Full-field characterization of helical Bloch modes guided in twisted coreless photonic crystal fiber.

It was recently reported that a photonic crystal fiber (PCF) with no structural core guides light if a permanent chiral twist is introduced by spinning the fiber preform during the draw. The intriguing guidance mechanism behind this novel effect has many remarkable features; for example, it intrinsically supports circularly polarized helical Bloch modes (HBMs) that carry multiple optical vortices, making twisted PCFs of interest in fields such as optical micro-manipulation, imaging, quantum optics, and optical communications. Here we report for the first time, to the best of our knowledge, that a twisted coreless PCF supports not just one but a family of guided HBMs, each member of which has a unique transverse field distribution and harmonic spectrum. By making detailed interferometric measurements of the near-field phase and amplitude distributions of HBMs, and expanding them as a series of Bessel beams, we are able to extract the amplitude of each azimuthal and radial HBM harmonic. Good agreement is found with the numerical solutions of Maxwell's equations. The results shed light on the properties of this curious new optical phenomenon.

Higher-order mode suppression in twisted single-ring hollow-core photonic crystal fibers.

A hollow-core single-ring photonic crystal fiber (SR-PCF) consists of a ring of capillaries arranged around a central hollow core. Spinning the preform during drawing introduces a continuous helical twist, offering a novel means of controlling the modal properties of hollow-core SR-PCF. For example, twisting geometrically increases the effective axial propagation constant of the LP01-like modes of the capillaries, providing a means of optimizing the suppression of HOMs, which occurs when the LP11-like core mode phase-matches to the LP01-like modes of the surrounding capillaries. (In a straight fiber, optimum suppression occurs for a capillary-to-core diameter ratio d/D=0.682.) Twisting also introduces circular birefringence (to be studied in a future Letter) and has a remarkable effect on the transverse intensity profiles of the higher-order core modes, forcing the two-lobed LP11-like mode in the untwisted fiber to become three-fold symmetric in the twisted case. These phenomena are explored by means of extensive numerical modeling, an analytical model, and a series of experiments. Prism-assisted side-coupling is used to measure the losses, refractive indices, and near-field patterns of individual fiber modes in both the straight and twisted cases.

Helically twisted photonic crystal fibres.

Recent theoretical and experimental work on helically twisted photonic crystal fibres (PCFs) is reviewed. Helical Bloch theory is introduced, including a new formalism based on the tight-binding approximation. It is used to explore and explain a variety of unusual effects that appear in a range of different twisted PCFs, including fibres with a single core and fibres with N cores arranged in a ring around the fibre axis. We discuss a new kind of birefringence that causes the propagation constants of left- and right-spinning optical vortices to be non-degenerate for the same order of orbital angular momentum (OAM). Topological effects, arising from the twisted periodic 'space', cause light to spiral around the fibre axis, with fascinating consequences, including the appearance of dips in the transmission spectrum and low loss guidance in coreless PCF. Discussing twisted fibres with a single off-axis core, we report that optical activity in a PCF is opposite in sign to that seen in a step-index fibre. Fabrication techniques are briefly described and emerging applications reviewed. The analytical results of helical Bloch theory are verified by an extensive series of 'numerical experiments' based on finite-element solutions of Maxwell's equations in a helicoidal frame.This article is part of the themed issue 'Optical orbital angular momentum'.

Current sensing using circularly birefringent twisted solid-core photonic crystal fiber.

Continuously twisted solid-core photonic crystal fiber (PCF) exhibits pure circular birefringence (optical activity), making it ideal for current sensors based on the Faraday effect. By numerical analysis, we identify the PCF geometry for which the circular birefringence (which scales linearly with twist rate) is a maximum. For silica-air PCF, this occurs at a shape parameter (diameter-to-spacing ratio of the hollow channels) of 0.37 and a scale parameter (spacing-to-wavelength) of 1.51. This result is confirmed experimentally by testing a range of different structures. To demonstrate the effectiveness of twisted PCF as a current sensor, a length of fiber is placed on the axis of a 7.6 cm long solenoid, and the Faraday rotation is measured at different values of dc current. The system is then used to chart the wavelength dependence of the Verdet constant.

Enhanced optical activity and circular dichroism in twisted photonic crystal fiber.

We demonstrate experimentally and theoretically that the core-guided mode in helically twisted photonic crystal fiber exhibits resonantly enhanced optical activity and circular dichroism in the vicinity of anti-crossings with leaky orbital angular momentum (OAM) modes in the cladding. This arises because the anti-crossings for left and right circularly polarized core modes occur at slightly different wavelengths.

Nonlinear amplification of side-modes in frequency combs.

We investigate how suppressed modes in frequency combs are modified upon frequency doubling and self-phase modulation. We find, both experimentally and by using a simplified model, that these side-modes are amplified relative to the principal comb modes. Whereas frequency doubling increases their relative strength by 6 dB, the growth due to self-phase modulation can be much stronger and generally increases with nonlinear propagation length. Upper limits for this effect are derived in this work. This behavior has implications for high-precision calibration of spectrographs with frequency combs used for example in astronomy. For this application, Fabry-Pérot filter cavities are used to increase the mode spacing to exceed the resolution of the spectrograph. Frequency conversion and/or spectral broadening after non-perfect filtering reamplify the suppressed modes, which can lead to calibration errors.

Raman-free nonlinear optical effects in high pressure gas-filled hollow core PCF.

The effective Kerr nonlinearity of hollow-core kagomé-style photonic crystal fiber (PCF) filled with argon gas increases to ~15% of that of bulk silica glass when the pressure is increased from 1 to 150 bar, while the zero dispersion wavelength shifts from 300 to 900 nm. The group velocity dispersion of the system is uniquely pressure-tunable over a wide range while avoiding Raman scattering-absent in noble gases-and having an extremely high optical damage threshold. As a result, detailed and well-controlled studies of nonlinear effects can be performed, in both normal and anomalous dispersion regimes, using only a fixed-frequency pump laser. For example, the absence of Raman scattering permits clean observation, at high powers, of the interaction between a modulational instability side-band and a soliton-created dispersive wave. Excellent agreement is obtained between numerical simulations and experimental results. The system has great potential for the realization of reconfigurable supercontinuum sources, wavelength convertors and short-pulse laser systems.

Optical activity in twisted solid-core photonic crystal fibers.

In this Letter we show that, in spectral regions where there are no orbital cladding resonances to cause transmission loss, the core mode of a continuously twisted photonic crystal fiber (PCF) exhibits optical activity, and that the magnitude of the associated circular birefringence increases linearly with twist rate and is highly reproducible. In contrast to previous work on twist-induced circular birefringence, PCF has zero linear birefringence and an on-axis core, making the appearance of circular birefringence rather unexpected. A theoretical model based on symmetry properties and perturbation theory is developed and used to show that both spin and orbital angular momentum play a role in this effect. It turns out that the degenerate left- and right-circularly polarized modes of the untwisted PCF are not 100% circularly polarized but carry a small amount of orbital angular momentum caused by the interaction between the core mode and the hollow channels.

Optimal storage and retrieval of single-photon waveforms.

We report an experimental demonstration of optimal storage and retrieval of heralded single-photon wave packets using electromagnetically induced transparency (EIT) in cold atoms at a high optical depth. We obtain an optimal storage efficiency of (49 ± 3)% for single-photon waveforms with a temporal likeness of 96%. Our result brings the EIT quantum light-matter interface closer to practical quantum information applications.

A dark-line two-dimensional magneto-optical trap of 85Rb atoms with high optical depth.

We describe the apparatus of a dark-line two-dimensional (2D) magneto-optical trap (MOT) of (85)Rb cold atoms with high optical depth (OD). Different from the conventional configuration, two (of three) pairs of trapping laser beams in our 2D MOT setup do not follow the symmetry axes of the quadrupole magnetic field: they are aligned with 45° angles to the longitudinal axis. Two orthogonal repumping laser beams have a dark-line volume in the longitudinal axis at their cross over. With a total trapping laser power of 40 mW and repumping laser power of 18 mW, we obtain an atomic OD up to 160 in an electromagnetically induced transparency (EIT) scheme, which corresponds to an atomic-density-length product NL = 2.05 × 10(15) m(-2). In a closed two-state system, the OD can become as large as more than 600. Our 2D MOT configuration allows full optical access of the atoms in its longitudinal direction without interfering with the trapping and repumping laser beams spatially. Moreover, the zero magnetic field along the longitudinal axis allows the cold atoms maintain a long ground-state coherence time without switching off the MOT magnetic field, which makes it possible to operate the MOT at a high repetition rate and a high duty cycle. Our 2D MOT is ideal for atomic-ensemble-based quantum optics applications, such as EIT, entangled photon pair generation, optical quantum memory, and quantum information processing.

Excitation of orbital angular momentum resonances in helically twisted photonic crystal fiber.

Spiral twisting offers additional opportunities for controlling the loss, dispersion, and polarization state of light in optical fibers with noncircular guiding cores. Here, we report an effect that appears in continuously twisted photonic crystal fiber. Guided by the helical lattice of hollow channels, cladding light is forced to follow a spiral path. This diverts a fraction of the axial momentum flow into the azimuthal direction, leading to the formation of discrete orbital angular momentum states at wavelengths that scale linearly with the twist rate. Core-guided light phase-matches topologically to these leaky states, causing a series of dips in the transmitted spectrum. Twisted photonic crystal fiber has potential applications in, for example, band-rejection filters and dispersion control.

Optical storage with electromagnetically induced transparency in a dense cold atomic ensemble.

We experimentally investigate optical storage with electromagnetically induced transparency in a dense cold (85)Rb atomic ensemble. By varying the optical depth (OD) from 0 to 140, we observe that the optimal storage efficiency has a saturation value of 50% as OD>50. Our result is consistent with that obtained from hot vapor cell experiments.

Optical precursor of a single photon.

We report the direct observation of optical precursors of heralded single photons with step- and square-modulated wave packets passing through cold atoms. Using electromagnetically induced transparency and the slow-light effect, we separate the single-photon precursor, which always travels at the speed of light in vacuum, from its delayed main wave packet. In the two-level superluminal medium, our result suggests that the causality holds for a single photon.

Bright spatially coherent wavelength-tunable deep-UV laser source using an Ar-filled photonic crystal fiber.

We report on the spectral broadening of ~1 µJ 30 fs pulses propagating in an Ar-filled hollow-core photonic crystal fiber. In contrast with supercontinuum generation in a solid-core photonic crystal fiber, the absence of Raman and unique pressure-controlled dispersion results in efficient emission of dispersive waves in the deep-UV region. The UV light emerges in the single-lobed fundamental mode and is tunable from 200 to 320 nm by varying the pulse energy and gas pressure. The setup is extremely simple, involving <1 m of a gas-filled photonic crystal fiber, and the UV signal is stable and bright, with experimental IR to deep-UV conversion efficiencies as high as 8%. The source is of immediate interest in applications demanding high spatial coherence, such as laser lithography or confocal microscopy.

Generation of narrow-band hyperentangled nondegenerate paired photons.

We report the generation of nondegenerate narrow-bandwidth paired photons with time-frequency and polarization entanglements from laser cooled atoms. We observe the two-photon interference caused by Rabi splitting with a coherence time of about 30 ns and a visibility of 81.8% which verifies the time-frequency entanglement of the paired photons. The polarization entanglement is confirmed by polarization correlation measurements which exhibit a visibility of 89.5% and characterized by quantum-state tomography with a fidelity of 90.8%. Taking into account the transmission losses and duty cycle, we estimate that the system generates hyperentangled paired photons into opposing single-mode fibers at a rate of 320 pairs per second.

Measurement of group-velocity dispersion of Bloch modes in photonic-crystal-fiber rocking filters.

We use low-coherence interferometry to measure the group-velocity dispersion (GVD) of the fast and slow Bloch modes of structural rocking filters, produced by twisting a highly birefringent photonic crystal fiber to and fro while scanning a focused CO(2) laser beam along it. The GVD curves in the vicinity of the resonant wavelength differ dramatically from those of the unperturbed fiber, suggesting that rocking filters could be used in the optimization of, e.g., four-wave mixing and supercontinuum generation. Excellent agreement is obtained between theory and experiment.

Pressure-controlled phase matching to third harmonic in Ar-filled hollow-core photonic crystal fiber.

We report tunable third-harmonic generation (THG) in an Ar-filled hollow-core photonic crystal fiber, pumped by broadband <2 microJ, 30 fs pulses from an amplified Ti:sapphire laser system. The overall dispersion is precisely controlled by balancing the negative dielectric susceptibility of the waveguide against the positive susceptibility of the gas. We demonstrate THG to a higher-order guided mode and show that the phase-matched UV wavelength is tunable by adjusting the gas pressure.

Stacked optical precursors from amplitude and phase modulations.

We report the generation of stacked optical precursors from a laser beam whose amplitude or phase is modulated by sequenced on-off step waveforms. Making use of the constructive interference between the precursors produced from different steps, as well as the main field, we generate optical transient pulses having peak powers of eight times the input power with electromagnetically induced transparency in laser-cooled atoms.

Two-photon free-induction decay with electromagnetically induced transparency.

We report the observation of coherent two-photon free-induction decay (FID) in a three-level Lambda system excited by a low-intensity square-modulated laser pulse. Using electromagnetically induced transparency in an Rb85 cold atomic cloud, for what we believe to be the first time, we observe FID signals with coherence time exceeding the relevant atomic excited-state natural lifetime. Because of the on-resonance enhancement, the two-photon FID signal can be observed at the falling edge without using heterodyne means.

Shaping biphoton temporal waveforms with modulated classical fields.

We experimentally demonstrate a technique for shaping the temporal quantum waveform of narrow-band biphotons generated in a cold atomic ensemble via four-wave mixing by periodically modulating the two input classical lasers. We show that it is possible to generate nonclassical paired photons with a predesigned shape of the correlation function.