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Historical note on glaciology and nanotechnology, by John F. Nye

This personal note, addressed to the glaciological community, is an addition to my lecture "Glaciology Sixty Five Years Ago" which is available to watch here.  I am a former glaciologist who is now working on optics and waves.  The transition happened in a quite logical and natural way.  I was interested in the radio-echo sounding of the Antarctic ice sheet when it first started.  At first, of course, it was not done from an aircraft or spacecraft but from a sledge down on the snow.  As you well know, a pulse of waves is sent out and you time how long it takes for the echo from the bed to come back.

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But the pulse that comes back is not exactly the same as the one that was sent out;  it is drawn out, with a long tail.  If the outgoing pulse contains 4 crests the echo might have 12 or many more crests in it.  The reason is simply that the rock bed is not just a mirror;  it is rough.  The front of the echo comes from just underneath the sledge but signals also echo back – are scattered back – by the more distant parts of the bed.  That gives the tail of the echo.

We knew from published photographs that the tail had a fine structure which changed rapidly as the sledge was moved, but to understand the details of how it would change Michael Walford, with two undergraduates, Robert Kyte and David Threlford, built a laboratory-sized analogue model [1] with a transmitter and receiver that used ultrasonic waves instead of radio waves.  Sound in air travels about 10,000 times slower than radio waves in ice, and the Antarctic ice sheet is also about 10,000 times thicker than a laboratory model, 1 m or so in depth.  So it scales down into the laboratory very nicely.  We simulated the rough rock bed by using crumpled cooking foil.  When we displayed the outgoing ultrasonic pulse and its echo on an oscilloscope they looked very like the radio versions.  But there was a feature of the received pulse that drew my attention;  it is shown in simplified form in the following animation.

The received pulse is very short in this example and contains just 4 crests.  But if the transmitter/receiver (carried by the sledge on the ice surface) is moved sideways by less than a wavelength the number of crests increases by 1.

At first there are 4 crests but then there are 5.  The following figure shows what the crests in the returning wave must look like in space.   

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The pulse must contain a dislocation very like an edge dislocation in a crystal, where a plane of atoms comes to an end.  The crests of the waves are the crystal planes.  4 crests sweep past point A, but an observer who moves to point B sees 5, as in the animation.  In the real problem the amplitude of the returning echo is a function of the three space variables x, y, z and the time t.  This example simplifies it to a function of x, z, t.  One can deduce that trains of waves in nature can contain dislocations (of mixed edge-screw type, in general).  That is a very broad conclusion, but it is justified because the cooking foil bed is sufficiently representative of a general scattering object.  Similar observations had been made before, most notably in the discovery as long ago as 1833-1840 by Whewell [2] of amphidromic points in the tides.   The new point was that dislocations are features to be expected in all waves.

This idea, developed with Michael Berry [3], has proved to be extraordinarily fruitful.  We and many others continue to pursue the topic of wave dislocations in optics and in monochromatic waves, where they are called optical vortices.  This is an academic study undertaken for its own inherent interest.  But the historical thread I want to follow here branched into an application of some importance when, following theoretical work by L. Allen, it was demonstrated [4] that a laser beam containing an optical vortex can turn a tiny object by transferring angular momentum to it.  The helical shape of the wavefronts was the operative feature.  It was already known that light can move an object by transferring linear momentum but here was the possibility, using a single laser beam, of a microscopic device, operating on a subwavelength scale, that could both move and turn an object even as small as a single atom – true optical tweezers.  As is well known, laser beams are now used for nano-assembly.  Nano-technology has begun, with all the exciting things it implies for the creation of new materials, and the new vistas it opens in the life sciences (manipulating single cells) and for quantum communication.  Thus the lineage can be traced back, from the manipulation of single atoms, molecules or cells and the nano-assembly of new materials, via optical vortices and dislocations in ultrasonic and other waves, to a study of radio-echo sounding in Antarctica – a scale change by a factor of 109.  Glaciologists may be pleased to know of this historical connection between their subject and nano-technology.

Correspondence

45 Canynge Road, Bristol BS8 3LH, UK.

Email: john.nye@bristol.ac.uk

References

[1] J. F. Nye, R. G. Kyte and D. C. Threlfall 1972, Proposal for measuring the movement of a large ice sheet by observing radio echoes, J. Glaciol. 11, No. 63, 319-325.

[2] S. Ducheyne 2010, Whewell's researches; scientific practice and philosophical methodology, Studies in History and Philosophy of Science A 41, (1), March, pp. 26-40.

[3] J. F. Nye and M. V. Berry 1974, Dislocations in wave trains, Proc. Roy. Soc. Lond A336, 165-190.

[4] R. Allen, M. W. Beijersbergen, R. C. J. Spreeuw and J. P. Woerdman 1992, Orbital angular momentum of light and the transformation of Laguere-Gaussian Modes, Phys. Rev. A45, 8185-8189.

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