THz Wave Modulators: A Brief Review on Different Modulation

J Infrared Milli Terahz Waves (2013) 34:1

–

27

DOI 10.1007/s10762-012-9946-2

THz Wave Modulators: A Brief Review on Different

Modulation Techniques

Marco Rahm & Jiu-Sheng Li & Willie J. Padilla

Received: 9 July 2012 / Accepted: 23 October 2012 /

Published online: 9 November 2012

#

Springer Science+Business Media New York 2012

Abstract We review different techniques for modulation of the electromagnetic properties of terahertz (THz) waves. We discuss various approaches for electronic, optical, thermal and nonlinear modulation in distinct material systems such as semiconductors, graphene, photonic crystals and metamaterials. The modulators are classified and compared with respect to modulation speed, modulation depth and categorized by the physical quantity they control as e.g. amplitude, phase, spectrum, spatial and temporal properties of the THz wave. Based on the review paper, the reader should obtain guidelines for the proper choice of a specific modulation technique in view of the targeted application.

Keywords Terahertz wave modulators . Metamaterials, graphene . Electronic modulation .

All-optical modulation . Photonic crystal modulators . Nonlinear tuning of metamaterials .

Magnetic field tuning

1 Introduction

Optics is one of the most foundational technologies fostering innovation and economic growth in a wealth of application disciplines. Certainly the most crucial technological advance in the field of optics was the invention of the laser [ 1 , 2 ] with applications spanning from material processing and machining, welding and drilling [ 3 ] to laser-optical precision

M. Rahm (

*

)

Department of Physics and Research Center OPTIMAS, University of Kaiserslautern,

Erwin-Schroedinger-Strasse, 67663 Kaiserslautern, Germany e-mail: mrahm@physik.uni-kl.de

M. Rahm

Fraunhofer Institute for Physical Measurement Techniques IPM, Heidenhofstrasse 8, 79110 Freiburg,

Germany

J.-S. Li

Centre for THz Research, China Jiliang University, Hangzhou 310018, China e-mail: jshli@126.com

W. J. Padilla

Department of Physics, Boston College, 140 Commonwealth Ave, Chestnut Hill, MA 02467, USA e-mail: Willie.Padilla@bc.edu

2 J Infrared Milli Terahz Waves (2013) 34:1

–

27 measurement systems and metrology [ 4 ], laser spectroscopy [ 5 , 6 ], bio sensing [ 7 ] and much more. Information technology continues to strongly benefit from laser technology which enabled the transition from comparably slow electronic telecommunication systems to alloptical, spectrally broadband optical communication networks with high data transmission rates up to multiple Terabits per second [ 8

–

11 ]. A key to high data transmission rates in optical fibers has been the development of efficient amplitude and/or phase modulators which are used to encode information in the carrier wave. However, such components do not only play a decisive role for optical networks, but are also irreplaceable for real-time manipulation of light and the technological advancement of adaptive optics in a wider context [ 12 ]. For example, modulators can be used to control the amplitude, phase, polarization state, spatial propagation direction, pulse shape, pulse length and many more characteristic properties of electromagnetic waves. While active modulators are well established and considered standard devices in the optical realm, the THz frequency regime is still in great demand for highly efficient, fast and versatile active light modulators. The progression of THz science and technology depends on the realization of efficient components such as adaptive lenses, filters, switchable mirrors, spatial light modulators, dynamic polarization controllers or amplitude and phase modulators.

The spectral frequencies of THz radiation are located in the range from 0.1 to 10 THz – wavelengths of 3 mm to 3 μ m. THz waves are strongly absorbed by water and they can penetrate through most dielectrics and intrinsic semiconductors [ 13 , 14 ]. Terahertz radiation is thus ideally suited for non-invasive testing of multilayer dielectric stacks for quality control

[ 15

–

18 ] and security screening of concealed substances behind plastics, cardboard, paper, textiles etc. [ 19 ]. Since the spectral bandwidth of pulsed THz waves can be of the order of several hundred percent, (compared to the center frequency), THz light is a promising candidate for short-distance data transmission at high bit rates [ 20 ]. In all proposed uses, reliable and versatile THz measurement systems require adequate optical components, i.e. modulators, for active adaptive control of the electromagnetic properties of the radiation.

Modulators can be categorized by the physical quantity they control, as e.g. amplitude, phase, pulse length and shape, spectrum, spatial and temporal properties or by the technique or material system which is employed to modulate the wave. In most cases, modulators manipulate multiple properties of the THz wave at once, either on purpose or as a consequence of an undesired side effect.

In this review article, we provide a brief overview of various techniques for the modulation of THz waves which have been investigated and demonstrated in the last few years.

Our survey is not intended to cover every single technique and prior publication, but rather to highlight some recent notable work. In section 2 we concentrate on all-optical THz wave modulation in semiconductors and metamaterials before overviewing electronically driven semiconductor and metamaterial-based modulators as well as graphene-based material systems in sections 3 and 4. In section 5 we focus on thermal modulation and modulators with memory effects. In section 6, we review concepts on magnetic tuning and nonlinear wave modulation in metamaterials while we elucidate theoretical concepts for THz wave modulation in linear and nonlinear photonic crystals in section 7. The article closes with a final conclusion and outlook in section 8.

2 All-Optical Modulation in Semiconductors and Metamaterials

Semiconductor scattering processes usually occur on time scales that are of the order of picoseconds and femtoseconds [ 21 ]. When optical radiation is incident upon a semiconductor,


–

27 3 free carriers may be produced so long as the energy of light ( h w

) exceeds the band gap energy

(E g

) of the semiconductor, i.e.

h w

E g

. These “ photo-generated ” carriers – consisting of electrons and holes – live for an amount of time termed the recombination time ( t

). The density of the photo-generated carriers ( n ) can be taken to be proportional to the fluence (energy per unit area) of incident photons and can often be described by a Drude model [ 22 ], where the complex conductivity is given as, e w "

0 w 2 p t

1 i wt

ð

1

Þ where ( w 2 p

¼ ne 2 = "

0 m ) is the plasma frequency squared,

ε

0 is the permittivity of free space, t is the scattering rate, m is the electron mass and e is the electron charge. The plasma frequency is a characteristic frequency below which materials act

“ metallic

” and above which they are transparent to light. If the fluence of light incident upon a semiconductor is sufficient such that w p

2 p

1 THz , then our semiconductor will be opaque for electromagnetic waves less than

1THz and for time scales up to t

0 t

. An ultrafast laser has pulse widths which are similar in time to semiconductor processes. Thus optically doped semiconductors used in combination with ultrafast lasers, may be used as ultrafast THz modulators.

In the past, semiconductors have proven to be suitable for all-optical modulation of electromagnetic waves. Generally, optical pulses may be used to modulate THz radiation by the following method: a laser pulse is incident on a semiconductor and produces a temporary region of high reflectance. THz light, co-incident on this area of high reflectivity, is thus modulated. In the 90 ’ s silicon was used as a semiconductor for THz modulation, and pulse widths of 28 ms [ 23 ] and 430 ns [ 24 ] were shown at 2.5THz. In other studies both gallium arsenide (GaAs) and Si were used for demonstration of pulse widths of 10 ns [ 25 ] and 5 ns

[ 26 ] for 1.4 THz radiation. In a more recent approach, spatially modulated laser light was used to induce one- and two-dimensional, tunable optical gratings in high-resistivity silicon to modulate terahertz waves [ 27 , 28 ].

In studies mentioned above, various lasers were used including an electronically controlled CW Nd:YAG [ 25 ] and a Q-switched Nd:YAG laser [ 21 , 22 ]. Although ultrafast lasers can yield near time bandwidth product limited pulses of a few femtoseconds, a number of factors enter into the ultimate switching speeds possible in semiconductors, including dark resistivity, carrier mobility, and carrier lifetime [ 29 ]. Silicon has a recombination time of several hundred ns and GaAs a few ns. Other semiconductors such as low-temperature grown GaAs and erbium doped super lattices grown in GaAs, permit much faster pico and sub-picosecond recombination times. Thus although modern lasers are sufficiently fast enough to permit THz modulation of THz frequencies, the carrier recombination time of semiconductors sets the ultimate limit. More recently an optically controllable THz filter was demonstrated using a GaAs/AlAs multiple-quantum-well structure [ 30 ]. Broadband changes in THz transmission where shown with average values of about 60 %.

In addition to their intrinsic use as large-aperture modulators, semiconductors can also be employed to actively control the electromagnetic transmissive and/or reflective properties of metallic structures with extraordinary transmission properties. Thin metal films with a twodimensional periodic array of subwavelength holes can exhibit transmission efficiencies far in excess of unity at wavelengths greater than the lattice parameter of the surface [ 31 ]. This behavior is not predicted by standard aperture theory, as developed by Bethe in 1947 [ 32 ]; however the theoretical consensus for enhanced transmission is that it is the result of excited surface plasmon polaritons which couple on either side of the metal, thus creating enhanced transmission.


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27

Fabrication of 2D metallic hole arrays or 1D metallic gratings on semiconducting substrates, or fabricated directly from semiconductors, permits modulation of THz radiation.

In 2005 researchers fabricated a grating structure in 130 μ m thick InSb with a periodicity of

300

μ m and a side length of 65

μ m [ 33 ]. Applied ultrafast pulses produced carrier densities of order 10

16 –

10

17 cm

-3 which resulted in changes of THz transmission of 0.25 % and 1 % at room temperature and 240 K, respectively. A similar work used a metal grating fabricated on a silicon substrate and showed THz modulation on picosecond time scales [ 34 ].

Taking this approach one step further, it was shown that semiconductors are suitable for active tuning of the optical properties of metamaterials at THz frequencies. Metamaterials

– designer materials consisting of sub-wavelength periodic metallic inclusions

– may be fashioned to exhibit exotic electromagnetic effects, including negative index of refraction

[ 35 , 36 ], invisibility cloaking [ 37 ] and perfect absorption [ 38 ]. Metamaterials are not limited by and do not depend on the particular properties of the materials they are fashioned from, but rather obtain their exotic properties from their geometry. Designs proven in a particular band of the electromagnetic spectrum may be scaled in size to operate in another range.

Metamaterials are a design concept and give one direct access to independently tailor the two parameters that couple light matter interaction in Maxwell ’ s Equations, ε and μ .

Metamaterials are thus a bottom-up approach where one pieces together a material through the assembly of ‘ designer atoms ’ , each of which have specifically programmed electromagnetic properties. The electromagnetic properties exhibited by individual element are preserved in the larger macroscopic material.

The two canonical metamaterial elements utilized to yield permeability and permittivity frequency dependent responses are shown in Fig.

1(a) and (b) , respectively. Each structure produces a resonant frequency dependent response – similar to a Lorentz oscillator – and the wavelength at resonance is significantly larger than the physical dimensions of the unit cell.

In transmission a metamaterial resonance would appear as a minimum, due to the peak of the imaginary portion of the Lorentz oscillator located at

ω

0

. A Lorentz oscillator takes the form, e w "

1

þ w 2

0 w 2 p w 2 i wg

ð 2 Þ where

ω

0 is the center frequency of the oscillator,

γ is the damping frequency, and

ε

∞ dielectric function at frequencies much greater than

ω

0

. In Fig.

1(c) is the we show the real (blue) and imaginary (red) terms of Eq.

2 for a metamaterial dielectric resonant response with parameters: w p

¼ 4 : 0 THz , w

0

¼ 2 : 5 THz , g ¼ 0 : 15 THz , "

1

¼ 1 : 0 , and a thickness of

3.5

μ m. The geometric structure of the Lorentz oscillator and the orientation of the exciting electric field are shown in Fig.

1(b) . The transmission, reflection, and absorption are plotted in Fig.

1(d) for the Lorentz oscillator described above. As can be observed, the minimum in transmission is located near the peak of the imaginary term in the dielectric function and absorption of about 35 % is realized.

Single unit cells are often fashioned on top of a carrier substrate and replicated to fill space, typically in two or three dimensions. Each metamaterial element, shown in Fig.

1(a) and (b) , consists of an inductive loop, and a split gap. The resonance of a metamaterial can be well described as an LC resonator where the resonance frequency is given as w

0

2 ¼

1

=

LC

The resonance frequency of the metamaterial element significantly depends on the dielectric

.

properties of materials placed near the capacitive gap. Thus by dynamically altering the substrate dielectric, the electromagnetic properties of metamaterials may be controlled. For example metamaterials fabricated on Si or GaAs could be photodoped thereby altering their


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27 5

Fig. 1 (a) A split ring resonator (SRR) metamaterial which yields a resonant magnetic response to an applied magnetic field as shown. ( b ) A metamaterial which achieves a resonant response to an applied electric field as shown. ( c ) Real (blue) and imaginary (red) portions of an electric Lorentz resonance excited by an electric field as shown in ( b ), with parameters as described in the text. ( d ) The corresponding reflection, transmission, and absorption for the Lorentz oscillator shown in ( c ).

transmissive value

– either by shifting of the resonance frequency (frequency modulation), or shunting of the capacitive response (amplitude modulation).

In 2006 split ring resonator metamaterials were fabricated on semi-insulating gallium arsenide (SI-GaAs), intended for operation near 0.56 THz [ 39 ]. Experiments were carried out with optical-pump terahertz probe spectroscopy, and a 50 fs 800 nm pulse was used to excite carriers across the 1.42 eV band gap. As previously mentioned, the lifetime of photodoped carriers in GaAs is a couple of nanoseconds, thus permitting characterization of the steady state THz response of the metamaterials. At zero applied fluence the metamaterials yielded a strong resonance with a transmission minimum of 15 %. However at small applied fluences of 1

μ

J/cm

2 and 2

μ

J/cm

2 the transmission increased to about

T

0

50 % and 75 %, respectively. The authors noted that these metamaterials could be used as dynamical devices such as an optically controlled THz bandpass element. For example, at


–

27

560 GHz a 2

μ

J/cm

2 pump pulse increases the transmission by 60 % and changes the metamaterial from absorbing to transparent, thus demonstrating THz amplitude modulation.

Amplitude modulation results in the metamaterials discussed above are inherently slow due to the long recombination time in SI-GaAs. However, a similar metamaterial structure was fabricated on ErAs/GaAs superlattice semiconducting substrates, which permit designer carrier lifetimes of a few ps [ 40 ]. A transmission change of 30 % was demonstrated at 0.75

THz with a switching recovery time of 20 ps. In another work, optical photodoping in metamaterials with silicon incorporated into the capacitive gap of a split ring resonator was demonstrated at microwave frequencies and shown to be capable of creating a three channel dynamical filter [ 41 ]. Rather than use a bulk semiconductor for switching, other studies used carbon nanotubes applied to metamaterials to realize optical switching [ 42 ]. Here it was shown that modulation depths of 10 % can be achieved by optical photodoping at NIR wavelengths of 1.8

μ m.

Another study investigated frequency modulation of metamaterials using a hybrid metamaterial/semiconductor structure. Silicon-on-sapphire (SOS) was used to form the capacitive regions of an electric ring resonator metamaterial

– see top panels of Fig.

2 . In this way the capacitance could be modified by optical doping, without shunting the capacitive response. The authors demonstrated a frequency tuning of the resonance of 20 % in bandwidth from 1.06 to

0.85 THz for increasing pump fluence [ 43 ]. It has also been shown possible to fabricate metamaterial / semiconductor structures in which the resonance blue shifts with applied optical photodoping [ 44 ]. A tri-gap electric ring resonator structure utilized silicon in outer gaps which permitted modification of the inductive term of the metamaterial [ 36 ] while another study used more conventional split ring resonators fabricated on SI-GaAs for a similar demonstration [ 45 ].

The use of SOS in other studies was directly incorporated into the gaps of split ring resonator materials which permitted amplitude modulation values of 60 % at 600 GHz [ 46 ].

3 Electronic Modulation in Semiconductors and Metamaterials

Although great progress in optically based THz modulators has been achieved, as described above, an all-electronic approach is an attractive proposition, especially with a view toward applications. Similar to the underlying principle of THz wave modulation by photo-doping of semiconductors, the carrier concentration in semiconductors can be changed by electric injection or depletion of charge carriers. In the last decade the use of two-dimensional electron gases (2DEGs) in semiconductors has proven useful for control of THz waves and the high electron mobility transistor (HEMT) is an often used architecture. A HEMT is a field effect transistor which utilizes 2DEGs at the heterojunction of a highly doped donor supply semiconductor (AlGaAs being typical) and a pristine undoped semiconductor

(GaAs). In this way the HEMT avoids carrier scattering which arises in heavily doped semiconductors, as the donated carriers lie in the quantum well at the interface.

In 2004, Kleine-Ostmann et al. demonstrated a room-temperature electrically driven THz wave modulator based on electron density modulation in a gated two-dimensional electron gas [ 47 ]. The epitaxial structure of the HEMT-like device is shown in Fig.

3(a) . A 2DEG of only few nanometers thick is concentrated near the GaAs/AlGaAs surface and can be depleted by application of a negative gate voltage which induces an increase of the transmittance through the device. Figure 3(b) shows the time trace of the modulation signal for different applied gate voltages. At a gate voltage of -10 V, the amplitude transmittance of the THz pulse increased by 3 % over a spectral range from 0.1 to 2 THz. As expected, the modulation depth of the reported device was fairly small since the 2DEG had a thickness of


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27 7

Fig. 2 The top left shows an SEM image of a hybrid metamaterial consisting of gold and silicon parts

– as labeled. Top right SEM image shows a larger field of view. Bottom panel shows the experimental results, as described in the text

– after [ 39 ].

only a few nanometers. Investigation into HEMTs as THz devices has demonstrated emission [ 48 ] detection [ 49 ], and modulation [ 47 ] of electromagnetic waves.

A useful implementation of HEMTs can be obtained by making the channel physically small in size. In this case the HEMTs have a resonant response to incident radiation, where the frequency is set by the geometry of the channel and carriers are considered to undergo

“ ballistic transport

”

. It should be noted that ballistic transport can be achieved both when the device size is made to be smaller than the mean-free-path, but also when the frequency of incident radiation is larger than the scattering frequency, i.e.

ωτ

>1. However, here electrons in HEMTs are highly doped and thus undergo many collisions. Thus, in this case individual carriers cannot be considered ballistic, but rather the 2DEG will act “ ballistically ” – similar to a localized surface plasmon [ 50 , 51 ]. Ballistic HEMTs have been fabricated with metal wire gratings and have demonstrated broadband THz detection at room temperatures, due in part to the non-radiative nature of 2DEG plasma oscillations [ 52 ].

Other various methods have been utilized to achieve amplitude and frequency modulation in semiconductor/metamaterial devices including; electronic control for amplitude [ 53 , 54 ],


–

27

Fig. 3 ( a ) Epitaxial structure of an electrically driven, room-temperature THz wave modulator. The modulator is similar to high electron mobility transistors (HEMTs). ( b ) Time trace of the modulation signal for different gate voltages. A maximum modulation of 3 % was observed over a frequency range from 0.1 to 2

THz [ 47 ].

spatial [ 55 ] and phase [ 56 ] modulation. These metamaterial devices rely on n-doped gallium arsenide (GaAs) and initial studies have demonstrated the potential of these systems for high speed telecommunications [ 57 ], spectroscopy, and imaging [ 55 ]. To-date THz metamaterials have shown modulation at frequencies low in the megahertz (MHz) range, and higher speed modulation has been hindered by large device capacitance - effects which can be possibly overcome from patterning the semiconducting regions. One of the first works used electric ring resonators patterned to form a square array with wires as inter-unit cell connections

– see Fig.

4(a) . Thus the entire metamaterial array could function as a grid for biasing of the underlying semiconductor. The metamaterial was fabricated on top of a 2 μ m thick epitaxial n-doped GaAs layer with the electron density of 2·10

16 cm

-3 grown on a supported SI-GaAs wafer [ 53 ]. The metal-semiconductor interface forms a Schottky diode permitting depletion underneath the metamaterial (Fig.

4(b) ). The carrier density can be actively controlled by applying a voltage bias between the metal and substrate. Thus the metamaterial device could be used for modulation of THz waves, as the conductivity of the substrate could be modified which then switches the resonance of the metamaterials. At zero applied bias the resonance response is damped owing to the lossy conductive n-doped GaAs region. However a reverse voltage bias was shown to sufficiently deplete the lossy carriers such that the metamaterial resonance could be re-established. As shown in Fig.

4(c) an intensity transmission modulation over 50 % at 720 GHz was demonstrated.

A similar structure was fabricated in which a hole array functioned as the GaAs epilayer

[ 58 ]. Here the authors demonstrated extra-ordinary transmission where the transmission peak was tuned by 2 % in frequency. Another work fabricated a similar structure and demonstrated a maximum transmission modulation depth of 52 % [ 59 ]. Ring apertures fabricated in silicon were shown to yield transmissive values of 60 %. A thin layer of free carriers in the underlying silicon substrate were shown to suppress the transmission by

18 dB, thus suggesting fabrication of THz modulators by CMOS architectures [ 60 ].

Several improvements may be made over the GaAs metamaterials Schottky modulators described above. For example, some shortcomings are that the metamaterial only works for one polarization and, additionally, can only achieve relatively slow modulation speeds.

Although amplitude modulation may be useful for various THz devices, high speed polarization independent switching is desirable for high bandwidth communications. One work, shown in Fig.

5 , presented a symmetric metamaterial design based on a Schottky / n-doped

GaAs device [ 61 ]. A modulation speed of 100 kHz at 630 GHz was demonstrated and shown


–

27 9

Fig. 4 ( a ) Schematic of an electronically driven metamaterial-based terahertz wave modulator. The electric resonators form a Schottky contact with the n-doped GaAs substrate. ( b ) By application of a reverse bias field between the Schottky and ohmic contact in ( a ), a voltage-dependent carrier depletion zone can be created in the split gap of the electric resonators and the strength of the metamaterial resonance and thus the terahertz wave transmission can be controlled. ( c ) Scheme of electronic modulation of terahertz waves. The terahertz pulses are incident on the modulator and the transmission through the metamaterial is controlled by the applied voltage between the Schottky and ohmic contacts [ 53 ].

to be polarization independent. Another study, also in n-doped GaAs, focused on increasing the modulation speed further. This was obtained by minimizing the device RC time constant, where R is the forward resistance of the Schottky diode (about 100

Ω in their device), and C is its depletion capacitance. An interdigitated Ohmic metamaterial contact was fabricated and a 2 MHz modulation speed was shown [ 62 ]. In a further study, HEMTs were monolithically integrated into the electric resonators of a metamaterial and a modulation depth of

23 % was achieved at a center frequency of 0.46 THz. A modulation bandwidth of up to

10 MHz was demonstrated [ 63 ].

4 Electronic Modulation in Graphene

More recently, it was found that graphene can be superior to semiconductors when used as an electrically driven modulator [ 64

–

68 ]. Graphene has raised tremendous interest in the last few years due to its unique band structure which exhibits a linear dispersion relation between energy and crystal momentum. As a result electrons are expected to behave as massless quantities and thus are described by the Dirac Hamiltonian [ 69 , 70 ]. Therefore graphene exhibits extremely high carrier mobilities of up to 20000 cm

2

V

-1 s

-1 for both holes and electrons. Furthermore, outstandingly high carrier concentrations up to 1×10

14 cm

-2 can be obtained in graphene as well as extremely low carrier concentration at the Dirac point [ 68 ]. Thus, the carrier concentration can be tuned by applying an external electric field to the graphene layer. Recently, Sensale-Rodriguez et al. reported an electronically driven graphene terahertz wave modulator based on modification of the conductivity of graphene by controlling intraband transitions in a single graphene layer or alternately in graphene-semiconductor stacks [ 68 ]. Figure 6(a) shows the conical band structure of graphene.

Since the energy of THz photons is too low to drive interband transitions, intraband transitions dominate the induced absorption of THz radiation. The Fermi level and thus the available density of states for intraband transitions can be tuned by applying a gate voltage V g

. In the experiment, graphene was processed on top of a SiO

2

/p-Si substrate. The conductivity of graphene was modified


–

27

Fig. 5 ( a ) A schematic of a polarization insensitive THz metamaterial / semiconductor modulator. ( b )

Schematic showing a side view perspective of the device highlighting the depletion of the semiconductor beneath the metamaterial. ( c ) Optical photograph of the fabricated device. ( d ) amplitude transmittance and phase [ 61 ].

by applying a voltage between the top contact and the ring-shaped back gate (see Fig.

6(b) ). The p-Si was only slightly doped at a concentration of 1×10

15 cm

-3 to avoid significant absorption of

THz radiation in the substrate. Figure 6(c) illustrates the intensity transmittance through the


–

27 11

Fig. 6 ( a ) Conic band diagram of graphene. The Fermi level can be tuned by an external gate voltage V

G which changes the conductivity and thus the absorption and reflectance of THz radiation. ( b ) Schematic of the graphene modulator. Single-layer graphene was processed on a SiO

2

/p-Si substrate. The gate voltage was applied between the top contact and a ring back gate. ( c ) Calculated intensity transmittance of THz radiation through graphene. The absorption and Fresnel reflections in the substrate were subtracted. The intensity modulation depth was 16 % [ 68 ].

modulator at gate voltages V

G

0

0 V and 50 V, respectively. In this graph, the Fresnel reflection and free carrier absorption of THz radiation in the substrate were subtracted to obtain the pure absorption in the graphene layer. Since the Dirac point and hence the minimum of the conductivity in the p-type graphene was obtained at a gate voltage V transmittance shows a maximum at this voltage while for V

G

G

0

50 V, the intensity

0

0 V the transmittance dropped to about 80 % due to an increased free carrier concentration in graphene. The intensity modulation depth was calculated to be about 16 % in the frequency range from 570 GHz to 630 GHz, where

½ max

T min

Þ = T max

. The device offered a 3 dB operation bandwidth of about 20 kHz.

At this point it should be noted that the definition of the modulation depth has not been used consistently throughout the literature and care is advised for any comparison or evaluation of the achieved modulation depth. It is necessary to distinguish between amplitude modulation depth and intensity modulation depth. The first describes the modulation of the electric field amplitude while the latter determines the modulation of the intensity, i.e. the square of the electric field amplitude. Further, one should take note of the reference value of the modulation depth. In some publications, the amplitude modulation depth M

A1

¼ ð

E max

E min

Þ =

E min has been referenced to the minimum E min of the transmitted field amplitude while in other publications the reference value is the maximum E max amplitude modulation depth is defined as M

A2

¼ ð E of the transmitted field and hence the max

E min

Þ = E max

. In consequence, the first definition allows modulation depth values in the range from 0 % to infinity per cent while the latter definition is more intuitive with values in the range from 0 to 100 %.

Figure 7(a) shows a conversion graph between the amplitude modulation depths M

A1 and M

A2

As can be seen, the values obtained from both definitions don

’ t differ considerably as long as the

.

modulation depth M between M

M

A1

= ð

1

þ

A1

M

A1

A1 is in the range from 0 to 10 %. For higher values of M

A1

, the difference and M

A2 increases corresponding to the conversion formula M

A2

%

Þ

100 . Figure 7(b) displays the dependence of the corresponding intensity modulation depth M

I1

¼¼ E 2 max

E 2 min

= E 2 min and M

I2

¼¼ E 2 max

E 2 min

= E 2 max on the amplitude modulation depth M

M h

A1

1 by M

1

= ð

1

I1

þ

%

M

A1

Þ 2 i

ð 1 þ M

100 .

A1

Þ 2

A1

1 i I1 can be derived from the amplitude modulation depth

100 and can be converted to M

I2 by M ¼


–

27

Fig. 7 ( a ) Conversion graph between amplitude modulation depth as defined by M and M

A2

¼ ð

E max

E min

Þ =

E max

, where E the minimal transmitted field amplitude. ( b ) Conversion graph between the amplitude modulation depth M and the intensity modulation depth M

I1 max

¼¼

E

2 max

E

2 min

=

E

2 min and M

I2

A1

¼¼

E

2

¼ ð

E max max min

E min

=

E

2

Þ =

E min is the maximal transmitted electric field amplitude and E

E

2 min max

.

is

A1

In a very recent study, Lee et al. demonstrated terahertz wave switching in gate-controlled graphene metamaterials [ 71 ]. The graphene metamaterial was composed of single-layer graphene on top of a metamaterial with a hexagonal unit cell deposited on a polyimide substrate as depicted in Fig.

8(a) . The top and bottom electrodes were designed to support extraordinary transmission for THz radiation to avoid signal attenuation in the electrode material. The graphene metamaterial was free-standing and embedded in a dielectric material. Figure 8(c) illustrates the dependence of the spectral amplitude transmittance (panel a), the amplitude modulation depth and the relative phase shift of the modulator on the applied gate voltage V

G

. The dashed line indicates the voltage V

CNP at the charge neutral point where the amplitude transmittance reaches a minimum at resonance frequency of the graphene metamaterial. The amplitude modulation depth was defined as the ratio between the transmittance change (T-T

CNP

) and the transmittance

T

CNP at the charge neutral point. (Note that, based on this definition, the amplitude modulation depth can yield values between zero and infinity at the resonance frequency.) As can be seen in

Fig.

8(c) , the resonance frequency shifted to lower frequencies for increasing modulus of V

G

. At the same time, the transmission at resonance increased due to resonance damping caused by an increasing conductivity in the graphene layer while the transmission decreased off-resonance due to carrier absorption. In addition to amplitude modulation, phase modulation occurred and a maximum phase shift of 40 deg at a frequency of 0.65 THz was observed. A maximum amplitude modulation depth of 90 % was achieved at the resonance frequency of 0.68 THz as indicated in Fig.

8(b) . This value corresponds to an amplitude modulation depth of 47.5 % when the modulation depth is defined as the ratio between the transmission change (T-T

CNP

) and the maximal transmission T for which, in contrast to the authors

’ definition, the amplitude modulation depth cannot exceed 100 %. In the same paper the authors studied the modulation behavior of a multilayer graphene metamaterial for which they observed a maximum amplitude modulation depth of 140 % and a maximum phase shift of 70 deg at resonance frequency. The amplitude modulation depth corresponds to a value of 58.5 % when referenced to the maximum transmission instead of the transmission minimum.

5 Thermal Modulators and Memory Effects

The propagation of a THz wave can be actively manipulated via direct control of the transmissive or reflective electromagnetic response of an optical material. In this manner,


–

27 13

Fig. 8 ( a ) Sketch of the graphene metamaterial. The metamaterial is composed of hexagonal unit cell structures covered by single-layer graphene. Electrodes that support extraordinary THz wave transmission are desposited on the top and bottom side of the graphene metamaterial. The device is embedded in two dielectric cover sheets. ( b ) Amplitude modulation depth defined by the ratio between the amplitude transmission change (T-T

CNP

)

/ and the transmission at the charge neutral point T

CNP as (T-T

CNP

)/T

CNP

. Note that the transmission is minimal at the charge neutral point. The amplitude modulation depth was determined at the resonance frequency of the metamaterial at 0.86 THz. ( c ) Amplitude transmission spectrum ( a ), amplitude modulation depth ( b ) and relative phase shift ( c ) in dependence on the gate voltage V g

[ 71 ].

the modulator material imprints the specific transmission or reflection characteristics onto the THz wave. One method of THz modulation is to thermally tune the electrical conductivity and thus the optical response of semiconductors or metal oxides [ 72

–

76 ], special insulator materials with metallic phase transition [ 77 – 81 ], or superconductors [ 82 – 84 ]. In many cases these materials are used to control the optical response of metamaterials which can be designed to exhibit a very specific, pre-defined optical response to THz waves. As a major disadvantage, thermal modulation is comparably slow with time constants in the range of several tens of milliseconds or longer.

An example of a thermally tunable metamaterial modulator is shown in Fig.

9 [ 78 ]. The modulator consists of an array of gold split ring resonators (SRRs) on top of vanadium dioxide (VO

2

), (see Fig.

9(b) ), deposited on a sapphire substrate. By changing the temperature, VO

2 undergoes a phase transition from the insulating to the metallic phase by forming percolating metallic grains (green spots in Fig.

9(a) ), thus slowly filling the gap of the SRRs.

When excited by an external THz beam, the SRRs, which themselves form an inductivecapacitive (LC) resonator, oscillate at their resonance frequency which is specific to the geometry of the gold SRRs, and therefore the inductance L and the capacitance C. In effective medium theory, the collective response of the SRR array defines the average electromagnetic response to external electromagnetic fields and thus the reflection and transmission of the material. The resonance frequency of the SRRs can be tuned by active


–

27

Fig. 9 ( a ) Percolation of metallic grains (green) during phase transition of vanadium dioxide from the insulating to the metallic phase (VO

2

). The metallic grains start filling the gap of the split ring resonator

(SRR). ( b ) Array of SRRs on top of VO

2 which was processed on a sapphire substrate. The array is used to modulate the transmissive properties of a THz beam. ( c ) Electric field in the gap of an SRR penetrating and interacting with VO

2

[ 78 ].

control of the capacitance of the SRRs. Since the local electric field of the SRRs penetrates

VO

2

, it is possible to vary the capacitance by changing the conductivity of VO

2 via temperature tuning. As a result, the resonance frequency of the SRR array shifts as shown in Fig.

10(a) [ 77 ]. In this case, the thickness of the VO

2 film was 90 nm. Interestingly, the insulator-metal transition of VO

2 and therefore the DC resistance of VO

2

, is hysteretic and reveals memory effects, as can be observed from Fig.

10(b) , where the temperaturedependent DC resistance of VO

2 is plotted. In consequence, the resonance frequency of the SRR array red-shifts when the temperature is increased around a pre-defined operating point however, due to a flat slope in the hysteresis curve during the cooling process, the shift persists when the heating is switched off. Essentially the metamaterial

‘ memorizes

’ the

Fig. 10 ( a ) Red shift of the resonance frequency of the SRR array when the temperature is increased. Due to hysteresis, the metamaterial memorizes the temperature change even after the heating source has been switched off. ( b ) Hysteresis of the DC resistance of a 90 nm thick VO

2 film on the temperature. By changing the resistance in the capacitive gap of the SRRs, the capacitance can be changed and the metamaterial can be tuned while inheriting the hysteretic characteristics of VO

2

[ 77 ].


–

27 15 frequency red-shift, even when the heating signal subsides. This hysteretic effect is the origin of the term ‘ memory metamaterial ’ .

In a similar approach to modulate the resonance frequency, optical absorption and reflection of metamaterials rely on temperature tuning of the electric conductivity of high-

Fig. 11 ( a ) Spectral amplitude transmission of a metamaterial made from epitaxial YBCO for different temperatures. ( b ) Spectral amplitude and frequency of the transmission minimum in dependence on the temperature. The inset displays the dependence of the real and imaginary part of the conductivity on the temperature [ 82 ].


–

27 temperature (high-T c

) superconductors [ 82 ]. Figure 11(a) illustrates the amplitude transmission spectrum of a metamaterial consisting of symmetric electric split ring resonators

(ELCs). The ELCs were made from epitaxial YBa

2

Cu

3

O

7δ

(YBCO) high-temperature superconducting films with

δ 0

0.05 and had a thickness of 180 nm. The transition temperature of the superconductor was T c

0

90 K. It is obvious that a major drawback of this modulation scheme lies in the fact that operation at cryogenic temperatures is a necessity.

Nevertheless, by changing the temperature from 20 to 84 K, a red shift of the resonance frequency from 0.61 to 0.55 THz was observed accompanied by a decrease of the resonance strength. This corresponds to a relative tuning range of 10 %. At temperatures between 84 K and 100 K, the resonance frequency increased again while the resonance strength kept decreasing. This behavior is depicted in Fig.

11(b) where the transmission minimum and the resonance frequency of the transmission minimum have been plotted for different temperatures. The non-monotonic shift of the resonance frequency to lower and higher frequencies for increasing temperature was described by considering the underlying real and imaginary part of the conductivity of the superconductor. (Due to the limited scope of this review, we refrain from reiterating this explanation at this point.) For thinner superconducting YCBO films the tuning range could be further increased. It was shown that the resonance frequency could be tuned from f max

0 0.48 THz at 20 K to f min a relative tuning range of (f max

-f min

)/f max

0 35 %.

0 0.31 THz at 78 K which corresponds to

An alternative scheme for thermal tuning of the optical response of a metamaterial can be established by thermally induced spatial reorientation of the unit cells of a metamaterial [ 85 ,

86 ]. Provided the unit cell is designed to possess electromagnetic anisotropy, the electromagnetic response of the unit cell strongly depends on the angle between the electric field, magnetic field and the wave vector of the incident THz wave and the relevant tensorial components of the tensor of the dielectric permittivity

ε ij and the magnetic permeability

μ ij

.

Further, if the metamaterial unit cell exhibits bianisotropic properties, the electric field can cross-couple to spatial components of the magnetic polarizability and similarly the magnetic field can cross-couple to electric dipole excitation. While all these aspects are discussed in detail in [ 85 ], we restrict ourselves to discuss the tuning of the anisotropic response of an

SRR array for simplicity. For this purpose we consider an SRR array as depicted in Fig.

12

(a) . The free-standing gold SRRs are connected to the substrate by bi-material cantilever legs. This permitted the orientation of the SRRs, i.e. the angle between the SRRs and the substrate, to be actively controlled by changing the applied temperature. Figure 12(a) shows the orientation of the SRRs for the in-plane configuration and at temperatures ranging from

350 °C to 450 °C in steps of 50 °C. The corresponding transmission spectra of the metamaterial are shown in Fig.

12(b) . The spectra were measured for the electric field vector

E parallel to the closed arms of the SRR and the magnetic field vector H in the plane of the substrate as illustrated in Fig.

12(c) . The wave travelled in the direction of the wave vector k along the normal of the substrate. In this configuration, the magnetic resonance of the SRRs cannot be excited as long as they lie in the plane of the substrate since the magnetic field vector has no component along the normal of the SRR. As soon as the cantilevers are heated, the SRRs tilt out of the plane of the substrate and the magnetic field vector component penetrating the metamaterial becomes non-zero, thus exciting the magnetic resonance. In consequence, the transmission minimum becomes more pronounced at higher temperatures due to an increase in the magnetic field component along the normal of the SRRs (see

Fig.

12(b) ). In contrast to the aforementioned thermal modulators, the bi-material metamaterial modulator only provides amplitude modulation and does not affect the phase of the

THz wave. This is characteristic for the specific configuration that was used to exploit the anisotropy of the metamaterial but need not be a restriction in general.


–

27 17

Fig. 12 ( a ) SEM picture of the SRRs connected to the substrate by bimaterial cantilevers. The color on the bottom of the SEM pictures relates to the temperatures in the legend of Fig. 12( b ). ( b ) Transmission spectra of the SRR metamaterial for different temperatures and thus different orientations of the SRR array. ( c ) Spatial configuration which was used to measure the transmission spectra depicted in Fig. 12( b ). The electric field was perpendicular to the gap of the SRRs while the magnetic field was lying in the plane of the substrate. The wave propagated along the wave vector k normal to the substrate [ 85 ].

6 Prospective Techniques: Magnetic and Nonlinear Modulation

In the following, we review techniques for magnetic and nonlinear tuning of the optical response of metamaterials. To-date these methods have been applied at microwave frequencies. Nonetheless, it is of some utility to discuss this approach, as it would be desirable to transfer to the THz regime. Notably, modulators with nonlinear optical properties in the THz frequency range would offer new possibilities for intensity-dependent modulation of the amplitude and the phase of THz radiation in an unprecedented manor.

Magnetic tuning can be achieved by a number of different approaches including external tuning of the stop band of photonic crystals by self-assembling of magnetizable conducting spheres [ 87 ], tuning of semiconductor-based split ring resonator metamaterials by an external magnetic field [ 88 ], shifting the resonance of superconductor-based metamaterials

[ 89 ] and metamaterials with embedded liquid crystals [ 90 ] as well as magnetic modulation of the band gap of nonlinear metamaterials [ 91 ] and magnetic control of the orientation of cantilever-based metamaterials [ 92 ].

Another promising technique is to modulate the electromagnetic properties of a metamaterial by embedding ferrites in the metamaterial structure and applying an external magnetic field [ 93 – 96 ]. In such a configuration, the inductance rather than the capacitance of the metamaterial unit cell can be tuned due to the proportionality of the inductance L to the permeability

μ of the surrounding medium. At this point, we should mention that magnetic tuning has not been demonstrated for THz waves yet due to the necessity for a ferrite material with magnetic response in the THz frequency range. However, the magnetic response of conventional ferrites vanishes at frequencies of several tens GHz and therefore has been demonstrated for microwaves, but could become possibly relevant for the higher

THz frequency range.


–

27

Figure 13 shows an example of magnetic tuning of the electric resonance of an electric split ring resonator (ELC) metamaterial [ 93 ]. In order to sensitize the metamaterial for magnetic field tuning, ferrite rods made from yttrium iron garnet (YIG) have been embedded in the metamaterial unit cell (see Fig.

13(a) ). The real part Re(

μ x,am

) and imaginary part Im

(

μ x,am

) of the permeability

μ x depend on the applied magnetic field as shown in Fig.

13(b) .

This dependence can be categorized in three distinct regimes: the low frequency regime below resonance, the resonant regime and the high frequency regime above resonance. Due to electromagnetic coupling between the fields surrounding the ferrite rods and the metamaterial, tuning of the permeability of YIG immediately influences the resonant behavior of the ELC metamaterial. Figure 13(c) illustrates frequency tuning of the resonance of the hybrid ELC-ferrite metamaterial for the low-frequency regime. The resonance frequency blueshifts from 11.6 GHz to 12.0 GHz when the magnetic field is changed from 0 Oe to

200 Oe. The inset of Fig.

13(c) shows that the resonance shift is caused by the corresponding tuning of the real part of the effective electric permittivity of the hybrid metamaterial.

Nonlinear tuning requires the inclusion of nonlinear materials in the metamaterial structure and high electric field intensities to drive the nonlinear polarization of such materials

[ 97 – 99 ]. Since table-top THz sources only deliver radiation with comparably low electric field amplitude and, due to a lack of nonlinear materials in the THz frequency range,

Fig. 13 Electric split ring resonator (ELC) metamaterial with ferrite rods. ( b ) Real part Re(

μ imaginary part Im(

μ x,am

) and x,am

) of a single yttrium iron garnet (YIG) rod in dependence on the frequency. The frequency ranges 1, 2 and 3 indicate the frequency regime below resonance, the resonant regime and the frequency regime above the resonance frequency. ( c ) Amplitude transmission spectrum S

21 for different magnitudes of the externally applied magnetic field in the low frequency regime indicated in Fig. 13( b ). The resonance frequency blue-shifts for increasing magnetic field strength [ 93 ].


–

27 19 nonlinear tuning becomes a difficult task. One promising approach may be the specific design of metal-insulator-metal (MIM) diodes as nonlinear inclusions in a metamaterial. In the microwave regime, it is by far easier to find elements with nonlinear response to an external stimulus. Due to the availability of lumped nonlinear components and sufficiently large feature sizes of the metamaterial structures, nonlinear elements as e.g. varactors, diodes etc. can be readily embedded in the metamaterial unit cells to provide them with a nonlinear response.

Nonlinear tuning has been successfully demonstrated at microwave frequencies by

Shadrivov et al. [ 97 ], and Fig.

14(a) illustrates the SRR metamaterial. Varactor diodes were

Fig. 14 ( a ) Double split ring resonator (SRR) metamaterial with varactor diodes as nonlinear inclusions. ( b )

Nonlinear tuning of the amplitude transmission spectrum of S

21 dependent on the incident power. The resonance frequency of the SRR metamaterial shifts to higher frequencies for increasing power levels. ( c )

Modulation of the transmission amplitude S

21 depending on the operating point. For 3.195 GHz, the resonant transmission minimum shifts away from the working point and the transmission increases while for a frequency of 3.468 GHz, the minimum is tuned towards the operating point and the transmission decreases for increasing power levels [ 97 ].


–

27 embedded in the gap of the double split rings to provide them with a nonlinear response to external electric fields. The resonance minimum of the SRR array could be frequency-tuned by variation of the incident microwave power. Figure 14(b) depicts the spectral transmission amplitude and the observed frequency shift of the resonance minimum for power levels of -2 dBm, 23 dBm and 33 dBm. The resonance minimum shifts to higher frequencies for increasing power levels due to the nonlinear response of the hybrid metamaterial.

Figure 14(c) shows the transmitted amplitude of the electric field and its dependence on the incident microwave power for two different operating points of 3.195 GHz and

3.468 GHz. For 3.195 GHz, the resonance minimum is tuned away from the working point for increasing power, thus resulting in an increased transmission. For 3.468 GHz, the transmission amplitude decreases for increasing power levels since the resonance minimum shifts towards the operating point. It should be noted, that the transmission of the demonstrated nonlinear modulator is determined by the incident power of the transmitted wave itself rather than by an external modulation source. However, in general, nonlinear tuning can also be achieved by cross-modulation of the nonlinear response of the metamaterial by means of an external light source. As a major advantage, nonlinear processes appear almost instantaneous and thus allow high modulation rates.

7 Photonic Crystal Modulators

Photonic crystals (PCs) offer the possibility to modulate THz radiation at high speeds within a narrow transmission band. PCs are composed of alternating layers with different refractive indices [ 100 ]. By design, the thickness and refractive indices of the alternating layers can be chosen to obtain a very specific band structure. They may exhibit a so-called photonic band gap, i.e. a range of frequencies for which the propagation of electromagnetic waves is forbidden. At the same time, it is possible to enable propagation of electromagnetic waves in the band gap within a narrow transmission band according to a so-called defect mode by breaking the periodicity of the photonic crystal [ 101 – 103 ].

In 2007, L. Fekete et al.

[ 104 , 105 ] demonstrated the possibility of ultrafast modulation of terahertz radiation using a one-dimensional PC with a GaAs defect. The PC was composed of three building blocks which are indicated as blocks P, S and Q in Fig.

15(a) [ 104 ]. Blocks

P and Q contain alternating layers of crystalline quartz and magnesium oxide with a refractive index of n

L

0 2.1 and n

H

0 3.12. In the middle of the structure, gallium arsenide

(GaAs) was introduced as a defect layer. Since crystalline quartz and magnesium oxide are both transparent for radiation in the THz and optical frequency range it is possible to excite free carriers near the surface of the GaAs defect by means of ultrashort 810 nm laser pulses.

As a result, the transmission of THz waves through the PC can be efficiently modulated by the external switching beam. This is shown in Fig.

15(b) where the spectral power transmission ratio between photo-excited PC and PC in the ground state is plotted for different pump fluences [ 105 ]. As a major advantage of this scheme, the modulation effect is significantly enhanced due to a high confinement of the THz electric field near the surface of the defect layer. In consequence, it is expected that a modulation depth of about 50 % can be obtained at incident pulse energies of the modulating laser source of 10 nJ which is considerably low. Furthermore, high modulation speeds of up to 100 ps have been observed.

However, a disadvantage is that THz radiation can only be modulated within a narrow transmission band, which is defined by the width of the defect mode, and therefore does not allow broad band modulation of THz waves. To date, both one- and two-dimensional photonic crystals have been employed as terahertz wave modulators.


–

27 21

Fig. 15 ( a ) Schematic of the photonic crystal. Regions P and Q are composed of alternating layers of a low

(L, white) and a high (H, dark) refractive index material. The region S represents the GaAs defect layer [ 33 ].

( b ) Ratio between the transmitted power of the photo-excited PC and the PC in ground state in dependence on the frequency for different pump pulse fluences (

μ

J/cm

2

): ( a ) 0.4, 1.0; ( b ) 0.8, 2.0; ( c ) 2.4, 6.1; ( d ) 5.3, 13.5;

( e ) 8.0, 20; ( f ) 26, 66 [ 105 ].

An optically controlled terahertz wave modulator based on nonlinear photonic crystals was theoretically proposed in [ 106 ]. The novel optically-controlled terahertz modulator relied on a nonlinear photonic crystal consisting of line and point defects as well as an organic polymer with fast nonlinear response, polyaniline, which was embedded in the point defects. As determined by the Kerr effect, the refractive index of polyaniline changes rapidly under the control of an applied pump intensity. In effect, the mode frequency in the point defect shifts dynamically and on/off modulation of terahertz waves can be realized. The

Fig. 16 ( a ) Top view of the two-dimensional photonic crystal (PC). The PC is composed of holes in silicon.

The holes are filled with a liquid crystal. Upon application of an electric field on the electrodes, the photonic band gap of the PC can be tuned and the transmission of a THz wave can be controlled and, as can be seen in

Fig. 16( b ), can be switched off. ( c ) Photonic band gap of the PC without application of an electric field and ( d ) with application of an electric field [ 107 , 108 ].


–

27 modulation rate of the device was calculated to be about 2.5 GHz. Although nonlinear PCs seem promising candidates for fast THz wave modulation, no experimental results verifying this prediction have been presented to date.

Other proposed modulation schemes are targeted toward active tuning of the photonic band gap of a PC. The basic idea is to modify the refractive-index contrast of the alternating

PC layers by using a pump laser, electric field, magnetic field or by variation of temperature.

Recently, Li et al. [ 107 , 108 ] theoretically proposed a new kind of terahertz wave modulator by using two-dimensional PCs. The terahertz wave modulator consists of a silicon photonic crystal slab comprised of a triangular lattice of air holes filled with a liquid crystal. The ON-

OFF mechanism roots in a dynamic band gap shift induced by an applied electric field.

Figure 16(a) shows a top view of the proposed terahertz wave modulator and the spatial electric field distribution of a traveling THz wave along the PC. Upon application of an electric field at the electrodes the refractive index of the liquid crystals is changed from n

1.53 and n

LC

LC

0

0

1.75 and the transmission of the THz wave can be switched on and off as can be seen by comparing the electric field distribution in Fig.

16(a) and (b) . As illustrated in

Fig.

16(c) and (d) the modulation effect relies on tuning of the photonic band gap from a lower and upper frequency boundary of 0.272-0.324(a/ l

) to 0.265-0.292(a/ l

) by photoinducing a refractive index shift of the liquid crystals from n

LC

0 1.53 to n

LC

0 1.75. Hereby, a is the lattice constant of the PC and l is the wavelength. Calculations showed that the extinction ratio was as high as 29.9 dB at response times of 100

μ s. The terahertz wave

Table 1 The table summarizes some characteristic quantities of optically, electrically and thermally driven terahertz wave modulators for various material systems. The modulators are evaluated with respect to the modulation bandwidth f

Mod and the relaxation time t as well as the operating frequency f . Furthermore, approximate values of the modulation depth are estimated. The modulation depth was defined by M

ð

E max

E min

Þ =

E max

, where E max is the maximal transmitted electric field amplitude and E min

A2

¼ is the minimal transmitted field amplitude. The last column refers to the reference number as listed in the reference section.

Method Material

τ or f

Mod

Operating Frequency f Mod Depth M

A2

Ref

Optical

Optical

Optical

Optical

Optical

Optical

Optical

Optical

Electrical

Electrical

Electrical

Electrical

Electrical

Electrical

Electrical

Electrical

Thermal

Thermal

Silicon

Silicon

GaAs

Silicon

InSb (grating)

Meta/GaAs

Meta/ErAs/GaAs

Meta/SOS

GaAs/AlGaAs (2DEG)

Meta/nGaAs

GaAs (hole array)

Meta/nGaAs

Meta/nGaAs

Meta/HEMT

Graphene

Meta/Graphene

Meta/VO2

Meta/YBCO

-

-

-

28 ms

430 ns

10 ns

5 ns

~ps

-

20 ps

-

-

-

-

100 kHz

2 MHz

10 MHz

-

2.5 THz

2.5 THz

1.4 THz

1.4 THz

-

0.56 THz

0.75 THz

0.6 THz

0.1-2 THz

0.72 THz

-

0.63 THz

-

0,46

0.57-0.63 THz

0.68 THz

1.0 THz

0.61-0.55 THz

-

-

-

0.25 %,1 %

80 %

35 %

70 %

3 %

30 %

33 %

36 %

-

33 %

9 %%

59 %

70 %

90 %

[ 61 ]

[ 62 ]

[ 63 ]

[ 68 ]

[ 71 ]

[ 77 ]

[ 82 ]

[ 23 ]

[ 24 ]

[ 25 ]

[ 26 ]

[ 34 ]

[ 39 ]

[ 40 ]

[ 46 ]

[ 47 ]

[ 53 ]

[ 59 ]


–

27 23 modulator can operate at room-temperature. Although not shown to date, it is expected that these devices can be readily fabricated using Si-based large-scale integrated technology.

8 Conclusion

We reviewed and compared different modulation techniques for manipulation of the electromagnetic properties of waves in the terahertz frequency regime. Modulators have been generally categorized considering three different properties. First of all, we classified the modulators with respect to the physical quantity to be modulated, as e.g. amplitude, phase and frequency modulation, polarization and pulse shape control etc. Second of all, we distinguished between the different material systems that are employed for the conception of terahertz wave modulators such as semiconductors, graphene, photonic crystal structures and metamaterials or combinations of the aforementioned materials and third of all we discussed a variety of modulation schemes such as electronic, all-optical, thermal, magnetic and nonlinear modulation. Furthermore, we compared the modulator devices with respect to modulation speed and modulation depth and discussed the pros and cons of the different approaches. The results are summarized in Table 1 . Based on the review paper, the reader should obtain guidelines for the proper choice of a modulation scheme in the light of the specific demands of the targeted application.

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