Delay of Light in an Optical Bottle Resonator with Nanoscale Radius Variation: Dispersionless, Broadband, and Low Loss

It is shown theoretically that an optical bottle resonator with a nanoscale radius variation can perform a multinanosecond long dispersionless delay of light in a nanometer-order bandwidth with minimal losses. Experimentally, a 3 mm long resonator with a 2.8 nm deep semiparabolic radius variation is fabricated from a $19\mu \mathrm{m}$ radius silica fiber with a subangstrom precision. In excellent agreement with theory, the resonator exhibits the impedance-matched 2.58 ns (3 bytes) delay of 100 ps pulses with $0.44\mathrm{dB}/\mathrm{ns}$ intrinsic loss. This is a miniature slow light delay line with the record large delay time, record small transmission loss, dispersion, and effective speed of light.

Figure 1

(a) Illustration of an optical bottle resonator delay line. Light is coupled into the resonator from a transverse waveguide (microfiber) and experiences whispering gallery mode propagation along the resonator surface. Inset shows the magnified profile of the fiber radius variation. (b) Semiparabolic variation of a bottle resonator radius used in the numerical simulations.

Figure 2

(a),(b) Surface plots of the transmission amplitude and group delay near the edge $z=z_{t1}$ of the bottle resonator calculated with the coupling parameters defined in the text. (c),(d) Transmission amplitude and group delay spectra at the coupling point $z_c=z_1$ shown in (a) and (b), respectively. (e) The output signal amplitude (solid line) calculated for the input 100 ps pulse (dashed line). The pulse spectrum is determined by the bold line in (c).

Figure 3

(a) Illustration of an optical bottle resonator delay line. Inset shows the magnified profile of the fiber radius variation. (b) Experimentally measured surface plot of the transmission amplitude measured at microfiber positions spaced by $10\mu \mathrm{m}$ along the fiber axis, which was used to determine the bottle resonator radius variation (bold line).

Figure 4

(a),(b) Surface plots of the transmission amplitude and group delay near the edge $z=z_{t1}$ of the fabricated bottle resonator measured after the optimization of coupling parameters by translation of the microfiber with respect to the resonator. (c),(d) Transmission amplitude and group delay spectra at the coupling point $z_c=z_1$ corresponding to minimum spectral oscillations in (a) and (b), respectively. (e),(f) The same as (c),(d) but at the coupling point $z_c=z_2$, which corresponds to the semiparabolic part of the potential $V(z)$. (g),(h) The output signal amplitudes (solid line) calculated for the input 100 ps pulse (dashed line) from the spectra measured at points $z_1$ and $z_2$, with the pulse spectrum determined by the bold line in (c) and (e), respectively.