Progress toward third-order parametric down-conversion in optical fibers

Optical fibers have been considered an optimal platform for third-order parametric down-conversion since they can potentially overcome the weak third-order nonlinearity by their long interaction length. Here we present, in the first part, a theoretical derivation for the conversion rate both in the case of spontaneous generation and in the presence of a seed beam. Then we review three types of optical fibers and we examine their properties in terms of conversion efficiency and practical feasibility.

Figure 1

SEM image of the hybrid fiber (a) and its inner core structure (b).

Figure 2

Dispersion curves of the photonic band-gap mode and the infrared fundamental mode of the hybrid fiber. The insets show the calculated spatial distributions of the modes.

Figure 3

Normalized spectra and near-field intensity distributions of the third harmonic (a) and the pump (b) for the hybrid fiber. The insets show the near field at the output of the fiber.

Figure 4

SEM picture of the hollow-core structure (a) with a detailed view of a capillary (b).

Figure 5

The calculated (red dashed line) and measured (blue continuous line) loss for the single-ring PCF designed for the photon triplet generation.

Figure 6

Difference between the refractive indices for 532 and 1596 nm vs the Xe pressure in a single-ring PCF. The insets show the simulated intensity distributions of the modes. The insets show the near field at the output of the fiber.

Figure 7

Phase matched third-harmonic high-order modes generated by changing the xenon pressure inside the gas chamber [from (a) to (c)]. Simulated Poynting vector of the guided modes [from (d) to (f)].

Figure 8

Normalized spectra and measured near-field intensity distributions of the TH (a) and the pump (b) for Xe-filled PCF at 8.7 bars.

Figure 9

Maximal angle allowing an adiabatic transition for ${\mathrm{HE}}_{11}$ and ${\mathrm{HE}}_{12}$, with the pump in the visible and the generated signal in the IR. The taper should be designed such that the local angle always lies within the shaded area to ensure adiabaticity. The red dots correspond to the maximum angle to avoid coupling from the IR ${\mathrm{HE}}_{11}$ to the next relevant higher-order mode ${\mathrm{HE}}_{12}$. The green triangles (blue squares) are the criterion for the visible light to avoid coupling between the ${\mathrm{HE}}_{12}$ and the next relevant lower- (higher-) modes.

Figure 10

Normalized spectra and measured near-field intensity distributions of the TH (a) and the pump (b) for tapered single-mode fiber in vacuum. The insets show the Poynting vector distributions at the output of the fiber.

Figure 11

(a) Proposed device based on 460HP and SMF28 fibers spliced together, with a taper in the SMF28 stretch. (b) ${\mathrm{HE}}_{11}$ mode propagating in the 460HP fiber, ${\mathrm{HE}}_{12}$ mode propagating in the SMF28 fiber, and diametrical section of both modes.

Figure 12

Left: ${\mathrm{HE}}_{11}$ and ${\mathrm{HE}}_{12}$ modes in the SMF28 fiber. Middle: Resulting intensity pattern in the $zy,xz$, and $xy$ planes. Right: Resulting intensity pattern in the $xz$ plane.

Figure 13

Imaged intensity pattern at the output of the fiber during taper fabrication, obtained from a video recorded by a charge-coupled device camera, with a $90\text{−}\mathrm{ms}$ time between frames, corresponding to a $\sim 75\mu \mathrm{m}$ taper length differential between frames.

Figure 14

The spectral density $S({\omega }_1,{\omega }_2)$ for the hybrid-core fiber at different pump frequencies.

Figure 15

The spectral density $S({\omega }_1,{\omega }_2)$ for the hollow-core fiber at different xenon pressures.

Figure 16

The spectral density $S({\omega }_1,{\omega }_2)$ for the tapered fiber at different taper diameters.