The interaction of THz phonon-polariton waves with
microstructures observed using quantitative, phasesensitive imaging
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Werley, Christopher A. et al. “The Interaction of THz Phononpolariton Waves with Microstructures Observed Using
Quantitative, Phase-sensitive Imaging.” IEEE, 2009. 1–2. ©
Copyright 2009 IEEE
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http://dx.doi.org/10.1109/ICIMW.2009.5324752
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Detailed Terms
The interaction of THz phonon-polariton waves with microstructures
observed using quantitative, phase-sensitive imaging
Christopher A. Werleya, Kebin Fanb, Andrew C. Strikwerdab, Qiang Wuc, Kung-Hsuan Lind,
Richard D. Averittb, and Keith A. Nelsona
a
Massachusetts Institute of Technology, Cambridge, MA 02139 USA
b
Boston University, Boston, MA 02215 USA
c
Nankai University, Tianjin 300457, P. R. China
d
Industrial Technology Research Institute South, Liujia Shiang 73445, Taiwan
I. INTRODUCTION AND BACKGROUND
P
HONON-polarition waves (PPWs) result from the
coupling of electromagnetic waves and optic phonons.
High amplitude THz frequency PPWs can be generated in the
ferroelectric crystal lithium niobate (LN) due to its large
electrooptic coefficients. These same coefficients also cause
the THz electric field to induce significant changes in the
crystal’s optical properties. Because of these characteristics and
the simplicity of material patterning with air gaps or metal
microstructures, it has been shown that LN slab waveguides
provide a particularly versatile platform for PPW generation,
manipulation, and detection [1]. Time-resolved imaging, used
to generate a movie of PPW propagation, has been a fruitful
detection technique because of the wealth of information
present when complete spatial and temporal evolution is
measured. Previous methods involved out-of-focus imaging
[1], which made it impossible to measure quantitative field
profiles. An additional drawback of the previous method was
that fabricated structures in the waveguide were blurry,
obscuring the interaction of the THz field with these structures.
We have adapted the technique of phase contrast imaging [2] to
enable high sensitivity, in-focus, quantitative measurement of
the THz field, E ( x, z , t ) .
II. RESULTS
The experimental setup is shown in fig 1a. The THz field
changes the index of refraction of the LN crystal, which
introduces a spatially dependent phase shift in the expanded
probe beam. To detect this phase shift, we must perform
phase-to-amplitude conversion, which is accomplished by a
phase plate located in the focal plane of a lens separated by 1f
from the sample. The phase plate introduces a λ/4 shift between
the 0th order beam and the light diffracted off of the THz wave,
which are spatially separated in this plane. When the 0th order
beam and the diffracted light recombine at the camera in the
image plane, they interfere, bringing about phase-to-amplitude
conversion.
Figure 1b shows one frame of a movie recorded using this
978-1-4244-5417-4/09/$26.00 ©2009 IEEE
technique, which shows the THz wave undergoing waveguide
dispersion as it propagates through a thin LN slab. By
extracting the THz field profile from each image in such a
movie and placing it in one row of a matrix, it is possible to
build up the full spatiotemporal evolution of the wave. The
two-dimensional Fourier transform of this matrix gives the
waveguide dispersion curve.
Figure 1c shows the
experimentally measured dispersion curve overlaid with
analytical theory. The figure shows the smooth response of the
imaging technique and the excellent agreement between
experiment and theory.
a
f1
dichroic
mirror
f1
f2
f2
camera
cyl.
lens
sample
blue
filter
phase
plate
diffracted
light
b
1.5
frequency (THz)
Abstract— We apply newly developed, phase-sensitive imaging
to enable sharply focused visualization of terahertz waves in
electro-optic media.
This approach allows quantitative
characterization of THz waves as they interact with
microstructures on or in the sample, yielding new insight into these
interactions.
c
1
0.5
0
0
Bulk LN
vacuum
waveguide modes
50
100
β (rad/mm)
Figure 1. The experimental setup is diagramed in
(a). (b) shows a typical snapshot from a movie
showing propagating THz fields acquired using
this setup. The THz propagates as waveguide
modes in the thin LN slab. In (c), the theoretical
dispersion curves for these modes are overlaid on
the experimentally measured ones.
150
In addition to looking at unstructured crystals like the one
shown in fig. 1b, the in-focus nature of phase contrast imaging
enables us to study structured crystals. One family of structures
involves air gaps, which can be cut into the LN with
femtosecond laser machining [3]. Because of the very large
index contrast between LN ( nTHz = 5.1 ) and air (n = 1), these
III. CONCLUSIONS
LN slabs are a versatile platform for THz generation,
detection, and control. The phase contrast technique enables in
–focus imaging and quantitative measurement of the THz field,
which makes possible a wide range of experiments studying the
interactions between THz fields and structured samples.
b
c
0.2
0.1
∆I/I0
structures are very effective for reflecting and guiding THz
waves. Figure 2a shows a THz wave propagating through one
such structure. In this “Y” coupler, part of the THz wave
(incident from the left) is guided down each arm of the Y, and
the two parts interfere at the intersection. The superimposed
wave is then guided down the stem of the Y. The clear
resolution of both the wave and the structure was not possible
using previous imaging techniques.
Another powerful way to control the field is to deposit metal
microstructures onto the crystal surface. Such structures have
previously been used to enhance electric fields and confine them
to spots smaller than the diffraction limit, as in bowtie antennas
[4], and to modify bulk material properties, as in metamaterials
[5]. Our imaging technique allows us to directly observe the
electric field of the THz wave as it interacts with these exciting
structures (fig, 2b,c).
We use finite difference time domain (FDTD) simulations to
design microstructures resonant at a design frequency, and
deposit them onto the surface of a thin LN slab. The evanescent
field of the waveguide mode interacts strongly with these
structures as the wave propagates down the crystal. Figure 2b
shows a single vertical stripe of electrically resonant
microstructures (shown in the inset, 40 µm on a side) which has
reflected most of a THz wave whose center frequency was tuned
to the microstructure resonance. Non-resonant THz waves
display only weak interactions with these structures.
Figure 2c shows a 200 GHz wave incident on a 200 µm tall
bowtie antenna with a 30 µm gap. As has been previously
demonstrated at visible frequencies [4], the antenna enhances
peak field strengths and localizes the field to a region much
smaller than the diffraction limit. Figure 2d shows a time-trace
of the field between the lobes of the antenna (blue) and above
the microstructure (green), clearly demonstrating that the
electric field is enhanced in the gap.
a
d
0
-0.1
-0.2
-0.3
0
bowtie tip
outside bowties
5
10
15
20
25
30
time (ps)
Figure 2. a-c show THz fields in structured and
patterned samples. a. A Y-coupler cut into a 50
µm thick LN slab. b. A vertical stripe of 40 µm
wide, electrically resonant gold microstructures
deposited on a 33 µm thick LN slab. c. A 200 µm
tall bowtie antenna with a 30 µm gap deposited on
a 33 µm thick LN slab showing field enhancement
in the gap. d. A time trace of the THz field given
by the image intensity above (green) and in (blue)
the bowtie gap, showing field enhancement.
REFERENCES
[1] T. Feurer et al, Annual Review of Materials Research 37, 317-350 (2007).
[2] Q. Wu et al, Opt. Express 17, 9219-9225 (2009).
[3] D. W. Ward et al, Appl. Phys. A 86, 49-54 (2007).
[4] E. Cubukcu et al., IEEE J Sel Top Quant 14, 1448-1461 (2008).
[5] W. J. Padilla et al., Phys. Rev. B 75, 041102(R) (2007).