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PUBLISHED ONLINE: 22 FEBRUARY 2009 | DOI: 10.1038/NPHOTON.2009.3

A metamaterial solid-state terahertz

phase modulator
Hou-Tong Chen1 *, Willie J. Padilla2, Michael J. Cich3, Abul K. Azad1, Richard D. Averitt4
and Antoinette J. Taylor1
Over the past two decades, terahertz time-domain spectroscopy1 and quantum-cascade lasers2 have been two of the
most important developments in terahertz science and technology. These technologies may contribute to a multitude of
terahertz applications that are currently under investigation
globally3. However, the devices and components necessary to
effectively manipulate terahertz radiation require substantial
development beyond what has been accomplished to date.
Here we demonstrate an electrically controlled planar hybrid
metamaterial device that linearly controls the phase of terahertz radiation with constant insertion loss over a narrow
frequency band. Alternatively, our device may operate as a
broadband terahertz modulator because of the causal relation
between the amplitude modulation and phase shifting. We
perform terahertz time-domain spectroscopy, in which our
hybrid metamaterial modulator replaces a commercial mechanical optical chopper, demonstrating comparable broadband
performance and superior high-speed operation.
The controllable properties of engineered metamaterials facilitate
novel opportunities for manipulating electromagnetic radiation4.
Electromagnetic phenomena achieved with metamaterials include
negative index of refraction5,6, super-resolution in optical
imaging7,8, and electromagnetic invisibility9. The resonant electromagnetic response originates from patterned metallic subwavelength structures, in which the dimensions can be appropriately
scaled to operate at terahertz frequencies10,11 where natural material
response is somewhat rare. As such, metamaterials provide the basis
for the construction of novel terahertz devices. Terahertz metamaterial devices have been demonstrated as state-of-the-art frequency-agile far-infrared lters12,13, all-optical switches and
modulators14,15, and perfect absorbers16,17. Room-temperature,
voltage-controlled metamaterial devices consisting of a single unit
cell layer in the propagation direction have also been shown and
are of particular interest here18,19.
Despite the rapid progress in terahertz technology generally, a
component largely unavailable as yet is an efcient terahertz
phase shifter. Its counterparts at microwave and optical frequencies
have many important applications, including, for example, phased
array antennas and high-speed Mach Zehnder modulators.
However these congurations are, in general, difcult to extend to
the terahertz regime. There have been a few attempts to demonstrate
terahertz phase shifters, including using semiconductor quantumwell structures at cryogenic temperatures20,21, or liquid crystals
with very low speed22. The single-layer planar hybrid metamaterial
phase modulator presented in this paper overcomes these shortcomings. Although phase shifting of terahertz radiation may be inferred

from our earlier work13,18, where frequency tuning of a metamaterial

resonance and amplitude modulation were reported, phase modulation was not explicitly discussed or explored. Here we present
the rst experimental demonstration of a room-temperature solidstate phase modulator at terahertz frequencies as well as an investigation of its potential applications. Our new device achieves a
voltage-controlled linear phase shift of p/6 radians at 16 V.
Moreover, the causal relation between amplitude switching and
phase shifting enables broadband modulation.
A single unit cell of the device is illustrated schematically
in Fig. 1a. Metallic electric split-ring resonators (SRRs)23 were
patterned to form a square array and connected by metal wires.
They were fabricated on a 1-mm-thick epitaxial n-doped GaAs
layer with an electron density of 2  1016 cm23 grown on an
intrinsic GaAs wafer. The SRRs and semiconductor form the
Schottky diode structure that can, upon application of an external
voltage, actively modify the depletion zone (see Supplementary
Information). The control of the carrier density in the depletion
zone permits tuning of the local dielectric properties near the
gaps of the SRRs. This results in changes of the transmission (amplitude, phase, or both) of the metamaterial device. The micro-fabrication of the device has been described previously18,19; an optical
microscopy image is shown in Fig. 1b. For this design, the SRR
gaps are located at the four outer corners and are directly connected
to the ohmic contact through the n-GaAs epilayer. This maximizes
depletion of electrons near the metamaterial gaps upon application
of bias voltage, which is essential to control the metamaterial resonances. In an earlier metamaterial switch18, the split gap was located
at the centre of an electric SRR and was surrounded by a closed
outer ring. This reduced the voltage available for effective charge
depletion within the split gap, which limited device performance.
(See Supplementary Information for further details of the device.)
Conventional terahertz time-domain spectroscopy24 (see
Supplementary Information) was used to characterize the device.
Resonances at 0.81 and 1.7 THz (driven by the electrical component
of the terahertz radiation as indicated in Fig. 1b) are obtained as
shown in Fig. 2a and b. The resonance at 0.81 THz arises from
the individual SRRs and is due to the inductivecapacitive coupling
of the circulating currents (Fig. 1c), while the resonance at 1.7 THz
originates from a collective dipolar resonance (Fig. 1d), where the
resonance frequency also depends on the SRR periodicity25. At
zero voltage bias the resonances are weak because carriers in the
substrate shunt the metamaterial capacitive gaps, thereby damping
the response. Under reverse bias voltage an increase in depletion
occurs, reducing the damping and causing an increase in oscillator
strength for both resonances. The depletion near the split gaps plays

Center for Integrated Nanotechnologies, Materials Physics & Applications Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545,
USA, 2 Department of Physics, Boston College, 140 Commonwealth Avenue, Chestnut Hill, Massachusetts 02467, USA, 3 Sandia National Laboratories,
MS1085, Albuquerque, New Mexico 87185, USA, 4 Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215,
USA; * e-mail: chenht@lanl.gov

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Figure 1 | Design of the electrically driven terahertz metamaterial phase

shifter. a, Schematic of device unit cell and its cross-section, indicating the
principle of operation. b, Optical microscopy image of the active area of the
device with gold thickness 200 nm, linewidth 4 mm, split gap spacing 2 mm,
outer dimension 36 mm, and period 50 mm. The polarization of the normally
incident terahertz radiation is also indicated. c,d, Numerical simulations of
surface current density excited from the inductivecapacitive (c) and
collective dipolar (d) resonances at 0.81 and 1.7 THz, respectively.

a critical role in restoring resonances, as illustrated in Fig. 1c and d

of the resonant surface current density.
In comparison to previously published results on metamaterial
switches18, this device has a higher modulation index of the transmission amplitude. At 16 V, the amplitude of the transmitted terahertz
electric eld at 0.81 THz, indicated by the dashed vertical line, has
decreased from t0V 0.56 to t16V 0.25, a change of 55% (intensity
change of 80%), as shown in Fig. 2a. This is an 83% performance
improvement over the earlier demonstration. The transmission amplitude at 1.7 THz has decreased from t0V 0.48 to t16V 0.30. Between
the two resonances the reverse voltage bias signicantly increases the
terahertz transmission amplitude. In short, the improved device performance results from more effective depletion of charge carriers in
the split gaps under an external voltage bias.
Voltage switching of the metamaterial device yields another
important functionalityphase shifting of the terahertz radiation.
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Amplitude modulation index

50.0 m

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Figure 2 | Electrically controllable terahertz transmission spectra.

a,b, Transmission amplitude (a) and phase spectra (b) at 0 V and reverse
bias voltages of 4 and 16 V. The solid vertical line indicates the frequencies
having a large phase shift and unchanged amplitude, and the dashed vertical
line indicates the frequencies having maximum amplitude switching and
minimum phase shifting. c, Voltage dependence of the phase shift at
0.89 THz and amplitude switching (modulation depth) at 0.81 THz.
The straight line is to guide the eye and indicates a linear dependence.

As shown in Fig. 2b, at 0.89 THz, indicated by the solid vertical line,
the phase of terahertz transmission is f16V 0.51 rad under a
reverse bias voltage of 16 V as compared to f0V 0.05 rad with no
voltage bias, resulting in a shift of Df 0.56 rad. The phase shift
occurs over a bandwidth of 23 GHz (that is, 0.8800.903 THz)
with a change in amplitude of less than 10% over this range. This
phase change occurs within a single metamaterial unit cell in the
propagation direction. A multi-layer phase shifter based on our
design would enable the ultimate goal of a 2p phase shifter.
Additionally, at the operational frequency of the phase shifter, the terahertz transmission amplitude is near 60% without consideration of
the substrate insertion loss and is almost independent of the applied
voltage bias. This is advantageous because the terahertz phase shifter
can operate with reasonably high and constant terahertz transmission
amplitude. The substrate insertion loss could be lowered with metamaterial impedance-matched layers26.
Various interconnect schemes would permit addressing individual
SRR elements, thus permitting application of, for example, a voltage
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Figure 3 | Broadband modulation of terahertz radiation. a, Time-domain

measurements of the terahertz modulation (differential) signal with a
square-wave voltage bias alternating between 0 and 16 V. The reference
terahertz signal is measured through a bare substrate using the terahertz
time-domain system with a mechanical chopper. b, After Fourier
transformation, the complex modulation in frequency domain is divided by
the reference so that the modulation amplitude spectrum is obtained. In the
frequency range roughly between the two resonances, the terahertz signal is
most effectively modulated.

gradient (and associated phase shift) to the array. This would allow for
real-time beam steering, focusing and other manipulations of terahertz
radiation for applications such as personnel screening in airports,
or locking a terahertz beam from a moving satellite to a specic
receiver. Therefore, it is important to characterize the phase shift,
Df(v) jfV(v) 2 f0V(v)j as a function of the applied bias voltage.
Figure 2c reveals a linear phase shift as a function of the bias voltage
over the range 016 V at 0.89 THz. Saturation sets in at higher
voltage as the resonance is restored, and because of a reduction in
the Schottky resistance resulting from increased leakage currents. In
Fig. 2c we also plot the voltage-dependent amplitude modulation
index, M jtV(v) t0V(v)j/t0V(v) at 0.81 THz, which reveals a
similar linear dependence. We note that the metamaterial device
directly manipulates terahertz waves. This is an important distinction
because alternative methods yield modulation during the terahertz
generation process27,28, that is, modulated sources. Thus our metamaterial device is a true terahertz component, and can be combined with
various terahertz sources such as backward wave oscillators or terahertz quantum-cascade lasers.
We now turn towards a demonstration of our metamaterial device as
a terahertz modulator by replacing a commercial modulator (that is, a
mechanical optical chopper) in a terahertz time-domain spectroscopic
system. Figure 2 indicates that amplitude switching and phase shifting in
our terahertz metamaterial device are inherently narrowbanda result
of the resonant nature of metamaterials. However, as shown in Fig. 2a
150

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Figure 4 | Terahertz time-domain spectroscopy using the broadband

metamaterial modulator. a, Amplitude spectral ratio of two subsequent
measurements (100% lines) using the metamaterial device or a mechanical
optical chopper as the modulator in a terahertz time-domain system, both at a
modulation frequency of 377 Hz. The grey shaded area indicates the + 2.5%
noise deviation. b, Terahertz transmission amplitude spectra through a second
metamaterial sample (unit cell shown in the inset) using the metamaterial
modulator (377 Hz and 30 kHz) or a mechanical optical chopper (377 Hz).

and b, the transmission amplitude and phase are not independent of

each other, but are causally connected, as manifested by Kramers
Kronig (KK) relations29. Specically, the phase is proportional to the
derivative of the amplitude with respect to the frequency. Near frequencies where the amplitude is not strongly dependent on the applied bias
voltage, but its slope is, the phase experiences a maximum shift, and vice
versa. Thus, although the amplitude modulation and phase shifting
response are inherently narrowband and strongly frequency dependent,
the KK relations specify that the metamaterial depicted in Fig. 1a will
modulate over an extended range. Thus, our device can be used as a
broadband modulator.
The frequency-dependent modulation of terahertz transmission
is given by




jD~t vj tV1 veifV1 v  tV2 veifV2 v 

showing that the amplitude and phase contribute to the modulation.

Figure 3a presents the experimental results of the metamaterial
device acting as a broadband modulator. The time-domain waveform of the terahertz modulation (differential) signal is shown as
the red curve for application of a square-wave voltage bias alternating between 0 and 16 V. The mechanical optical chopper has been
removed from the terahertz time-domain system. As a reference, the
terahertz transmission signal through a bare GaAs substrate is also
measured. The modulated terahertz spectrum produced by the
metamaterial device is shown in Fig. 3b and displays a broadband
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and rather at response of Dt(v)  25% between 0.8 and 1.7 THz,
beyond which the terahertz radiation is also modulated but with
decreasing modulation depth. These frequencies correspond to the
two metamaterial resonances shown in Fig. 2. By using methods
to increase the frequency span between the two resonances30, it is
possible to further broaden the modulation bandwidth.
This terahertz modulator can be implemented into a terahertz
time-domain spectrometer, replacing the typical mechanical
optical chopper. To further evaluate the performance, in Fig. 4a
we plot the division of two subsequent measurements, a so-called
100% line, at the modulation frequency of 377 Hz. This quantity
represents the frequency-dependent noise of the system as deviations from 100%. We take as our evaluation point deviations of
+2.5%, indicated by the grey area of Fig. 4a. The same procedure
is also performed for a mechanical optical chopper at the same
modulation frequency. The mechanical chopper yields a range
from 93 GHz to 2.32 THz in this particular terahertz system,
where the noise is mainly from the long-term system stability.
The metamaterial modulator range is from 161 GHz to 1.88 THz.
For a more restrictive criterion of +1%, the metamaterial device
achieves a modulation range from 0.61 to 1.69 THz, roughly
between the two resonance frequencies. The signal-to-noise ratio
is not as good as the mechanical chopper, which achieves a 100%
modulation depth with no insertion loss, and has, in principle, innite bandwidth. We also note that operating this device as a broadband modulator requires phase-sensitive detection. However, the
compact metamaterial modulator has no moving parts, is only
1 mm thick (one layer of active material), and has been demonstrated to operate up to 2 MHz (ref. 19), which can reduce the
signal acquisition time. In contrast, mechanical optical choppers
are bulky and are limited to kilohertz modulation rates.
As a further test, we performed terahertz transmission measurements through a second metamaterial sample (see inset to Fig. 4b)
using our metamaterial device as a chopper (377 Hz). In Fig. 4b the
transmitted amplitude spectra are shown, clearly identifying the
metamaterial resonance near 1 THz. The results are comparable
to those measured using a mechanical chopper (377 Hz). The agreement in Fig. 4 conrms the applicability of this metamaterial modulator as a functional device. Figure 4b also shows results at 30 kHz,
signicantly exceeding the operational frequency of mechanical
choppers. Comparable performance to the results obtained at
377 Hz demonstrates the high-speed modulation capability.
In conclusion, we have demonstrated a single-layer, electrically
controllable terahertz metamaterial phase shifter yielding up to
Df 0.56 rad with constant insertion loss. The phase shifting, as
well as the amplitude modulation index, reveal a linear dependence
on the applied voltage bias. It is possible to individually address the
metamaterial elements, which could be useful for future terahertz
devices such as voltage-controlled arrays for active beam steering
and focusing. This metamaterial device has been shown to modulate
a complex transmission signal, and we have demonstrated its use as
a high-speed broadband modulator in a terahertz time-domain
spectrometer.

Received 24 November 2008; accepted 20 January 2009;

published online 22 February 2009
References
1. Grischkowsky, D., Keiding, S., van Exter, M. & Fattinger, Ch. Far-infrared timedomain spectroscopy with terahertz beams of dielectrics and semiconductors.
J. Opt. Soc. Am. B 7, 2006 2015 (1990).
2. Kohler, R. et al. Terahertz semiconductor-heterostructure lasers. Nature 417,
156 159 (2002).
3. Tonouchi, M. Cutting-edge terahertz technology. Nature Photon. 1,
97 105 (2007).
4. Smith, D. R., Pendry, J. B. & Wiltshire, M. C. K. Metamaterials and negative
refractive index. Science 305, 788 792 (2004).

NATURE PHOTONICS | VOL 3 | MARCH 2009 | www.nature.com/naturephotonics

5. Veselago, V. G. The electrodynamics of substances with simultaneously negative

values of 1 and m. Sov. Phys. Usp. 10, 509 514 (1968).
6. Shelby, R. A., Smith, D. R. & Schultz, S. Experimental verication of a negative
index of refraction. Science 292, 77 79 (2001).
7. Pendry, J. B. Negative refraction makes a perfect lens. Phys. Rev. Lett. 85,
3966 3969 (2000).
8. Fang, N., Lee, H., Sun, C. & Zhang, X. Sub-diffraction-limited optical imaging
with a silver superlens. Science 308, 534 537 (2005).
9. Schurig, D. et al. Metamaterial electromagnetic cloak at microwave frequencies.
Science 314, 977 980 (2006).
10. Yen, T. J. et al. Terahertz magnetic response from articial materials. Science 303,
1494 1496 (2004).
11. Azad, A. K., Dai, J. & Zhang, W. Transmission properties of terahertz pulses
through subwavelength double split-ring resonators. Opt. Lett. 31,
634 636 (2006).
12. Chen, H.-T. et al. Complementary planar terahertz metamaterials. Opt. Express
15, 1084 1095 (2007).
13. Chen, H.-T. et al. Experimental demonstration of frequency-agile terahertz
metamaterials. Nature Photon. 2, 295 298 (2008).
14. Padilla, W. J., Taylor, A. J., Highstrete, C., Lee, M. & Averitt, R. D. Dynamical
electric and magnetic metamaterial response at terahertz frequencies. Phys. Rev.
Lett. 96, 107401 (2006).
15. Chen, H.-T. et al. Ultrafast optical switching of terahertz metamaterials
fabricated on ErAs/GaAs nanoisland superlattices. Opt. Lett. 32,
1620 1622 (2007).
16. Landy, N. I., Sajuyigbe, S., Mock, J. J., Smith, D. R. & Padilla, W. J. Perfect
metamaterial absorber. Phys. Rev. Lett. 100, 207402 (2008).
17. Tao, H. et al. A metamaterial absorber for the terahertz regime: Design,
fabrication and characterization. Opt. Express 16, 7181 7188 (2008).
18. Chen, H.-T. et al. Active terahertz metamaterial devices. Nature 444,
597 600 (2006).
19. Chen, H.-T. et al. Hybrid metamaterials enable fast electrical modulation of
freely propagating terahertz waves. Appl. Phys. Lett. 93, 091117 (2008).
20. Libon, I. H. et al. An optically controllable terahertz lter. Appl. Phys. Lett. 76,
2821 2823 (2000).
21. Kersting, R., Strasser, G. & Unterrainer, K. Terahertz phase modulator. Electron.
Lett. 36, 1156 1158 (2000).
22. Hsieh, C.-F., Pan, R.-P., Tang, T.-T., Chen, H.-L. & Pan, C.-L. Voltage-controlled
liquid-crystal terahertz phase shifter and quarter-wave plate. Opt. Lett. 31,
1112 1114 (2006).
23. Padilla, W. J. et al. Electrically resonant terahertz metamaterials: Theoretical and
experimental investigations. Phys. Rev. B 75, 041102(R) (2007).
24. OHara, J. F., Zide, J. M. O., Gossard, A. C., Taylor, A. J. & Averitt, R. D.
Enhanced terahertz detection via ErAs:GaAs nanoisland superlattices, Appl.
Phys. Lett. 88, 251119 (2006).
25. Acuna, G. et al. Surface plasmons in terahertz metamaterials. Opt. Express 16,
18745 18751 (2008).
26. Lee, J. W. et al. Invisible plasmonic meta-materials through impedance matching
to vacuum. Opt. Express 13, 10681 10687 (2005).
27. Zhao, G., Schouten, R. N., van der Valk, N., Wenckebach, W. Th.
& Planken, P. C. M. Design and performance of a THz emission and detection
setup based on a semi-insulating GaAs emitter. Rev. Sci. Instrum. 73,
1715 1719 (2002).
28. Cai, Y. et al. Coherent terahertz radiation detection: Direct comparison between
free-space electro-optic sampling and antenna detection. Appl. Phys. Lett. 73,
444 446 (1998).
29. Jackson, J. D. Classical Electrodynamics 3rd edn (John Wiley & Sons, 1998).
30. Azad, A. K., Taylor, A. J., Smirnova, E. & OHara, J. F. Characterization and
analysis of terahertz metamaterials based on rectangular split-ring resonators.
Appl. Phys. Lett. 92, 011119 (2008).

Acknowledgements
We thank I. Brener for coordinating the sample fabrication, J.F. OHara for discussions and
the use of the terahertz system, and D. Lippens for useful discussions. We acknowledge
support from the Los Alamos National Laboratory LDRD Program. This work was
performed, in part, at the Center for Integrated Nanotechnologies, a US Department of
Energy, Ofce of Basic Energy Sciences Nanoscale Science Research Center operated jointly
by Los Alamos and Sandia National Laboratories. Los Alamos National Laboratory, an
afrmative action/equal opportunity employer, is operated by Los Alamos National
Security, LLC, for the National Nuclear Security Administration of the US Department of
Energy under contract DE-AC52-06NA25396.

Additional information
Supplementary Information accompanies this paper at www.nature.com/naturephotonics.
Reprints and permission information is available online at http://npg.nature.com/
reprintsandpermissions/. Correspondence and requests for materials should be
addressed to H.T.C.

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