CHAPTER 4. ATOMICALLY THIN ELECTRO-OPTIC POLARIZATION MODULATOR
4.5 CAVITY DESIGN AND BROADBAND NATURE OF BIREFRINGENCE IN TLBP
4.5 CAVITY DESIGN AND BROADBAND NATURE OF
polarization conversion (either in the azimuthal orientation or the ellipticity or both). The difference in the trajectories are intimately related to the critical coupling between the cavity and the incoming polarization. For all the presented trajectories, the azimuthal orientation was aligned nearly 45 degrees to the AC and ZZ direction of the TLBP flake. For each normalized Poincaré sphere, the blue arrows mark the beginning of the spectral scan (1410nm for D1-4, 1500 for D5) and the red arrows mark the end (1520nm for D1-4, 1575 for D5)–also shown as stars in x-axis of (E).
We next designed a heterostructure for polarization conversion by integrating the TLBP in an optically resonant cavity geometry which enhances the degree of polarization conversion. A transfer matrix calculation of a typical Fabry-Pérot cavity design, schematically shown in side view in Fig. 4.4A, yields the complex reflection phasor, amplitude and phase spectra, as illustrated in Fig. 4.4B, C, D respectively. From the phasor diagram in Fig. 4.4B, a prominent and different complex reflectivity feature is seen along the two polarizations. A clear resonance from the cavity is seen at 1479 (1470) nm for the AC (ZZ) direction in the reflection amplitude in Fig. 4.4C, along with a weaker excitonic absorption feature at shorter wavelengths (1398 nm), seen only along the AC direction. Interestingly, the reflected phase along the AC and ZZ, in Fig. 4.4D shows strong differences near the cavity resonance. Taken together, these results indicate the potential for significant polarization conversion of the reflected light. The cavity parameters used in Fig. 4.4B- D are not a unique choice. In fact, the optical anisotropy in TLBP is broadband, enabling operation over the entire wavelength range of the telecommunication E, S and C-bands with appropriate changes in the cavity parameters–primarily via adjustment of the thicknesses of the dielectric medium (hBN or PMMA) and the top Au mirror. Both parameters are important in determining the resonance wavelength and the reflection extinction ratio.
We present numerical results on the effect of the top Au and PMMA thickness on the cavity performance. Here, the thickness of the bottom Au, bottom hBN, TLBP and top hBN were fixed at 100 nm, 120 nm, 1.59 nm, and 52 nm. The refractive indices of Au were adopted from Johnson and Christy, while n=2.17 was used for hBN with no dispersion. For PMMA, n=1.478 was used.
AC response of TLBP was modelled with a single exciton with the following parameters–
resonance wavelength = 1398.2 nm, oscillator strength = 2.5 meV, broadening/linewidth = 45.1 meV (as extracted from measurements discussed in Fig 2.). 𝛜∞ = 12.5 and 10.2 were used for the
AC and ZZ direction, respectively. The ZZ direction permittivity was assumed to be constant, with no excitonic feature. No thickness dependence was assumed for the complex refractive index for any of the layers. Transfer matrix calculations were run with sweeps of the PMMA thickness and the top Au thickness. Fig. 4.5A shows the evolution of the cavity resonance. As the PMMA thickness is swept, the cavity resonance redshifts due to the overall increase in the optical length of the cavity. As the top Au thickness is increased, the resonance frequency blueshifts because of the change in the reflectivity of the top mirror (higher reflectivity for thicker top Au). Fig 4.5B shows the effect of the top Au and PMMA thickness on the reflection amplitude at the resonance along the AC direction. A trajectory is seen with low reflectivity highlighting the critical coupling condition. This is the physical set of parameters which correspond to the maximal energy transfer to the cavity. Finally, the maximum achieved phase shift difference between the AC and ZZ directions as a function of top Au and PMMA thickness is discussed in Fig. 4.5C. Strong phase difference is seen along the “critical coupling” trajectory. In this work, cavities were fabricated with target critical coupling to the AC direction because that is the electrically tunable polarization direction, while the ZZ remains passive, for all doping conditions.
Figure 4.5. Amplitude and phase shift dependence on cavity parameters. Effect of the top Au and PMMA thickness are studied on the cavity performance. (A) Resonance of the cavity (along the AC direction) showing redshifts with increasing PMMA thickness and blueshifts with increasing metal thickness. (B) Reflection amplitude of the cavity (along the AC direction) showing the
“critical coupling” trace as a function of top Au and PMMA thickness. (C) Maximum phase shift difference between the AC and ZZ direction plotted as a function of top Au and PMMA thickness.
Strong phase shift difference traces follow the reflection amplitude trace, highlighting the importance of critical coupling.
To experimentally demonstrate the broadband nature of the TLBP anisotropy, reflection intensities (S0) measured from five representative heterostructures are shown in Fig. 4.4E. The PMMA thickness was sequentially tuned to redshift the cavity resonance, spanning approximately 100 nm across the E, S, and C–telecommunication band. For each heterostructure device (D1 to D5), a
corresponding spectral trajectory on the normalized Poincaré sphere is shown in Fig. 4.4F-J, respectively. The blue (red) arrows mark the beginning (end) of the measured spectral trajectory, corresponding to 1410 (1520) nm for D1 to D4 and 1500 (1575) nm for D5. Efficient polarization conversion can be seen for all the devices, confirming the broadband nature of the anisotropy in TLBP coupled with the cavity mode. The differences in the trajectories arise from where the cavity resonance wavelength is with respect to the beginning and ending point of the spectral scans. In addition, the arc length subtended by the trajectories on the normalized Poincaré sphere is intimately related to how well the cavity critically couples to the incoming free-space electromagnetic field and is dominated strongly by the top mirror reflectivity.