Exciton-Polariton Fano Resonance Driven by Second Harmonic Generation

Angle-resolved second harmonic generation (SHG) spectra of ZnO microwires show characteristic Fano resonances in the spectral vicinity of exciton-polariton modes. We observe a resonant peak followed by a strong dip in SHG originating from the constructive and destructive interference of the nonresonant SHG and the resonant contribution of the polariton mode. It is demonstrated that the Fano line shape, and thus the Fano asymmetry parameter $q$, can be tuned by the phase shift of the two channels. We develop a model to calculate the phase-dependent $q$ as a function of the radial angle in the microwire and achieve a good agreement with the experimental results. The deduced phase-to-$q$ relation unveils the crucial information about the dynamics of the system and offers a tool for control on the line shape of the SHG spectra in the vicinity of exciton-polariton modes.

Figure 1

(a) The SEM of a typical ZnO microwire. The angles defined as $\theta$ and $\varphi$ represent the two detection planes of the angle-resolved spectra. (b) The fundamental light wave irradiates the ZnO microwire from the back of the glass, and the SHG radiation is emitted from the top of the wire. (c) The dispersion of the 28th and 29th TM-polarized polariton modes, fitting with the white dashed lines.

Figure 2

(a) Angle $\theta$-resolved SHG spectra with the peak at 3.175, 3.172, 3.169, 3.155, and 3.151 eV from top to bottom. (b) The corresponding line curves at $\theta =0°$, fitting with the red solid lines by Eq. (1).

Figure 3

(a) Angle $\varphi$-resolved spectral patterns. The SHG and polariton mode are resonant at 3.169 eV. (b) $q$ values at each angle are obtained by fitting each line profile. The dashed lines are the boundaries where $q$ changes sign. (c) The typical line profiles taken at $\varphi =-27°$, $-15°$, $-8.3°$, 0°, 7.7°, 15°, and 27° from pattern (a). The black dotted lines are experimental data, and the red solid lines are fitted data. These curves show the different line shapes resulting from the Fano coupling in the system.

Figure 4

(a) The electric field distribution pattern for the 29th polariton mode in real space calculated using the finite element analysis. Inset: The equiphase surface is marked by the dashed and solid lines for the white rectangle area. (b) The Fourier transform of pattern (a). The dashed lines mark the angles where the phase of the emission electric field in pattern (a) changes sign. (c) The phase $\phi$ vs $\varphi$ curve obtained with the use of the phase information in (a). (d) The theoretical pattern calculated by using Eq. (3) with $A_p/{\mathrm{\Gamma }}_p$ being the amplitude against $\varphi$ obtained from (b) and $A_s/{\mathrm{\Gamma }}_s$ being the same order of $A_p/{\mathrm{\Gamma }}_p$. ${\mathrm{\Gamma }}_p$ and ${\mathrm{\Gamma }}_s$ are the FWHM (in the frequency domain) of the 29th polariton mode (1.3 meV) and SHG (12 meV), respectively. (e) The $q$ variation obtained by fitting each line of pattern (d) (red solid line) and $q(\phi )=-\cot (\phi /2)$ (green dashed line).