Abstract

We report fabrication of a THz phonon-polariton resonator in a single crystal of LiNbO3 using femtosecond laser machining with high energy pulses. Fundamental and overtone resonator modes are excited selectively and monitored through spatiotemporal imaging. The resonator is integrated into a single solid-state platform that can include THz generation, manipulation, readout and other functionalities.

© 2004 Optical Society of America

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References

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Appl. Phys. Lett.

N.S. Stoyanov, T. Feurer, D.W. Ward, and K.A. Nelson, "Integrated diffractive terahertz elements,�?? Appl. Phys. Lett. 82, 674-676 (2003).
[CrossRef]

Chem. Phys. Lett.

A.J. Markels, A. Roitberg, and H.C. Heilweil, "Pulsed terahertz spectroscopy of DNA, bovine serum albumin and collagen between 0.1 and 2.0 THz,�?? Chem. Phys. Lett. 320, 42-48 (2000)
[CrossRef]

IEEE J. Quant. Electron.

J.E. Pedersen and S.R. Keiding, "THz time-domain spectroscopy of nonpolar liquids,�?? IEEE J. Quant. Electron. 28, 2518-2522 (1992)
[CrossRef]

IEEE Trans. Antennas Propag.

K.S. Yee, IEEE Trans. Antennas Propag. 14, 302 (1966)

J. Chem. Phys.

R.M. Koehl, S. Adachi, and K.A. Nelson, "Real-space polariton wave packet imaging,�?? J. Chem. Phys. 110, 1317-1320 (1999)
[CrossRef]

J. Opt. Soc. Am

W.D. Montogomery, �??Self imaging objects of infinite aperture,�?? J. Opt. Soc. Am., 57, 772-778 (1967)
[CrossRef]

J. Opt. Soc. Am. B

J. Opt. Soc. Am. B.

T.P. Dougherty, G.P. Wiederrecht, and K.A. Nelson, "Impulsive stimulated Raman scattering experiments in the polariton regime,�?? J. Opt. Soc. Am. B. 9, 2179-2189 (1992).
[CrossRef]

J. Phys. Chem A

M.C. Beard, G.M. Turner, and C.A. Schmuttenmaer, "Measuring intramolecular charge transfer via coherent generation ot THz radiation,�?? J. Phys. Chem A 106, 878-883 (2002)
[CrossRef]

Meas. Sci. Technol.

C.B. Schaffer, A. Brodeur, and E. Mazur, "Laser-induced breakdown and damage in bulk transparent materials induced by tightly-focused femtosecond laser pulses,�?? Meas. Sci. Technol. 12, 1784-1794 (2001)
[CrossRef]

MRS Symposium Proceedings

D.W. Ward, E. Statz, N. Stoyanov, and K.A. Nelson, "Simulation of Phonon-Polariton Propagation in Ferroelectric LiNbO3,�?? in Engineered Porosity for Microphotonics and Plasmonics: MRS Symposium Proceedings, Vol. 762, R. Wehrspohn, F. Garcial-Vidal, M. Notomi, and A. Scherer, ed. (Materials Research Society, Pittsburgh, PA, 2003), pp.C11.60.1-6.

D.W. Ward, E. Statz, J.D. Beers, N. Stoyanov, T. Feurer, R.M. Roth, R.M. Osgood, and K.A. Nelson, "Phonon- Polariton Propagation, Guidance, and Control in Bulk and Patterned Thin Film Ferroelectric Crystals,�?? in Ferroelectric Thin Films XII: MRS Symposium Proceedings, Vol. 797, A. Kingon, S. Hoffmann-Eifert, I.P. Koutsaroff, H. Funakubo, and V. Joshi, ed. (Materials Research Society, Pittsburgh, PA, 2003), pp. W5.9.1-6. /condmat/ 0401049

Nature Materials

N.S. Stoyanov, D.W.Ward, T. Feurer, and K.A. Nelson, "Terahertz polariton propagation in patterned materials,�?? Nature Materials, 1, 95-98 (2002)
[CrossRef]

Opt. Lett.

Philos. Mag.

H.F. Talbot, "Facts relating to optical science, No. IV,�?? Philos. Mag. 9, 401-407 (1836)

Phys. Rev. B

T. Qiu and M. Maier, "Long-distance propagation and damping of low-frequency phonon polaritons in LiNbO3,�?? Phys. Rev. B 56, R5717-R5720 (1997)
[CrossRef]

Phys. Rev. Lett.

B. B. Hu, X.-C. Zhang, and D.H. Auston, "Terahertz radiation induced by subband-gap femtosecond optical excitation of GaAs,�?? Phys. Rev. Lett. 67, 2709-2712 (1991)
[CrossRef] [PubMed]

K.P. Cheung, D.H. Auston, "Excitation of coherent phonon polaritons with femtosecond optical pulses,�?? Phys. Rev. Lett. 55, 2152-2155 (1985)
[CrossRef] [PubMed]

Science

T. Feurer, J.C. Vaughan, and K.A. Nelson, "Spatio temporal coherent control of lattice vibrational waves,�?? Science 299, 374-376 (2003)
[CrossRef] [PubMed]

Other

M. Bor Philos., K. Huang, Dynamical Theory of Crystal Lattices (Oxford Classic Texts, New York, 1988)

E.D. Palik, "Handbook of Optical Constants of Solids," (Academic Press, Orlando, 1985), pp. 695-702

A. Taflove and S.C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artec House, Boston, 2000)

Supplementary Material (2)

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Figures (6)

Fig. 1.
Fig. 1.

(a) Experimental setup used to generate and monitor narrow-band phonon polaritons inside the resonator. A phase mask (LHS illustration) or a third cylindrical lens (RHS) is used to project several optical interference fringes or a single line of excitation light onto the resonator, permitting generation of a selected harmonic or the fundamental frequency respectively. (b) Machined structure. The resonator is formed by the crystalline material between the two carved out rectangles. The distances indicated are approximate values. As evident, the resonator walls are not perfect and it turns out that the side surfaces are tilted by about 6 to 8 degrees due to the laser machining process. The air gaps also form resonators which may be coupled to the central crystalline resonator.

Fig. 2.
Fig. 2.

(a) Schematic illustration of the coupled system of resonators with tilted side surfaces. The excitation pulse (in red) passes through the center of the LiNbO3 resonator and generates two polariton waveforms (in green) propagating in opposite lateral direction with a forward component. (b) Calculated frequency response. The two modes observed in the experiments are indicated by two gray bars, where the width corresponds to the uncertainty in the measured frequency.

Fig. 3.
Fig. 3.

(a) A phonon-polariton response with approximately 80 µm wavelength has been generated inside the resonator. A well-defined standing wave and its confined oscillations at a frequency of (0.67±0.02) THz ((1.50±0.05) ps period) are clearly observed. (b) (1544 KB) Evolution of the polariton inside the resonator.

Fig. 4.
Fig. 4.

Each horizontal line is constructed from images at different time steps, such as those in Fig. 3, by averaging the signal along the resonator length where the signal extends.

Fig. 5.
Fig. 5.

(a) Line excitation inside the resonator and subsequent recurrences. As evident from the figure, recurrences occur on average every (3.9±0.4) ps. The dotted line between the last two images indicates that they are separated by two recurrence periods. (b) (1929 KB) Evolution of the polariton inside the resonator.

Fig. 6.
Fig. 6.

Each horizontal line is constructed from images at different time steps, such as those in Fig. 5, by averaging the signal along the resonator length where the signal extends.

Tables (1)

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Table 1. Values of parameters used in FDTD simulations.

Equations (6)

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2 Q ¯ j t 2 = ω ̿ T j 2 Q ¯ j Γ ̿ j Q ¯ j t + ε f ω ̿ T j 2 S ̿ j E ¯
P ¯ = j ε f ω ̿ T j 2 S ̿ j Q ¯ j + ε f ( ε ̿ 1 ) E ¯
E j t = 1 ε f ε ( ( × H ¯ ) j ε f ( ε 0 j ε j ) ω T j Q j t )
H j t = 1 μ f ( × E ¯ ) j
2 Q j t 2 = ω T j 2 Q j Γ j Q j t + ε f ( ε 0 j ε j ) ω T j E j + F ISRS
F ISRS = 1 2 N μ ε f ( α x ) E Laser 2

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