Coherent Control of Ultrahigh-Frequency Acoustic Resonances in Photonic Crystal Fibers

Ultrahigh frequency acoustic resonances ($\backsim 2\mathrm{GHz}$) trapped within the glass core ($\backsim 1\mu \mathrm{m}$ diameter) of a photonic crystal fiber are selectively excited through electrostriction using laser pulses of duration 100 ps and energy 500 pJ. Using precisely timed sequences of such driving pulses, we achieve coherent control of the acoustic resonances by constructive or destructive interference, demonstrating both enhancement and suppression of the vibrations. A sequence of 27 resonantly-timed pulses provides a 100-fold increase in the amplitude of the vibrational mode. The results are explained and interpreted using a semianalytical theory, and supported by precise numerical simulations of the complex light-matter interaction.

Figure 1

Coherent control of acoustic phonons. The cladding pitch and core diameter are 1.67 and $1.27\mu \mathrm{m}$ for PCF no. 1 (top row), and 1.92 and $1.75\mu \mathrm{m}$ for PCF no. 2 (bottom row). The white bars are $1\mu \mathrm{m}$ long. (b) Response for a single pulse excitation of PCF no. 1 (blue curve), excitation by two pulses spaced by 260 ps (red curve) and excitation by two pulses spaced by 512 ps (green curve). (e) The same as (b) but for PCF no. 2 and pulse separations of 329 ps for the red curve and 658 ps for the green curve. The cartoons in (b) and (e) illustrate the corresponding pump pulse sequence schemes. (c),(f) The Fourier transform power spectra corresponding to the time waveforms shown in (b) and (e), corresponding curves share the same color; the arrows indicate the multiplication factor used in each curve.

Figure 2

Multipulse excitation of ARs. (a) Response of PCF no. 1 when excited by a single pulse (red curve) and a train of 27 pulses (black curve). (b) Same as (a) but for PCF no. 2. (c) Fourier transform power spectra obtained from the response of PCF no. 1 to a single pulse (red dashed curve) and a sequence of 27 pulses (black solid curve); the arrow indicates the multiplication factor used in the red curve. (d) Spectral power amplitude for the target AR as the number of pulses increases. The black and red curves represent PCF no. 1 and PCF no. 2, respectively. The dots represent the experimental data, the dashed line the expected amplification, and the solid line the expected amplification with saturation parameter $S=0.06$.

Figure 3

Numerically calculated electrostriction excitation and elasto-optic refractive index modulation for PCF no. 1. (a) Electrostrictive excitation for pump light polarized linearly (blue curve) and circularly (red curve); the arrows indicate the most optically active modes, shown in parts (c) and (d). (b) Real (red dashed curve) and imaginary (black solid curve) parts of the refractive index perturbation spectrum; the inset shows the temporal response. (c) $\Delta {ϵ}_{xx}+\Delta {ϵ}_{yy}$ for the $R_{01}$-like mode at 2.318 GHz. (d) $\Delta {ϵ}_{xy}$ for the $T{R}_{21}$-like mode at 1.956 GHz. The black solid lines represent the undeformed fiber geometry used in the calculation. The mesh deformation in the transverse plane was scaled for clarity.