.5 nm. The successful implementation of the FTS chip based on a matured and low-cost silica planar lightwave circuit process makes it quite promising to realise mass production and widespread application.

1. Introduction A spectrometer is a rather versatile sensing tool because the spectra ranging from ultraviolet to far infra-red can reflect numerous important information in various domains including space exploration, environmental protection, industrial and agricultural production, medical diagnosis, biological and chemical analysis, and optical communication [1– 8]. In recent decades, abundant effort has been made to minimise the traditional bulky and expensive spectrometer, aiming to realise an inexpensive and portable spectral analysis tool, which can dramatically promote the prominence of a spectrometer [9–12]. A micro-electromechanical system (MEMS) [9,10] and planar waveguide chip [11,12] are two main structures to attain the above-mentioned objective. Compared to MEMS, a planar waveguide chip is more attractive because it has the potential to form a high-degree integration device with a photodetector array and electronic processing circuits on a single chip. Thus, it can be sufficiently small to be embedded into small mobile devices like smart phones [13,14]. To build spectrometer chips, numerous structures on planar waveguides have been proposed, including photonic crystal structures [12], arrayed waveguide gratings [15], echelle diffraction gratings [16], and micro-cavity resonators [17]. However, each of the above structures has its own deficiency restricting its rapid spread in applications.

For instance, photonic-crystal spectrometers frequently require highresolution lithography, resulting in a high fabrication expenditure. Moreover, micro-cavity resonator-based spectrometers are extremely sensitive to fabrication imperfections, meaning they have a low yield. Dispersion-grating-based spectrometers have a single input and multiple outputs, leading to decomposition of the input light and thereby a dramatic degradation of the detection limit. An Mach–Zehnder interferometer (MZI)-array-based Fourier-transform spectrometer (FTS) chip is a competitive alternative to the above counterparts owing to its intrinsic high throughput and large fabrication tolerance [18]. Numerous works have been conducted since the FTS chip was first demonstrated in 2007 [18], including developing different material platforms [19– 21], condensing the layout [3], and improving the retrieval algorithm [22]. However, until now, almost all the reported FTS chips are dedicated to operate in the infra-red band; to the best of our knowledge, an FTS chip that can analyse the visible spectrum is yet to be explored. This is despite its significance in various visible-spectrum analysis applications including LED measurement, wine quality qualification, and dental surgery. In this article, we demonstrate that an MZI-based FTS chip can work in the entire visible band on silica-based planar waveguides. To ensure a wide-band operation with a short central wavelength, bending

∗ Corresponding author. E-mail address: [email protected] (J.-J. He).

https://doi.org/10.1016/j.optcom.2019.124599 Received 21 June 2019; Received in revised form 17 August 2019; Accepted 18 September 2019 Available online 20 September 2019 0030-4018/© 2019 Elsevier B.V. All rights reserved.

X. Ma, J. Zou, Q. Shao et al.

Optics Communications 456 (2020) 124599

In a real FTS chip, the number of MZIs is finite and assumed to be N here. The arm length difference of each MZI is discretely distributed from 0 to (𝑁 − 1)𝛥𝐿. Moreover, the mode and material dispersions cannot be neglected any more. Thus, based on Eqs. (2), (4) should be rewritten in a discrete format as 𝑆(𝜎) = 2

𝑁−1 ∑

𝐹 (𝑚𝛥𝐿)𝑐𝑜𝑠(2𝜋𝜎𝑁𝑒𝑓 𝑓 (𝜎)𝛥𝐿)𝛥𝐿 + 𝑆𝑎𝑙𝑙 𝛥𝐿.

(5)

𝑚=1

In Eq. (5), a finite summation is performed, which implies that a truncation will exist in the output interferogram. This will cause unwanted ripples in the retrieved spectrum. To mitigate this negative effect, an apodisation function can be introduced into the equation [23]. In addition, for an FTS chip operating in a wide band and with a small ratio of the central wavelength to the FSR, which is the scenario encountered in this work, the wavenumber or wavelength-dependent loss cannot be neglected and must be compensated. The compensation coefficients can be obtained by comparing the transmission wide-band spectrum of No. 0 MZI with the original input spectrum. The accurate values of the MZI channel-dependent loss are not available in our Yjunction coupler-based FTS and can be managed to eliminate furthest by improving the fabrication. Therefore, herein we will only consider the output interferogram truncation and wavenumber-dependent loss effect, and transform Eq. (5) to the following equation:

Fig. 1. Global schematic diagram of our FTS chip.

arms that can support high-order modes in a short wavelength range are employed to confine the overall chip size. The experimental result proves the ability of our FTS chip to analyse the entire visible spectrum with a minimum resolution of better than 10 nm and to reproduce the spectrum with an accuracy of less than 0.5 nm.

𝑆(𝜎) = 𝑣(𝜎)(2

2. Principle

𝐹 𝑆𝑅

where 𝑣(𝜎) is the compensation coefficient for the wavenumberdependent loss and 𝑊 (𝑚𝛥𝐿) is the apodisation function to reduce the truncation ripple. Eq. (6) is the formula that we will use to retrieve the original input spectrum. As we already know, in an FTS chip, an input light with a monochromatic Littrow wavenumber, 𝜎𝐿 , can result in a constant interferometric output along the output plane. If we want to produce i fringes in the output interferogram of the FTS chip, then we should inject the light with the wavenumber, 𝜎𝑖 , that satisfies the following relation:

∫0

𝑆(𝜎) (1 + 𝑐𝑜𝑠(2𝜋𝜎𝑁𝑒𝑓 𝑓 (𝜎)𝑚𝛥𝐿))𝑑𝜎, 2

(1)

where m is the order number of the MZI. 𝐼(𝑚𝛥𝐿) represents the output power of the 𝑚th MZI. 𝑆(𝜎) represents the input spectral power density at a shifted wavenumber, 𝜎, which equals 𝜎 − 𝜎𝐿 . 𝜎𝐿 is the Littrow wavenumber. At the Littrow wavenumber, the output intensities in all the MZIs are uniform at their maxima. 𝑁𝑒𝑓 𝑓 (𝜎) is the waveguide effective refractive index of the bending arm waveguide at 𝜎. Now, we make the following assumptions: (a) the input spectral power density, 𝑆(𝜎), vanishes outside the FSR, (b) the arm length difference change, 𝛥L, between adjacent MZIs diminishes infinitely, the maximum arm length difference increases infinitely, and the number of MZIs is infinitely large, (c) the mode and material dispersions are neglected. With the above assumptions, Eq. (1) can be transformed to the following formula:

|𝑁𝑒𝑓 𝑓 (𝜎𝑖 ) ∗ (𝑁 − 1)𝛥𝐿𝜎𝑖 − 𝑁𝑒𝑓 𝑓 (𝜎𝐿 ) ∗ (𝑁 − 1)𝛥𝐿𝜎𝐿 | = 𝑖, 𝑖 = 0, 1, 2, … , (𝑁 − 1)∕2.

∫−∞

𝑆(𝜎)𝑐𝑜𝑠(2𝜋𝜎𝑥)𝑑𝜎,

𝛿𝜎𝑖 = (|𝜎𝑖−1 − 𝜎𝑖+1 |)∕2, 𝑖 = 1, 2, … , (𝑁 − 1)∕2 − 1 𝛿𝜎0 = |𝛿𝜎0 − 𝛿𝜎1 |, 𝛿𝜎(𝑁−1)∕2 = |𝛿𝜎(𝑁−1)∕2−1 − 𝛿𝜎(𝑁−1)∕2 |.

(2)

+∞

𝑆(𝜎)𝑑𝜎 =

∫0

∫−∞

𝑆(𝜎)𝑑𝜎 = 𝐼(0 ⋅ 𝛥𝐿).

(3)

𝑙𝜋 <= 2𝜋𝜎𝑚𝑖𝑛 𝑁𝑒𝑓 𝑓 (𝜎𝑚𝑖𝑛 )𝛥𝐿 < 2𝜋𝜎𝑚𝑖𝑛 𝑁𝑒𝑓 𝑓 (𝜎𝑚𝑎𝑥 )𝛥𝐿 <= (𝑙 + 1)𝜋,

𝑥 is a continuous variable representing the arm length difference of each MZI. 𝑆𝑎𝑙𝑙 represents the total power in the analysed spectral range. In No. 0 MZI, the optical path differences (OPD) between the two arms is 0. Therefore, based on Eq. (1), 𝐼(0 ⋅ 𝛥𝐿) is equivalent to 𝑆𝑎𝑙𝑙 . 𝐹 (𝑥) is a modified interferometric output. Formally, Eq. (2) is a standard Fourier cosine transform. Assuming that 𝐹 (𝑥) is symmetric with respect to x = 0, 𝑆(𝜎) can be expressed in the form of an inverse Fourier cosine transform as follows:

𝑙 = 0, ±1, ±2, … .

3. Design

∫0+

(4)

0+

+∞

=2

The target of our work is to realise an FTS chip that can analyse the entire visible spectrum and be implemented on a silica waveguide platform with a refractive index difference of 0.75% between the core and cladding waveguides. The dispersion functions of the refractive

𝐹 (𝑥)𝑐𝑜𝑠(2𝜋𝜎𝑥)𝑑𝑥

∫−∞

𝐹 (𝑥)𝑐𝑜𝑠(2𝜋𝜎𝑥)𝑑𝑥 +

∫0−

(9)

Eq. (9) defines the variation range of the phase difference between the two arms in No. 1 MZI, and it can be used to determine 𝛥𝐿 when the FSR is decided and vice versa.

+∞

𝑆(𝜎) =

(8)

Assuming that the largest and smallest wavenumbers we analysed are 𝜎𝑚𝑎𝑥 and 𝜎𝑚𝑖𝑛 , respectively, the FSR is defined as 𝜎𝑚𝑎𝑥 − 𝜎𝑚𝑖𝑛 . In Eq. (1), the cosine function used is symmetrical to 𝑙𝜋, where 𝑙 represents arbitrary positive or negative integers. If there are two wavenumbers 𝜎𝑝 and 𝜎𝑛 in the FSR forming the cosine value in Eq. (1) to be symmetrical to 𝑙𝜋 in No. 1 MZI, then 𝜎𝑝 and 𝜎𝑛 will also form a cosine value that is symmetrical to 𝑚𝑙𝜋 in any No. m MZI. This implies that we cannot distinguish 𝜎𝑝 and 𝜎𝑛 in the retrieved spectrum. To avoid the above scenario, 𝜎𝑚𝑎𝑥 and 𝜎𝑚𝑖𝑛 have to satisfy the following relation:

where 𝐹 𝑆𝑅

(7)

Based on the sampling theorem, the spectral resolution, 𝛿𝜎𝑖 , of the FTS chip at 𝜎𝑖 can be defined with the adjacent 𝜎𝑖−1 and 𝜎𝑖+1 as

+∞

𝐹 (𝑥) = 2𝐼(𝑥) − 𝑆𝑎𝑙𝑙 =

𝑆𝑎𝑙𝑙 =

𝐹 (𝑚𝛥𝐿)𝑊 (𝑚𝛥𝐿)𝑐𝑜𝑠(2𝜋𝜎𝑁𝑒𝑓 𝑓 (𝜎)𝛥𝐿)𝛥𝐿 + 𝑆𝑎𝑙𝑙 𝛥𝐿), (6)

𝑚=1

An MZI array is the key component of the FTS chip. The arm length difference of each MZI equally increases across the array by a constant value, 𝛥L. For a lossless case with 50:50 splitting and combining ratios, the transmission function of the 𝑚th MZI can be expressed as [18]: 𝐼(𝑚𝛥𝐿) =

𝑁−1 ∑

𝐹 (𝑥)𝑐𝑜𝑠(2𝜋𝜎𝑥)𝑑𝑥. 2

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Optics Communications 456 (2020) 124599

Fig. 2. Detailed structure of the MZI. Fig. 3. Simulated coupling loss curves of the fundamental mode light between straight and bending arm waveguides with and without a matching curve.

indices of the core and cladding waveguides are estimated by fitting the data provided in Handbook of Optical Constants of Solids [24] as follows: 𝑛𝑐𝑙𝑎𝑑𝑑𝑖𝑛𝑔 = 1.0029𝜆4 −2.5872𝜆3 + 2.5428𝜆2 − 1.1575𝜆 + 1.6661, 𝑛𝑐𝑜𝑟𝑒 = 1.0075 ⋅ 𝑛𝑐𝑙𝑎𝑑𝑑𝑖𝑛𝑔 ,

(10)

where the unit of 𝜆 is μm. Fig. 1 shows the global schematic of our FTS chip. N MZIs with arm length differences from 0 to (𝑁 − 1)𝛥𝐿 are arrayed from the top to the bottom. The arm length difference is accomplished by two parallel waveguides with the same rotation angle but different radii. This arrangement can cause the two arms to come extremely close to each other everywhere, thus maximally mitigating the intensity and phase errors resulting from fabrication nonuniformity. For the outside coupling light, inverse tapers are employed in the input end of the chip to increase the receiving aperture size. The splitter and combiner of the MZI are constructed by a Y-junction coupler, because compared to a directional coupler or multi-mode interferometer (MMI), it has a better wide-band performance, which is highly desired here. Almost all the reported work on MZI-based FTS chips employs single-mode waveguides as the MZI arms to prevent the interference of a high-order mode light [3,18,20,22]. However, for an FTS chip covering the entire visible band corresponding to a large ratio of the central wavelength to the FSR, a wider arm waveguide that can support multimode propagation particularly in the short wavelength end of the FSR is necessary to constrain the chip size. This is because when the ratio of the central wavelength to the FSR is large, the mode properties in the short and long wavelength ends differ significantly. If we affirm designing a single-mode waveguide in the entire FSR, then some difficult problems will be encountered. For example, in our design, when we fix the core-channel-waveguide height as 1.3 μm, for a light at 380 nm and 780 nm, the waveguide width should be no longer than 1.4 μm and 4.1 μm, respectively, to support only the fundamental mode. If we choose 1.4 μm as the waveguide width to ensure singlemode light propagation in the entire FSR, then to obtain a theoretically acceptable bending-arm-waveguide loss of less than 0.05 dB/cm, the waveguide radius should be longer than 900 μm and 15 000 μm for a light at 380 nm and 780 nm respectively. A bending-arm-waveguide radius of 15 000 μm is not practical because it will result in an extremely large chip size. Therefore, in our design, based on a trade-off, we determine the core channel waveguide width as 3 μm and the radius of the bending arm waveguide as 4000 μm. At the turning points of the straight and bending waveguides, the high-order modes are excited and a fundamental mode mismatch exists. Both the phenomena will cause attenuation of the fundamental mode light, thus augmenting the on-chip loss. To deal with these negative effects, a section of the matching curve is inserted between a straight and bending waveguide [25], as shown in Fig. 2. A matching curve has a radius twice the bending waveguide. Its length is optimised via simulation with the beam propagation method (BPM), and its function of improving the coupling efficiency of the fundamental mode light between the straight and bending waveguides is presented in Fig. 3. In Y-junction couplers, in an entire FSR, the waveguides

Fig. 4. Simulated relation curves between the arm phase difference of No. 1 MZI and wavelength for the different 𝛥𝐿 values of 0.1 μm, 0.2 μm, 0.27 μm, and 0.3 μm, respectively.

Fig. 5. Simulated spectral resolution of our FTS chip.

should be single-mode waveguides; otherwise, a high loss will occur in the splitting and coupling processes. The mode transformation between the narrower Y-junction coupler waveguide and wider MZI arm waveguide is satisfied by a taper. The residual high-order mode light existing in the arm waveguides will be eliminated when passing through the single-mode waveguide in the Y-junction couplers. The phase difference between the two arms of No. 1 MZI changes with the wavelength. Their relation is illustrated in Fig. 4 for four different 𝛥𝐿 values of 0.1 μm, 0.2 μm, 0.27 μm, and 0.3 μm, respectively. Based on Eq. (9), to form an FTS chip covering the visible band, both the 𝛥𝐿 values of 0.1 μm and 0.27 μm can be chosen. The 0.1 μm𝛥𝐿 corresponds to an FSR far beyond our requirement, which will result in a worse spectral resolution for the same number of MZIs. Hereby, we determine 𝛥𝐿 as 0.27 μm, related to an FSR from 399 nm to 786.5 nm, where 399 nm is the Littrow wavelength. In our chip, 101 MZIs with arm length differences from 0 to 27 μm are incorporated, and the spectral resolutions at the wavelengths that produce an interferogram with integer-number fringes can be calculated by Eqs. (7) and (8). 3

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Optics Communications 456 (2020) 124599

Fig. 6. Schematic of the FTS chip manufacturing process.

Table 1 Key design parameters of the FTS chip. Parameter

Value

Parameter

Value

Parameter

Value

𝑊𝑖𝑛 (μm) 𝐿𝑡𝑎𝑝1 (μm) 𝑅1 (μm) 𝛥𝐿 (μm)

17 450 4015 0.27

𝑊𝑠𝑝 (μm) 𝐿𝑡𝑎𝑝2 (μm) 𝑅2 (μm) N

1.25 100 3985 101

𝑊𝑎𝑟𝑚 (μm) 𝐿𝑚 (μm) 𝑅𝑚 (μm) 𝐻𝑐𝑜𝑟𝑒 (μm)

3 70 8000 1.3

cladding layer is covered in three cycles of PECVD deposition and thermal annealing. Fig. 6 displays the schematic of the FTS chip manufacturing process. The overall size of the FTS chip is 2.8 cm by 1.3 cm. For some detailed structures, photos of the fabricated FTS chip and its optical micrographs are presented in Fig. 7. In Fig. 7(c) and 7(d), waveguides between the adjacent splitters and combiners are accompanying the waveguides used to improve the fabrication uniformity, with actually no light being transmitted inside. The fabrication process is completely compatible to the well-known and matured planar lightwave circuit (PLC) process.

Fig. 7. (a) Photograph of the quartz-based FTS chip alongside a quarter; (b) Optical micrograph of the inverse tapers in the input end; (c) Microscope image of the Y-junction splitters; (d) Microscope images of the Y-junction combiners.

5. Characterisation and discussions The measurement set-up includes a supercontinuum source (YSL photonics SC-5 series), a variable line-width filter (VLT), a pair of Nufern SMJ-S405 fibres, an optical spectrum analyser (Ando AQ6315A), and a photodetector (Newport Model 2931). The experimental principle structure diagram is shown in Fig. 8. As the emitted light from the supercontinuum source is much weak below 450 nm, in this work, we only analyse the chip spectrum for the spectra above 450 nm. By setting the VLT with a wide linewidth covering the FSR, we first measure the transmission spectra of all the MZIs. As indicated in Fig. 8, an optical spectrum analyser is used to receive the output light and resolve the spectra. The transmission spectra are normalised to that

These are illustrated in Fig. 5. Table 1 lists the key design parameters of the chip. 4. Fabrication The FTS is fabricated on a 1.2-mm-thick quartz wafer, which is also a natural low-cladding waveguide layer. A 1.3-μm-thick germaniumdoped silica core layer is deposited via plasma-enhanced vapour chemical deposition (PECVD). The waveguide structure is then formed via contact lithography and successive inductively coupled plasma (ICP) etching. Finally, an 18-μm-thick boron–phosphor-codoped upper

Fig. 8. Experimental principle structure diagram.

4

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Optics Communications 456 (2020) 124599

of No. 0 MZI, and then presented as a two-dimensional (2D) colour scaling graph in Fig. 9. From Fig. 9, we can see that the long wavelength end of the FSR is 787 nm, which is quite close to the theoretically calculated value of 786.5 nm. By comparing the transmission spectrum of No. 0 MZI and the input spectrum, we can determine that the nonuniformity of the wavelength-dependent loss is 2.4 dB. Most of this is caused by the Y-junction splitter and combiner. To accurately obtain the actual dispersion equation for the effective refractive index of the MZI bending-arm waveguide, we analyse the normalised transmission spectrum of No. 100 MZI, as shown in Fig. 10. The red points at the peaks of the spectrum in Fig. 10 correspond to the wavelengths at which the OPDs are integer multiples of the wavelengths. In our chip, based on Eq. (7), we can deduce that the integers range from 50 to 88 and we calculate the effective refractive index at each wavelength, which are then fitted to obtain the dispersion equation in the analysing spectral range. The dispersion equation is as follows:

Fig. 9. Two-dimensional colour scaling graph for the transmission spectra of all the MZIs in our chip. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

𝑁(𝜆) = 4.9041 × 10−8 𝜆2 − 1.0711 × 10−4 𝜆 + 1.5113.

(11)

Then, we incorporate three narrow spectra centred at 497.5 nm, 619.5 nm, and 750.5 nm in our FTS chip to test its spectrum retrieving ability. As shown in Fig. 8, a photodetector is used here to obtain the output powers of all the MZIs that form the interferogram. The output interferogram is further employed to retrieve the original spectrum by an inverse discrete cosine Fourier transform based on Eq. (6). The input spectra and output interferograms at the three wavelengths are presented in Fig. 11, and the corresponding retrieved spectra are shown in Fig. 12. From Fig. 12, we can see that the full widths at half-maximum (FWHMs) of the original spectra are 7 nm, 11 nm, and 13.5 nm, respectively, and those of the retrieved spectra are 8.5 nm, 13 nm, and 16 nm, respectively. The minor broadening of the FWHMs is attributed to the apodisation function used in Eq. (6) to flatten the side lobes. The accuracy of the retrieved spectral peak is within the spectrum sampling resolution of 0.5 nm. The noise level is approximately 10 dB, which is mainly caused by the measurement instability and intensity and phase

Fig. 10. Transmission spectrum of No. 101 MZI.

Fig. 11. Three groups of input spectra centred at 497.5 nm, 619.5 nm, and 750.5 nm and their corresponding simulated and measured interferograms.

5

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Optics Communications 456 (2020) 124599

Fig. 12. Three normalised narrow input spectra and their respective retrieved spectra centred at 497.5 nm, 619.5 nm, and 750.5 nm.

References

errors in the MZI array originating from fabrication imperfections. The noise level can be reduced by applying a pseudoinverse algorithm [3] when the full transmission spectra of all the MZIs in the entire FSR are available after the measurement instrument is upgraded.

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6. Conclusion In summary, we have presented a detailed description of the design, fabrication, and characterisation of an FTS chip based on silica planar waveguides, covering the entire visible band. Spectral analysis between 450 and 787 nm was demonstrated. A minimum spectral resolution better than 10 nm and spectral peak bias of less than 0.5 nm are obtained. By upgrading our measurement instrument, we can further measure the spectra below 450 nm and utilise the pseudoinverse algorithm, which can inherently calibrate the intensity and phase error of the MZI array to decrease the noise level. Owing to the compatibility with the low-cost and mature PLC fabrication process, the proposed silica-based visible-band FTS chip is a highly promising measurement tool with the ability to realise mass production and widespread applications. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements We thank Jinpeng Pang and Xiang Xia for their helpful discussions. This work was supported in part by the National Natural Science Foundation of China under Grant 61535010, the National Natural Science Foundation of China under Grant 61605172, the Public Project of Zhejiang Province under Grant 2016C33074, and in part by the research fund from Zhejiang Lightip Electronics Technology Co., Ltd.

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