[[Image:]]Laser Physics and Quantum Optics Research at Sussex. Les Allen
Introduction. I was a founder member of the Department, appointed in October 1962. My research has always been characterised by a very close link between theory and experiment. For many years the experimental work was conducted in my laboratory at Sussex and was always directed at verifying, or finding the limitations of, theory. Similarly, my theoretical work has been framed so as to encourage experimental investigation. Over the last decade of my research career, in the absence of a laboratory of my own, such experiments have usually been carried out by individuals with whom I have directly interacted.
Laser Physics. I began the study of laser physics before the first laser was made and built the second (ruby) laser in this country in 1962, in collaboration with my colleague O S Heavens, at Royal Holloway College, London, where I was an Assistant Lecturer. I worked at RHC from 1960-1962 and then went to a Lectureship at Sussex. Geoff Jones (DGC Jones) was appointed at Sussex on condition that he join an existing research group. He elected to work with me.
Because gas systems allowed easy variation of pressure, partial pressure, discharge voltage and current and so on we decided to work on gas lasers at Sussex. Solid-state systems depended too much on other people’s ability/willingness to grow optically perfect crystals; not a skill the UK possessed at that time. We built a large number of different types of laser which enhanced our insight into the detailed mechanisms involved in laser action.
We first made a distinctive, original, mark with a careful experimental investigation of the Lamb theory of gas lasers, during which time Willis Lamb spent a crucial month at Sussex. The study of the variation with cavity Q of the beat frequency between axial modes of a gas laser, mode self-locking and the intensity of a single mode as a function of cavity Q all interpreted and verified Lamb theory, [1, 2] which was also used to consider the optimisation of output coupling and the time development and competition between modes in a gas laser. An understanding of the theory led subsequently to an examination of the extent to which mode locking might automatically create -pulses. Other fundamental laser studies associated spatial coherence with mode structure, [3]; showed how spatial coherence is enhanced by propagation in bounded media; and explained the granularity of scattered laser light.[4]. The understanding gained led to Geoff Jones and I co-authoring the first book devoted to gas lasers and the first to include Lamb theory. When Willis Lamb visited in the autumn of 1968 for several weeks, he was asked to give some lectures on the theory of the laser. Sussex theoreticians turned up in force and were surprised to hear him say “Well, of course, it is all in the book” . Their mystification was complete when they found out who had written it and who Lamb was praising. They were no worse at recognizing the importance of lasers than any other group of theoreticians, but they did not expect (humble) experimenters to recognize the importance when they did not. This important work was conducted with Geoff Jones and 3 students; there was no group technician and no Post-Doc Fellow.
Amplified Spontaneous Emission and Coherent Interactions. Detailed studies of the difference between amplified spontaneous emission, ASE, and superradiance, an issue which had a very considerable but very confused literature, led to work of some depth in both areas The study of coherent interactions between laser light and atom ensembles produced research on self-induced transparency in self-chirped media, [5]; incoherent bleaching and self-induced transparency; and, most important, to what has become the classic, much cited, book on the subject “Optical Resonance and Two-level Atoms” by L.Allen and JH Eberly [6]. [Eberly was based at Rochester, NY, USA where I worked on many occasions.] The threshold condition, the connection with laser theory and the intensity and saturation of ASE became an extensive investigation, [7]. The connection was made between ASE and models of OH radiation in the interstellar medium and published in Nature and the Astrophysical Journal. The best of the work concerns the spatial and frequency distributions of pulsed ASE, [8], which gives great insight into the temporal and spatial nature of spontaneous emission. During this period when we were still actively pursuing alternative laser systems, money was obtained for useful expenditure on equipment and, most important, to appoint a laboratory Assistant, Peter Pollard. I went to the USA for a year to work with Leonard Mandel at Rochester, NY and came back to find that as the funding had ended Pollard had been allocated to the general electronics workshop. It set the scene, however, for one workshop (mechanical) technician, Jeff Holloway, to be assigned with special emphasis to my group. As time went along he became increasingly thought of as my technician even though he was never formally given that assignation. During this period Geoff Jones had moved on to other interests in Physics and my “Group” was typically myself, the technician Jeff Holloway and 3 students. There was still no Post – Doctral assistance because funding never permitted it. Geoff and I had co-authored a book and 16 papers in a very successful partnership.
This was an important period in Laser Physics in general and for me. What could have been an even more successful period was blighted by ER Pike FRS, of Malvern. I simply could not raise any funding. I suspected this was due to Pike sitting on the committee and this was finally confirmed after about three years by a telephone call from SRC telling me that ‘”as Dr Pike had now left the Committee” I should probably do well to apply for funding. I applied and got some money at last. The field, however, had moved on.
Some years later, arguing publically about the way SRC (SERC) allocated its funding, I criticised the way they had handled Pike. The secretariat must have known he was deliberately stopping me getting funded, but did nothing. In an article I wrote in Physics World, I told the same story and specifically named Pike (why not the story was true) but they would not name him. How we ever competed on the world stage in laser physics at Sussex I do not know; but we did. Significantly, although it was never for large sums of money, the in-house funding at Sussex proved to be very important. Without it, it is unlikely that very much of this work would have got done.
Multiphoton Absorption The work on ASE and Coherent Interactions was followed by a significant period of time studying the broadening and saturation of atomic transitions in n-photon absorption from n- independent lasers, I was lucky enough, finally, to get SRC funding to bring CR Stroud. Jr to the Group from Rochester for six months. [9]. This theoretical work was substantiated and confirmed by experimental examinations of the time development of adiabatic two-photon absorption in the low intensity and rate equation regimes. Subsequent work led to studies of the maximum yield in multiphoton ionisation, [10] and to the role of real intermediate states in the multi-photon process, which allowed the identification of a new electric dipole selection rule, [11]. Stroud was my only SRC funded post-doc in more than 20 year’s research at Sussex. About 4 students were involved at this time.
During the same period I co-authored a book on quantum optics. Soon after that I began five years in senior academic administration in London and my research output during that period was concomitantly low. Premature early retirement led to a decade or more of peripatetic research as a well deserved antidote before I settled into a series of Visiting appointments.
Orbital Angular Momentum. For the last ten years and more, my work has been concentrated on the study of the orbital angular momentum, or o.a.m, of light. It was known for a long time that electromagnetic fields could possess orbital as well as spin angular momentum. But it was only recognised in 1992 by myself and co-authors in Leiden that specific, readily realisable, laboratory fields such as Laguerre-Gaussian modes and Bessel beams had orbital angular momentum of per photon, where l is an integer, and would permit its properties to be elucidated in depth, [12]. It was shown experimentally that the usual Hermite-Gaussian laser beam could be converted by means of a mode convertor into a Laguerre-Gaussian beam and that such a beam possessed angular momentum characteristics independent of, but analogous to, polarisation, [13], and that the act of mode conversion was equivalent to putting waveplates in the path of a polarised beam. The theory of o.a.m was then extended to non-paraxial beams with the unapproximated Maxwell equations, [14]. The scope of the work was broadened to a comprehensive study of the interaction of atoms with beams possessing o.a.m. This work shows that there is an azimuthal Doppler shift in the resonant frequency of the atom, that the radiation pressure force is modified and that there is an associated torque on the atom, all introduced by orbital angular momentum, [15]. This work has been extended to various atom cooling and pumping regimes and includes a study of the role of multiple Laguerre-Gaussian beams and polarisation in atom-field dynamics.
Amongst my other work on this subject, there is laboratory proof that not only is the frequency of the light doubled in second harmonic generation but so, too, is the o.a.m of the transmitted beam: the maximum value of orbital angular momentum is unconstrained which is not the case for spin. Spin and orbital angular momentum have been shown to be mechanically equivalent when and a rotational frequency shift, proportional to the sum of spin and orbital angular momentum, has been observed in a rotating light beam, [16]. A matrix formulation analogous to the Jones matrices has been derived for the propagation of light with both spin and o.a.m, [17], and their intrinsic and extrinsic nature elucidated, [18]. More recently two-photon entanglement of orbital angular momentum states has been the subject of investigation, [19]. A recent book by Allen, Barnett and Padgett “Optical Angular Momentum”, [20], shows the current state of this subject and something of my contribution to it. It is now a major research field and in March 2010 a three day Conference at York was devoted entirely to the subject. I am looked on by many as the founding father of the subject because although it began with two papers at Leiden the subject only continued by my interaction with UK workers. Of the first 40 papers on the subject 25 had my name on them. Although I have been associated with Leiden, Utrecht, Colorado, Essex, St. Andrew, Glasgow, Strathclyde etc., during the last 20 years, there is little doubt that my earlier 20 years of hands-on research at Sussex where I produced 4 books and 79 papers, provided the vital underpinning of the work. The field is still developing quickly and in 2009 I was awarded the Institute of Physics’ Young Medal and Prize, jointly with Prof. Miles Padgett, Glasgow, for our “pioneering work on the orbital angular momentum of light.”
References Les Allen
1. VARIATION WITH CAVITY Q OF THE BEAT FREQUENCY BETWEEN AXIAL MODES OF A GAS LASER
L. Allen, D.G.C. Jones and M.D. Sayers
J. Phys. A (Proc. Phys. Soc.) [2], 2, 2, 87-94, January 1969
2. AMPLITUDE, COMPETITION, SELF-LOCKING, BEAT FREQUENCY, AND TIME DEVELOPMENT IN A THREE MODE GAS LASER
M.D. Sayers and L. Allen
Phys. Rev. A. 1, 6, 1730-1746, June 1970
3. SPATIAL COHERENCE AND MODE STRUCTURE IN THE HE-NE LASER
D.C.W. Morley, D.G. Schofield, L. Allen and D.G.C. Jones
Brit. J. App. Phys. 18, 10, 1419-1422, October 1967
4. AN ANALYSIS OF THE GRANULARITY OF SCATTERED OPTICAL MASER LIGHT
L. Allen and D.G.C. Jones
Phys. Letts. 7, 321-323, 15 December 1963
5. Self-induced Transparency in Self-Chirped Media
C.R. Stroud, Jr., C.M. Bowden and L. Allen
Opt. Commun. 67, 5, 387-390, 1 August 1988
6. “OPTICAL RESONANCE AND TWO-LEVEL ATOMS”
L. Allen and J.H. Eberly
Dover. New York. 1987, [Reprinted and corrected; unabridged.] Wiley. New York. 1975
[Also in Russian and Chinese translation; in a Japanese edition with N. Takatsuji; in a Polish edition with K. Rzazewski.]
7. AMPLIFIED SPONTANEOUS EMISSION AND EXTERNAL SIGNAL AMPLIFICATION IN AN INVERTED MEDIUM
L.Allen and G.I.Peters
Phys. Rev. A 8, 2031-2047, October 1973
8. THE SPATIAL AND FREQUENCY DISTRIBUTIONS OF THE INTENSITY OF PULSED AMPLIFIED SPONTANEOUS EMISSION
L. Allen, S.P. Kravis and J.S. Plaskett
J.O.S.A. 69, 1, 167-175, January 1979
9. BROADENING AND SATURATION IN n-PHOTON ABSORPTION
L. Allen and C.R. Stroud Jr
Phys. Reps. 91, 1, 1-29, November 1982
10. Laser Intensity for Maximum Yield in Multiphoton Ionisation
L. Allen, R.W. Boyd, J. Krasinski, M.S. Malcuit and C.R. Stroud,Jr.
Phys. Rev. Letts. 54, 4, 309-312, 28 January 1985
11. Two-Photon Electric-Dipole Selection Rules and Non-Degenerate Real Intermediate StateS
N. Melikechi and L. Allen
J.O.S.A. B, 3, 1, 41-44, January 1986
12. Orbital Angular Momentum of Light and the Transformation of Laguerre-Gaussian Laser Modes
L. Allen, M.W. Beijersbergen, R.J.C. Spreeuw and J.P. Woerdman
Phys. Rev. A 45, 11, 8185-8189, 1 June 1992
13. Astigmatic Laser Mode Converters and Transfer of Orbital Angular Momentum
M.W. Beijersbergen, L. Allen, H.E.L.O. van der Veen and J.P. Woerdman
Opt. Commun. 96, 1-3, 123-132, 1 February 1993
14. Orbital Angular Momentum and Non-Paraxial Light Beams
Stephen M. Barnett and L. Allen
Opt. Commun. 110, 5-6, 670-678, 1 September 1994
15. Atomic Motion in Light Beams Possessing Orbital Angular Momentum
W.L. Power, L. Allen, M. Babiker and V.E. Lembessis
Phys. Rev. A. 52, 1, 479-488, July 1995
16. Rotational frequency shift of a light beam
J. Courtial, D.A. Robertson, K. Dholakia, L. Allen and M.J. Padgett
Phys. Rev. Letts. 81, 22, 4828-4830, 30 November 1998
17. A matrix formulation for the propagation of light with orbital and spin angulaR momenta
L. Allen, J. Courtial and M.J. Padgett
Phys. Rev. E 60, 6, 7497-7503, December 1999
18. THE INTRINSIC AND EXTRINSIC NATURE OF THE ORBITAL ANGULAR MOMENTUM OF A LIGHT BEAM
A T O’Neil, I MacVicar, L Allen and M J Padgett
Phys. Rev. Letts. 88, 5, 053601- 4, 4 Feb 2002
19. TWO-PHOTON ENTANGLEMENT OF ORBITAL ANGULAR MOMENTUM STATES
Sonja Franke-Arnold, Stephen M Barnett, Miles J Padgett and L Allen
Phys. Rev A 65, 3, 0338231-6, March 2002
20. “OPTICAL ANGULAR MOMENTUM”,
L Allen, Stephen M Barnett and M J Padgett
IOP, Bristol, 2003