Different MZI sensors have been designed to convert the change in the waveguide's effective index to a sensible quantity for COVID-19 detection. The Si3N4 waveguide surface will be functionalized with the virus antibodies. In this case, the COVID virus in the sample will be selectively captured by the waveguide. COVID virus binding will change the refractive index of the 80 nm layer covering the waveguide core. Accordingly, a wavelength shift (Δλ) in the transmission spectrum of the MZI will occur, from which the virus concentration can then be determined.
For a MZI device with power evenly devided to its arms the transmission spectrum can be derived to be [27]:
where Δφ the phase difference of the MZI arms; neff,sens, neff,ref and Lsens, Lref are the waveguide mode effective index and length of the sensing and reference arms of the MZI sensor, respectively.
From which we can get the peak wavelengths as:
Accordingly, the free spectral range (FSR), full-width half maximum (FWHM), sensitivity (S) and FOM of the MZI sensor can be derived as follows [27]:
FOM is the main performance parameter of any RI sensor as it determines the minimum detectable refractive index change. Table 1 shows the dimensions and FOM of different symmetric MZI (s-MZI) sensors designs, Lsens=Lref=LMZI, at different wavelengths with AR≈1, LMZI=500µm and ideal y-junction for comparison. The optimized strip waveguides from the previous analysis with the virus layer around the core are used as the sensing arm with width wsens. Oxide capped waveguides are used as the reference arm with width wref. These results are obtained using a FDE solver to determine neff(λ) of the sensing and reference waveguides. Next, integrated photonics circuit simulator [28] is used to determine T(λ) at different nlayer (virus concentration) from which S, FWHM and FOM are then calculated. Results exhibit the same response as Fig. 5 with around 8 times greater FOM at the lower (blue) wavelength. Table 1 also shows FOM at λ=450 nm for different AR, reaching a maximum of 1231 RIU-1 at AR=2.88. As mentioned before, at higher waveguide widths, TM mode was used as it can reach higher Swg than TE mode, see Fig. 2(c). Note that, MIR range was discarded due to its low Swg and high (water absorption) losses.
Table 1. FOM of S-MZI sensors with LMZI = 500 µm. *Representing TM mode.
λ (nm)
|
AR
|
Dimensions (nm)
|
FOM (RIU-1)
|
450
|
0.13*
|
wsens=550, wref=520 and h=70
|
501
|
0.37*
|
wsens=270, wref=300 and h=100
|
553
|
1
|
wsens=138, wref=145 and h=140
|
812
|
2.88
|
wsens=104, wref=104 and h=300
|
1231
|
650
|
1.1
|
wsens=203, wref=230 and h=220
|
454
|
980
|
1.2
|
wsens=300, wref=360 and h=360
|
244
|
1550
|
1
|
wsens=512, wref=850 and h=500
|
100
|
Although small waveguide dimensions in the visible range exhibit high sensing performance, the fabrication of such waveguides require complex and expensive lithography systems like electron beam or deep UV lithography. Hence, we want to determine a sensor's performance with a feature size above 1µm, which will allow for easy and cheap fabrication. While lower wavelengths exhibit higher performance, the blue wavelength has almost zero sensitivity for small AR waveguides with wopt>1µm. Hence, we choose to compare two designs both with TM mode. The first design is operating at low (red) wavelength λ=650 nm exhibiting Swg of 0.115, and the second is operating at a higher wavelength at λ=980 nm but demonstrating slightly higher Swg of 0.13. Table 2 shows the dimensions and the FOM of both MZI sensor designs. We can see that the first design operating at lower (red) wavelength with AR=0.05 has a higher FOM of 158 RIU-1 even if it exhibits slightly lower Swg.
Table 2. FOM of S- MZI sensors with large feature size using TM mode at LMZI = 500 µm.
λ (nm)
|
Dimensions
(nm)
|
FOM
(RIU-1)
|
650
|
wsens=1500, wref=1000 and h=80
|
158
|
980
|
wsens=1500, wref=1100 and h=160
|
127
|
The minimum detectable index change of the virus layer can be calculated from [29] as Δnmin=1/FOM. These values can then be converted to minimum detectable virus coverage rmin using (1). Table 3 shows Δnmin and rmin for the MZI sensors designs at the blue wavelength with different AR and the design at red wavelength optimized for large dimensions (AR=0.05) with LMZI=500µm. Note that lower virus concentrations (coverage r) can be detected by increasing the FOM by increasing the MZI sensor length as given in (7).
It is important to note that, silicon nitride waveguides with film thickness great than 300 nm suffer large stress, and different techniques are used to overcome this problem [30-32]. However, our analysis shows that thin silicon nitride waveguides, with h<300 nm, in the visible range are of better sensing performance. In this case, such stress is reduced and a homogeneous index and thickness can be obtained using low-pressure chemical vapor deposition (LP-CVD) [32].
Table 3. Δnmin and Rmin of S-MZI sensors with LMZI = 500 µm. *Representing TM mode.
λ (nm)
|
AR
|
Δnmin
|
rmin (%)
|
450
|
0.13*
|
2.0×10-3
|
1.29
|
0.37*
|
1.8×10-3
|
1.16
|
1
|
1.2×10-3
|
0.79
|
2.88
|
8.1×10-4
|
0.52
|
650
|
0.05*
|
6.3×10-3
|
3.73
|
Finally, different MZI configurations were studied and compared for sensing, namely symmetric MZI (s-MZI), asymmetric MZI (a-MZI) and loop terminated MZI (LT-MZI) shown in Fig. 6. The simulated results of the different configurations are summarized in Table 4 for the design of TM mode with wsens=270 nm, h=100 nm and wref=300 nm at λ=450 nm and Lsens=500 µm. While s-MZI (Lsens=Lref) sensitivity is determined only by its waveguide structures, i.e. Δneff=neff,sens-neff,ref, a-MZI (Lsens=Lref+ΔL) sensitivity can be engineered using ΔL=Lsens-Lref, according to (6). However, both structures will exhibit almost the same FOM for the same Lsens. On the other hand, LT-MZI is a recently proposed design [33] that consists of a conventional MZI with a loop connecting the output directional coupler arms, reflecting back the wave to the interferometer. For the same waveguide structure and Lsens, LT-MZI will exhibit the same sensitivity with the conventional MZI while the FWHM will reduce to half resulting in twice the FOM. The LT-MZI directional couplers are also assumed to be ideal 3-dB couplers. The asymmetric LT-MZI can also be used to control the sensitivity using ΔL as in the a-MZI case.
Table 4. FOM and S of the TM mode for different MZI sensors configurations with wsens=270 nm, h=100 nm and wref =300 nm at λ=450 nm and Lsens=500µm.
|
S (nm/RIU)
|
FOM (RIU-1)
|
s-MZI
|
3098
|
553
|
a-MZI
|
ΔL=30µm
|
1316
|
540
|
ΔL=5µm
|
5579
|
530
|
LT-MZI
|
3098
|
1106
|