Polarisation-vortex beams over a broad wavelength region are generated by nonlinear transformation of a radially-polarized mode in a specially-designed optical fiber. The beams are produced by stimulated Raman scattering from 20-ns 1064-nm laser pulses, and up to the 4th order Stokes shift is observed. Measurements of polarization-selected intensity profiles of individual Stokes components show that the generated light maintains the desired spatial intensity distribution and radial polarization of the pump mode. At the highest pump power, 300 W, the process creates a coherent vortex beam from 1064 nm to 1310 nm, which is a span of nearly 250 nm.
© 2010 OSA
In the last decade, perhaps the most extensively studied complex beam-shape of light is the class of vortex beams, which possess phase or polarization singularities [1,2]. These beams have several potential scientific and technological applications, such as laser-based electron and particle acceleration , single-molecule spectroscopy , higher-dimensional quantum encryption , optical tweezers that can apply torques , sub-wavelength focusing , and metal machining . Here, we report on the observation of intra-pulse Raman scattering of a polarization vortex beam up to the 4th Stokes order without any degradation in its distinctive polarization-singularity-possessing characteristic. The key enabler is a specially designed optical fiber that supports stable propagation, over distances of at least 100 meters, of a desired optical vortex mode. This allows utilizing long propagation lengths to build up a relatively weak nonlinear effect such as Raman scattering, leading to nonlinear generation of a coherent vortex beam with a record 250-nm spectral width.
All the interest in optical vortices not withstanding, few of these applications have sufficiently advanced, primarily because creating a polarization vortex beam is very hard - in free-space or in fibers. Likewise, there is no report, to the best of our knowledge, of nonlinear optical pulse shaping (or indeed, of observing any nonlinear optical phenomena) with these beams - a critical requirement if several of the proposed applications with ultra-short pulses are to be realized.
Traditionally vortex beams have been generated by using free-space components on a conventional laser beam [9,10]. These techniques are generally limited by the power or wavelength at which vortex beams can be realized. Vortex modes have been created in optical fibers, but until recently this phenomenon was limited by its ability to guide the vortex mode stably for more than a few centimeters, and that too, only in straight fibers . While the traditional approaches produce a vortex beam by the coherent combination of multiple interfering modes, the present approach utilizes the fact that polarization vortices are true eigenmodes of optical fibers, albeit fundamentally unstable in conventional fibers. This instability arises from the near degeneracy of a variety of polarization vortices, which, over any reasonable propagation length (e.g. more than a few meters) in fibers, serve to mix with each other, thus destroying the distinctive polarization singularity each individual mode possesses.
In the present paper, a radially-polarized beam as sketched in Fig. 1(a) is investigated. As first demonstrated in , the stable, mode-coupling-free transmission of a selected polarization vortex can be achieved by employing an annular refractive-index profile as shown in Fig. 1(b). In a conventional fiber, the vortex modes (TM01, TE01 and HE21) are usually separated in effective indices (neff ) by ~10−6, and this near degeneracy is the primary reason for their instability. In contrast, Fig. 1(c) shows that for the new fiber, the neff of the desired radially-polarized mode (TM01) is separated from the other states by more than 10−4 over a large wavelength range exceeding 300 nm. The strong outer ring in the refractive index profile is what separates the vortex modes, as the different polarization states of these modes will interrogate this ring differently: depending on the orientation of the electric field relative to the abrupt change in refractive index, different boundary conditions apply . The effective refractive index difference between the different modes illustrated in Fig. 1(c), can be measured as described in . The measurements indicate that, once excited, a polarization vortex beam in this fiber will stably propagate over long lengths, agnostic to its wavelength of operation - a key feature for studying nonlinear optical phenomena.
The measurement setup used in the experiment is shown in Fig. 2 . The output of a Q-switched Nd:YAG (Yttrium-Aluminum Garnet) laser with a pulse duration of ~20 ns at a wavelength of 1064 nm and a 10-Hz repetition rate is coupled into a standard single-mode fiber (SMF). This fiber is spliced onto the vortex fiber. A mechanical grating with a grating period of 560 µm excites the light from the fundamental mode to the desired radially-polarized vortex mode, as described in .
The conversion efficiency of this process is as high as 99%. The very high conversion efficiency, combined with the stability of an optical fiber, makes this a very good platform for shaping beams, and gives an output of the vortex fiber that is a very pure radially-polarized mode. In order to get an efficient non-linear conversion of the vortex mode inside the specialty fiber, a 100-m-long fiber is used. Even with fiber-bend radii less than 7 cm, the mode propagated stably to the end of the fiber. The radially-polarized light at the output of the fiber is collimated with a 40x microscope objective and sent onto a silicon CCD, an optical spectrum analyzer (OSA), or a power-meter, respectively. The spectral properties of the transmitted light are measured with the OSA and can be seen in Fig. 3 .
We observe the formation of new wavelengths in the form of clearly separated peaks with a spacing of more than 50 THz, at peak powers of 300 W, corresponding to the Raman splitting in fused silica. Depending on the power of the pump laser coupled into the fiber, we observe different orders of the non-linear Raman interaction. With peak powers up to 300 W, the 4th order Stokes shift is clearly seen. With a transmission of ~90% through the vortex fiber, only fairly limited amounts of power were lost during the non-linear wavelength conversion. The SRS is probed by spontaneous Raman scattering generated in the fiber, starting out with a single photon. The threshold power for SRS can be estimated from the effective mode area, the fiber length and the Raman gain coefficient as Pth = 16⋅Aeff/gR⋅L , which gives a value of 93 W in excellent agreement with the experimentally observed threshold.
The Raman gain is dependent on whether the polarizations of the pump and signal are copolarized or orthogonal, with copolarized pumping being far more efficient . It usually requires a polarization maintaining fiber to get copolarized SRS in a fiber, but the same can be achieved by the stable polarization state of the radially-polarized mode. Therefore, it is expected that the light generated at other wavelengths by SRS will be copolarized with the pump, and thus maintain the radially-polarized mode.
To confirm that the generated wavelengths are produced in pure vortex modes with shape and polarization properties inherited from the pump mode, a tunable bandpass filter (interference filter), is added to the setup to view the beam at the different wavelengths separately. The filter allows transmission up to a wavelength of 1200 nm. Figure 4 shows the wavelength spectrum, measured with the OSA, with different settings of the bandpass filter. The filter clearly separates the different Stokes-shifted components generated by SRS. At each wavelength, we obtain an image with the silicon charge-coupled-device (CCD) camera to confirm that the spatial intensity distribution has maintained the doughnut shape that is expected if the radially-polarized modes are conserved in the nonlinear process. In order to confirm the polarization properties of the mode, a polarizer is added to the setup. As demonstrated by Fig. 4, the intensity pattern obtained by selecting a given polarization direction is as expected for a radially-polarized beam. When rotating the selected polarization direction, the observed intensity distribution rotates accordingly. This confirms that the new wavelengths are in fact produced in the desired radially-polarized mode. The power can be measured at each wavelength, and we observe that at a pump intensity of 200 W, the pump, the 1st, and the 2nd order Stokes-shifted components all carry the same amount of power, signifying high power-conversion efficiency.
In summary, we have used a specially-designed optical fiber to create a vortex mode, and have shown that the vortex mode propagates stably through 100 m of fiber, which is, to the best of our knowledge, the largest demonstrated propagation-length of a radially-polarized field in any medium other than free space. During propagation, new wavelengths were generated by SRS. These wavelengths were created so that they maintained the radial polarization of the pump light. They propagated with low losses through the optical fiber and exited the fiber end in a high-quality radially-polarized mode. At peak powers of 300 W, we observed up to the 4th order Stokes shift, and measurements confirmed that the light from the pump, the 1st, and the 2nd order Stokes shift (1064 nm, 1115 nm, and 1175 nm) exhibited the expected spatial intensity distribution and polarization. At the highest pump power, the process created a coherent vortex beam from 1064 nm to 1310 nm, which is a span of nearly 250 nm. On the one hand, one would expect nonlinear optical processes to be polarization sensitive, and thus especially well-suited in maintaining polarization distributions under nonlinear transformations, as has been observed here. However, nonlinear optical processes also act as momentum scatterers that can strongly perturb an optical eigenmode. Remarkably, the strong nonlinear transformations that we observe are bereft of such inter-modal scattering, the usual bane of even linear or “gentle” manipulation of vortex beams in conventional fibers or setups, owing to the existence of multiple near-degenerate states.
These results represent the groundbreaking demonstration of a vortex beam undergoing a stable non-linear interaction. This clearly points to the applicability of these beams for two applications that especially rely upon nonlinear optics with vortex beams, namely, the ability to shape ultra-short pulses of radially polarized beams for particle acceleration, and the ability to create correlated photon pairs in vortex modes for quantum cryptography. In addition, this demonstration also points to a new and simple way to produce these beams at the spectral range of choice, depending on the application - a capability especially valuable in wavelength ranges that do not have easily available lasing materials.
This work was supported by The Danish Council for Independent Research | Natural Sciences (FNU). M. F. Yan is gratefully acknowledged for fruitful discussions regarding the development of optical fibers used in this report. S. R. gratefully acknowledges the support of K. Rottwitt and the Danish Technical University for facilitating this collaboration.
References and links
2. Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon. 1(1), 1–57 (2009). [CrossRef]
3. Y. I. Salamin, “Electron acceleration from rest in vacuum by an axicon Gaussian laser beam,” Phys. Rev. A 73(4), 043402 (2006). [CrossRef]
5. A. Vaziri, J.-W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, “Concentration of higher dimensional entanglement: qutrits of photon orbital angular momentum,” Phys. Rev. Lett. 91(22), 227902 (2003). [CrossRef]
8. A. V. Nesterov and V. G. Niziev, “Laser beams with axially symmetric polarization,” J. Phys. D 33(15), 1817–1822 (2000). [CrossRef]
9. G. Machavariani, Y. Lumer, I. Moshe, A. Meir, and S. Jackel, “Efficient extracavity generation of radially and azimuthally polarized beams,” Opt. Lett. 32(11), 1468–1470 (2007). [CrossRef]
10. M. A. Ahmed, J. Schulz, A. Voss, O. Parriaux, J. C. Pommier, and T. Graf, “Radially polarized 3 kW beam from a CO2 laser with a intracavity resonant grating mirror,” Opt. Lett. 32(13), 1824–1826 (2007). [CrossRef]
11. G. Volpe and D. Petrov, “Generation of cylindrical vector beams with few-mode fibers excited by Laguerre-Gaussian beams,” Opt. Commun. 237(1-3), 89–95 (2004). [CrossRef]
13. J. D. Jackson, Classical Electrodynamics, 3rd edition, (John Wiley & Sons, New York 1999)
14. G. P. Agrawal, Nonlinear Fiber Optics, 4th edition, (Academic Press, San Diego 2007)