Sensing Performance of Two-Dimensional Phoxonic Crystal Heterostructure Cavity

Fig. 1. Model of the sensing structure of phoxonic crystal. (a) Model diagram; (b) schematic of single cells (grey area is air, blue area is silicon matrix); (c) first Brillouin zone (radius of intermediate circular hole is measured in the lattice constant a)

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Fig. 2. Dispersion curves of a cell with radius of $r = 0.45 a$ . (a) Optical TE mode; (b) optical TM mode; (c) acoustic mode

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Fig. 3. Supercell model diagrams of 1×11 phoxonic crystal in y direction and phonon and photon surface wave bands and their modal diagrams. (a) Unidirectional supercell model; (b) acoustic mode (solid black line represents the body-wave band); (c) optical TE mode; (d) optical TM mode (light grey shaded areas represent light cones); (e) modal diagram of four surface wave bands of acoustic mode; (f) modal diagram of three surface wave bands of optical TE mode; (g) modal diagram of surface wave energy band of optical TM mode

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Fig. 4. Phonon and photon surface wave band curves. (a) Photons (light gray shade represents the light cone); (b) phonons (red dotted line represents the surface wave band of $h = 0.4 a$ , $d = 0.275 a$ ; blue dotted line represents the surface wave band of $h = 0.25 a$ , $d = 0.4 a$ ; cyan shade represents the mode gap)

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Fig. 5. Transmission spectrum of water and electric field intensity distribution corresponding to the formant peak. (a) Transmission spectrum of water; (b) electric field intensity distribution

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$Transmission spectra of three solutions and the relationship between refractive index and resonant wavelength. (a) 1-propanol solution; (b) sodium chloride solution; (c) glucose solution; (d) relationship between refractive index and resonant wavelength$

Fig. 6. Transmission spectra of three solutions and the relationship between refractive index and resonant wavelength. (a) 1-propanol solution; (b) sodium chloride solution; (c) glucose solution; (d) relationship between refractive index and resonant wavelength

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Fig. 7. Diagrams of transmission loss of water and three absorption peaks and their corresponding vibrational modes and acoustic field profiles. (a) Diagram of water transmission loss; (b) vibrational mode diagrams and acoustic field distribution diagrams of three absorption peaks

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$Transmission loss plots of mode A and mode B at different mass fractions of three solutions. (a) Mode A of 1-propanol solution; (b) mode A of sodium chloride solution; (c) mode A of glucose solution; (d) mode B of 1-propanol solution; (e) mode B of sodium chloride solution; (f) mode B of glucose solution$

Fig. 8. Transmission loss plots of mode A and mode B at different mass fractions of three solutions. (a) Mode A of 1-propanol solution; (b) mode A of sodium chloride solution; (c) mode A of glucose solution; (d) mode B of 1-propanol solution; (e) mode B of sodium chloride solution; (f) mode B of glucose solution

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Fig. 9. Peak frequency of modes A and B as a function of sound velocity

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Table 1. Acoustic and optical material parameters for three solutions

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Table 1. Acoustic and optical material parameters for three solutions

Solution	Solution mass fraction /%	Refractive index n	Velocity v /（m·s^-1）	Density ρ $/$ （kg·m^-3）
Water	0	1.3333	1490	997.02
1-propanol	6.67	—	1545	990
	13.67	1.3451	—	—
	27.47	—	1531	956
	35.76	1.3609	—	—
	38.48	—	1472	933
	49.89	—	1421	908
	52.61	1.3696	—	—
	76.95	1.3792	—	—
Sodium chloride	5	1.3425	1548.9	1040
	10	1.3515	1619.3	1062
	15	1.3605	1672.5	1110
	20	1.3710	1746.3	1159
Glucose	20	1.3639	1558	1084
	40	1.3999	1671	1180
	60	1.4419	1781	1273

Table 2. Optical sensing performance parameters of 1-propanol solution

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Table 2. Optical sensing performance parameters of 1-propanol solution

Mass fraction of 1-propanol /%	0 （water ）	13.67	35.76	52.61	76.95
$λ_{r} / n m$	1653.17	1662.88	1675.88	1682.94	1690.81
${d_{F W H M}}_{, r} / n m$	0.47	0.47	0.47	0.46	0.46
$S / (n m \cdot R I U^{- 1})$	—	822.88	822.78	811.49	819.79
$Q$	3517.38	3538.04	3565.70	3658.57	3675.67
$η_{F O M} / R I U^{- 1}$	—	1761.09	1750.59	1764.11	1782.15

Table 3. Optical sensing performance parameters of sodium chloride solution

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Table 3. Optical sensing performance parameters of sodium chloride solution

Mass fraction of sodium chloride /%	0 （water ）	5	10	15	20
$λ_{r} / n m$	1653.17	1660.76	1668.15	1675.51	1684.16
${d_{F W H M}}_{, r} / n m$	0.47	0.47	0.47	0.46	0.46
$S / (n m \cdot R I U^{- 1})$	—	825.00	821.10	817.80	823.81
$Q$	3517.38	3533.53	3549.26	3642.41	3661.22
$η_{F O M} / R I U^{- 1}$	—	1755.32	1747.02	1777.82	1790.89

Table 4. Optical sensing performance parameters of glucose solutions

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Table 4. Optical sensing performance parameters of glucose solutions

Mass fraction of glucose /%	0 （water ）	20	40	60
$λ_{r} / n m$	1653.17	1678.32	1707.55	1741.25
${d_{F W H M}}_{, r} / n m$	0.47	0.43	0.41	0.42
$S / (n m \cdot R I U^{- 1})$	—	821.89	811.94	809.52
$Q$	3517.38	3903.07	4164.76	4145.83
$η_{F O M} / R I U^{- 1}$	—	1911.37	1980.34	1927.43

Table 5. Acoustic sensing performance parameters of 1-propanol solution

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Table 5. Acoustic sensing performance parameters of 1-propanol solution

Mass fraction of 1-propanol /%	0 （water）	6.67	27.47	38.48	49.89
$f_{r, A} / G H z$	4.0461	4.1951	4.1516	3.9881	3.8464
$f_{r, B} / G H z$	4.2773	4.4347	4.3905	4.2181	4.0687
$S_{A} / [M H z / (m \cdot s^{- 1})]$	3.222	3.107	2.573	2.778	—
$S_{B} / [M H z / (m \cdot s^{- 1})]$	3.289	3.157	2.761	2.929	—

Table 6. Acoustic sensing performance parameters of sodium chloride solution

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Table 6. Acoustic sensing performance parameters of sodium chloride solution

Mass fraction of sodium chloride /%	0 （water ）	5	10	15	20
$f_{r, A} / G H z$	4.0461	4.2127	4.4077	4.5602	4.7695
$f_{r, B} / G H z$	4.2773	4.4522	4.6572	4.8154	5.0346
$S_{A} / [M H z / (m \cdot s^{- 1})]$	—	2.829	2.770	2.867	2.836
$S_{B} / [M H z / (m \cdot s^{- 1})]$	—	2.969	2.912	2.974	2.970

Table 7. Acoustic sensing performance parameters of glucose solutions
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Table 7. Acoustic sensing performance parameters of glucose solutions
Mass fraction of glucose /% 0 （water ） 20 40 60
$f_{r, A} / G H z$ 4.0461 4.2438 4.5670 4.8825
$f_{r, B} / G H z$ 4.2773 4.4839 4.8194 5.1501
$S_{A} / [M H z / (m \cdot s^{- 1})]$ — 2.907 2.860 2.868
$S_{B} / [M H z / (m \cdot s^{- 1})]$ — 3.038 2.969 2.868

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Xu Wang, Miao Tian, Zhenmeng Ma, Lei Zhang. Sensing Performance of Two-Dimensional Phoxonic Crystal Heterostructure Cavity[J]. Acta Optica Sinica, 2024, 44(14): 1426002

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