SILICON FOURIER TRANSFORM SPECTROMETER AND OPTICAL SPECTRUM RECONSTRUCTION METHOD

Abstract

A silicon Fourier transform spectrometer and an optical spectrum reconstruction method are disclosed. The spectrometer includes a waveguide input coupler, cascaded optical switches, unbalanced subwavelength grating (SWG) waveguide pairs, and a germanium silicon detector, where the cascaded optical switches are connected through unbalanced SWG waveguide pairs. The state of the optical switches are adjusted to digitally configure the optical path, so as to constitute a series of unbalanced Mach-Zehnder interferometer (MZI) arrays with different optical path differences, to realize a Fourier transform spectrometer based on spatial heterodyne. The optical spectrum is reconstructed by using a compressed sensing algorithm.

Claims

1. A silicon Fourier transform spectrometer, comprising: a waveguide input coupler (101), cascaded optical switches (102), unbalanced subwavelength grating (SWG) waveguide pairs (103), a germanium silicon detector (104), and an external multi-channel power supply, wherein the waveguide input coupler (101), the cascaded optical switches (102), the unbalanced subwavelength grating (SWG) waveguide pairs (103), and the germanium silicon detector (104) are prepared on a silicon-on-insulator (SOI) platform; the cascaded optical switches (102) comprise N+1 2×2 optical switches, each of the 2×2 optical switches comprises two 3-dB couplers (102a), two balanced waveguides (102b), and one phase shifter (102c), two output terminals of the former 3-dB coupler (102a) are separately connected to one waveguide (102b), one of the balanced waveguides (102b) is integrated with the phase shifter (102c), and the other terminals of the two balanced waveguides (102b) are connected to two input terminals of the latter 3-dB coupler (102a); there are N pairs of unbalanced SWG waveguide pairs (103), each pair of unbalanced SWG waveguide pairs comprises two unbalanced SWG waveguides, the two waveguides have different widths and lengths, the optical path difference of an i.sup.th unbalanced SWG waveguide pair is OPD.sub.i=2.sup.i−1OPD.sub.1, and the temperature-dependent phase difference shift is 0; the output terminal of the waveguide input coupler (101) is connected to one input terminal of the first-stage optical switch of the cascaded optical switches (102), and the two output waveguides of a former-stage optical switch are connected to the two input waveguides of a latter-stage optical switch through the unbalanced SWG waveguide pair (103); and the germanium silicon detector (104) adopts a PIN structure, and is connected to one output terminal of the last-stage 2×2 optical switch of the cascaded optical switches (102), where control terminals of the N+1 2×2 optical switches are connected to the external multi-channel power supply.

2. The silicon Fourier transform spectrometer as described in claim 1, wherein the waveguide input coupler (101) adopts an inverse taper structure or a gating coupler structure, and an optical spectrum signal to be measured is input to a chip through optical fiber coupling.

3. The silicon Fourier transform spectrometer as described in claim 1, wherein the cascaded switch quantity N+1 is related to the quantity of resolvable wavelength points of the spectrometer.

4. The silicon Fourier transform spectrometer as described in claim 1, wherein the 2×2 optical switch adopts a 2×2 balanced Mach-Zehnder (MZI) structure, the 3-dB coupler (102a) adopts a multimode interference (MMI) structure or a directional coupler structure, and the phase shifter (102c) adopts a metal resistance or a waveguide resistance structure based on the thermo-optic effect.

5. The silicon Fourier transform spectrometer as described in claim 1, wherein different unbalanced SWG waveguide pairs (103) adopt a same waveguide structure, and the length is increased proportionally, so that the optical path difference of the i.sup.th unbalanced SWG waveguide pair is OPD.sub.i=2.sup.i−1OPD.sub.1.

6. The silicon Fourier transform spectrometer as described in claim 1, wherein a mode spot converter is provided at the connection between the SWG waveguide and the 2×2 optical switch to reduce reflection loss of a device.

7. The silicon Fourier transform spectrometer as described in claim 1, wherein the 2×2 optical switch is controlled through the external multi-channel power supply, to work at the state of 3-dB splitting, cross or bar. In this condition, two optical switches in a path are at the 3-dB splitting state, and the rest are at the bar or cross state, thereby constituting an unbalanced MZI structure with different optical path differences, wherein the optical path difference changes to (1˜2.sup.N−1)OPD.sub.1.

8. A method for obtaining a reconstructed optical spectrum of a light source by using the Fourier transform spectrometer on a silicon substrate as described in claim 1, comprising: (i) inputting monochromatic optical signals in the wavelength range to be measured into the MZIs with different optical path differences, forming an interference pattern through optical-to-electrical conversion, and constituting a calibration matrix A with the spectra of all the MZIs; (ii) inputting an optical signal x to be measured, and measuring an output signal y using the germanium silicon detector in cases of different optical path differences; and (iii) reconstructing the original optical spectrum by using a reconstruction algorithm by setting a reasonable regular penalty term and a corresponding hyperparameter, to improve the quality of the reconstructed spectrum.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0024] FIG. 1 shows the structure of the silicon Fourier transform spectrometer according to the present invention.

[0025] FIG. 2 shows the structure of the silicon-based optical switch according to one embodiment of the present invention.

[0026] FIG. 3 shows the structure of the unbalanced SWG waveguide pair according to the present invention.

[0027] FIGS. 4A to 4D show the working principle of the four-stage reconfigurable on-chip Fourier transform spectrometer according to one embodiment of the present invention, where FIG. 4A shows that, when SE.sub.1 and SE.sub.2 operate at the 3-dB splitting state, the device is equivalent to an MZI with an optical path difference of OPD.sub.1; FIG. 4B shows that, when SE.sub.1 operates at the cross state and SE.sub.2 and SE.sub.3 operate at the 3-dB splitting state, the device is equivalent to an MZI with an optical path difference of 2OPD.sub.1; FIG. 4C shows that, when SE.sub.1 and SE.sub.3 operate at the 3-dB splitting state and SE.sub.4 is at the bar state, the device is equivalent to an MZI with an optical path difference of 3OPD.sub.1; and FIG. 4D shows the longest optical path difference.

[0028] FIG. 5 shows the typical calibration matrix A according to one embodiment of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

[0029] To further clarify the objectives, technical solutions, and core advantages of the present solution, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be noted that the following specific embodiments are merely for explanatory purposes and are not intended to limit the present invention. In addition, technical features involved in the various embodiments can be combined with each other provided that they do not conflict with each other.

[0030] As shown in FIG. 1, the silicon Fourier transform spectrometer in the present invention comprises a waveguide input coupler 101, cascaded optical switches 102, unbalanced SWG waveguide pairs 103, a germanium silicon detector 104, and an external multi-channel power supply. The waveguide input coupler 101, the cascaded optical switches 102, the unbalanced SWG waveguide pair 103, and the germanium silicon detector 104 are prepared on a silicon-on-insulator platform.

[0031] The cascaded optical switches 102 include N+1 2×2 optical switches. The 2×2 optical switch includes two 3-dB couplers 102a, two balanced waveguides 102b, and one phase shifter 102c. Two output terminals of the former 3-dB coupler 102a are separately connected to one waveguide 102b, one of the balanced waveguides 102b is integrated with the phase shifter 102c, and the other terminals of the two balanced waveguides 102b are connected to two input terminals of the latter 3-dB coupler 102a.

[0032] There are N pairs of unbalanced SWG waveguide pairs 103. Each pair of unbalanced SWG waveguide pair includes two unbalanced SWG waveguides. The two waveguides have different widths and lengths, an optical path difference of an i.sup.th unbalanced SWG waveguide pair is OPD.sub.1=2.sup.i−1OPD.sub.1, and the temperature-dependent phase difference shift is 0.

[0033] An output terminal of the waveguide input coupler 101 is connected to one input terminal of the first-stage optical switch of the cascaded optical switches 102, and two output waveguides of a former-stage optical switch are connected to two input waveguides of a latter-stage optical switch through the unbalanced SWG waveguide pair 103; and the germanium silicon detector 104 adopts a PIN structure, and is connected to one output terminal of the last-stage 2×2 optical switch of the cascaded optical switches 102, where control terminals of the N+1 2×2 optical switches are connected to the external multi-channel power supply.

[0034] The waveguide input coupler 101 adopts an inverse taper structure or a gating coupler structure, and an optical spectrum signal to be measured is input to a chip through optical fiber coupling.

[0035] The cascaded switch quantity N+1 is related to the quantity of resolvable wavelength points of the spectrometer.

[0036] The 2×2 optical switch adopts a 2×2 balanced Mach-Zehnder interferometer (MZI) structure, the 3-dB coupler 102a adopts a multimode interferometer (MMI) structure or a directional coupler structure, and the phase shifter 102c adopts a metal resistance or a waveguide resistance structure based on the thermo-optic effect.

[0037] Different unbalanced SWG waveguide pairs 103 adopt a same waveguide structure, and a length is increased proportionally, so that the optical path difference of the i.sup.th unbalanced SWG waveguide pair is OPD.sub.1=2.sup.i−1OPD.sub.1.

[0038] A mode spot converter is provided at the connection between the SWG waveguide and the 2×2 optical switch to reduce reflection loss of the device.

[0039] The 2×2 optical switch is controlled through the external multi-channel power supply, to work at the state of 3-dB splitting, cross or bar. In this condition, two optical switches in a path are at the 3-dB splitting state, and the rest are at the bar or cross states, thereby constituting an unbalanced MZI structure with different optical path differences, wherein the optical path difference changes to (1˜2.sup.N−1)OPD.sub.1.

[0040] A method for obtaining a reconstructed spectrum of a light source by using the silicon Fourier transform spectrometer is provided, and the method includes the following steps: first, inputting monochromatic optical signals in the wavelength range to be measured into the MZIs with different optical path differences, forming an interference pattern through optical-to-electrical conversion, and constituting a calibration matrix A with the spectra of all the MZIs; ; then, inputting an optical signal x to be measured, and measuring an output signal y using the germanium silicon detector in cases of different optical path differences; and finally, reconstructing an original optical spectrum by using a reconstruction algorithm by setting a reasonable regular penalty term and a corresponding hyperparameter, to improve the quality of reconstructed spectrum.

[0041] In one embodiment of the present invention, the cascaded optical switches 102 comprise the N+1 2×2 optical switches, and the cascade quantity N+1 is related to the bandwidth and spectral resolution of the spectrometer. Each stage of the cascaded optical switches adopts a 2×2 balanced Mach-Zehnder interferometer (MZI) structure, and the structure is shown in FIG. 2, and comprises two 3-dB couplers 102a, two balanced waveguides 102b, and a phase shifter 102c. The external power supply is used to power up the phase shifter on the optical switch to change a phase difference between two arms, and the switch can be configured to the cross state, the bar state, and the 3-dB splitting state. The two output waveguides of the former-stage optical switch is connected to the two input waveguides of the latter-stage of optical switch through the unbalanced SWG waveguide pair 103.

[0042] Therefore, there are a total of N pairs of unbalanced SWG waveguide pairs 103, each pair comprises two unbalanced SWG waveguides, and the two waveguides have different widths and lengths, so that the two waveguides have an optical path difference OPD.sub.i (where i is a sequence number of an unbalanced SWG waveguide pair). Therefore, the state of the optical switch is changed, to digitally switch the optical path, and in combination with the unbalanced SWG waveguide pair, an asymmetric MZI structure with different optical path differences can be reconstructed.

[0043] The final output optical signal is detected by the germanium silicon detector 104, which is connected to one output terminal of the last-stage 2×2 optical switch of the cascaded optical switches. The optical power signal is converted into the electrical signal.

[0044] Based on the foregoing solution, the structure of the unbalanced SWG waveguide pair is shown in FIG. 3. To eliminate temperature sensitivity, according to an expression of the temperature-dependent phase difference shift ∂Δφ/∂T of the device:

[00001]$\frac{\partial \mathrm{\Delta \phi }}{\partial T}=\frac{2\pi }{{\lambda }_0}\left(\frac{\partial n_{\mathrm{eff}}}{\partial T}\Delta L+\frac{\partial \Delta n_{\mathrm{eff}}}{\partial T}L\right)$

where Δn.sub.eff represents the effective refractive index difference n.sub.eff 1−n.sub.eff 2 between two SWG waveguides with different widths, and therefore ∂Δn.sub.eff/∂T is the difference between thermo-optic coefficients of the two SWG waveguides, and ∂n.sub.eff/∂T is the thermo-optic coefficient of a conventional channel waveguide. The first term in brackets on a right side of an equal sign in the expression is greater than 0, and ∂Δn.sub.eff/∂T in the second term may be less than 0. Therefore, the period, the duty cycle, and the waveguide width of SWG waveguides on two arms are designed, to adjust waveguide dispersion, so that the temperature-dependent phase difference shift of the device can be 0, thereby achieving a thermal condition within a relatively wide wavelength range. Through design, the optical path difference OPD.sub.i of the first-stage SWG waveguide pair is:

OPD.sub.i=n.sub.gΔL+(n.sub.g1−n.sub.g2)L

where n.sub.g1 and n.sub.g2 are group refractive indices of the upper and lower SWG waveguides. For the i stage, if an optical path difference of 2.sup.i−1OPD.sub.1 is to be realized, it is only necessary to correspondingly increase the length of the waveguide to satisfy the length difference 2.sup.i−1ΔL between waveguides of the same size, and the length of the waveguides with different widths is 2.sup.i−1L.

[0045] Based on the foregoing solution, a four-stage optical switch is used as an example to illustrate a specific working principle of the Fourier transform spectrometer:

[0046] As shown in FIGS. 4A through 4D, the structure comprises four 2×2 cascaded optical switches, and is named as SE.sub.k (k=1,2,3,4). Two optical switches are connected by using two unbalanced SWG waveguides. Optical path differences of the two unbalanced SWGs are OPD.sub.i (i=1, 2, 3, 4), where OPD.sub.i=2.sup.i−1OPD.sub.1. As shown in FIG. 4A, when SE.sub.1 and SE.sub.2 operate at the 3-dB splitting state, the device is equivalent to an MZI with an optical path difference of OPD.sub.1.

[0047] As shown in FIG. 4B, when SE.sub.1 operates at the cross state, and SE.sub.2 and SE.sub.3 operate at the 3-dB splitting state, the device is equivalent to an MZI with an optical path difference of 2OPD.sub.1.

[0048] As shown in FIG. 4C, when SE.sub.1 and SE.sub.3 operate at the 3-dB splitting state, and SE.sub.2 is at the bar state, the device is equivalent to an MZI with an optical path difference of 3OPD.sub.1. The reset is deduced by analogy. The longest optical path difference is shown in FIG. 4D. When SE.sub.1 and SE.sub.4 operate at the 3-dB splitting state, and SE.sub.2 and SE.sub.3 operate at the bar state, the device is reconstructed as an MZI with an optical path difference of 7OPD.sub.1. For this four-stage cascaded optical switch structure, a total of seven MZIs with different optical path differences from 1OPD.sub.1 to 7OPD.sub.1 can be realized.

[0049] The embodiment shows that for (N+1)-stages cascaded optical switches and N-stages unbalanced SWG waveguide pairs, through digital selecting of optical paths, a total of 2.sup.N−1 MZIs with different optical path differences can be reconstructed, and the optical path differences are respectively (1˜2.sup.N−1) OPD.sub.1. Therefore, the structure only needs to use N unbalanced waveguides and N+1 2×2 optical switches to achieve the same bandwidth and spectral as 2.sup.N−1 unbalanced MZI arrays. It greatly simplifies design complexity of the chip and reduces a device size.

[0050] Based on the foregoing solution, the Fourier transform spectrometer needs to be calibrated before a formal test. States of all optical switches are adjusted, and there are a total of 2.sup.N−1 unbalanced MZIs with different optical path differences. A tunable laser source scans the wavelength in the optical spectrum range to be measured, and there are a total of m wavelength points. The monochromatic continuous wave from the tunable laser source is input into each MZI, and the optical signal after the interferometer is converted into the electrical signal through the on-chip germanium silicon detector, and then is recorded by a data acquisition card. In the way, a (2.sup.N−1)×m calibration matrix A can be obtained, where each row in the matrix represents a transmission spectrum, and each column represents discrete sampling points of an interference pattern. A typical calibration matrix is shown in FIG. 5. In addition to being used for regularization reconstruction of input spectrum, the calibration matrix can also eliminate the phase errors caused by manufacturing and different fringe contrast caused by waveguide loss. A polychromatic optical signal x to be measured is a vector with m elements, and each element represents power at the corresponding wavelength and can be expressed as y=Ax, where y is the measured interference pattern and is a vector with 2.sup.N−1 elements. Therefore, information about the optical spectrum of polychromatic light to be measured can be recovered by obtaining x from y.

[0051] Based on the foregoing solution, because m is far greater than 2.sup.N−1, there are many solutions in the foregoing matrix equation x, but an accurate solution often cannot be obtained by using a conventional pseudo-inverse matrix method. In the present invention, a machine learning algorithm is used to accurately reconstruct the optical spectrum to be measured. Different regularized regression algorithms have different advantages, disadvantages, and trial ranges. Table 1 lists several common reconstruction algorithms.

TABLE-US-00001 TABLE 1 Algorithm name Problem solving Ridge min.sub.x{∥y − Ax∥.sub.2.sup.2 + α.sub.2∥x∥.sub.2.sup.2} Lasso min.sub.x{∥y − Ax∥.sub.2.sup.2 + α.sub.1∥x∥.sub.1} BPDN min.sub.x{0.5 × ∥y − Ax∥.sub.2.sup.2 + α.sub.1∥x∥.sub.1} RBF Network [00002]${\min }_c\left\{{.Math.y-A{h}_c.Math.}_2^2\right\},h_c=\mathrm{Kc}=\underset{d=1}{\overset{D}{.Math.}}{C}_d{e}^{-\beta {.Math.\lambda -{\lambda }_d.Math.}^2}$ Elastic-Net min.sub.x, x>0 {∥y − Ax∥.sub.2.sup.2 + α.sub.1∥x∥.sub.1 + α.sub.2∥x∥.sub.2.sup.2} Elastic-D1 min.sub.x, x>0 {∥y − Ax∥.sub.2.sup.2 + α.sub.1∥x∥.sub.1 + α.sub.2∥x∥.sub.2.sup.2 + α.sub.3∥D.sub.1x∥.sub.2.sup.2}

[0052] Because some of optical spectra to be measured are relatively sparse (including only a few discrete wavelength components), and some have a large quantity of continuous spectrum, applicability of different algorithms should be considered when an algorithm is selected. The L.sub.1 norm term is mainly used to increase sparsity, which has a good effect on reconstructing the sparse spectrum. And the L.sub.2 norm term mainly prevents overfitting. The foregoing two terms have a good effect on reconstructing the sparse optical spectrum. However, due to lack of a constraint on optical spectrum continuity, a continuous optical spectrum cannot be accurately recovered by including only the L.sub.1 and L.sub.2 norm terms. Introducing the L.sub.2 norm term of a first-order difference matrix of the optical spectrum can increase the continuity of the optical spectrum to a certain extent. Therefore, among the foregoing several algorithms, the Elastic—D1 algorithm can be used to reconstruct various types of different optical spectra more accurately. However, because values of the three hyperparameters need to be calculated, the calculation complexity is increased. However, each term in the algorithm is greater than 0, so that a standard convex optimization tool can be used for calculation.

[0053] The foregoing content is the specific implementation solution of the silicon Fourier transform spectrometer chip in the present invention and can be easily understood by persons in scientific research or industrial departments in the same field. The foregoing content is merely preferred embodiments of the present invention and is not intended to limit the present invention. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

[0054] Compared with a conventional passive MZI array structure, this can effectively reduce the size of the chip and improve the performance of the device; and the unbalanced SWG waveguide pairs can effectively improve temperature stability of the chip. The present invention can meet an application requirement of the Fourier transform spectrometer on miniaturization and portability, and can resolve a problem that a spectrometer on an existing silicon platform is generally sensitive to temperature.