Hybrid photonic-crystal fiber

This article offers an extensive survey of results obtained using hybrid photonic-crystal fibers (PCFs) which constitute one of the most active research fields in contemporary fiber optics. The ability to integrate novel and functional materials in solid- and hollow-core PCFs through various postprocessing methods has enabled new directions toward understanding fundamental linear and nonlinear phenomena as well as novel application aspects, within the fields of optoelectronics, material and laser science, remote sensing, and spectroscopy. Here the recent progress in the field of hybrid PCFs is reviewed from scientific and technological perspectives, focusing on how different fluids, solids, and gases can significantly extend the functionality of PCFs. The first part of this review discusses the efforts to develop tunable linear and nonlinear fiber-optic devices using PCFs infiltrated with various liquids, glasses, semiconductors, and metals. The second part concentrates on recent and state-of-the-art advances in the field of gas-filled hollow-core PCFs. Extreme ultrafast gas-based nonlinear optics toward light generation in the extreme wavelength regions of vacuum ultraviolet, pulse propagation, and compression dynamics in both atomic and molecular gases, and novel soliton-plasma interactions are reviewed. A discussion of future prospects and directions is also included.

Figure 1

Chronological overview of the most important breakthrough in the fields of PCF and hybrid PCF. [1] [213], [2] [197], [3] [211], [4] [205] and [483], [5] [49], [6] [223], [7] [89], [8] [473], [9] [429], [10] [37], [11] [251], [12] [382], [13] [84], [14] [384], [383], [15] [355], [16] [31], and [17] [41].

Figure 2

Cross sections and refractive index profiles of (a) a conventional step-index optical fiber and (b) a solid-core PCF. The gray and black regions correspond to silica material and air, respectively. The photonic-crystal cladding is an ideal triangular lattice with parameters pitch $\mathrm{\Lambda }$, i.e., the distance between air holes and inner hole diameter $d$ which is related to the air-filling fraction. The core diameter is defined as $\sim 2\mathrm{\Lambda }$.

Figure 3

(a) Propagation diagram of a conventional step-index fiber with a Ge-doped core and pure silica cladding. (b) Propagation diagram for a triangular hole lattice in silica glass with air-filling fraction 45%. The green line in both plots corresponds to the air line. (c) Schematic representation of how the air holes act as bars keeping the fundamental mode confined (left) while the higher-order modes are leaking out (right). Adapted from [370].

Figure 4

(a) Numerically calculated density of states (DOS) plot for a triangular HC-PCF cladding lattice. Black represents zero DOS and white maximum DOS. The slanted colored lines show several cladding mode trajectories. Mode trajectories for the cladding modes on the edges of the photonic band gap are represented in red for the interstitial apexes mode (B), in blue for the strut mode (C), and in green for the hexagonal air-holes mode (D). The dash-dotted white line represents $n_{\mathrm{eff}}\sim 0.995$. (b)–(d) The near-field pattern of the modes calculated for $n_{\mathrm{eff}}\sim 0.995$ in (b) and (c) for the apex and strut modes, respectively, and for $n_{\mathrm{eff}}\sim 0.973$ in (d) for the hexagonal air-holes mode. (e) Unit cell of the cladding structure of a honeycomb triangular lattice of air holes indicating the struts and apexes. Adapted from [83].

Figure 5

(a) Scanning electron micrograph of a kagome-style HC-PCF. (b) Star-of-David pattern (light gray). The highlighted region represents the unit cell. (c) Calculated effective indices for a one ring kagome structure in comparison with a capillary model. The inset shows the HE11 mode at 800 nm with the structure superimposed. Adapted from [39] and [329].

Figure 6

(a), (b) Principle of ARROW guidance when light is in antiresonance or off-resonance state light remains confined in the core. At resonance state, light couples to the high-index cylinders and thus escapes from the core introducing a dip in the transmission spectra. (c) Examples of the transmission spectrum of a high-index infiltrated solid-core PCF (top) and antiresonant hollow-core fiber (bottom). Inset images: White-light near-field profiles of the propagating light in the core of the fibers.

Figure 7

(a) A twisted coreless PCF. (b) Scanning electron micrograph of the coreless microstructured PCF. (c) Experimental and simulated Poynting vector distributions at 818 nm at different twist rates. Adapted from [41].

Figure 8

(a) Transmission spectrum of a solid-core PCF filled with LCs (highlighted areas indicate the on-resonance state in which the light is coupled to the high-index rods). (b) Thermal tuning of the fiber filled with LCs from 20 °C up to 80 °C. The plot shows the spectral position of the notch in the long 1300–1600 nm wavelength edge. Inset: Near-field profile of the LC-PCF. Adapted from [386].

Figure 9

Blue- and red-edge band-gap tunability with respect to the applied voltage. Inset: An integrated LC-filled PCF sandwiched between the two electrodes used to drive the device at 1600 nm wavelength edge. Adapted from [9]; inset image adapted from [266].

Figure 10

(a) A rf phase shift and relative power change vs the driving voltage for different modulation frequencies. (b) A rf phase shift and corresponding time delay vs the modulation frequency for different driving voltages (the top flat line corresponds to 100 $V_{\mathrm{rms}}$ in both panels). Adapted from [471].

Figure 11

The laser wavelength is shifted toward longer wavelengths as $V_{\mathrm{rms}}$ increases. At 160 $V_{\mathrm{rms}}$ parasitic lasing sets in at shorter wavelengths ($\sim 1035\mathrm{nm}$). A total shift of 25 nm is observed. Adapted from [335].

Figure 12

(a) Schematic of the directional coupler. (b) Optical images of the empty and filled PCFs with the high-index inclusion. Transmission as a function of wavelength for (c) 50.7 °C and (d) 51.7 °C of the selectively filled hybrid PCF based refractive index sensor. Inset of (c): Measured near-field profile of the core and high-index waveguide mode profiles. Adapted from [479].

Figure 13

(a) Schematic representation of the hybrid chalcogenide glass-silica PCF. (b) SEM image of the hybrid PCF. (c) Transmission spectrum of the unfilled (black line) and the hybrid PCF (red line). Points A and B correspond to the output mode patterns at 630 and 700 nm, respectively. Adapted from [161].

Figure 14

Cross-section SEM image of the core of a solid-core PCF with deposited ${\mathrm{As}}_2{\mathrm{S}}_3$ layers. (b) Zoomed-in SEM image of a single hole. Adapted from [293].

Figure 15

(a) SEM image of the core of a solid-core PCF with a single high-index Ge wire. (b) Zoomed-in SEM image of the cross section of the fiber. (c) Transmission spectra with respect to the wavelength at various positions of the output polarizer. (d) Transmission profile of the ratio between the two orthogonal polarization states as a function of a wavelength. Inset: Intensity response with respect to the analyzer angle at a fixed wavelength (950 nm). Adapted from [441].

Figure 16

(a) A Schottky $\mathrm{Pt}/n\text{−}\mathrm{Si}$ junction formed in a capillary by multimaterial deposition using HPCVD of phosphorus-doped $n^{+}\text{−}\mathrm{Si}$, $n^{-}\text{−}\mathrm{Si}$, and Pt layers. (b) Fundamental guiding mode in the $n^{-}\text{−}\mathrm{Si}$ layer. (c) Electrodes in the $\mathrm{Pt}/n\text{−}\mathrm{Si}$ Schottky junction formed using a FIB. (d) Photodetection response of the diode triggered with $\sim 10$-ps laser pulses at wavelengths of 1310 nm (blue) and 1550 nm (red) and measured using an oscilloscope. Inset: Internal photoemission process, carrier transport, and collection scheme. Adapted from [178].

Figure 17

(a) Real and (b) imaginary parts of permittivity of gold from 200 up to 1300 nm. The green line is calculated using the Drude model (lowest line). The black circles and red line are the experimental data from Johnson and Palik, respectively. The blue line is the fit of the experimental data. Adapted from [255].

Figure 18

SEM images of a Au-filled (a) solid-core PCF showing the metal wires sticking out (b) after polishing the end facet of the fiber with a focus ion beam. Selectively Au-filled (c) polarization-maintaining (PM) PCF and (d) kagome hollow-core fiber. Adapted from [390], [255], and [443].

Figure 19

(a) Measured transmission spectrum in $y$ polarization of 6 mm (blue) and 24.5 mm (orange) lengths of a PM-PCF. (b) Calculated dispersion of the relevant modes. (Black line) Initial PM-PCF. (Colored lines) Modes ($m=2–5$) of an isolated wire embedded in silica. (c) Near-field profiles at 546 nm (A) and 907 nm (B), superimposed on to an SEM of the structure. Adapted from [258].

Figure 20

(a) Concept of the azimuthal polarization excitation in a metal-filled PCF. (b) SEM image of the PCF with the integrated central Au wire. (c) Calculated loss spectra of the three core modes, together with the imaginary part of the gold (purple dashed line). The gray area is the zoomed section showing the experimental cutback loss of the azimuthal mode (orange line) compared with theory (red line). The orange-shaded area shows the experimental error range. Adapted from [443].

Figure 21

Experimentally observed output diffraction pattern and soliton localization in a liquid-infiltrated PCF at (a) low and (b) high input powers. Adapted from [360].

Figure 22

(a) Schematic representation of the optofludic coupler. (b) Optical images of the actual filled strands of a PCF with ${\mathrm{CCl}}_4$. (c) Measured intensity distributions at the output of the nonlinear coupler at different powers: (A) 3.5 kW, (B) 24.2 kW, and (C) 58.7 kW. (d) Experimentally measured and normalized power distribution between the two channels $S1$ (blue) and $S2$ (red) of the optofluidics coupler vs input power. The solid lines are the theoretically calculated dependences of the power distribution. Adapted from [451].

Figure 23

(a) Simulated and (b) measured spectral evolution vs increasing input power of the high-index filled PCF showing the redshifting generated soliton and the dispersive wave when pumped close to its ZDW. The output was recorded using a frequency-resolved optical gating (FROG) system. Adapted from [147].

Figure 24

(a) Optical image of the selectively single strand filled PCF with ${\mathrm{CCl}}_4$. (b) Near-field profile superimposed on a cross section of the fiber. (c) Spectral evolution for different input powers of a 26 cm long fiber with a single strand filled with and diameter of 2.5 m. (d) Spectral broadening of the same structure with a glass core (red curve, light gray) and a liquid ${\mathrm{CCl}}_4$ core (blue curve, dark gray). For comparison, the linear refractive index and the dispersion properties are deliberately set to be identical. Adapted from [451].

Figure 25

(a) Example of the usual setup for free-space coupling into a gas-filled HC-PCF, allowing for vacuum propagation and pressure gradients between the cells. (b) One realization of the setup, showing side scattering at the point of UV emission (as described in Sec. 3g5).

Figure 26

The properties of gases and gas-filled HC-PCFs. (a) The variation of number density as a function of pressure, at 293 K, for gases commonly used to fill HC-PCFs. He and ${\mathrm{H}}_2$ are close to ideal gases, whereas Xe is far from an ideal gas at pressures over 10 bar. Calculated using refprop ([260]). (b) Equation (24) as a function of angular frequency (equivalent wavelength range 200–4000 nm) for commonly used gases. (c) GVD curves for various filling gases and pressures at 293 K, in a $30\mu \mathrm{m}$ core diameter broadband-guiding HC-PCF, illustrating tuning of the zero dispersion point from $\sim 300$ to $\sim 1200\mathrm{nm}$. (d) The nonlinear refractive index of common gases as a function of pressure (silica glass is added as a reference line).

Figure 27

Pulse compression results in gas-filled broadband-guiding HC-PCFs or similar fibers using SPM spectral broadening and chirped mirrors for phase compensation. The arrows start at the input pulse duration and peak power and point to the final compressed pulse duration and peak power. The references and repetition rates are indicated beside the arrows.

Figure 28

(a) Temporal intensity evolution through the fiber for soliton-effect self-compression from 30 to $\sim 1\mathrm{fs}$ in a $26\mu \mathrm{m}$ core diameter broadband-guiding HC-PCF filled with 28 bar He. The initial pulse has an energy of $3.54\mu \mathrm{J}$, corresponding to an $N=3.5$ order soliton. (b) Corresponding peak intensity. (c) Corresponding full width at half maximum (FWHM) pulse duration.

Figure 29

Phase-matched RDW wavelengths as a function of gas-filling pressure in a $30\mu \mathrm{m}$ core diameter broadband-guiding HC-PCF, for an 800 nm, 30 fs pump pulse with energy tuned for an input soliton order of $N=4$.

Figure 30

Pulse propagation simulations of RDW emission for parameters similar to [208] (see text). (a) The temporal intensity evolution along the fiber length. (b) The spectral intensity evolution along the fiber length, including self-steepening. (c) As for (b) but without the self-steepening term; in this case the RDW is much weaker.

Figure 31

Experimental spectra of RDW emission from a kagome HC-PCF collated from [280] and [127].

Figure 32

Group velocity dispersion of 10 bar Ar in a $30\mu \mathrm{m}$ core diameter broadband-guiding HC-PCF with the indicated ionization fractions.

Figure 33

(a)–(c) Ionization of 10 bar Ar with a 10 fs Gaussian pulse with peak intensity $2\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$. (a) The electric field, (b) the ionization rate, and (c) the accumulated free-electron density. (d)–(f) Ionization of 28 bar He with the self-compressed pulse from Fig. 28 (1.2 fs duration, $6.6\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$). (f) The rise time of the free-electron density step is 200 as.

Figure 34

(a) Experimental and (b) numerical output spectra of a broadband-guiding HC-PCF ($26\mu \mathrm{m}$ core diameter) filled with 1.7 bar of argon as a function of input pulse energy (65 fs, 800 nm). In region (i) there is no ionization; at (ii) a blue shoulder emerges, moving to higher frequencies as the pulse energy increases; at (iii) a second ionization stage starts; and at (iv) spectral interference between the two blueshifting pulses is apparent. (a), (b) Adapted from [186]. (c) Temporal and (d) spectral evolution during fundamental soliton self-frequency blueshift; (e) cross-correlation frequency-resolved optical gating traces [at the positions marked with dashed lines in (c), (d)] showing the pulse compression and frequency shifting. (c)–(e) Adapted from [69].

Figure 35

The spectra corresponding to Fig. 28 are shown (a) with and (b) without the influence of ionization. These parameters correspond to the experimentally observed VUV RDW emission shown in Fig. 31. The dashed black lines mark the zero dispersion wavelength (340 nm) and $N$ and $A$ indicate normal and anomalous dispersion. Without ionization the VUV RDW is not emitted. Adapted from [127].

Figure 36

Experimental VUV supercontinuum generation results in a He-filled broadband-guiding HC-PCF. (a) (Linear scale) for core diameters of (i) $28\mu \mathrm{m}$ and (ii) $26\mu \mathrm{m}$; (inset) the same data on a logarithmic scale, including the spectra recorded through a sapphire filter (black lines). (b) The full supercontinuum corresponding to (i) in (a). The solid black line is the simulated spectrum. The dashed vertical line marks the ZDW ($N=\text{normal}$ and $A=\text{anomalous}$ GVD). From [127].

Figure 37

Several major results for Raman frequency comb generation and broadening in ${\mathrm{H}}_2$-filled HC-PCFs. (a) Image and spectrum of the generated and transmitted rovibrational Raman comb through a $\sim 1\mathrm{m}$ long hydrogen-filled ($\sim 20\mathrm{bar}$) broadband-guiding HC-PCF for a circularly polarized laser input (12 ns, 1064 nm). From [84]. (b) Image of a Raman comb generated in a $\sim 3\mathrm{m}$ long broadband-guiding HC-PCF filled with a mixture of ${\mathrm{H}}_2$ (5 bar) and ${\mathrm{D}}_2$ (8 bar) for a circularly polarized laser input (1 ns, 532 nm). From [187]. (c) Spectrum of a Raman comb generated in a broadband-guiding HC-PCF filled with a mixture of ${\mathrm{H}}_2$, ${\mathrm{D}}_2$, and Xe. More than 135 lines are generated in a visible spectral region. From [187]. (d) A vacuum UV till IR supercontinuum generated in a $\sim 15\mathrm{cm}$ long hydrogen-filled (5 bar) broadband-guiding HC-PCF pumped with ultrashort pulses (50 fs, 800 nm). From [31].