**6. References**


Slow light engineered structures perform better than material-based methods for high bandwidths. On the other hand, their feasibility into devices for practical applications is higher, due to the materials employed and their operation conditions. In particular, photonic crystals are proving to be a suitable technology to take slow light into practice. Small operating power, compact footprint, and the possibility of monolithic integration with electronics and CMOS fabrication are some of their strong points. Along this Chapter the capabilities of fast and efficient switching using electro-optic effects have been justified on

So far our work in this field has been focused on high-index contrast photonic crystal structures, exploiting the use of materials as silicon and lithium niobate. Our future research lines will explore the use of *intelligent* materials such as hydrogel polymers and chalcogenide glass (Eggleton et al.,2011), in order to achieve added functionalities to the

In spite of all these promising and almost magic properties of photonic band gap materials, they still remain at research stage. Some difficulties such as high propagation losses in the slow light regime, dispersive effects, coupling inefficiencies and fabrication roughness or inaccuracies are somehow hampering their evolution to commercial devices. Recent advances in dispersion engineering and loss reduction-oriented design approaches, together with the continuous improvement of fabrication processes, are taking slow light in photonic crystal closer to practical applications. In addition to this, the refinement of nanoimprint lithography, as an alternative for accurate mass production, herald a brighter future for real

This work has been partially supported by the Spanish Administration organism CDTI,

Andonegi, I., Blanco, A., Garcia-Adeva, A. (2011). Characterization of Slow Light Regime in

Baba, T. (2008). Slow Light in Photonic Crystals. *Nature Photonics,* Vol.2, (August 2008), pp.

Biallo, D. et al. (2007). High Sensitivity Photonic Crystal Pressure Sensor. *Journal of the European Optical Society*, Vol. 2, ( May 2007), pp. 1-5, ISSN 1990-2573 Bigelow, M. S., Lepeshkin, N. N. & Boyd, R. W. (2003). Observation of Ultraslow Light

Blanco, A., Beltrán, P., & Zubía, J. (2009). Slow Light Buffers for Future All-Optical Packet

*Magnetooptics - ImagineNano 2011*, Bilbao, Spain, April 12 - 17, 2011

90, No. 11, (March 2003), pp. 1139031-4, ISSN 1079-7114.

Petersburg, Russia, October 12-14, 2009

2D Photonic Crystal Waveguides, *Proceedings of PPM 2011 Photonics, Plasmonics and* 

Propagation in a Ruby Crystal at Room Temperature. *Physical Review Letters*, Vol.

Switched Networks, *Proceedings of ICUMT 2009 International Conference on Ultra Modern Telecommunications & Workshops*, pp. 1-6, ISBN 978-1-4244-3942-3, Saint

the basis of computing and simulations.

photonic crystal devices.

slow-light photonic crystal devices.

under project CENIT-VISION 2007-1007.

465-473, ISSN 1749-4885

**5. Acknowledgements** 

**6. References** 


**0**

**4**

*Italy*

**Manipulation of Photonic Orbital Angular**

Eleonora Nagali and Fabio Sciarrino

*Dipartimento di Fisica, Sapienza Universitá di Roma*

**Momentum for Quantum Information Processing**

More than a century ago, pioneering works carried out by Poynting (1909) and other physicists have provided the evidence of the validity of Marxwell equations for an electromagnetic field, showing how a beam of light carries energy and momentum, both in the linear and angular components. In particular the angular momentum of light, related to the generator of rotations in quantum mechanics, has been typically associated with its polarization, and more specifically with its circular polarization components. An optical beam traveling in the positive direction of the *z* axis that is circularly polarized, carries a *z*-component angular momentum content *σ* = ±*h*¯ per photon, which is positive if the circular polarization is left-handed and negative if it is right-handed. This angular momentum content is not just a formal property, but a very concrete one that can have significant mechanical effects as for example an observable induced rotation by absorption to a material particle Beth (1936); Friese

At the same time, calculations of angular momentum for a free electromagnetic beam gave rise to a *second* contribution not related to photon spin, to which was attributed the name of *orbital angular momentum* (OAM). Unlike the spinorial angular momentum (SAM), considered as the intrinsic part of angular momentum since it does not depend on the specific reference frame, the orbital component is associated to the transverse spatial structure of the wavefront. More precisely, this angular momentum appears when the beam wavefront acquires a helicoidal structure, or equivalently, its field spatial dependence contains a helical phase factor having the form *eimϕ*, where *ϕ* is the azimuthal phase of the position vector *r* around the beam axis *z* and *m* is any integer, positive or negative, providing the direction and the "velocity" of the phase spiraling along the beam direction. It can be shown that in this case the optical beam carries an angular momentum along its axis *z* equal to *mh*¯ per photon, in addition to the polarization one *σ*. When *m* is nonzero, the helical phase factor imposes the existence of an optical vortex at the center of the beam where the light intensity vanishes. Although the fundamental concept of orbital angular momentum associated with a light field was already known since the early forties, the research on the orbital angular momentum of light has begun only in 1992, with the appearance of a seminal publication carried out by Allen et al. (1992). In this work, Allen et al. demonstrated experimentally that a particular set of solutions of Helmoltz equation in paraxial approximation, the Laguerre-Gauss modes (LG), carry a fixed amount of orbital angular momentum. Moreover, such beam could be

**1. Introduction**

et al. (1998)

*International Conference on Group IV Photonics*, pp. 40 – 42, ISBN: 978-1-4244-4402-1, San Francisco, CA, USA, September 9-11, 2009

