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  • Classical and quantum dynamics of

    optical frequency conversion

    By

    Andrew G. White

    A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

    OF THE AUSTRALIAN NATIONAL UNIVERSITY

    DEPARTMENT OF PHYSICS MARCH 1997

  • c© Andrew G. White, 1997

    Typeset in Palatino by TEX and LATEX 2ε.

  • To my parents

    Who encouraged me to find out about dinosaurs

  • Declaration

    This thesis is an account of research undertaken in the Department of Physics, Faculty

    of Science, Australian National University and the Fakultät für Physik, Universität Kon-

    stanz, Germany, between March 1991 and October 1996.

    Except where acknowledged in the customary manner, the material presented in this

    thesis is, to the best of my knowledge, original and has not been submitted in whole or

    part for a degree in any university.

    Andrew G. White

    Friday 28th March, 1997

  • Abstract

    A second harmonic generator is constructed to investigate the power and noise behaviour

    of optical frequency conversion.

    Strong squeezing of the second harmonic is demonstrated. It is found that pump

    noise critically affects the squeezing, with attenuation of the pump noise significantly

    improving the squeezing. A modular modelling approach is used to describe and quan-

    tify this effect, and excellent agreement is found between theory and experiment.

    Two methods of SHG are possible, passive (occurs external to a laser) and active (oc-

    curs within a laser). Theoretically exploring the possible squeezing regimes, the effect of

    laser noise on both methods is considered. It is concluded that active SHG is not feasible,

    as the high dephasing of practical lasers totally destroys the squeezing.

    It is shown that the second harmonic generator can simultaneously support multiple,

    interacting, second order nonlinear processes. Two categories of interaction are iden-

    tified: competing, where the interacting processes do not share all of the modes; and

    cooperating, where they do.

    Competing nonlinearities are evident in the system as triply resonant optical paramet-

    ric oscillation (TROPO): where second harmonic generation (SHG) and non-degenerate

    optical parametric oscillation (NDOPO) occur simultaneously. Power clamping of the

    second harmonic and nondegenerate frequency production in both the visible and in-

    frared are observed and explained, again obtaining good agreement between theory and

    experiment. Design criteria are given that allow TROPO to be avoided in future efficient

    SHG systems.

    The second harmonic squeezing is observed to be degraded by TROPO, with a max-

    imum value occurring just before the onset of TROPO – in contrast to predictions for

    closely related systems. A model is developed that shows this is due to two effects: a

    noise eating effect related to the second harmonic clamping; and low frequency noise

    added by the additional TROPO modes.

    A model of cooperating nonlinearities is developed that shows a wide variety of third

    order effects, including cross- and self phase modulation (Kerr effects) and two photon

    and Raman absorption, are in principle possible in the second harmonic generator. A

    strong third order effect is demonstrated experimentally: the system is phase mismatched

    and optical bistability is observed that is shown to be due to the Kerr effect.

    Arguments are presented to prove that, in principle, the system acts as a Kerr medium

    even at the quantum level. A model of Kerr squeezing is developed that allows consider-

    ation of the effect of pump noise: it is shown that the predicted squeezing is sensitive to

    both the amplitude and phase quadratures of the pump. Strong classical noise reduction

    (but no squeezing) is observed on light reflected from the cavity. It is speculated that the

    squeezing is masked by excess phase noise from the laser.

    Due to the quantitative and qualitative agreement between experiment and theory,

    and the experimental reliability of the system, it is concluded that SHG is now a well un-

    derstood and practical source of squeezed light. The potential for future systems, given

    the availability of new nonlinear materials, is discussed.

    vii

  • Papers by author

    Accepted papers resulting from work in this thesis

    • A. G. White, P. K. Lam, M. S. Taubman, M. A. M. Marte, S. Schiller, D. E. McClelland and H.-A. Bachor. Classical and quantum signatures of competing χ(2) nonlinearities. Phys-

    ical Review A, 55, no. 6, p. 4511 - 4515, 1997

    • S. Schiller, R. Bruckmeier, and A. G. White. Classical and quantum properties of the subharmonic-pumped parametric oscillator. Optics Communications, 138, nos 1-3, p. 158

    - 171, 1997

    • A. G. White, T. C. Ralph, H.-A. Bachor. Comment on “Noiseless amplification in cavity based optical systems with an internal two-photon process”. Journal of Modern Optics, 44,

    no. 3, p. 651 - 652, 1997

    Published papers resulting from work in this thesis

    • A. G. White, M. S. Taubman, T. C. Ralph, P. K. Lam, D. E. McClelland, H.-A. Bachor. Experimental test of modular noise propagation theory for quantum optics. Physical Review

    A, 54, no. 4, p. 3400 - 3404, 1996

    • A. G. White, J. Mlynek and S. Schiller. Cascaded second-order nonlinearity in an optical cavity. Europhysics Letters, 35, no. 6, pp. 425 - 430, 1996

    • A. G. White, T. C. Ralph, H.-A. Bachor. Active versus passive squeezing via second har- monic generation. Journal of the Optical Society of America B, 13, no. 7, pp. 1337 - 1346,

    1996

    ix

  • x

    • H.-A. Bachor, T. C. Ralph, M. S. Taubman, A. G. White, C. C. Harb, D. E. McClelland. Progress in the search for the optimum light source: squeezing experiments with a frequency

    doubler. Journal of Quantum and Semiclassical Optics, 7, no. 4, pp. 715 - 726, 1995

    • T. C. Ralph, M. S. Taubman, A. G. White, D. E. McClelland, and H.-A. Bachor. Squeezed light from second harmonic generation: experiment versus theory. Optics Letters, 20, no. 5,

    pp. 1316 - 1318, 1995

    • T. C. Ralph and A. G. White. Retrieving squeezing from classically noisy light. Journal of the Optical Society of America B, 12, no. 5, pp. 833 - 839, 1995

    Published papers resulting from work in Honours thesis

    • N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White. Generation of optical phase singularities by computer-generated holograms. Optics Letters, 17, no. 3, pp. 221 - 223,

    1992

    • A. G. White, C. P. Smith, N. R. Heckenberg, H. Rubinsztein-Dunlop, R. McDuff, C. O. Weiss, and Chr. Tamm. Interferometric measurements of phase singularities in the output of

    a visible laser. Journal of Modern Optics, 38, no. 12, pp. 2531 - 2541, 1991

    Other published papers

    • A. E. Stuchbery, A. G. White, G. D. Dracoulis, K. J. Schiffer, and B. Fabricius. Gyromag- netic ratios of low-lying rotational states in Gd156 , Gd158 , Gd160 . Zeitschrift für Physik A

    - Atomic Nuclei, 338, no. 2, pp. 135 - 138, 1991

  • Acknowledgements

    It is not so much our friends’ help that helps us as the confident knowledge that they will help us

    Epicurus

    I have been gifted with the friendship and support of a great number of people during

    the course of this thesis, and now is my chance, in ever so humble a way, to thank them.

    Firstly I wish to thank Dianna Gould for her love and belief. She has endured my

    stress and our separation due to this thesis, and responded with understanding and lov-

    ing company. Thank you, you made it all worthwhile.

    To my family – mum, dad, nanna, pa, Damian and Natalie – your unstinting love

    and support has been my crutch in the lean times, and I cannot think how to repay you,

    except maybe to try and see you much more often (oh, OK, and to get my nose out of a

    book occasionally while I’m there!).

    To paraphrase Rumpole, a number of my friends from Queensland have gone on to

    “join the legions of those I like, but never see”. Tracey and James, Jacinta and Mark,

    thank you for your understanding and regular Christmas cards. A special thank you to

    Matthew Molineux, whose continued efforts to stay in touch have kept our friendship

    alive and well across several continents despite my habit of regularly losing his contact

    address (well, you will move so often).

    To the old gang from uni: Margaret Wegener, Alan Monaghan, Sam Meyer, Bradley

    Ellis, (and the others I’ve forgotten because it’s 4 o’clock in the morning, but you know

    who you are) thank you for continuing phone calls, emails, and hurried dinners at Christ-

    mas. A most special thank you to Craig Smith (who was my laboratory partner in Hon-

    ours), for both the regular, sanity inducing, contact, and for reminding me of the im-

    portant things in life. For their friendship and for acting as a mirror to my soul when

    required, thank you to Rebecca Farley and Steven Siller (atque in perpetuum, frāter, avē

    atque valē).

    Thank you to Wayne and Pippa Rowlands and Joe and Janet Hope for their welcome

    and for restoring my faith in humanity - it was appreciated guys!

    Being a student in a town far from my home state, I have been in more