Publications

Preprints

Position, spin and orbital angular momentum of a relativistic electron,
K Y Bliokh, M R Dennis & F Nori   (arXiv: 1706.01658)

 Constructing a polynomial whose nodal set is any knot or link,
B Bode & M R Dennis   (arXiv: 1612.06328)

 Zernike amplitude pupil apodization for vortex coronography with obscured apertures,
G J Ruane, M R Dennis & G A Swartzlander   (arXiv: 1412.8731)

Refereed Scientific Publications

2017

[88] Knotted fields and explicit fibrations for lemniscate knots,
B Bode, M R Dennis, D Foster & R P King  Proceedings of the Royal Society of London A 475 (2017) 20160829 (arXiv: 1611.02563)

[87] Constructing a polynomial whose nodal set is the three-twist knot 52,
M R Dennis & B Bode J Phys A 50 (2017) 265204  (arXiv: 1612.06801)

[86] A random wave approach to the Aharonov-Bohm effect,
A J H Houston, M Gradhand & M R Dennis, J Phys A 50 (2017) 205101  (arXiv: 1612.01839)

[85] A ray-optical Poincaré sphere for structured Gaussian beams,
M A Alonso & M R Dennis, Optica 4 (2017) 476-86  (arXiv: 1612.06824)

[84] Proteins analysed as virtual knots,
K Alexander, A J Taylor & M R Dennis, Scientific Reports 7 (2017) 42300 (arXiv: 1611.06185)

[83]  Swings and roundabouts: Poincaré spheres for polarization and Gaussian beams,
M R Dennis & M A Alonso, Philosophical Transactions of the Royal Society A 375 (2017) 20150441   (Theme issue ‘Optical orbital angular momentum’; arXiv: 1611.10245)

[82] Editorial: Singular optics and topological photonics,
M Soskin, A V Boriskina, Y Chong, M R Dennis & A Desyatnikov, Journal of Optics 19 (2017) 010401 (editorial to special issue)

[81] Vortices, natural and deliberate,
M V Berry & M R Dennis, in “Roadmap on structured light”,
H Rubinsztein-Dunlop & A Forbes, eds, Journal of Optics 19 (2017) 013001

2016

[80] Weaving knotted vector fields with tunable helicity,
H Kedia, D Foster, M R Dennis & W T M Irvine, Physical Review Letters 117 (2016) 274501   (arXiv: 1610.02463)

[79] Vortex knots in tangled quantum eigenfunctions,
A J Taylor & M R Dennis, Nature Communications 7 (2016) 12346 (arXiv:1608.00909)

[78] Generation and application of Bessel beams in electron microscopy,
V Grillo, J Harris, G C Gazzadi, R Balboni, E Mafakheri, M R Dennis, S Frabboni,
R W Boyd & E Karimi, Ultramicroscopy 166 (2016) 48-60 (arXiv: 1505.07815)

[77] Direct measurement of the extraordinary optical momentum using a nano-cantilever,
M Antognozzi, S Simpson, R Harniman, J Senior, R Hayward, H Hoerber, M R Dennis, A Y Bekshaev, K Y Bliokh & F Nori, Nature Physics 12 (2016) 731-5 (arXiv: 1506.04248)

2015

[76] Nodal areas in coherent beams,
G L Ruane, G A Swartzlander, S Slussarenko, L Marrucci & M R Dennis,
Optica 2 (2015) 147-50 (arXiv: 1312.3983)

2014

[75] Geometry and scaling of tangled vortex lines in three-dimensional random wave fields,
A J Taylor & M R Dennis, Journal of Physics A 47 (2014) 465101 (arXiv: 1410.0383)

[74] Eigenpolarizations for giant transverse optical beam shifts,
J B Götte, W Löffler & M R Dennis, Physical Review Letters 112 (2014) 233901
(arXiv: 1401.5505)

[73] Generation of non-diffracting electron Bessel beams,
V Grillo, E Karimi, G C Gazzadi, S Frabboni, M R Dennis, & R W Boyd,
Physical Review X 4 (2014) 011013

2013

[72] Propagation-invariant beams with quantum pendulum spectra: from Bessel beams to Gaussian beam-beams,
M R Dennis & J D Ring, Optics Letters 38 (2013) 3325-8 (arXiv: 1307:7180)

[71] Limits to superweak amplification of beam shifts,
J B Götte & M R Dennis, Optics Letters 38 (2013) 2295-7 (arXiv: 1303.5038)

[70] Singular values, nematic disclinations, and emergent biaxiality,
S Čopar, M R Dennis, R D Kamien & S Žumer, Physical Review E 87 (2013) 050504(R)   (arXiv: 1302.3159)

[69] Incomplete Airy beams: finite energy from a sharp spectral cutoff,
J D Ring, C J Howls & M R Dennis, Optics Letters 38 (2013) 1639-41

[68] Super-oscillatory optical needle,
E T F Rogers, S Savo, J Lindberg, T Roy, M R Dennis & N I Zheludev,
Applied Physics Letters 102 (2013) 031108

[67] Beam shifts for pairs of plane waves,
M R Dennis & J B Götte, Journal of Optics 15 (2013) 014015
(Special issue “Beam shifts”)

2012

[66] Topological aberration of optical vortex beams: determining dielectric interfaces by optical singularity shifts,
M R Dennis & J B Götte, Physical Review Letters 109 (2012) 183903   (arXiv: 1205.6457)

[65] Spontaneous knotting of self-trapped waves,
A S Desyatnikov, D Buccoliero, M R Dennis & Y S Kivshar,
Scientific Reports 2 (2012) 771.1-7

[64] Auto-focusing and self-healing of Pearcey beams,
J D Ring, J Lindberg, A Mourka, M Mazilu, K Dholakia, & M R Dennis,
Optics Express 20 (2012) 18955-66

[63] Generalized shifts and weak values for polarization components of reflected light beams,
J B Götte & M R Dennis, New Journal of Physics 14 (2012) 073016 (arXiv: 1204.0315)

[62] The analogy between optical beam shifts and quantum weak measurements,
M R Dennis & J B Götte, New Journal of Physics 14 (2012) 073013 (arXiv: 1204.0327)

[61] Aberration-like cusped focusing in the post-paraxial Talbot effect,
J D Ring, J Lindberg, C J Howls & M R Dennis, Journal of Optics 14 (1012) 075702
(arXiv: 1204.5994)

[60] Reconnections of wave vortex lines,
M V Berry & M R Dennis, European Journal of Physics 33 (2012) 723-31

[59] A super-oscillatory lens optical microscope for subwavelength imaging,
E T F Rogers, J Lindberg, T Roy, S Savo, J E Chad, M R Dennis & N I Zheludev,
Nature Materials 11 (2012) 432-35

2011

[58] Paraxial and nonparaxial polynomial beams and the analytic approach to propagation,
M R Dennis, J B Götte, R P King, M A Morgan & M A Alonso,
Optics Letters 36 (2011) 4452-4   (arXiv: 1108.5906)

[57] Relativistic electron vortex beams: angular momentum and spin-orbit interaction,
K Y Bliokh, M R Dennis & Franco Nori, Physical Review Letters 107 (2011) 174802
(arXiv:1105.0331)

[56] Fermionic out-of-plane structure of polarization singularities,
M R Dennis, Optics Letters 36 (2011) 3765-7  (arXiv: 1108.5759)

[55] Knotted and tangled threads of darkness in light beams,
M J Padgett, K O’Holleran, R P King & M R Dennis, Contemporary Physics 52 (2011) 265-79

[54] All-optical discrete vortex switch,
A S Desyatnikov, M R Dennis & A Ferrando, Physical Review A 83 (2011) 063822

[53] Stream function for optical energy flow,
M V Berry & M R Dennis, Journal of Optics 13 (2011) 064004
(special issue ‘Optical Angular Momentum’)

[52] Weak value distributions for spin 1/2,
M V Berry, M R Dennis, B McRoberts & P Shukla, Journal of Physics A 44 (2011) 205301

[51] Entangled optical vortex links,
J Romero, J Leach, B Jack, M R Dennis, S Franke-Arnold, S M Barnett & M J Padgett,
Physical Review Letters 106 (2011) 100407

2010

[50] Gaussian random wavefields and the ergodic mode hypothesis,
M R Dennis, Chapter 4 in New Directions in Linear Acoustics and Vibration: Quantum Chaos, Random Matrix Theory and Complexity, M Wright and R Weaver eds,
Cambridge University Press (2010) pp 59-76 (Publisher homepage)

[49] Suppression of collapse for spiralling elliptic solitons,
A S Desyatnikov, D Buccoliero, M R Dennis & Y S Kivshar
Physical Review Letters 104 (2010) 053902

[48] Isolated optical vortex knots,
M R Dennis, R P King, B Jack, K O’Holleran & M J Padgett
Nature Physics 6 (2010) 118-21

2009

[47] Optical vortices,
K O’Holleran, M R Dennis & M J Padgett,
Chapter 7 in Tutorials in Complex Photonic Media, M Noginov, M W McCall, G Dewar & N I Zheludev eds, SPIE Press, Bellingham WA (2009) pp 118-21 (Publisher homepage)

[46] Methodology for imaging the 3D structure of singularities in scalar and vector optical fields,
K O’Holleran, F Flossmann, M R Dennis & M J Padgett
Journal of Optics A 11 (2009) 094020 (special issue ‘Singular Optics’)

[45] On the Burgers vector of a wave dislocation,
M R Dennis, Journal of Optics A 11 (2009) 094002
(special issue ‘Singular Optics,’ arXiv: 0905.0111)

[44] Singular Optics: More ado about nothing,
M R Dennis, Y S Kivshar, M S Soskin & G A Swartzlander Jr,
Journal of Optics A 11 (2009) 090201
(editorial for special issue ‘Singular Optics’)

[43] Near integrable systems,
E Bogomolny, M R Dennis & R Dubertrand, Journal of Physics A 42 (2009) 335102
(arXiv:0902.2089)

[42] Singular Optics: Optical Vortices and Polarization Singularities,
M R Dennis, K O’Holleran & M J Padgett, Progress in Optics 53 (2009) 293-363

[41]  Topology of light’s darkness,
K O’Holleran, M R Dennis & M J Padgett, Physical Review Letters 102 (2009) 143902

[40] Density and correlation functions of vortex and saddle points in open billiard
systems,
R Höhmann, U Kuhl, H-J Stöckmann, J-D Urbina, M R Dennis
Physical Review E 79 (2009) 016203 (arXiv: 0808.2945)

[39] Natural superoscillations in monochromatic waves in D dimensions,
M V Berry & M R Dennis, Journal of Physics A 42 (2009) 022003

2008

[38] Superoscillation in speckle patterns,
M R Dennis, A C Hamilton & J Courtial, Optics Letters 33 (2008) 2976-8
(arXiv: 0810.1948)

[37] Polarization singularity anisotropy: determining monstardom,
M R Dennis, Optics Letters 33 (2008) 2572-4 (arXiv: 0810.2002)

[36] Polarization singularities in 2D and 3D speckle fields,
F Flossmann, K O’Holleran, M R Dennis & M J Padgett,
Physical Review Letters 100 (2008) 203902

[35] Boundary-condition-varying circle billiards and gratings: the Dirichlet singularity,
M V Berry & M R Dennis, Journal of Physics A 41 (2008) 135203 (journal page)

[34] Fractality of light’s darkness,
K O’Holleran, M R Dennis, F Flossmann & M J Padgett,
Physical Review Letters 100 (2008) 053902

[33] Probability density of the multipole vectors for a Gaussian cosmic microwave background,
M R Dennis & K Land, Monthly Notices of the Royal Astronomical Society 383 (2008) 424-34   (arXiv: 0704.3657)

2007

[32] Poincaré sphere representation for the twist of phase singularities and its application to optical vortex metrology for fluid mechanical analysis,
W Wang, M R Dennis, R Ishijima, T Yokozeki, A Matsuda, M Takeda & S G Hanson,
Optics Express 15 (2007) 11008-19

[31] The plasmon Talbot effect,
M R Dennis, N I Zheludev & F J Garcia de Abajo, Optics Express 15 (2007) 9692-700
(arXiv: 0706.1439)

[30] Nodal densities of planar gaussian random waves,
M R Dennis, European Physical Journal – Special Topics 145 (2007) 191-210
(issue devoted to Chladni’s 250th anniversary)

[29] A three-dimensional degree of polarization based on Rayleigh scattering,
M R Dennis, Journal of the Optical Society of America A 24 (2007) 2065-9
(arXiv: physics/0702105)

[28] Topological events on wave dislocation lines: birth and death of loops, and reconnection,
M V Berry & M R Dennis, Journal of Physics A 40 (2007) 65-74

2006

[27] Stokes parameters in the unfolding of an optical vortex through a birefringent crystal,
F Flossmann, U T Schwarz, M Maier & M R Dennis, Optics Express 14 (2006) 11402-11

[26] Illustrations of optical vortices in three dimensions,
K O’Holleran, M R Dennis & M J Padgett,
Journal of the European Optical Society – Rapid Publications 1 (2006) 06008

[25] Rows of optical vortices from elliptically perturbing a high-order beam,
M R Dennis, Optics Letters 31 (2006) 1325-7 (arXiv: physics/0602066)

[24] Topology of optical vortex lines formed by the interference of three, four, and five plane waves,
K O’Holleran, M J Padgett & M R Dennis, Optics Express 14 (2006) 3039-44

[23] Angular momentum of optical vortex arrays,
J Courtial, R Zambrini, M R Dennis & M Vasnetsov, Optics Express 14 (2006) 938-49

2005

[22] Polarization singularities from unfolding an optical vortex through a birefringent crystal,
F Flossmann, U T Schwarz, M Maier & M R Dennis, Physical Review Letters 95 (2005)
253901

[21] Geometry of Călugăreanu’s theorem,
M R Dennis & J H Hannay, Proceedings of the Royal Society of London A 461 (2005) 3245-54
(arXiv: math-ph/0503012)

[20] Vortex knots in light,
J Leach, M R Dennis, J Courtial & M J Padgett, New Journal of Physics 7 (2005) 55.1-11
(arXiv: physics/0411121)

[19] Correlations between Maxwell’s multipoles for Gaussian random functions on the sphere,
M R Dennis, Journal of Physics A 38 (2005) 1653-8
(arXiv: math-ph/0410004)

2004

[18] Knotted threads of darkness,
J Leach, M R Dennis, J Courtial & M J Padgett, Nature 432 (2004) 165

[17] Polarization singularities in the clear sky,
M V Berry, M R Dennis & R L Lee Jr, New Journal of Physics 6 (2004) 162.1-14

[16] Canonical representation of spherical functions: Sylvester’s theorem, Maxwell’s multipoles and Majorana’s sphere,
M R Dennis, Journal of Physics A 37 (2004) 9487-500 (arXiv: math-ph/0408046)

[15] Local phase structure of wave dislocation lines: twist and twirl,
M R Dennis, Journal of Optics A 6 (2004) S202-8
(special issue ‘Singular Optics,’ arXiv: physics/0309069)

[14] Quantum cores of optical phase singularities,
M V Berry & M R Dennis, Journal of Optics A 6 (2004) S178-80
(special issue ‘Singular Optics’)

[13] “The plurality of optical singularities,”
Michael Berry, Mark Dennis & Marat Soskin, Journal of Optics A 6 (2004) S155-6
(editorial for special issue ‘Singular Optics’)

[12] Geometric interpretation of the 3-dimensional coherence matrix for nonparaxial polarization,
M R Dennis, Journal of Optics A 6 (2004) S26-31
(special issue ‘Polarization Optics,’ arXiv: physics/0309019)

[11] Black polarization sandwiches are square roots of zero,
M V Berry & M R Dennis, Journal of Optics A 6 (2004) S24-5
(special issue ‘Polarization Optics’)

2003

[10] Braided nodal lines in wave superpositions,
M R Dennis, New Journal of Physics 5 (2003) 134.1-8
(arXiv: physics/0307139)

[9] Correlations and screening of topological charges in Gaussian random fields,
M R Dennis, Journal of Physics A 36 (2003) 6611-28
(arXiv: math-ph/0302024)

[8] The optical singularities of birefringent dichroic chiral crystals,
M V Berry & M R Dennis, Proceedings of the Royal Society of London A 459 (2003) 1261-92

[7] Saddle points in the chaotic analytic function and Ginibre characteristic polynomial,
M R Dennis & J H Hannay, Journal of Physics A 36 (2003) 3379-84
(special issue ‘Random Matrix Theory,’ arXiv: nlin.CD/0209056, )

2002

[6] Polarization singularities in paraxial vector fields: morphology and statistics,
M R Dennis, Optics Communications 213 (2002) 201-21

2001

[5] Knotting and unknotting of phase singularities: Helmholtz waves, paraxial waves and waves in 2+1 spacetime,
M V Berry & M R Dennis, Journal of Physics A 34 (2001) 8877-88

[4]  Knotted and linked phase singularities in monochromatic waves,
M V Berry & M R Dennis, Proceedings of the Royal Society of London A 457 (2001) 2251-63

[3] Phase critical point densities in planar isotropic random waves,
M R Dennis, Journal of Physics A 34 (2001) L297–L303

[2] Polarization singularities in isotropic random vector waves,
M V Berry & M R Dennis, Proceedings of the Royal Society of London A 457 (2001) 141-55

2000

[1] Phase singularities in isotropic random waves,
M V Berry & M R Dennis, Proceedings of the Royal Society of London A 456 (2000) 2059-79

Books etc :

 The Princeton Companion to Applied Mathematics,
N J Higham, M R Dennis, P Glendinning, P A Martin, F Santosa & J Tanner, editors,
Princeton University Press, 2015.  Wrote articles including Tensors & Manifolds,       Invariants & Conservation Laws, Maxwell’s equations and Dirac equation.
(Publisher website)

Topological singularities in wave fields,
Ph D thesis, Bristol University 2001

Other Publications, including Conference Proceedings :

[c20]  Supervisor’s forward to
A J Taylor Analysis of Quantised Vortex Tangle, Springer Thesis Series, 2017.
My notes on hyperspherical harmonics were included as Appendix A1.

[c19] Beam shifts to reflected light beams and their axial structure,
M R Dennis & J B Götte, SPIE Proceedings 9441 (2014) 94410M
(19th Polish-Slovak-Czech Optical Conference on Wave and Quantum Aspects of Contemporary Optics)

[c18] Editorial to Special Issue on Singular Optics,
A S Desyatnikov, T A Fadeyeva & M R Dennis, Journal of Optics 15 (2013) 040201

[c17]  “Weaving dark threads in light beams into knots and links,
M R Dennis & R P King, in Experience-centered Approach and Visuality in the Education of
Mathematics and Physics,
 J Barallo, M Budin, A Durity, F Kristof, S Jablan,
A Klingne Takaks, L Radovic, R Sazdanovic, E Stettner eds, published by Kaposvar
University, Hungary (2012), pp 100-2.

[c16] Probing quantum cores of optical vortices with atoms,
J B Goette & M R Dennis, SPIE Proceedings 6950 (2011) 6950-0U
(Complex Light and Optical Forces V)

[c15] Scalar Goos-Haenchen shift for Robin boundary conditions,
M R Dennis & J B Goette, SPIE Proceedings 6950 (2011) 6950-0J
(Complex Light and Optical Forces V)

[c14]  Quantum phases: 50 years of the Aharonov-Bohm effect and 25 years of the
Berry Phase,
Mark Dennis, Sandu Popescu and Lev Vaidman, Journal of Physics A 43 (2010) 350301,
Forward to Special Issue

[c13] Topological configurations of optical phase singularities,
M R Dennis, Topologica 2 (2009) 007

[c12] Topology of generic polarization singularities in birefringent crystals,
U T Schwarz, F Flossmann & M R Dennis, Topologica 2 (2009) 006

[c11] Natural superoscillation of random functions in one and more dimensions,
M R Dennis & J Lindberg, SPIE Proceedings 7394 (2009) 73940A
(Plasmonics: Metallic Nanostructures and Their Optical Properties VII)

[c10] Concerning the path of light upon total reflection,
U T Schwarz and M R Dennis, Journal of Optics A 11 (2009) 090401,
special issue ‘Singular Optics,’ translation of
H Wolter, “Zur Frage des Lichtweges bei totalreflexion,”
Zeitschrift fur Naturforschung 5a (1950) 278-83,

[c9] Metamaterials: A cat’s eye for all directions,
M R Dennis, News & Views in Nature Materials, 8 (2009) 613-4

[c8] Paraxial and non-paraxial self-imaging of band-limited waves,
J Lindberg & M R Dennis, summary of presentation at Koli Workshop on Partial
Electromagnetic Coherence and 3D Polarization, Koli, Finland, May 24-27, 2009.
Published by University of Joensuu, Department of Physics and Mathematics, Finland,
2009, A T Friberg, J Turunen, J Tervo eds, pp62-3

[c7] Skylight polarization maps and three-dimensional scattering,
M R Dennis, summary of invited lecture at Koli Workshop on Partial Electromagnetic
Coherence and 3D Polarization, Koli, Finland, May 24-27, 2009.
Published by University of Joensuu, Department of Physics and Mathematics, Finland,
2009, A T Friberg, J Turunen, J Tervo eds, pp36-7

[c6] The fractal shape of speckled darkness,
M R Dennis, K O’Holleran & M J Padgett, SPIE Proceedings 6905 (2008) 69050C
(Complex Light and Optical Forces II)

[c5] Fluid mechanics measurement based on the anisotropic core structure of pseudophase
singularities in analytic signal representation of speckle pattern,
W Wang, M R Dennis, R Ishijima, T Yokozeki, A Matsuda, S G Hanson & M Takeda,
SPIE Proceedings 6616 (2007) 66160W (Optical Measurement Systems for Industrial Inspection V)

[c4]  The topology of vortex lines in light beams,
M J Padgett, K O’Holleran, J Leach, J Courtial & M R Dennis, in Topology in Ordered Phases:
Proceedings of the 1st International Meeting on TOP 2005 Sapporo, Japan 7-10 March 2005
,
S Tanda, T Matsuyama, M Oda, Y Asano, K Yakubo eds, World Scientific, pp 287-294.

[c3] Polarization singularities in paraxial and nonparaxial fields,
M R Dennis & M V Berry, summary of oral presentation at ICO Topical Meeting on
Polarization Optics, Polvijärvi, Finland, June 30-July 3, 2003.
Published in Department of Physics, Collected Papers 8, 2003, University of Joensuu,
Finland, A A Friesem, J Turunen eds, p20.

[c2] The singularities of crystal optics,
M V Berry & M R Dennis, summary of invited lecture by M V Berry at ICO Topical
Meeting on Polarization Optics, Polvijärvi, Finland, June 30-July 3, 2003.
Published in Department of Physics, Collected Papers 8, 2003, University of Joensuu,
Finland, A A Friesem, J Turunen eds, pp18-19.

[c1]  Local Properties and statistics of phase singularities in generic wavefields,
Mark Dennis, SPIE Proceedings 4403 (2001) 13-23
(Second International Conference on Singular Optics (Optical Vortices): Fundamentals and Applications)