Measuring twisted light

Measuring light’s orbital angular momentum has been a field of active research in the last 20 years and there are now many possible techniques.

Post contributed by:
Mark Siemens, 
University of Denver, 
USA

In order to take full advantage of twisted light in light-matter interactions, it is critical for researchers to have full control and characterization of the orbital angular momentum (OAM) of their lasers. The last 25 years have seen the development of a large assortment of methods for measuring light’s OAM, which can be generally separated into three categories: qualitative methods for identifying the nearest-integer value of OAM, quantitative techniques for identifying average OAM in beams containing more than a single mode, and modal decomposition methods capable of measuring the spectrum of OAM modes.

The challenge in measuring OAM is that it is carried by the helicity of the phase, which cannot be measured with an intensity-only image. The simplest and oldest method for characterizing OAM is interference with a known reference beam. The spiral pattern is a clear indicator of twisted light [1], while the number of interference minima reveals the nearest-integer OAM value and the OAM sign can be can be inferred from the direction of the spiral if there is a radius of curvature difference between the beam under test and the reference. Diffraction from non-round apertures that break the azimuthal symmetry of a beam with OAM also yield a qualitative estimate of the OAM [2,3].

Direct quantitative measurement of the average OAM is also possible, but requires considerable care in alignment and interpretation. This is important for measuring beams that don’t have single-integer-valued OAM, which is inevitable for all experimental systems because small misalignments or optical irregularities deform the mode and change the OAM spectrum. Fractional OAM also arises when a spiral phase plate is inserted into a laser beam with a wavelength different from the design wavelength of the spiral phase plate. Recent experiments showed that the average fractional OAM can be measured quantitatively with a single cylindrical lens by calculating higher-order moments of the intensity pattern formed at the focal plane of the lens, see Fig. 1 [4].

Figure 1: OAM measurements with a single cylindrical lens.

OAM measurements can be pushed even further by decomposing a beam into its OAM spectral components, which is exciting and important for a number of applications including communications. The first method demonstrated for measuring an OAM spectrum uses a programmable spatial light modulator (SLM) onto which various forked grating patterns can be projected [5]. When the topological charge of a forked grating is opposite to the OAM of light incident on the grating, the helical phase on the light is flattened and there will be a peak in the center of the far-field intensity (or at the focus of a lens). Then if the forked grating is scanned through all OAM values of interest, an OAM spectrum can be measured. More recently, Miles Padgett’s group showed that a series of SLMs can be used to make a geometrical transformation between the azimuthal phase and linear position, which allows for real-time measurement of the OAM spectrum by recording the light intensity at different locations [6]. Later work showed that the same operation could be performed with a patterned refractive optic [7].

Of course, there are many other ways for measuring the OAM of light. Current research is mostly focused on accurate, efficient, and stable methods of measuring OAM spectra down to a single photon level, which opens up exciting opportunities of studying twisted light-matter interactions.


REFERENCES

[1] Soskin, M. S., Gorshkov, V., Vasnetsov, M., Malos, J., & Heckenberg, N. (1997). Topological charge and angular momentum of light beams carrying optical vortices. Physical Review A, 56(5), 4064–4075. http://doi.org/10.1103/PhysRevA.56.4064
[2] Guo, C.-S., Lu, L.-L., & Wang, H.-T. (2009). Characterizing topological charge of optical vortices by using an annular aperture. Optics Letters, 34(23), 3686–3688. http://doi.org/10.1364/OL.34.003686
[3] Anderson, M. E., Bigman, H., de Araujo, L. E. E., & Chaloupka, J. L. (2012). Measuring the topological charge of ultrabroadband, optical-vortex beams with a triangular aperture. Journal of the Optical Society of America B, 29(8), 1968–1976. http://doi.org/10.1364/JOSAB.29.001968
[4] Alperin, S. N., Niederriter, R. D., Gopinath, J. T., & Siemens, M. E. (2016). Quantitative measurement of the orbital angular momentum of light with a single , stationary lens. Optics Letters, 41(21), 5019–5022.
[5] Mair, A., Vaziri, A., Weihs, G., & Zeilinger, A. (2001). Entanglement of the orbital angular momentum states of photons. Nature, 412(6844), 313–316. http://doi.org/10.1038/35085529
[6] Berkhout, G. C. G., Lavery, M. P. J., Courtial, J., Beijersbergen, M. W., & Padgett, M. J. (2010). Efficient sorting of orbital angular momentum states of light. Physical Review Letters, 105(15), 8–11. http://doi.org/10.1103/PhysRevLett.105.153601
[7] Lavery, M. P. J., Robertson, D. J., Berkhout, G. C. G., Love, G. D., Padgett, M. J., & Courtial, J. (2012). Refractive elements for the measurement of the orbital angular momentum of a single photon. Optics Express, 20(3), 2110–5. http://doi.org/10.1364/OE.20.002110