Giant Enhancement of the Goos-Hänchen Shift Assisted by Quasibound States in the Continuum

We achieve reflection-type bound states in the continuum (BICs) in the compound grating waveguide structure by tuning the excitation of the guided modes. Assisted by the quasi-BICs with ultrahigh Q factors, the Goos-Hänchen (GH) shift can be greatly enhanced to larger than or equal to four orders of wavelength. In addition, different from the large GH shift based on the Brewster dip or transmission-type resonance, the maximum GH shift assisted by the reflection-type quasi-BIC is located at the reflectance peak with unity reflectance, which can be more easily detected in the experiment. Based on the quasi-BIC-assisted giant GH shift, we propose an ultrasensitive temperature sensor with a minimum resolution in the order of ${10}^{-4}$ °C. Our work provides a route, under the current experimental conditions, to design ultrasensitive sensors, light information storage devices, wavelength division de/multiplexers, optical switches, and polarization beam splitters based on this giant GH shift together with high reflectance.

Figure 1

Schematic of the unit cell of the compound grating waveguide structure. The first layer is a four-part periodic grating layer with the grating period $\mathrm{\Lambda }$ and the thickness $h_1$. The widths of the first and third parts are the same value $d_a$, while those of the second and fourth parts are $d_b=d+\Delta d$ and $d_c=d-\Delta d$, respectively. The second layer is a waveguide layer with the thickness $h_2$.

Figure 2

(a) GMR excitation of the compound grating waveguide structure. $k_{x,i}$ and $\beta$ represent the tangential components of the wave vectors in the grating and the waveguide layer, respectively. (b) Dispersion relations of the TE₀ guided mode in the waveguide layer (blue solid line), $k_x=k_{0x}$ in the air background (black dashed line), and $k_x=k_{x,i}(i=-1,-2)$ in the grating (red and green dashed lines).

Figure 3

Reflectance spectra (zero-order diffraction) around ${\lambda }_A$ of the structure for different values of $\delta$ at $\theta =5^{\circ }$ for TE polarization. The right insets represent the $|E_y|$ distributions corresponding to the reflectance peaks.

Figure 4

(a) Dependence of Q factor on $\delta$. (b) Linear relationship between Q factor and $1/{\delta }^2$. The red dashed line is a linear fitting line.

Figure 5

Reflectance angular spectra for (a) $\delta =0.3$ at ${\lambda }_0=658.2\mathrm{nm}$, (d) $\delta =0.2$ at ${\lambda }_0=659.1\mathrm{nm}$, and (g) $\delta =0.1$ at ${\lambda }_0=659.6\mathrm{nm}$. (b), (e), and (h): corresponding reflection phase angular spectra. (c), (f), and (i): corresponding GH shift angular spectra.

Figure 6

(a) Dependence of peak value of GH shift on $\delta$. (b) Linear relationship between peak value of GH shift and Q factor. The red dashed line is a linear fitting line.

Figure 7

(a) Schematic of the unit cell of the proposed temperature sensor. (b) GH shift angular spectra of the proposed sensor at T = 25 °C and T = 25.2 °C. (c) GH shift of the proposed sensor versus temperature. (d) Temperature-dependent sensitivity of the proposed sensor.

Figure 8

Dependence of minimum temperature resolution on Q factor.

Figure 9

Reflectance spectra around ${\lambda }_B$ of the structure for different values of $\delta$ at $\theta =5^{\circ }$ for TE polarization.

Figure 10

Dependence of Q factor on $\delta$.