We used newly developed experimental methods to collect educational video clips of electromagnetic waves propagating at the speed of light. The terahertz frequency waves were generated and detected in LiNbO3 crystals structured to reproduce classic optical geometries and experiments, such as two-slit interference and diffraction from a grating. Direct visualization of the phase fronts as the electromagnetic pulses propagate, reflect, diffract, and interfere helps develop intuition and understanding about the fundamental behavior of light and waves. We believe these videos will be a valuable addition to lectures on introductory optics and physics, because they bring contemporary research to the classroom and provide clear and direct experimental demonstrations of light and wave behavior.
REFERENCES
1.
Y. J.
Dori
and J.
Belcher
, “How does technology-enabled active learning affect undergraduate students’ understanding of electromagnetism concepts?
,” J. Learn. Sci.
14
, 243
–279
(2005
). 2.
Computational Electrodynamics: The Finite-Difference Time-Domain Method
, 3rd ed., edited by A.
Taflove
and S. C.
Hagness
(Artech House
, Boston, MA
, 2005
). 3.
M.
Sipos
and B. G.
Thompson
, “Electrodynamics on a grid: The finite-difference time-domain method applied to optics and cloaking
,” Am. J. Phys.
76
, 464
–469
(2008
). 4.
D. W.
Ward
, E. R.
Statz
, N. S.
Stoyanov
, and K. A.
Nelson
, “Simulation of Phonon-Polariton Propagation in Ferroelectric LiNbO3 Crystals
,” in Engineered Porosity for Microphotonics and Plasmonics, MRS Symposium Proceedings
, 2003
, Vol. 762
, pp. C11
–60
1
–6
. 5.
J. D.
Joannopoulos
, S. G.
Johnson
, J. N.
Winn
, and R. D.
Meade
, Photonic Crystals, Molding the Flow of Light
, 2nd ed. (Princeton U. P.
, Princeton, NJ
, 2008
), Chap. 2. 6.
D.
Auston
and M.
Nuss
, “Electrooptic generation and detection of femtosecond electrical transients
,” IEEE J. Quantum Electron.
24
, 184
–197
(1988
). 7.
D.
Grischkowsky
, S.
Keiding
, M.
van Exter
, and Ch.
Fattinger
, “Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors
,” J. Opt. Soc. Am. B
7
, 2006
–2015
(1990
). 8.
Q.
Wu
, T. D.
Hewitt
, and X.-C.
Zhang
, “Two-dimensional electro-optic imaging of THz beams
,” Appl. Phys. Lett.
69
, 1026
–1028
(1996
). 9.
Z.
Jiang
and X.-C.
Zhang
, “Terahertz imaging via electrooptic effect
,” IEEE Trans. Microwave Theory Tech.
47
, 2644
–2650
(1999
). 10.
R. M.
Koehl
, S.
Adachi
, and K. A.
Nelson
, “Direct visualization of collective wavepacket dynamics
,” J. Phys. Chem. A
103
, 10260
–10267
(1999
). 11.
T.
Feurer
, N. S.
Stoyanov
, D. W.
Ward
, J. C.
Vaughan
, E. R.
Statz
, and K. A.
Nelson
, “Terahertz polaritonics
,” Annu. Rev. Mater. Res.
37
, 317
–350
(2007
). 12.
T.
Feurer
, N. S.
Stoyanov
, D. W.
Ward
, and K. A.
Nelson
, “Direct visualization of the Gouy phase by focusing phonon polaritons
,” Phys. Rev. Lett.
88
, 257402
–1
(2002
). 13.
T.
Feurer
, J. C.
Vaughan
, and K. A.
Nelson
, “Spatiotemporal coherent control of lattice vibrational waves
,” Science
299
, 374
–377
(2003
). 14.
K.-H.
Lin
, C. A.
Werley
, and K. A.
Nelson
, “Generation of multicycle THz phonon-polariton waves in a planar waveguide by tilted optical pulse fronts
,” Appl. Phys. Lett.
95
, 103304
(2009
). 15.
N. S.
Stoyanov
, T.
Feurer
, D. W.
Ward
, and K. A.
Nelson
, “Integrated diffractive THz elements
,” Appl. Phys. Lett.
82
, 674
–676
(2002
). 16.
N. S.
Stoyanov
, D. W.
Ward
, T.
Feurer
, and K. A.
Nelson
, “Terahertz polariton propagation in patterned materials
,” Nature Mater.
1
, 95
–98
(2002
). 17.
N. S.
Stoyanov
, T.
Feurer
, D. W.
Ward
, E. R.
Statz
, and K. A.
Nelson
, “Direct visualization of a polariton resonator in the THz regime
,” Opt. Express
12
, 2387
–2396
(2004
). 18.
P.
Peier
, S.
Pilz
, and T.
Feurer
, “Time-resolved coherent imaging of a THz multilayer response
,” J. Opt. Soc. Am. B
26
, 1649
–1655
(2009
). 19.
P.
Peier
, H.
Merbold
, V.
Pahinin
, K. A.
Nelson
, and T.
Feurer
, “Imaging of THz waves in 2D photonic crystal structures embedded in a slab waveguide
,” New J. Phys.
12
, 013014
(2010
). 20.
P.
Peier
, S.
Pilz
, F.
Müller
, K. A.
Nelson
, and T.
Feurer
, “Analysis of phase contrast imaging of terahertz phonon-polaritons
,” J. Opt. Soc. Am. B
25
, B70
–B75
(2008
). 21.
Q.
Wu
, C. A.
Werley
, K.-H.
Lin
, A.
Dorn
, M. G.
Bawendi
, and K. A.
Nelson
, “Quantitative phase contrast imaging of THz electric fields in a dielectric waveguide
,” Opt. Express
17
, 9219
–9225
(2009
). 22.
C. A.
Werley
, Q.
Wu
, K.-H.
Lin
, C. R.
Tait
, A.
Dorn
, and K. A.
Nelson
, “Comparison of phase-sensitive imaging techniques for studying terahertz waves in structured LiNbO3
,” J. Opt. Soc. Am. B
27
, 2350
–2359
(2010
). 23.
D.
Strickland
and G.
Mourou
, “Compression of amplified chirped optical pulses
,” Opt. Commun.
56
, 219
–221
(1985
). 24.
25.
Y. R.
Shen
, The Principles of Nonlinear Optics
(John Wiley & Sons
, Hoboken, NJ
, 2003
). 26.
T. P.
Dougherty
, G. P.
Wiederrecht
, and K. A.
Nelson
, “Impulsive stimulated Raman scattering experiments in the polariton regime
,” J. Opt. Soc. Am.
9
, 2179
–2189
(1992
). 27.
D. W.
Ward
, E. R.
Statz
, and K. A.
Nelson
, “Fabrication of polaritonic structures in LiNbO3 and LiTaO3 using femtosecond laser machining
,” Appl. Phys. A
86
, 49
–54
(2007
). 28.
C.
Mack
, Fundamental Principles of Optical Lithography: The Science of Microfabrication
(John Wiley & Sons
, Hoboken, NJ
, 2007
). 29.
H. J.
Eichler
, P.
Günter
, and D. W.
Pohl
, Laser-Induced Dynamic Gratings
(Springer-Verlag
, Berlin
, 1986
). 30.
G. R.
Fowles
, Introduction to Modern Optics
, 2nd ed. (Dover Publications
, Mineola, NY
, 1989
), Chap. 5. 31.
R.
Resnik
, D.
Halliday
, and K. S.
Krane
, Phyiscs
, 5th ed. (John Wiley & Sons
, New York
, 2002
). 32.
We rederived the Fresnel Kirchhoff formula following the derivation in Ref. 30, but in two dimensions instead of three because wave behavior in the waveguide follows two-dimensional behavior. Making the additional assumption that plane waves are incident on the aperture, the Green’s function is G(x,z) = −Y0(2πρ/λ)[x/ρ + 1] with Y0 a Bessel function of the second kind and ρ2 = x2 + z2 the radius in two dimensions. The E -field can then be calculated by performing a numerical convolution of the aperture function with the Green’s function E(x,z,t) = [A(z) ⊗ G(x,z)]exp(−iωt).
33.
34.
L. G.
Gouy
, “Sur une propriété nouvelle des ondes lumineuses
,” C. R. Acad. Sci. Paris
110
, 1251
–1253
(1890
). 35.
N. J.
Cronin
, Microwave and Optical Waveguides
(Institute of Physics
, Philadelphia, PA
, 1995
). 36.
C.
Yang
, Q.
Wu
, J.
Xu
, K. A.
Nelson
, and C. A.
Werley
, “Experimental and theoretical analysis of THz-frequency, direction-dependent, phonon polariton modes in a subwavelength, anisotropic slab waveguide
,” Opt. Express
18
, 26351
–26364
(2010
). 37.
nelson.mit.edu/ under “movietheater.”
© 2012 American Association of Physics Teachers.
2012
American Association of Physics Teachers
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