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We demonstrate extremely efficient excitation of linearly-, radially-, and azimuthally-polarized modes in a hollow-core photonic band-gap fiber with femtosecond laser pulses. We achieve coupling efficiencies as high as 98% with linearly polarized input Gaussian beams and with high-power pulses we obtain peak intensities greater than 1014 W/cm2 inside and transmitted through the fiber. With radially polarized pulses, we achieve 91% total transmission through the fiber while maintaining the polarization state. Alternatively with azimuthally-polarized pulses, the mode is degraded in the fiber, and the pure polarization state is not maintained.
©2009 Optical Society of America
Since the development of hollow-core photonic band-gap fibers (HC-PBGFs) [1], an array of applications for these air-guiding structures has been demonstrated [2–10]. The unique geometry of these fibers allows for an unprecedented tight confinement in air-guided transmission and thus for intense light fields with modest pulse energies. This capability makes HC-PBGF’s ideal for investigating intense light-matter interactions when the core is filled with a gaseous medium. Several studies [3,11–15] have explored the limits on high-power propagation, and damage in these fibers at nanosecond pulse lengths has been investigated [12–15], with 370-μJ pulses being delivered [13], but no extensive studies have been performed in the femtosecond regime.
Here we investigate the transmission of linearly-, radially- and azimuthally-polarized (RP and AP) beams in HC-PBGF with femtosecond laser pulses. We observe highly efficient coupling into HC-PBGFs with linearly-polarized Gaussian beams and use amplified, femtosecond Ti:sapphire pulses to investigate the damage threshold of these fibers. With this improved coupling we demonstrate peak powers exceeding 1014 W/cm2, which we believe to be the highest peak power observed inside a HC-PBGF. We also experimentally investigate the excitation of polarization vortices in HC-PBGF with femtosecond pulses. We show, for the first time to our knowledge, that by injecting an ultrafast RP pulse into a HC-PBGF it is possible to obtain efficient coupling and transmission with relatively high mode purity at the output.
Optical polarization vortices display intriguing properties both in the linear and nonlinear propagation regimes. The basic form of polarization vortices is a purely radially or azimuthally polarized beam with a Laguerre-Gaussian TEM01 ring-shaped intensity distribution and a polarization singularity at the center. These basic polarization vortices can also be described as a superposition of two-phase vortices with opposite circular polarization and helicity. In the linear paraxial propagation regime, these beams are eigenmodes of both free space and cylindrical waveguides. Under tight-focusing conditions, the RP (AP) beams produce strong longitudinal electric- (magnetic-) field components at the focus [16], which could be beneficial for various applications such as trapping and acceleration of particles [17,18], microscopy [19], and laser processing [16]. In the nonlinear optical regime, a few theoretical and experimental studies with RP and AP beams have been reported, which include vortex-driven surface second-harmonic generation [17], propagation in Kerr-type medium [20–23], and theoretical work on RP and AP dark solitons in defocusing Kerr media [24].
Generation of RP and AP beams has been demonstrated by a variety of methods. These include coherently combining two linearly polarized degenerate LG beams [25], coherently combining two circularly-polarized phase vortices [25], exploiting special laser resonator schemes [26,27], using a segmented wave plates [19,28], liquid crystals [29], holographic elements [30], sub-wavelength gratings [31], and selective excitation in fibers [32]. These methods differ in their complexity, efficiency, mode purity, and power handling capability. So far excitation of RP and AP modes in optical fibers has been pursued mainly with low power CW lasers and standard step index fibers [32–34]. Recent results have demonstrated coupling into HC-PBGF using CW generated optical vortices [35].
We first investigate the maximum coupling and damage threshold of these fibers with linearly polarized Gaussian beams. Typical damage in coupling from free space into a HC-PBGF with femtosecond laser pulses is shown in Fig. 1b . Mismatching the mode size or shape of the incoming laser beam with that of the HC-PBGF causes this catastrophic interaction. To minimize this, careful measures are taken to match the mode profile of the fiber used in this experiment. This procedure drastically increased the coupling efficiency into the HC-PBGF and resulted in higher peak intensity within the fiber core prior to optical breakdown.
Fig. 1 (a). SEM image of HC-800-02 fiber (Crystal Fibre) used in this experiment and (b) damage that occurred when a high-energy, mismatched mode is coupled into a similar fiber HC-PBGF designed to operate at 1550-nm center wavelength.
The HC-PBGF used in this investigation (Crystal Fibre, HC-800-02, Fig. 1a) operates at a center wavelength of 835 nm and exhibits an attenuation of 0.25 dB/m for a 70-nm region surrounding that wavelength. This fiber has a core diameter of 6.8 μm and a measured mode-field diameter (1/e-width) of 5.0 μm. In addition, and important for this particular investigation, is that the fundamental mode exhibited a strong Gaussian shape allowing for appropriate mode matching with standard optics.
For this experiment we used an amplified Ti:Sapphire laser (Coherent Hydra) operating at 1-kHz repetition rate producing 40-fs pulses centered at 810 nm and capable of 1-mJ pulse energies. The setup for this work is shown in Fig. 2 . After passing through an aperture, the amplified laser is spatially filtered and then attenuated using a combination of quarter- and half-wave plates followed by a thin-film polarizer. Coupling in and out of the fiber is performed with a pair of 16 × (0.25 NA) aspheric lenses with the 30-cm length of fiber mounted on three-axis flexure stages. To match the mode of the HC-PBGF, the aperture size and position of L2 are adjusted in an iterative process to produce the highest coupling. In order to avoid damaging the front face of the fiber, the initial coupling uses relatively low pulse energies (~2 nJ), which are then increased once the fundamental mode is properly excited.
Fig. 2 Experimental setup for linear polarization studies. An amplified Ti:sapphire system is spatially filtered and then coupled into the HC-800-02 fiber using a pair of aspheric lenses (AL) held inside an evacuated chamber
In order to measure coupling with optimal mode matching, we operate with pulse energies well below damage threshold for this fiber and without the vacuum chamber shown in Fig. 2. Using 100-nJ pulses we achieve 98% coupling, which to our knowledge is the highest value observed in HC-PBGF when accounting for the transmission loss of the fiber. At higher pulse energies, the three-axis stages and fiber are placed inside of a chamber and evacuated to a pressure of 5 mTorr to avoid ionization effects. The results of this work are shown in Fig. 3 where we have plotted input pulse energy at the face of the fiber and output energy as measured at the back end of the fiber. The actual experimental coupling achieved inside the chamber was reduced to 93.5%, as shown in the plot. We attribute this reduction as compared to the lower energy results outside the chamber to aberrations of the beam caused by the chamber windows. As shown in the plot (Fig. 3), the highest measured pulse energy at the output was 1.8 μJ, which for a 40-fs pulse corresponds to a peak intensity of 1.6 × 1014 W/cm2 and is, to our knowledge, the highest peak intensity observed inside a hollow-core photonic band-gap fiber. To verify that the fidelity of the pulse is maintained during transmission through the evacuated fiber, a frequency-resolved optical gating (FROG) measurement [36] of the input and output of the fiber is shown in Fig. 4 . The observed broadening of the pulse width is consistent with the combined dispersion of the waveguide and the two 3-mm thick Sapphire windows on the vacuum chamber.
Fig. 3 Transmitted pulse energy through a 30-cm length of evacuated HC-800-02 fiber as a function of input pulse energy. The dashed black line represents perfect coupling
Fig. 4 Retrieved temporal profiles from the FROG measurements of the input (left) and output (right) pulses for a 30-cm-long piece of HC-800-02 PBGF.
We next consider the propagation characteristics of polarization vortices for our PBGF sample. The experimental setup is shown in Fig. 5 in which the output of a Ti:Sapphire laser oscillator (80-MHz repetition rate, 50-fs pulses, centered at 810 nm) is converted into a linearly-polarized degenerate TEM01 Laguerre-Gaussian beam using a 0-π phase plate and a spatial filter. The beam is then split into two arms, where one is rotated by 90 degrees with a periscope, before being interferometrically recombined with the other to achieve a RP beam. Time and phase alignment is achieved by controlling the delay with a high-precision stage.
Fig. 5 Experimental setup for the vortices studies. A linearly-polarized Gaussian beam from a Ti:sapphire oscillator is converted to a radially- or azimuthally-polarized donut beam and then focused into the HC-PBGF. Elements in red are in a different plane.
An AP beam is obtained by rotating the phase plate by 90 degrees. This beam is then focused with a 10 × (0.16 NA) aspheric lens into a 20-cm length of commercially available HC-PBGF (Crystal Fibre, HC-800-01). The fiber core is hexagonal with a total width of 9.2 μm and 9.5 μm along the short and long axes, respectively. The output face of the fiber is imaged onto a 12-bit CCD with either a 10 × or a 40 × aspheric objective.
The measured intensity distributions of the RP beam before the fiber are shown in Fig. 6(a)-6(e). The beam has the expected TEM01 donut shape, and the two-lobe pattern formed after passing through a polarizer rotates according to the angular position of the polarizer, which is indicative of radial polarization. The corresponding measured intensity distributions just after the output face of the fiber are shown in Fig. 6(f)-6(j), and it is evident that the beam maintains its donut shape and its radial polarization. Figure 7 shows the intensity distribution precisely at the output face of the fiber. Altering the input polarization of the beam by slightly changing the time alignment of the two arms has a minor effect on the output.
Fig. 6 Experimental intensity distributions of a RP beam before and after the PBGF. [(a)-(e)] Intensity distributions in front of the focusing objective; [(f)-(j)] intensity distributions just after the fiber output face. White arrows indicate the orientation of a linear polarizer placed before the CCD, and the yellow dashed line indicates the fast axis of a quarter-wave plate placed before the polarizer. Color scale is different for each image, where red (blue)represents high (low) intensity.
Fig. 7 Experimental intensity distributions of the radially polarized beam at the HC-PBGF output face region. (a) The intensity distribution detected by the CCD camera as the 40× objective is moved towards the fiber tip; (b) the intensity distribution exactly at the fiber output face.
The effective transmission of the RP beam through the fiber, including the coupling losses, is measured to be 91%, which we believe to be the highest efficiency reported so far for the excitation of a RP beam in any optical fiber with ultrafast pulses. All the experiments are conducted at fiber input pulse energies between 0.75 and 62.5 pJ.
When trying to excite the hybrid radial-azimuthal donut modes by applying a π/2 phase shift to one arm, the output intensity distribution deteriorates (nonzero intensity at the center), indicating a non-pure mode at the output. When the input beam is AP, we observe azimuthal polarization at the output of the fiber, but the mode is also less pure. Figure 8 shows the output intensity distributions in the case of input azimuthal polarization. Instead of a donut shape with zero intensity at the center, we observe a circular distribution with a slight dip at the center and after passing through a polarizer, the lobes are slightly rotated compared to their expected position. Thus, in this specific fiber, we observe a clear tendency for support of radial polarization over azimuthal polarization.
Fig. 8 Experimental intensity distributions of AP beam after the PBGF. The white arrows indicate the orientation of a linear polarizer placed before the CCD. Color scale is different for each image, where red (blue) represents high (low) intensity.
The discrimination between radial and azimuthal polarization in this fiber could originate from the non-perfect cylindrical cross-section of the fiber. Figure 9 shows the typical near-field intensity distribution from the fiber as advertised in the data sheet. The distribution is not radially symmetric and is characterized by two different widths. This can result in larger losses or scattering for the azimuthal polarization versus the radial polarization.
Fig. 9 Typical near-field intensity distribution from a HC-800-01 fiber, as published by the manufacturer (Crystal Fiber datasheet [HC-800-01]).
For the linearly polarized mode we measure a peak transmitted intensity of 1.6 × 1014 W/cm2 using 40-fs pulses and a coupling efficiency of 98%, while for the radially polarized mode we measure a 91% coupling efficiency which, to our knowledge are the highest reported coupling efficiencies for these polarization distributions. In addition, we demonstrate experimentally that ultrafast laser pulses with pure radial polarization can be efficiently coupled into a HC-PBGF. In contrast to the radially polarized mode, the azimuthal one is not preserved as it propagated along the fiber. Although the reason behind this degradation is not clear, we believe it may arise due to the non-perfect cylindrical cross section of the fiber. The low-loss coupling of linear and radial polarization beams should extend the capabilities of these fibers for studying intense nonlinear light-gas interactions and beam delivery of high peak power femtosecond laser pulses.
Acknowledgments
This work was supported by the Air Force Office of Scientific Research supported by NSF under contract number F49620-03-1-0223, by the Center for Nanoscale Systems under award number EEC-0117770, and by the NSF grant PHY-0703870. CJH acknowledges financial support from Lawrence Livermore National Laboratories through the National Physical Science Consortium. The LEO 1550 SEM was originally funded by the Keck Foundation, with additional support from the Cornell Nanobiotechnology Center (STC program, NSF award number ECS-9876771).
*These authors contributed equally to this work.
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