A systematic and accurate measurement of the diffracted light at large distances behind a diffracting edge – an overdue experiment for clearing beyond any doubt the old and major controversy regarding the origin of the diffracted inside or outside of the diffracting edges, or equivalently, for clearing the controversy regarding the physical reality of waves/ wave functions for light.

 

Corneliu I. Costescu, Ph.D., The Agora Laboratory, 1113 Fairview Ave, Urbana, IL 61801 USA, Ionel Rata, UIUC, USA

 

1. Introduction. An old and major unsolved controversy regards the origin of the diffracted light. The alternative views in this debate are as follows. i) The diffracted light is born inside of the diffracting edge. This view was initiated by Thomas Young in 1802 and many scientists in our days (for instance J.W. Goodman, Introduction to Fourier Optics, pg 46 – McGraw-Hill 1968) believe that this is the case. Due to the prevalence of the next alternative view – see (ii) below, no specific complete analysis and theory were developed yet for this view. Rather, this view is implemented in the Geometrical Theory of Diffraction (GTD) as a mixture between the concept of rays leaving from the diffracting edges and propagating in straight paths, with the wave concepts from the alternative (ii) below. For instance, in GTD the straight-path rays behave like waves (interfere) when they encounter other similar rays.  ii) The diffracted light is born mostly outside of any thick diffracting body (Huygens, Fresnel, quantum mechanics and quantum electrodynamics). by the specific diffractive behavior of waves of hundreds of nanometer wavelength – very large as compared with the atomic distances. An illustrative example is as follows. Assume that a plane wave falls on a perfectly conducting and infinitesimally-thin half-plane edge. Then the part of the plane wave that passes un-deviated spreads (diffracts) behind the diffracting edge such that at very large distances from this diffracting edge the wave is everywhere (both in the directly illuminated area and in the geometrical shadow of the diffracting edge) a plane-wave with an amplitude of half of its initial (incident) value. This example illustrates how in the wave description the diffracted light is born essentially outside of the diffracting edge for any kind of bodies.  The alternative (ii) is greatly analyzed and developed in the modern physics while, as mentioned already above, there is no complete analysis of the alternative (i).

 

No experiment was successful yet to indicate beyond any doubt where the diffracted light is born and hence to clear definitively this old and major controversy. This claim includes the interference experiments and the measurements of the diffracted light at short distances. Indeed, as we show in this proposal, even though the results from these experiments can be quantitatively described well by the mathematics for (ii), this can also be done, conceptually and quantitatively, on the line of the alternative (i).  The importance and the way of solving this controversy are discussed below.

 

The importance of clearing this controversy can be appreciated by the following three simple but very powerful arguments. First, if (i) is proven true then a systematic study of the (i) would force a practical view essentially different from (ii) and hence, it would force a corresponding development of the theory of light. Indeed, let us assume that the diffracted light is born inside the diffracting edges. Then the light can not be waves in free space. If it did, then the diffracted light would be necessarily born outside of the diffracting edges (as it was described above for the case of the diffraction of a plane wave by a half-plane edge), which contradicts the assumption we have started with. Therefore if the diffracted light is born in the diffracting edges then the electromagnetic/ quantum waves which we currently use for a light beam can not have a physical reality. In this case these waves become rather a powerful mathematical tool that is fit (for numerous and perfectly understandable reasons) for the description of the diffraction of light. In this case, a complete analysis of the direct consequences and a development of theory become necessary – we discuss in this proposal the relevant issues. Second, this controversy has affected in a major way every generation of students and professors. Every student and professor tries to find in vain the definitive answer to the question if the waves for light are real. The confirmation of the option (ii) means proving definitively the physical reality of waves/ wave functions. Third, this origin of the diffracted light is more than ever a major issue because of the need of a more detailed view of light phenomena in nanoscience and nanotechnology – we discuss relevant literature in this proposal. Therefore, it would be of great benefit if we can find a feasible experiment to settle this old debate in a definitive way.

 

Our proposal shows that the old edge-diffraction experiment can provide the crucial information for clearing beyond any doubt this controversy. Indeed, accurate measurements of light intensity at (very) large distances behind the diffracting edge in the geometrical shadow can verify in the most direct way if light spreads like waves. The most direct way would be to experiment with beam of light that can be described by a plane wave falling perpendicularly on a half-plane edge. For this case, the wave theory of light predicts that the diffracted light is described by the well known Fresnel-Cornu-Rayleigh-Sommerfeld formula. This formula shows the surprising result that the light intensity in the geometrical shadow behind the diffracting edge increases from zero to a quarter of the incident intensity of light as the distance from the diffracting edge (behind this edge i.e., in its geometrical shadow) increases from zero to infinity, on any line parallel with the beam axis. Such a behavior would be easy to verify. However, since there are no infinite plane-wave source of light, it is necessary to measure the light intensity behind the diffracting edge for two beams of very different thickness. According to the wave theory of light there must be differences, in the intensity of the diffracted light behind the diffracting edge, between these two cases of beam thickness. By measuring these differences we can provide a specific and simple answer of the type Yes or No to choosing between the alternatives (i) and (ii) from above.  As discussed above, the results from our experiment can be either the confirmation beyond any doubt of the current predictions for this experiment (and hence, proving definitively the physical reality of waves/ wave functions – a result sought in vain until now), or the negation of the current prediction for it. In the latter case, as we discussed above, the diffracted light is born inside the diffracting edge and cannot be of the wave type in free space.

 

Therefore, our experiment brings essential/ fundamental information no mater of which of the alternatives (i) and (ii) are confirmed. If the experimental results will confirm the alternative (ii) then we have a definitive proof of the physical reality of waves/ wave functions – a result sought in vain in the past. If the experimental results will negate the current prediction for this experiment (i.e., if they will prove the alternative (i) that the diffracted light is born in inside the diffracting edges) then a complete analysis of these results will necessarily suggest a new structure and new mechanisms, and will lead to new ways of experimentation for light propagation and diffraction. This complete analysis will also show why the current wave approach fits in the limits of the current way of experimenting. Our proposal also describes a research-education method that is necessary for accomplishing such a complete analysis. In conclusion and first, our experiment will eliminate beyond any doubt a major ongoing controversy and will likely open a new and major development for light. An adequate research-education method is defined for carrying out the experiment and its interpretation. Second, by providing new and accurate data for light diffraction at large distances this experiment is important in itself. Finally, our experiment will also measure the contribution of the scattering of light by the air along the laser beam to the measured light.

 

Section 2 below presents a general description of the proposed experiment and its interpretation.  The discussion in Section 3 provides information regarding the four NIST evaluation criteria for the proposal: the importance of the proposed research, the relation of our proposal with the ongoing work in NIST, the feasibility and the potential impact for our experiment and interpretation, and our qualifications.

 

2. A general description of the project. 

2.1 The main objectives

Our project pursues the following two main objectives:

a) A systematic and accurate measurement of the intensity of the diffracted light at very large-distances behind the diffracting edge in a laser - diffracting edge - detector system, and a systematic comparison of the results from two very different cases, a thin and a thick laser beam.  The very large distances for our measurements are those where the current theory predicts a difference between a thin and thick beam behind the diffracting edge. As mentioned above these measurements essentially test if light spreads as waves behind a diffracting edge.  Although very simple in principle, our systematic measurements at large distances have never been done in the past, due to the lack of very high quality light sources (a very stable laser beam with perfect circular symmetry) and of high quality light detectors. However, in our times these overdue measurements are feasible with the instruments described in the next subsection. Limited such experiments have been done in the near past for small distances behind the diffracting edge and hence, only limited data exists for the corresponding light intensity. These limited data seem to match the current predictions from electrodynamics of light and hence, it seems that they confirm the wave behavior. However, for a number of reasons as we discuss in the end of this section, these results could be only a quantitative match of the mathematical instruments of the current views with the experimental data, and which could be qualitatively and quantitatively better explained by a new view derived from assuming that the origin of the diffracted light is inside of the diffracting edge.

 

b) A systematic development of the interpretation of the results from the above experiment, and a systematic development of applications.  For this purpose we have developed a necessary and productive research-teaching method and instrument, as briefly described in Section 3.

 

2.2 Experimental details for our experiment

For reproducible results and easy alignment of the laser-edge-detector system on such large distances, in the experiment under (a) above we use a very high quality laser beam with circular symmetry around the beam axis, stable in intensity/ frequency/ direction, and small divergence (low power - 1 mW), (the He-Ne laser ML-1 from Microg-Lacoste).  A metallic plate that has a high quality (thin and straight) edge is placed perpendicularly in the laser beam such that the beam axis intersects the edge.  Two separate positions are used for this edge – one at 5 m and one at 25 m from the laser.  At these positions, the laser is seen as a point source and the beam diameter is respectively around 10 mm (thin beam) and around 100 mm (thick beam).  The employment of a point source prevents the straight paths from the laser volume from reaching the space behind the diffracting edge.  For each in-beam position of the diffracting edge, the diffracted light is accurately mapped at large distances, behind the diffracting edge, in its shadow.  These measurements are performed at those distances where the current wave theory of light predicts a difference between diffraction of a thin beam and a thick beam of light.  In contrast, at small distances and close to the beam axis, this theory predicts similar results for the two beams.  The detector is a Thorlabs PDF10A femtodiode, which is similar in sensitivity to a photomultiplier.  To study the contribution of the light scattered by the surrounding gas (air/ Ar/ He) to the light intensity measured at large distances from the diffracting edge and up to 30 cm off the beam axis, two diffusion pumps reduce the pressure inside the tunnel.  By reducing the gas pressure we obtain the bare edge-diffracted light intensities.  Finally, we normalize the edge-diffracted intensities to the intensity of the laser beam at the point where the axis of the beam intersects the diffracting edge.

 

 

2.3 A sketch of the theoretical and experimental background

In the current view (the alternative (ii) from the introduction) the diffracted light originates in the specific diffractive behavior of waves (Huygens, Fresnel, Sommerfeld, all modern physics). In 1815 - 1819, Fresnel successfully used the Huygens principle of propagating waves through the aperture, in which the diffracted light originates in the wave behavior around the diffracting edges. This view was combined with the electromagnetism and later was combined with quantum mechanics and was developed in quantum electrodynamics, as the modern physics on light [1-5]. In this case the diffraction of a plane wave on a simple metallic edge leads to the Fresnel – Kirckoff- Rayleigh - Sommerfeld (FKRS) formulae. Importantly enough this formulae show that the diffracted light (born outside of the diffracting edge by the specific behavior of waves) will exist even for a perfectly reflecting material in the edge – a claim-prediction which is out of the experimental reach. Such an out-or-reach prediction is a serious trouble for a theory. For the case of real materials the electromagnetic waves are also scattered/ absorbed by the material, and collective electron oscillations (plasmons for instance - on the body surface) are generated by the presence of the electromagnetic waves. It is worth for our proposal to mention here that, obviously in this current view these electron oscillations (including the plasmons) are regularly only an accompanying effect for the electromagnetic waves. An equilibrated set of references for the theoretical and experimental issues for light production, propagation and diffraction are Refs [6-39].  These references and relevant issues for our proposal are discussed in a later paragraph.

 

The alternative (i) from the introduction i.e., the origin of the diffracted light in the diffracting edges is present from time to time in the literature in different forms, beginning with Thomas Young in 1801 [40]. He proposed the principle of interference of waves emerging from inside the diffracting edges, and he calculated wavelengths. No mechanism was suggested for the production of the diffracted light inside the diffracting edges.  In1960 Andrews [41] and Norton [42] revived the idea of the diffracted light as waves originating from the diffracting edges, to show that it is simpler to use than the Fresnel-Huygens-Kirckoff approach.  In addition, Keller introduced in 1962 [43] the Geometrical Theory of Diffraction (GTD), which is still under development [44, 45]. GTD postulates that the diffracted rays are born in the diffracting edges, and calculates their intensity from comparison with the electromagnetic treatment. A similar approach is used by the theory of the boundary wave diffraction [46, 47].

 

There is a large body of experimental data for the diffraction pattern (interference experiments) and for edge diffraction at small, intermediate and large distances. Similar data are available for slit/ hole/ etc. The electromagnetic theory (elm) and the quantum theory (qm) can give a good quantitative description for these kind of results: interference patterns and light intensities. The situation is completely different at large distances behind a diffracting edge i.e., in the geometrical shadow however, in spite of the simplicity of the experimental case. Indeed, for this case no data is available for the intensity of the diffracted light.  Hence, we essentially do not know if elm/ qm can fit for the description of such data. In fact the controversy described above strongly suggests that the elm results for the edge diffraction could be wrong at large distances. As explained in the proposal a systematic measurement for this case would allow for a clear choosing between the two views above.

 

There is a wealth of experimental results at the nanometer level, which indicate that the edges of the diffracting bodies play by their collective electron-oscillations an essential role in the diffraction, and starting from here a complete analysis can suggest a more mechanism-type approach for the structure of the light beam.  The first two sets of results are as follows. 1) An un-expectedly strong and forwardly oriented, non-diffractive type transmission of light through sub-wavelength apertures in a very thin screen, and an unexpectedly strong dependence of the transmitted intensity on the screen material [6-13].  2) The detection of spatial details much smaller than half-wavelength (the wave resolution limit) in the near-field microscopy [14-22].  The theoretical treatment for both these limiting cases (small size metallic apertures) requires using collective electron oscillations (in excess to the incident EM waves) in the materials exposed to light to explain the observed features i.e., not only the regular EM wave solution in the free space for the regular metallic apertures. The need to treat in a completely different manner the small and the large apertures in EM is an indication that one or both these treatments are only a mathematical description.  In our proposal, the collective electron oscillations in the walls of the apertures are always (for both small size and large size apertures) the origin of the diffracted light. In our proposal, these collective electron oscillations are generated at the entrance surface by the incoming non-wave, periodic structure of the light beam in free space. This brings a considerable simplification and physical insight for the diffraction phenomenon for both large and small apertures of thin or thick wall. After their generation on the surface, they propagate by themselves – self-sustained electron oscillation propagation. In the above references [6-22] the collective electron oscillations are not recognized as the light beam carrier in condensed matter, i.e., they are still seen as the byproduct of the abstract EM wave propagation in matter. In fact, although the experiments are very suggestive toward recognizing this role, making this recognition would be impossible without performing an analysis similar to our proposal.

 

Refs. [23-28] are related in a way to the previous set [6-13].  The references [12, 23-28] report the modification of the spontaneous emission probability by either placing the atoms in small optical cavities or in spatially periodical modulated surfaces, where collective electron oscillations take place i.e., where light is propagating inside condensed matter. This modification of the rate of the spontaneous emission seems a very promising property to analyze in the context of the application of the bi-structure to the atomic spectroscopy – see the Section c. Indeed, we show in Section c that the steady-state Schrödinger equation can be obtained from the equation for the collective electron oscillation in a central potential.

 

The following experimental results also point to the need of a more detailed understanding of the light propagation and diffraction. The unexpected spotted structure (speckles) in a laser illuminated area on a material surface [29, 30]. The nature of a speckle is not fully clear. Interference effects are currently invoked. However, in our bi-structure, the laser beam has a naturally discontinuous intensity distribution, both transversally and longitudinally to propagation, and hence it would naturally produce speckles.  Moreover, the structure of a speckle spot might be discontinuous and flickering, which is a prediction of our bi-structure beam of light.

Surprising spectral changes are predicted in the propagation of light from multiple coherent sources (the Wolf effect, [31, 32]).  There is even a formation of multiple colors when a beam passes though an array of holes in a thin film. Spectral changes can occur in many ways with the bi-structure beam of light, especially in small pieces of material: by interference of electronic oscillations, or by the excitation of transitory electron oscillations in peripheral parts of small material bodies. 

Light emitted when a beam of fast moving electrons passes parallel and close to a metallic surface with fine gratings, perpendicularly to the gratings direction [33]. The color of the emitted light is dictated by the speed of electrons. This experiment should be analyzed in most detail since it seems that it produces (by the propagation of collective electron oscillations in the gratings) a beam of light similar with the diffracted light from the edge diffraction. It seems that it supports our claim that the formation and the propagation of collective electron oscillations inside the terminal shapes of the diffracting edges play the most important role in the formation of the diffracted light.

The fluorescent blinking of quantum dots [34] when illuminated by a laser beam seems a very promising test. It might play, for a new structure of light, a similar role as the Brownian motion played for the kinetic theory of heat.

 

References

[1] A. Sommerfeld, Optics, Lectures on Theoretical Phys. vol. IV (Academic Press Inc.,1954).

[2] M. Born, E. Wolf, Principles of Optics, 6th ed., (Pergamon Press, Oxford, 1980).

[3] A. Messiah, Quantum Mechanics, vol 1, (John Wiley & Sons, 1958).

[4] W. Heitler, The Quantum Theory of Radiation (Oxford Univ. Press, Printed in Great Britain, 1954). R.P. Feynman, QED, The Strange Theory of Light and Matter, (Princeton, New Jersey, 1985).

[5] A. Yariv, Optical Electronics in Modern Communications (Oxford University Press, 1997)

 

[6] T.W. Ebbessen, H.J. Lezec, H.F. Ghaemi, T. Thio, P.A. Wolff, “Extraordinary optical transmission through sub-wavelength hle arrays,” Nature, vol. 391, 667 (1998).

[7] D.E. Grupp, H.J. Lezec, T.W. Ebbessen, K.M. Pellerin, T. Thio, “Crucial role of metal surface in enhanced transmission through sub-wavelength apertures”, Appl. Phys. Lett.,77(11), 1569 (2000).

[8] H.J. Lezec, A. Degiron, E. Devaux, R.A. Linke, L. Martin-Moreno, F.J. Garcia-Vidal, T.W. Ebbessen, “Beaming Light from a Sub-wavelength Aperture”, Science, vol 297, 820 (2002)

[9] A Degiron, H.J. Lezec, W.L. Barnes,T.W. Ebbessen, Effects of hole depth on enhanced light transmission through sub-wavelength hole arrays”, Appl. Phys. Lett. 81(23), 4327 (2002).

[10] L. Martin-Moreno, F.J. Garcia-Vidal, H.J. Lezec, A. Degiron, T.W. Ebbessen, “Theory of Highly Directional Emission from a Single Sub-wavelength  Aperture Surrounded by Surface Corrugations”, Phys. Rev. Lett., 90 (16), 167401(4) (2003).

[11] F.J. Garcia-Vidal, L. Martin-Moreno, H.J. Lezec, T.W. Ebbessen, “Focusing light with single sub-wavelength aperture flanked by surface corrugations”, Appl. Phys. Lett., 83(22),4500 (2003).

[12] S.C. Kitson, W.L. Barnes, J.R. Sambles, “Full Photonic Band Gap for Surface Modes in the Visible”, Phys. Rev. Lett., 77(13), 2670 (1996).

[13] R.H. Ritchie, E.T. Arakawa, J.J. Cowan, R.N. Hamm, “Surface –Plasmon Resonance Effect in Grating Diffraction”, Phys. Rev. Lett., 21(22), 1530 (1968).

 

[14]Near Field Optics, Vol. 242 of NATO Advanced Studies Institute, Series E: Applied Sciences, edited by D.W. Pohl and D. Courjon (Kluwer, Dordrecht, 1993).

[15] R.D, Grober, T.D. Harris, J.K. Trautman, and E. Betzig, “Design and Implementation of low temperature near-field scanning optical microscope,” Rev. Sci. Instrum. 65, 626 (1994).

[16] R.D. Harris, R.D. Grober, U.K. Tautman, and E. Betzig, “Super-Resolution Imaging Spectroscopy”, Appl. Spectrosc. 48,14A (1994)

[17] C. Girard and A. Dereux, “Near Field optics theories,” Rep. Prog. Phys. 59, 657 (1996).

[18] J.L. Kann,T.D. Milster, F.F. Froechlich, R.W. Ziolkowski, J.B. Judkins, “Linear behavior of a near-field optical scanning system,” J. Opt. Soc. Am. A 12, 1677 (1995). “ Near-field optical detection of asperities in dielectric surfaces,”J. Opt. Soc. Am. A 12, 501 (1995).

[19] D. Van Labeke, D Barchiesi, and F. Baida, “Optical characterization of nanosources used in scanning near-field optical microscopy,” J. Opt. Soc. Am. A 12, 695 (1995).

[20] G.W. Bryant, E.L. Shirley, L.S. Goldner et al., “Theory of probing a photonic crystal with transmission near-field optical microscopy,” Phys. Rev. B, 58, 2131 (1998).

[21] H. A. Bethe, “Theory of Diffraction by Small Holes,” Phys. Rev. 66, 163, (1944).

[22] C.J. Bouwkamp, “On Bethe’s theory of diffraction by small holes,” Philos Res. Rep. 5, 321 (1950). “On the diffraction of electromagnetic waves by small circular disks and holes,” 5, 401 (1950).

 

[23] P. Goy , J.M. Raimond, M. Gross, S. Haroche, “ Obsevation of Cavity-Enhance Single-Atom Spontaneous Emission,” Phys. Rev. Lett., 50(24), 1903 (1983).

[24] F. DeMartini, G. Innocenti, G.R. Jacobobitz, P. Mataloni, “Anomalous Spontaneous Emission Time in Microscopic Optical Cavity,” Phys. Rev. Lett. 59(26), 2955 (1987).

[25] E. Yablonovitch, “Inhibited Spontaneous Emission in Solid-State Physics and Electronics,” Phys. Rev. Lett., 58(20) 2059 (1987).

[26] S. John, “Strong Localization of Photons in Certain Disordered Dielectric Superlatices,” Phys. Rev. Lett., 58, 2486 (1987).

[27] E. Yablonovitch, “Photonic band-gap structures,” J. Opt. Soc. Am. B10, 283 (1993)

[28] M.D. Tocci, M. Scalora, M.J. Bloomer, J.P. Dowling, C.M. Bowden, “Measurement of spontaneous-emission enhancement near the one-dimensional photonic band edge of semiconductor heterostructures,” Phys. Rev. A 53, 2799 (1996).

 

[29] G. Cloud, Optical Methods of Engineering Analysis ( Cambridge University Press, 1998)

[30] R. Petit (ed), Electromagnetic Theory of Gratings, (Springer-Verlag, Berlin, NY, 1980).

[30] E. Wolf, Phys. “Invariance of the Spectrum of Light on Propagation”, Rev. Lett., 56(13), 1370 (1986)

[31] G. Popescu, A. Dogariu, “Spectral Anomalies at Wave-Front Dislocations”, Phys. Rev. Lett., 88 (18), 183902 (2002).

[33] S.J. Smith, E.M. Purcell, “Visible Light from Localized Surface Charges Moving across a Grating”, Phys. Rev. Lett., 1069 (1953)

[34] M. Nirmal, L. Brus, “Luminescence photophysics in semiconductor nanocrystals”, Acc. Chem. Res. 32, 407 (1999).

[35] P.A. Franken, A.E. Hill, D.W. Peters, G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett. 7, 118 (1961).

[36] J.E. Pearson, T.C. McGill, S. Kurtin, A. Yariv, “Diffraction of Gaussian Beams by a Semi-Plane”, J. of the Opt. Society of America, 59, 11 (1440).

[37] L.E.R. Peterson, G.S. Smith, “Three-dimensional electromagnetic diffraction of a Gaussian beam by a perfectly conducting half-plane”, J. Opt. Soc. Am, A 19, 11 (2265).

[38] G.R. Wein, “A video technique for the quantitative analysis of the Poisson spot and other diffraction patterns”, Am. J. Phys. 67(3), 236 (1999).

[39] R.E. Haskell, “A simple experiment of Fresnel Diffraction”, Am. J. Phys. 38(8), 1039 (1970).

[40] T. Young, “On the Theory of Light Colors”, Paper presented before Royal Society in 1801. Miscellaneous works of the late Thomas Young, vol 1 p. 151 (John Murray, London, 1855).

[41] C.L. Andrews, Optics of the electromagnetic spectrum, (Prentice Hall, Inc., Englewood Cliffs, NJ, 1962.

[42] N. Norton, “Thomas Young and the theory of Diffraction”, Phys. Educ., vol 14, 19/9, 450 (1979).

[43] J.B. Keller, “Geometrical Theory of Diffraction”, J. Opt. Soc. Am. 52, pp.116 - 130 (1962).

[44] G.L. James, Geometrical Theory of Diffraction for Elm. Waves (Peter Peregrinus Ltd. 1986).

[45] V.A Borovikov, B.Ye. Kinber, “Geometrical Theory of Diffraction”, (The Institution of Electrical Engineers, 1994).

[46] A. Rubinovicz, ( ), Nature, 160, 150 (1957).

[47] K. Miyamoto, E. Wolf, “Generalization of the Maggi-Rubinovicz Theory of of Boundary Diffraction Wave – Part I”, J. Opt. Am. 52, pp. 615-625 (1962). Part II ibid, pp. 626 (1962).