Electric field, Magnetic field and Magnetization: THz time-domain spectroscopy studies

(1)

THz time-domain spectroscopy studies

Proefschrift

ter verkrijging van de graad van doctor aan de Technische Universiteit Delft,

op gezag van de Rector Magnificus prof. ir. K. C. A. M. Luyben, voorzitter van het College voor Promoties,

in het openbaar te verdedigen op maansdag 6 July 2015 om 12:30 uur

door Nishant Kumar Master of Science in Photonics

Cochin University of Science and Technology, Cochin, India geboren te Patna, India.

(2)

Prof. dr. P. C. M. Planken

Samenstelling promotiecommissie:

Rector Magnificus, voorzitter

Prof. dr. P. C. M. Planken, Technische Universiteit Delft/ARCNL, promotor Dr. A. J. L. Adam, Technische Universiteit Delft, copromotor Prof. dr. H. P. Urbach, Technische Universiteit Delft

Prof. dr. H. J. Bakker, FOM-Instituut voor Atoom- en Molecuulfysica Prof. dr. L. D. A. Siebbeles, Technische Universiteit Delft

Prof. dr. Ir. L. J. van Vliet, Technische Universiteit Delft Dr. W. A. Smith, Technische Universiteit Delft

This work was funded by the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO) and the Stichting voor Technische Wetenschappen (STW). Copyright c 2015 by N. Kumar

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means: electronic, mechanical, photocopying, recording or otherwise, without prior written permission of the author.

isbn:

Printed in the Netherlands by Ipskamp Drukkers, Enschede. A free electronic version of this thesis can be downloaded from: http://www.library.tudelft.nl/dissertations

(3)

(4)

(5)

1 Introduction 1

1.1 Terahertz radiation . . . 1

1.2 Applications of THz radiation . . . 2

1.3 THz time domain spectroscopy . . . 2

1.4 Generation of THz radiation. . . 4

1.4.1 Biased semiconductor emitters . . . 4

1.4.2 Photo-Dember effect . . . 6

1.4.3 Optical Rectification . . . 6

1.5 Terahertz detection mechanisms. . . 8

1.5.1 Electro-optic detection. . . 8

1.5.2 Magneto-optic detection . . . 9

1.6 Measuring the THz electric near-field. . . 9

1.7 Scope and organization of the thesis . . . 11

2 THz near-field Faraday imaging 13 2.1 Metamaterials. . . 13

2.1.1 Split-ring resonator. . . 15

2.2 Imaging the terahertz magnetic field . . . 17

2.2.1 Measuring the terahertz magnetic far-field. . . 17

2.2.2 Imaging terahertz magnetic near-field . . . 18

2.3 Experimental . . . 19

2.3.1 Sample fabrication . . . 19

2.3.2 Results and Discussions . . . 20

2.3.3 Single point measurement . . . 21

2.3.4 Two dimensional distribution . . . 23

2.4 Double Split Ring Resonator . . . 25

2.4.1 Single point measurements . . . 26

2.5 Conclusion . . . 27

2.6 Complementary split ring resonators . . . 29

2.6.2 Single point measurement . . . 31

(6)

3 THz emission from ferromagnetic metal thin films 35

3.1 Ferromagnetism. . . 35

3.2 Laser-induced ultrafast demagnetization . . . 37

3.2.1 Historical review . . . 37

3.3 THz emission from non-magnetic metal thin films. . . 41

3.4 THz emission from ferromagnetic metal thin films . . . 41

3.5.2 THz generation and detection setup . . . 43

3.5.3 Magnetic force microscopy. . . 44

3.6 Result and discussions . . . 45

3.6.1 THz emission from cobalt thin film . . . 45

3.6.2 Azimuthal angle dependence . . . 46

3.6.3 THz emission in back reflection . . . 48

3.6.4 Thickness dependent THz emission . . . 49

3.6.5 MFM measurements . . . 50

3.8 Effect of capping layer on the Terahertz emission . . . 54

3.8.1 THz emission from Pt/Co thin films . . . 55

3.8.2 Relation between the magnetic order and THz emission . . 56

3.8.3 Azimuthal angle dependence . . . 57

3.8.5 Effect of changing the order of the films on THz emission . 59 3.9 Conclusions . . . 60

4 THz emission from BiVO4/Au thin films 61 4.1 Motivation . . . 61

4.2 THz generation from semiconductors . . . 61

4.2.1 Surface field effect . . . 62

4.2.2 Photo-Dember effect . . . 64

4.3 Bismuth Vanadate . . . 65

4.3.1 BiVO4structure . . . 66

4.3.2 Preparation of BiVO4 thin film . . . 67

4.4.2 THz generation and detection setup . . . 68

4.5 Results and discussion . . . 70

5 Conclusions 77

Appendix 79

Bibliography 80

(7)

Samenvatting 97

Acknowledgements 101

(8)

(9)

1

Introduction

1.1 Terahertz radiation

Terahertz (THz) radiation is electromagnetic radiation which spans the frequency range from 0.1 THz to 10 THz. In terms of wavelengths, it ranges from 30 µm to 3 mm. The THz region of the electromagnetic spectrum lies between the microwave and the infrared regions, as shown in Fig.1.1. Until recently, this region was also known as the “THz gap” since efficient sources and detectors for THz radiation were not available. The THz region is located where both electronic means and optical means to generate light exist [1]. For example, low frequency THz radiation can be made by electronically multiplying a lower frequency source [2]. A methanol gas laser, on the other hand, is an example of an optical source of THz radiation [3]. THz radiation has many interesting applications. For example, it can pass through many dielectric materials which are opaque to visible radiation and can thus be used for imaging purposes. Unlike X-rays, THz radiation is non-ionizing and has little effect on biological samples [4]. Many crystalline organic materials have unique absorption spectra in the THz range which can be used as an optical fingerprint and therefore can be used to identify the chemical structure of the materials [5]. For example, Walther et al. showed that, by using THz radiation, polycrystalline sucrose can be easily differentiated from other sugars [6].

Radio

waves

Micro

waves

Visible

X-rays

Υ-rays

Electronics

Photonics

THz

gap

106

109 1012

1015

1018

1021

Frequency (Hz)

Infrared

1014

(10)

1.2 Applications of THz radiation

THz radiation is very effective for the analysis of solids, liquids or gases. Several materials have characteristic strong absorption lines in the THz frequency range. For many gas molecules, the energy required for the transitions between the ro-tational energy levels lies in the THz region. For example, dichloromethane has rotational lines with transitions up to 2.5 THz [7].

In the solid crystalline phase, the atoms or molecules are held close to their equi-librium positions which leads to collective lattice vibrations at certain frequencies. These low frequency vibrations of molecules in the solid state can often absorb THz radiation [7]. Furthermore, in the case of semiconductors, absorption of THz radiation is due to free electrons. THz radiation is non-ionizing radiation and can be used for non-invasive and non-destructive imaging and spectroscopy.

THz radiation can pass through many packaging materials such as cardboard, cloth, paper, ceramics and plastics. Hence, THz radiation can be used for package inspection, security screening and quality control. For example, in 1995, Hu et al. showed that THz radiation can be used to find defects in computer chips [8]. THz radiation is safe for humans and could be used for biomedical imaging [9]. It might be used for cancer detection, endoscopy and detection of tooth decay [10]. THz radiation is often used for the characterization of old paintings, the detection of explosives, drug screening, food inspection and to identify the chemical composition of materials [11,12]. THz radiation can not only image the hidden underlying paint layers but can also give spectroscopic information on different paint layers [13,14]. THz radiation also has potential applications in the field of near-field imaging. Using a THz near-field microscope, it is possible to achieve a subwavelength spatial resolution [15,16].

THz radiation has a lot of potential to be used for communication purposes. Compared to microwaves, the THz band provides a larger bandwidth and, conse-quently, a potentially higher transmission rate. The low power and low efficiency of THz sources and the strong absorption by water vapor present in the atmo-sphere are some disadvantages of using THz radiation. However, it is possible to use THz radiation for communication over shorter distances and for satellite to satellite communication, where atmospheric absorption is not a problem [17].

1.3 THz time domain spectroscopy

Terahertz time domain spectroscopy (THz-TDS) is a spectroscopic technique that uses THz radiation to probe the properties of materials. The basic idea of THz-TDS is that we measure the electric field of the THz pulse as a function of time. If the THz pulse passes through a material, its time profile gets changed compared to the reference pulse. The reference pulse can be a pulse propagating in vacuum or in a medium with known properties. By comparing the THz pulse transmit-ted through the medium with the reference THz pulse we can find the changes introduced by the material [18].

In Fig.1.2we show a typical experimental setup for THz generation and detec-tion. A femtosecond laser pulse is split into two parts using a 80:20 beam splitter.

(11)

The part of the beam with higher energy is called the pump beam and the lower energy one is called the probe beam. The pump pulse is incident on the emit-ter at a 45◦angle of incidence and the THz radiation is collected in the reflection direction. The experimental setup is described in detail in chapter 3 and chapter 4.

Electro-optic detection Sample THz Beam Pump Beam Probe Beam Beam Splitter Detection Crystal Quarter Waveplate Wollaston prism Differential Photodetectors Parabolic Mirrors Femtosecond Laser THz reflection setup

Figure 1.2: Terahertz far-field experimental setup.

A typical measurement of the THz electric field as a function of time is shown in Fig.1.3(a). The corresponding THz frequency spectrum is obtained by taking the Fourier transform of the emitted THz electric field, which is shown in Fig.1.3(b). THz-TDS measures the electric field instead of the intensity of a light pulse and hence gives information about both the amplitude and the phase of the light. Using THz-TDS, the absorption coefficient and the refractive index of a sample at different frequencies can be calculated simultaneously without the need for a physical model of the absorption [19].

(a) (b)

Figure 1.3: (a) Measured temporal waveform of a THz pulse generated in a gallium phosphide (GaP) (110) crystal by optical rectification and (b) the corresponding calculated frequency spectrum. As a detection crystal we have selected GaP, which is 300 µm thick.

(12)

1.4 Generation of THz radiation

There are different ways of generating THz radiation and in this thesis we will focus only on the optical methods of THz generation. This includes generation of THz radiation from biased semiconductor emitters, THz emission due to the photo-Dember effect and THz emission due to optical rectification.

1.4.1 Biased semiconductor emitters

When a femtosecond laser pulse is incident on a semiconductor, if the energy of the photons is greater than the bandgap energy of the semiconductor, electron-hole pairs are generated. Due to the applied bias these carriers accelerate and a transient photocurrent is formed on a subpicosecond time scale. The bias can be either an externally applied voltage, as in the case of a photoconductive antenna, or it can be an intrinsic electric field, as in the case of depletion field emitters.

Photoconductive antenna - The photoconductive antenna (PCA) is one of the most common and efficient sources of THz radiation. A schematic diagram of a PCA is shown in Fig.1.4. In a PCA, we have a semiconductor with two electrodes attached to the surface [20]. These electrodes are biased with an externally applied voltage. When charge carriers are excited using a fs laser pulse, this external bias accelerate the carriers to form a photocurrent J(t).

Electrodes +V -V fs laser pulse THz pulse SI-GaAs substrate Silicon lens -Current + -+ -+

Figure 1.4: Schematic diagram of generation of THz radiation from a photocon-ductive antenna. When a femtosecond laser pulse is incident on the semiconductor, electron-hole pairs are generated. These carriers are accelerated due to the applied bias and form a current on a sub picosecond time scale, which generates electro-magnetic radiation in the THz range.

Since, the mobility of electrons is usually much higher than the mobility of holes, the contribution of holes in the transient current can typically be neglected. The

(13)

magnitude of the transient photocurrent is described as [21] :

J (t) = N (t) |e| v(t) = N (t) |e| µEb, (1.1) where N(t) is the density of photoexcited electrons, e = 1.6 × 10−19C is the charge per electron, v(t) is the velocity of the electrons, µ is the mobility of the electrons and Eb is the bias electric field.

The photocarrier density is a function of time and depends both on the carrier life time τc and the shape of the laser pulse. The charge carriers recombine and the photocurrent decays. This transient photocurrent generates electromagnetic, pulsed radiation in the THz frequency range. The THz radiation is emitted in the direction of the propagation of the laser pulse and also in the direction of the reflected laser pulse. The polarization of the generated THz radiation is parallel to the applied bias field. The far electric field of the radiated THz radiation, ET Hz, is proportional to the first time derivative of the photocurrent J(t),

ET Hz∝ ∂J (t)/∂t = |e| [N (t)∂v(t)/∂t + v(t)∂N (t)/∂t]. (1.2) Equation 1.2 demonstrates that the time varying photocurrent and, hence, the THz emission depends on two phenomena: 1) acceleration of carriers and 2) ul-trafast variation in carrier density. The number of free carriers depends on the optical power provided by the laser pulse and on the material itself whereas the acceleration of these free carriers depends on the applied bias voltage. However, the laser power and the bias voltage can be increased only till a threshold limit because of the device saturation and/or the device breakdown [22].

In our setup, we have used semi insulating-GaAs as the semiconductor substrate for fabricating the photoconductive antenna. On the back of the GaAs substrate, we have used a hyperhemispherical silicon lens for coupling out and collimating the THz radiation efficiently. Also, instead of applying a DC bias voltage, we have used a 50 kHz, 400 V square wave ac bias voltage. When the voltage changes from -400 V to +400 V, the sign of the THz signal also changes. Hence, the signal detected by the lock-in is double the signal obtained with a DC bias voltage that changes from 0-400 V. As a result, the measured signal is increased without actually increasing the THz amplitude [23].

Depletion field emitter - THz emission from a depletion field is similar to THz emission from a photoconductive antenna. Charge carriers are generated by the photoexcitation of a semiconductor surface using a femtosecond laser. How-ever, instead of applying an external bias voltage as in PCA, in this case the charge carriers are accelerated due to an intrinsic electric field, present in the semiconduc-tor. This intrinsic electric field can be formed when a metal comes in close contact with an n-type semiconductor material. On contact, the electrons move from the semiconductor to the metal and an electric field is formed near the surface. This electric field is called the depletion field [24]. The direction of this field is from the semiconductor to the metal. The depletion field drives the two kinds of carriers in opposite directions and produces a photocurrent which leads to the formation of a dipole-like layer in the direction of the surface normal. This transient dipole emits a THz pulse [25]. The direction of the surface depletion field depends on

(14)

the type of doping. For n-type and p-type doping, the direction of the dipole is opposite and hence the polarities of the emitted THz pulses are opposite too. The formation of the depletion field and THz generation due to the depletion field are discussed in more detail in section 4.2.1 of this thesis.

1.4.2 Photo-Dember effect

In the case of narrow-bandgap semiconductors, when the depletion field is weak, THz generation is mostly due to the photo-Dember effect. In the photo-Dember effect, the laser light is strongly absorbed by the semiconductor material, so that the photoinduced electron-hole pairs form a concentration gradient close to the surface of the semiconductor. Since electrons often have a higher mobility than holes, they are able to diffuse faster. The combination of the concentration gradi-ent and the difference in mobilities generate a transigradi-ent dipole which emits THz radiation [26]. The electric field of the emitted THz radiation, ET Hz, is directly proportional to the derivative of the diffusion current Jd,

ET Hz ∝∂Jd

∂t . (1.3)

InAs and InSb are two examples of photo-Dember based THz emitters. Both materials have a very high ratio of electron to hole mobilities and a very narrow bandgap [27]. The photo-Dember effect is different from the depletion field effect. The polarity of THz radiation emitted by the photo-Dember effect does not depend on the doping type but it shows a strong dependence on temperature [28]. These differences make it possible to separate the contributions to the THz emission by the photo-Dember effect and from the current surge in the surface depletion region. THz generation due to the photo-Dember effect is discussed in more detail in section 4.2.2 of this thesis.

1.4.3 Optical Rectification

Another commonly used technique for the emission of THz radiation is optical rec-tification. The schematic representation of THz generation by optical rectification is shown in Fig.1.5. Optical rectification is a non-resonant method of generating THz radiation meaning that no absorption is needed to create THz light. It is ba-sically difference-frequency generation with the difference frequency close to zero. It is a second-order non-linear optical effect [21]. The dielectric polarization of the material is directly proportional to the applied electric field.

P = ε0χ(E)E (1.4)

Here, ε0 is the permittivity of free space and χ(E) is the electric susceptibility. The nonlinear optical properties of the material can be described by expanding the susceptibility χ(E) into a power series of the electric field E [18].

(15)

Here, optical rectification comes from the second term of the equation after the equality sign. If we consider an optical electric field E described by E = E0cos ωt, where E0 = E0(t) for a laser pulse, then the second-order nonlinear polarization P(2) _{is [}₁₈_]:

P(2)= ε0χ2E2= ε0χ2(E0cos ωt)2= ε0χ2E0 2 2 (1 + cos 2ωt) = P (2) OR+ P (2) SHG (1.6) The second-order nonlinear polarization is a sum of two terms. The first term is a quasi DC polarization (quasi, because E0 is not a constant but time-dependent since we are dealing with a laser pulse), which results from the rectification of the incident optical electric field by the second-order nonlinear electric susceptibility of the material. The second term shows a cos 2ωt dependence and describes second harmonic generation. Here, only the first term is relevant to the generation of THz radiation [18]. Optical rectification occurs only in those crystals that are not centrosymmetric – that is, crystals that do not display inversion symmetry. In such non-centrosymmetric crystals, the second-order non-linear susceptibility χ2 6= 0. When a femtosecond pulse is incident on such a crystal, due to the optical rectification of the femtosecond laser pulses, subpicosecond THz pulses are generated. In the far field, the radiated electric field E(t) is proportional to the second time derivative of P_OR(2) [21]:

ET Hz∝ ∂2P (2) OR/∂t 2 ∼ ∂2E0(2)/∂t 2 _(1.7)

Where, again, E0= E0(t)

Non-linear

optical crystal

Laser pulse

(fs)

THz pulse

(ps)

Figure 1.5: Schematic representation of THz generation by optical rectification. A femtosecond laser pulse is incident on a nonlinear optical crystal and due to optical rectification of the femtosecond laser pulses, THz pulses are generated.

One of the most important factors to take into account during THz genera-tion from non-linear non-resonant optical processes is phase matching. The phase matching condition is satisfied when the group velocity of the optical beam is equal to the phase velocity of the THz beam [21,29]. The advantage of using optical

(16)

rectification in non-absorbing materials, is that the response of the crystal is essen-tially instantaneous, in prinicple allowing for very short THz pulse durations. The bandwidth depends only on the width of the laser pulse and the phase matching conditions in the generation and detection crystals [21].

1.5 Terahertz detection mechanisms

The most common methods for detecting pulsed THz radiation are photoconduc-tive detection and electro-optic/magneto-optic detection. Here, we describe only the free-space electro-optic and magneto-optic detection methods in detail, be-cause only these detection methods are used in the experiments described in this thesis.

1.5.1 Electro-optic detection

The electro-optic detection method relies on a change of the polarization of the probe pulse induced by the instantaneous electric field of the THz pulse [30]. The schematic diagram for electro-optic detection of THz radiation is shown in Fig.1.6. Initially, when no THz radiation is incident on the electro-optic crystal, the linearly polarized probe beam remains linear even after passing through the crystal. Then, the linearly polarized probe beam passes through a quarter wave plate and becomes circularly polarized. A Wollaston prism splits this circularly polarized light into two beams with equal intensities and orthogonal polarizations. These two beams are focused on two photodiodes of a differential photodetector and since both components have the same intensity, the detector signal is zero. On the other hand, when THz radiation is incident on the electro-optic crystal, the electric field of the THz pulse induces a birefringence in the crystal which is proportional to the instantaneous THz field [31]. As a result of the birefringence, when the linearly polarized probe beam passes through the crystal, it becomes slightly elliptical. The quarter wave plate turns this into an elliptically polarized beam that deviates slightly from a circularly polarized beam. The Wollaston prism splits the elliptically polarized probe beam into two beams with orthogonal polarizations but, now, with unequal intensities. The output of the differential photodetector is proportional to the difference in the intensities of the two beams which is directly proportional to the instantaneous THz electric field. Hence, by measuring the change in the polarization of the probe beam as a function of delay between the probe pulse and the THz pulse, the THz electric field as a function of time can be measured, as shown in Fig.1.6[32].

Zinc telluride (ZnTe) and Gallium phosphide (GaP) are the most commonly used electro-optic crystals for THz detection. By increasing the thickness of the detection crystal we can increase the sensitivity of THz detection. However, in-creasing the thickness of the detection crystal also increases phase mismatching effects [18]. This leads to a smearing out of the detected THz field as a func-tion of time, which can have a negative effect on the shape of the detected THz spectrum [33].

(17)

Detection Crystal Quarter Waveplate Wollaston prism Differential Photodetector Probe beam THz beam Polarization states Probe THz pulse EO crystal ETHz(t) Iprobe(t)

Figure 1.6: Schematic diagram of THz detection using free space electro-optic sampling. The synchronised probe pulse samples the complete electric field of the THz pulse by varying the delay between the THz pulse and the probe pulse.

1.5.2 Magneto-optic detection

Similar to electro-optic detection we also have a magneto-optic detection scheme for THz radiation. In magneto-optic detection, instead of measuring the electric field of THz radiation, we measure the THz magnetic field using the Faraday effect. The linear polarization of the probe beam is rotated due to the THz magnetic field which is measured using a magneto-optic crystal [34,35]. The free space magneto-optic detection of THz radiation is discussed in more detail in section 2.2.1.

1.6 Measuring the THz electric near-field

THz radiation has been widely used for imaging applications. However, the spatial resolution that can be achieved when imaging with electromagnetic waves is limited by diffraction. The size of the smallest objects that can be spatially distinguished is theoretically about half of the wavelength of light. For a wavelength corresponding to a frequency of 1 THz, the far field spatial resolution of an image is limited to approximately 150 µm in vacuum. This constitutes a major issue in THz imaging of subwavelength-sized objects [36]. There are different techniques to break the diffraction limit and to achieve a better spatial resolution. One way to overcome this limit is to work in the near-field region of the sample [37]. When the size of the object is bigger or comparable to the wavelength of light, it has clearly a visible effect in the far-field, but when the object is of sub-wavelength dimensions,

(18)

it affects the field only in a volume around the object which is comparable to the size of the object itself. Hence, for the detection of subwavelength sized objects we need a measurement method which can measure the field in the immediate vicinity of the object. So, the idea is to capture the THz wave in the near field, very close to the sample surface [37]. The advantage of THz near-field imaging over optical near field imaging techniques is that it measures the electric field, rather than the intensity of the light. Many schemes have been proposed for imaging the THz electric near field, most of which involve an aperture, a tip or an electro-optic detection crystal [38]. In experiments related to the one described in chapter 2 of this thesis, electro-optic detection is used for imaging the THz near-field. For this reason, a brief description of this technique follows:

Electro-optic detection of the THz electric near-field : In near-field electro-optic detection, a tightly focused probe beam is used to detect the THz electric near-field in a small volume [39]. The schematic diagram for this is shown in Fig. 1.7. Gallium phosphide (GaP) is taken as a detection crystal [39]. On top of the GaP crystal a reflective coating for the 800 nm beam, which consists of 130 nm of SiO2 and 200 nm of Ge, is deposited. The sample in Fig. 1.7, il-lustrated as a hole in a gold film, is illuminated with a THz pulse from the top and a probe pulse is incident on the sample from below. The probe pulse samples the THz electric near-field of the structure and gets reflected due to the reflective coating. Then, the probe beam passes through a λ/4 waveplate and a Wollaston prism and is finally incident onto a differential detector. The coating also prevents any probe light from reaching the sample, getting scattered and measured by the detector [39]. The spot of the probe beam is used as a synthetic aperture and only that part of THz radiation is detected which is present in the path of the probe beam. The radius of the focal spot of the probe beam (800 nm) is related to its own wavelength which is much smaller than the THz wavelength. Thus, this method circumvents the THz diffraction limit [37,40]. By selecting the orientation of the detection crystal, it is possible to select for which component of the THz electric near-field vector an electro-optic detection setup is sensitive. For exam-ple, (100) oriented GaP or ZnTe crystals measure the component of the electric near-field which is perpendicular to the sample surface, being blind to the in-plane (x and y) components of the electric near-field [39]. Similarly, we can measure the in-plane (x and y) components using a (110) crystal orientation [33,37]. The electro-optic crystal is mechanically raster scanned in all three directions to mea-sure the electric near field and pixel by pixel an image is obtained. To obtain a high spatial resolution, the electro-optic crystal should be thin and the interaction region should be small. Hence, the probe beam should be well focused onto the detection crystal [38].

Adam et al. measured the THz electric near-field in the vicinity of subwavelength sized metallic spheres [40]. The same technique has been used for measuring the electric near-field of many other structures and to perform microspectroscopy in the THz frequency range [41–47].

In 2007, Bitzer et al. measured the in-plane electric near field distributions of split-ring resonators [48]. A split-ring resonator (SRR) is a single ring, or concen-tric rings, of metal containing a gap. Later, the same group showed THz elecconcen-tric

(19)

Ge SiO2 Gold GaP

THz

beam

Sample

scan

Detector

Probe

beam

Figure 1.7: Schematic diagram of THz detection using free space electro-optic sampling

near-field measurements of a complementary split-ring resonator (CSRR). They showed that the magnetic near-field of a SRR and a CSRR can be calculated from the electric near-field measurements [49]. Direct measurement of the mag-netic near-field at THz frequencies is very challenging. Until recently, only far field measurements of the THz magnetic field, using the Faraday effect, have been shown by Riordan et al. [35].

1.7 Scope and organization of the thesis

Till now, we have discussed the generation and detection of, mostly, the THz elec-tric field and the use of static elecelec-tric fields for the generation of THz light. In general, very little work has been done in the THz domain involving magnetic fields. In this thesis we study magnetic field aspects of THz generation and detec-tion. In Chapter 2, we report on the first direct measurement of the THz magnetic near-field of split ring resonators using a magnetic field sensitive material. The THz electric near-field of such a split-ring resonator has been measured before but the magnetic near-field of a split-ring resonator is relatively weak and has never been measured before. In chapter 3 we discuss emission of THz radiation due to ultrafast demagnetization of ferromagnetic thin films. The THz electric

(20)

field emitted from thin cobalt films changes sign when the sample is rotated by 180◦. However, for thicker cobalt layers, we observe the development of an az-imuthal angle-independent contribution to the THz emission. Hence, for thick cobalt films, the polarity remains unchanged with 180◦sample rotation. We corre-late these findings with a change in the magnetization of these films from in-plane, to out-of-plane for increasing Co layer thickness, as measured using magnetic force microscopy.

In contrast to the previous chapters, in chapter 4 the magnetic field does not play a role. In this chapter, we show generation of THz light from BiVO4/Au thin films. The motivation behind this study is that BiVO4 is a wide-bandgap semi-conductor, similar to Cu2O. Recently it has been shown that when femtosecond laser pulses with 800 nm wavelength are incident on Cu2O/metal interfaces, strong THz emission is observed. This is surprising, because the energy of the correspond-ing photons is much smaller than the bandgap of cuprous oxide. Therefore, it is interesting to try other large bandgap materials as well, especially BiVO4, which is technologically relevant. BiVO4 is widely used in the pigment industry and has potential applications for photoelectrochemical water splitting. We find that BiVO4/Au interfaces emit small amplitude THz pulses, when illuminated with below-gap femtosecond laser pulses. By studying the THz radiation emitted from these interfaces we propose that the most likely cause of the THz emission is the photo-Dember effect. Finally, chapter 5 summarizes the experiments described in this thesis.

(21)

2

THz near-field Faraday

imaging

2.1 Metamaterials

Recently, there has been a lot of interest in metamaterials because of their exotic properties and potential applications. These materials can manipulate light in remarkable ways and have optical properties which are not available in nature. Metamaterials provide a design-based approach to create novel electromagnetic functionality. This functionality spans the spectrum from the microwave domain to the visible domain with examples including cloaking and superlensing [50]. One can think of metamaterials as pseudo materials in which periodically or randomly distributed structures constitute the “atoms”. The size of the structures and the spacing between them is much smaller than the wavelength of the electromagnetic radiation. When electromagnetic radiation is incident on these materials, we can pretend that the material is electromagnetically homogeneous. The properties of a metamaterial are determined by the properties of the material from which each of the individual elements is formed, the shape or the structure of the individual ele-ments and the interaction between them. Metamaterials are characterized by two fundamental macroscopic parameters: relative permittivity (εr) and permeability (µr). The electric permittivity and magnetic permeability define the response of the material when an oscillating electric field or magnetic field is applied. In the case of metamaterials, the effective permittivity or permeability is an average or collective response of all the elements of which the metamaterial is made. By properly designing the structures we can control the relative permittivity and per-meability. This has been used recently for various applications like imaging with subwavelength spatial resolution, artificial magnetism, and to obtain a negative refractive index [51].

In Fig. 2.1 we show the optical properties of the materials for different signs of the permittivity (εr) and permeability (µr). In the case of ordinary optical materials, the permittivity and permeability are usually positive (εr> 0, µr> 0), as shown in the first (top-right) quadrant. The refractive index of such materials is given by n =√εrµr. In this case, the phase velocity is in the direction of the Poynting vector. The electric field ~E, the magnetic field ~H, and the wave vector ~_{k form a right handed set of vectors. Hence, these materials are also called right} handed materials, which support forward propagating waves.

(22)

μ

< 0,

Artificial Metamaterials

Evanescent decaying wave

Backward propagating wave

μ > 0

ε < 0, μ < 0

ε > 0,

Evanescent decaying wave

μ < 0

E

k H

S

Ordinary optical materials

μ > 0

> 0,

Forward propagating wave

E

H k

S

Metals, doped semiconductors

(below plasma frequency)

Some ferromagnetic metals

(up to GHz)

S S

(imaginary)

n =

(real)

ε

(ε μ )¹ ²

/

> 0

ε

r

r r r r r r

n = (ε μ )¹ ²

r r /

(real)

< 0

n = (ε μ )¹ ²

r r /

n = (ε μ )¹ ²

r r /

(imaginary)

r r r r

Figure 2.1: Classification of materials based on their permittivity, εr, and perme-ability, µr. Here, materials are divided into four different quadrants. (Quadrant I): Both, εr and µr are positive. Most ordinary optical materials fall in this quadrant. (Quadrant II): εris negative and µr is positive. Metals and heavily doped semicon-ductors below plasma frequency fall in this quadrant. (Quadrant III): Both, εr and µrare negative. No natural materials, only metamaterials show such characteristics (Quadrant IV): εris positive and µr is negative. Some ferromagnetic materials near resonance frequency belong to this quadrant. Here, ~E is the electric component of the plane wave, ~H is the magnetic component of the plane wave, ~k is the wave vector and ~S is the Poynting vector, where the Poynting vector is defined as ~S =

~ E× ~H.

However, metals form an exception having a negative value for the real part of the permittivity in a large range of the electromagnetic spectrum. Metals and doped semiconductors can display a negative permittivity and a positive

(23)

perme-ability (εr < 0, µr > 0), below the plasma frequency and fall in the second (top-left) quadrant. On the other hand, the permeability of ferromagnetic mate-rials is negative whereas their permittivity is positive (εr > 0, µr < 0), near the ferromagnetic resonance frequency [50] and they thus fall in the fourth (bottom-right) quadrant. For materials with either permittivity or permeability less than zero, the refractive index is imaginary, which supports the existence of evanescent waves.

In 1968, Veselago proposed the concept of materials having simultaneously a negative permittivity and a negative permeability (εr < 0, µr < 0, third quadrant/bottom-left quadrant), at a specific frequency [52]. In 1996, Pendry argued that a negative permittivity can be achieved by a periodic array of thin metallic wires and confirmed it experimentally in 1998 [53,54]. Subsequently, in 1999 Pendry showed that an effective negative permeability can be achieved by using split ring resonators [55]. In 2000, Smith et al. demonstrated that on com-bining an array of split-ring resonators (negative permeability), with an array of metallic thin wires (negative permittivity), a negative refractive index is achieved in the microwave regime, n = −√εrµr [56,57]. Hence, such materials are also called “double negative materials”. In this case, the phase velocity is opposite to the flow of energy or poynting vector, and instead of forming a right handed set of vectors, ~E, ~H, ~k forms a left handed set of vectors. Hence, these mate-rials are also called left handed matemate-rials, which support backward propagating waves [58]. In such materials, Snell’s law, the Doppler effect, Cherenkov radiation etc. are completely reversed with respect to materials with a positive refractive index. Lately, several metamaterial structures have been realized with various types of constituents such as thin wires, swiss rolls, split-ring resonators (SRRs), pairs of rods, pairs of crosses, fishnets etc [59].

2.1.1 Split-ring resonator

The split-ring resonator (SRR) is one of the most common and most widely used metamaterial elements. Typically, SRRs are fabricated using highly conducting metals and they are used to obtain a negative magnetic permeability. In Fig.2.2(a) we show the design of a single split ring resonator (sSRR) where d is the length of the arm, t is the width of the arm, g is the gap width and h is the thickness of the metal of the split-ring resonator. A SRR can be represented by an LC circuit. The equivalent circuit for a sSRR is shown in Fig.2.2(b). The capacitance C is associated with the charge accumulation at the gaps and the inductance L with the current circulating in the resonator [60]. The capacitance (C) of a SRR is generally calculated as [61],

C = ε0εght

g (2.1)

where ε0 is the vacuum permittivity, εg is the effective relative permittivity of the material in the gap. εg is influenced not only by the medium inside the gap but also by the dielectric constant of the substrate.

(24)

d g h t

L

C

Equivalent LC circuit

Capacitor Inductor

b)

a)

c)

dSRR

sSRR

d g t g

Figure 2.2: (a) Design of the single split ring resonator (sSRR) (b) Equivalent LC circuit (c) Design of the double split ring resonator (dSRR). The incident THz electric-field (blue) is polarized parallel to the gap. It generates current flowing in the arms of the resonator, leading to a single magnetic “dipole” for the sSRR and two opposite magnetic “dipoles” for the dSRR.

The inductance (L) of a SRR depends on the geometric shape of the ring. For a planar square split-ring resonator, it is given by [62],

L = N µd 2 h = µ0

d2

h (2.2)

Here, N (number of turns in coil)=1 and µ = µrµ0 (where µr=1 for air).

Where, µ is absolute permeability, µr is relative permeability and µ0 is the per-meability of free space.

The resonance frequency is given by [62],

fLC= 1

(25)

fLC= 1 2πd r g t 1 √ ε0µ0εg = 1 2πd r g t c0 √ εg (2.4) where c0is the velocity of light in vacuum.

The resonance wavelength is given by, λLC= c0 fLC = 2πd√εg r t g. (2.5)

The resonance frequency and wavelength of the SRR depend on the dimensions of the SRR and hence can be tuned by scaling the geometrical parameters of the SRR. When the incident electric field is parallel to the arm containing the gap of the SRR, the electric field capacitatively couples to the SRR and generates a current in the loop. This circulating current generates a magnetic field in the SRR. The magnetic field, induced by the current, is strongest at the resonance frequency of the SRR, which is determined by the loop inductance and gap capacitance as depicted in Fig.2.2(a) and2.2(b).

The single SRR (sSRR) in Fig.2.2(a) is but one of a myriad of design possibilities for subwavelength magnetically active resonators. For example, Fig.2.2(c) depicts a double SRR (dSRR) which is simply two sSRRs placed back-to-back. Electric field excitation drives counter circulating currents in this structure resulting in two oppositely directed “magnetic dipoles”. Thus, the magnetic dipoles cancel and the bulk effective response of an array of dSRRs is described by an effective electric permittivity. In short, the magnetic fields associated with these magnetic “dipoles” are of opposite sign, originate from a subwavelength area, and thus largely cancel in the far field.

2.2 Imaging the terahertz magnetic field

When electromagnetic radiation interacts with matter, usually the magnetic field component of light couples very weakly to the atoms compared to the electric field component. Thus, it is very difficult to detect the effect of a magnetic field com-ponent on matter. Enhanced magnetic light-matter interaction can be achieved by using artificial magnetic “atoms”. In metamaterials, by tailoring the geometry of the constituent resonating structures, an enhanced response to the magnetic field can, in principle, be achieved. Usually, when we study metamaterials, we study their response in the far-field which gives information about the macroscopic parameters, like effective relative permittivity and permeability. However, their unique optical properties are derived from the near-field interactions including magnetic near-field interactions. So, to understand the properties of metamateri-als, near-field information is important.

2.2.1 Measuring the terahertz magnetic far-field

When linearly polarized light passes through a transparent magneto-optic mate-rial placed in a uniform magnetic field, the transmitted light has its polarization

(26)

rotated. This effect is known as the Faraday effect (see Fig.2.3(a)). The rotation angle is proportional to the component of the magnetic field in the propagation direction of the probe beam. The rotation angle of the polarization of the probe beam is θ(t) = V B(t)Lcosγ, where V is the Verdet constant of the material, B(t) is the magnitude of the magnetic field, L is the interaction length of the THz and optical beams inside the crystal and γ is the angle between the direction of the magnetic field and the propagation direction of the probe beam. For maximum rotation, γ = 0, i.e. the propagation direction of the probe beam and the direction of the magnetic field are parallel to each other. In 1997, Riordan et al. measured the transient magnetic field component of THz radiation using free space magneto-optic sampling [35]. The authors demonstrated that the magnetic component of THz radiation induces a circular birefringence in the magneto-optical sensor via the Faraday effect and when a probe beam passes through the crystal, the linear polarization of the probe beam is rotated (see Fig.2.3(b)).

(a)

(b)

β B d Faraday’s rota"on Plane of polariza"on Plane of polariza"on rotated by angle THz beam Linearly polarized probe beam Magneto-op"c sensor β

Free space magneto-op"c sampling

E BTHz

Figure 2.3: (a) Faraday rotation (b) Free space magneto-optic sampling.

2.2.2 Imaging terahertz magnetic near-field

It is difficult to measure the electric and magnetic near-fields experimentally be-cause they are strongly localized and cannot be observed using conventional, far field, imaging techniques which cannot “see” objects smaller than half-of-a wave-length. Although, it is possible to calculate the magnetic near-field from mea-surements of the electric near-field [41,48,63], such a method amplifies noise and inaccuracies. In addition, a calculation of the magnetic near-field requires two measurements, namely that of Ex and Ey with equal sensitivity. At optical wave-lengths, only indirect measurements of the magnetic near-field [64], the amplitude of the magnetic field [65], or its polarization have been reported [66]. At microwave frequencies, only a simple microstrip line has been investigated [67] while no direct measurements have been reported at THz frequencies. In fact, for both sSRRs and dSRRs, the near-field magnetic distribution is expected to be non-trivial. Nev-ertheless it is important to have magnetic near-field information because deep subwavelength measurements of the magnetic near-field with high spatial resolu-tion can shed light on the strength and distriburesolu-tion of the local magnetic field and the near-field magnetic interaction between neighboring resonators.

(27)

2.3 Experimental

We directly measure the magnetic near field of SRRs that are resonant at ter-ahertz frequencies. This is accomplished using near-field terter-ahertz time domain spectroscopy (THz-TDS). Our structures are deposited on terbium gallium garnet (TGG) substrates. TGG is a magneto-optic crystal providing a linear Faraday rotation, that is, a rotation of the plane of polarization of an optical beam is lin-early proportional to the strength of an external magnetic-field pointing in the optical beam propagation direction. TGG doesn’t show any second order electro-optic effects and it is generally used as a polarization rotator or isolator. In combination with THz-TDS, TGG (Verdet constant of 60 radT−1m−1at 800 nm) has previously been used to measure the free-space time-dependent magnetic field component parallel to a probe beam [35]. Adapting this technique allows us to measure the two-dimensional spatial distribution of the magnetic near-field which strongly varies in a small region of space of only several tens of microns, about two orders of magnitude smaller than the wavelength of the THz light.

2.3.1 Sample fabrication

The sSRR and dSRR resonators (as shown in Fig. 2.4(a) and Fig. 2.4(b)) have been fabricated on TGG. Table 2.1 details the dimensions and simulated reso-nance frequencies of the SRRs. The resoreso-nance frequency given in the table is the resonance frequency of the resonator on TGG, not the resonance frequency of a resonator in free space. The presence of TGG lowers the resonance frequency. The numerical simulations were performed by using the commercial software package CST Microwave Studio. The measured and calculated resonance frequencies for different SRRs and a dSRR are also listed in the table.

For calculating the resonance frequency of a split-ring resonator analytically, we use the formula given in equation 2.4. As we can see from the equation, the calculated resonance frequency depends on the geometrical parameters of a split-ring resonator and also on the effective relative permittivity (εg) of the material in the gap, which is in air in this case. However, εg is also affected by the dielectric constant of the substrate, which is TGG. Hence, the actual εg should be some weighted average of the dielectric constants of the TGG substrate and air. We have calculated the resonance frequencies of SRRs for εg = εT GG = 12.4 and for εg= εair =1 and then we get a range in which the actual resonance frequency will be present, which is shown in table 2.1.

Before fabrication, we first deposit a reflective coating for the 800 nm beam consisting of 130 nm of SiO2 and 300 nm of Ge on top of a 1 mm thick (111) TGG crystal. Standard electron-beam lithography was used for patterning the resonators, which consists of 200 nm thick gold with a 10 nm layer of titanium for adhesion to the Ge layer. The design of the sample is shown schematically in Fig.2.5(a).

(28)

Table 2.1: Summary of the parameters of different single split resonators and the double split resonator simulated and measured in the near-field with the parameters indicated in the drawings below.

Sample Arm Arm Gap Resonance Resonance Resonance

Name length width width Frequency Frequency Frequency (range)

d t g Simulated Measured Calculated

(µm) (µm) (µm) (THz) (THz) (THz) sSRR-1 90 10 5 0.155 0.166 0.106 – 0.375 sSRR-2 90 15 15 0.185 0.181 0.150 – 0.530 sSRR-3 70 10 10 0.224 0.250 0.194 – 0.682 dSRR-1 90 10 5 0.170 0.174 – d d d d

Figure 2.4: (a) Schematic drawing of a sRR and (b) a dSRR

2.3.2 Results and Discussions

The schematic of the experimental setup is shown in Fig.2.5(b). In our experiment, a single-cycle, broadband THz pulse propagating in the ˆz-direction with an electric field polarization in the ˆy-direction, is incident on a single resonator. The single-cycle, broadband (0 - 3 THz) THz pulse is generated using a Ti:sapphire laser producing 15 fs pulses, which are focused on the surface of a semi-insulating GaAs crystal biased with a 50 kHz, ±400 V square wave. A silicon hyper-hemispherical lens is glued on the back of the crystal to collimate the emitted THz radiation. The THz beam is then further collimated and refocused using gold-plated parabolic mirrors [23]. The THz beam at focus covers a larger area than that of a single resonator. At the same time, a synchronized, femtosecond probe laser pulse prop-agating in the (−ˆz)-direction is focused in the crystal to an approximately 5 µm diameter spot immediately below the structure, using a reflective objective. The Ge/SiO2 reflection coating on the crystal reflects the probe beam. Due to the induced magnetic field of SRRs, the polarization of the probe beam experiences a Faraday rotation. The (111) orientation of the TGG crystal ensures that the probe pulse will only experience a Faraday rotation by a magnetic field component Hz aligned with the propagation direction of the probe beam. This means that the

(29)

a)

_b)

Figure 2.5: (a) Design of the sample (b) Rotation of the probe polarization due to the magnetic near-field present inside the TGG crystal.

setup is blind to both the incident magnetic field, polarized in the ˆx-direction, and any other magnetic field in the ˆy-direction. In practice, no change in probe polar-ization was detected in the absence of the metallic split-ring resonators. Therefore, we can safely assume that the probe beam polarization will be linearly rotated only in the presence of a longitudinal magnetic field Hzinside the crystal. A differential detector, combined with a λ/2 wave plate and a Wollaston prism measures this rotation [68]. The instantaneous THz magnetic field is linearly proportional to the differential detector signal.

The THz magnetic near-field as a function of time is obtained by optically & rapidly delaying the probe pulse via the optical delay stage, with respect to the THz pulse while measuring the Faraday rotation. This technique measures the field and thus both the amplitude and the phase of the magnetic near-field are obtained. Because the signal is weak, the time-dependent signal at a single position is an average over 200000 temporal scans and was obtained in less than an hour time. To measure the two-dimensional spatial distribution of the magnetic near-field, the sample is raster scanned in the xy-plane. The temporal average scan number is reduced to 10000 per pixel for the 2D-scan. A typical, 25 ps long scan of the THz magnetic near-field was obtained by stitching two 15 ps long scans together. 2.3.3 Single point measurement

Fig. 2.4(a) shows a drawing of the sSRR patterned on the TGG crystal. The incident electric field is polarized along the ˆy-axis, parallel to the arm containing the gap of the resonator. The sSSR covers an area of 90 µm by 90 µm, the width of each arm is 10 µm and the gap is 5 µm wide as shown in Table2.1.

In Fig. 2.6(a) we plot the measured magnetic near-field Hz(t) induced by the incident electric field at a single fixed position inside the sample sSRR-1, indi-cated by a cross in the insert of Fig. 2.6(a). To confirm that we measure the

(30)

0 5 10 15 20 25 Time (ps) Hz (arb. units) a) b) c) d) e) Current Distribution

at 166 GHz Amplitude of the Hat 166 GHz z field Phase of the Hat 166 GHz z field

0 max 180º 0º E E 0.1 0.2 0.3 0.4 0.5 Frequency (THz) 0 0.2 0.4 0.6 0.8 1 1.2 |Hz| (arb. units) sSRR-1 sSRR-2 sSRR-3

Figure 2.6: (a) Measurement of the time dependent out-of-plane magnetic near-field Hz(t), induced by the electric field incident for the two different orientations of the sSRR shown in the insets. Measurements are taken at the positions indicated by the crosses. (b) Amplitude spectra calculated from the time-dependent mag-netic field Hz(t) for the three different sSRR with dimensions given in Table2.1. (c) Calculated surface current density at the resonance and two dimensional spatial distribution of the calculated d) amplitude and e) phase of Hzat the crystal surface at the resonance frequency of 166 GHz. One can see the 180 degree phase difference between the fields on the inside and outside of the structure.

magnetic field induced by the structure, the structure is rotated by 180 degree around the z-axis. The incident electric field being unchanged, this should reverse the direction of the current and thus reverse the direction of the magnetic near-field vector. Indeed, the figure shows that the measured Hz(t) is opposite in sign compared to the previous measurement confirming that we indeed measure the magnetic near-field. The oscillations found in the two time traces indicate that the structure behaves like a resonator. Time traces of the magnetic near-field of two other sSRRs with dimensions shown in Table 2.1 have also been measured. The spectral content of the three measured magnetic field time traces, obtained by fast-Fourier transforming these traces, is shown in Fig.2.6(b). Each sSRR shows a single large peak in its frequency spectrum, which corresponds to the strong oscil-lations observed in the time trace of the magnetic near-field. The peak frequency for the three different sSRRs are 0.155, 0.185, and 0.224 THz, respectively. These

(31)

resonances correspond to the ones found in far-field transmission measurements of the LC response of arrays made of similar SRRs [69]. The peak frequency is a clear function of the sSRR dimensions: the smallest resonator (sSRR-3) exhibits the highest resonance frequency at 0.224 THz. To confirm that the measured peak frequencies correspond to the resonance frequencies of the SRRs, we have performed finite integration technique (FIT) simulations on these structures us-ing CST Microwave Studio , a commercial software package. The gold layer wasR taken as a perfect conductor, which is a reasonable assumption at THz frequencies. The reflective layers were neglected. The index of refraction of the TGG crystal at THz frequency was taken to be 3.75, equal to the value that we have measured. The peak positions calculated by the FIT simulations are at frequencies of 0.166, 0.181, and 0.250 THz respectively, which agrees well with the experimental val-ues. Fig. 2.6(c) shows the calculated surface current densities at the resonance frequency (166 GHz) of the sSRR-1 sample. When the single split-ring resonator is excited with an incident electromagnetic wave, a spatially circulating and tem-porally oscillating electric current is induced in the metallic ring. One can see that the strongest current is inside the long arm of the structure, and that it is particularly strong near the corner. This can be understood intuitively: the elec-trons flowing through the arm would prefer to take the shortest path, i.e. hugging the bend, resulting in a stronger current at the inside of the corner. This current creates a time-dependent magnetic field, which is oriented normal to that plane, i.e. along the z-axis. It corresponds to the field component that we measure in our magneto-optical detection setup.

2.3.4 Two dimensional distribution

We have also measured the two-dimensional spatial distribution of the magnetic near-field Hzat the resonance frequency. These 2D measurements give information about the distribution of the field inside and outside the ring. As we can see in the measurement in Fig.2.7, the field is only measurable inside the resonator and within our measurement accuracy no field was measured at positions outside the sSRR. The strongest field is measured in a region opposite the gap, close to the long arm. Both observations can be understood by the fact that the current is stronger in the long arm than in the arm containing the gap. This leads to a stronger magnetic near-field near the long arm, on the inside of the ring. This is supported by the calculations shown in Fig. 2.6(d) and 2.6(e) where we plot the calculated amplitude and phase of Hz in the plane below the structure at the resonance frequency. Interestingly, these calculations predict a 200 times stronger magnetic field near the corner, close to the long arm, compared to the incident magnetic field strength. The calculated 2D magnetic field distribution plotted in Fig.2.6(d), however, differs from the measured 2D distribution. In the calculation, the field is strongly localized near the long arm, whereas the magnetic field has expanded to fill the resonator in the measurement. To better understand the discrepancy between experiment and simulation, we have calculated 2D spatial distributions of the magnetic near-field inside the TGG crystal at four different distances from the surface at z = 0, -10, -20 and -30 µm. These results are shown

(32)

0 -10 -20 -30 z (µm) -194 0 194 0 28 -28 0 11 -11 0 16 -16 130 µm 130 µm 130 µm 130 µm 130 µm 130 µm 130 µm

Figure 2.7: Measured (left) and calculated (right) two-dimensional spatial distribu-tions of the magnetic near-field Hz at the resonance frequency of sample sSRR-1: for z = 0, -10, -20 and -30 µm. The 2D measurement agrees mostly with the calculated spatial distributions between 10 and 20 µm below the surface.

in Fig.2.7 along with the measurement. In both cases, the total area covered is 130 µm by 130 µm.

Although the field is mainly concentrated near the edge of the metal at the plane z = 0, it gradually changes into an uniform distribution when the distance z to the structure increases. One can see that the measurement resembles the calculation for a distance between 10 to 20 µm from the surface. This shows that we measure directly in the near-field, at a distance much smaller than the size of the object. We reach a spatial resolution of about 10 µm, much smaller than the 1.88 mm vacuum wavelength that corresponds to the resonance frequency of 0.16 THz. This corresponds to a value of about λ/200, more than two orders of magnitude below the diffraction limit.

As the simulations also show, the longitudinal component of the magnetic field amplitude decreases rapidly with distance from the surface but at 30 µm below, the calculated magnetic field strength is still 5 times larger than the incident field strength. At the average depth where we measure the magnetic field, the calculated enhancement explains why we are able to measure the magnetic near-field at all, despite the fact that we sample the field in a very small volume only.

In principle, our measurement method doesn’t sample the field at a single depth only but, it integrates the field over the entire length of the crystal. To understand

(33)

0 50 100 150 200 250 300 Depth (µm) 0 0.05 0.1 0.15 0.2 0.25 |Hz| 130 µm b) a) 130 µm -100 0 100 (A rb . units)

Figure 2.8: (a) Magnitude of the magnetic near-field, Hz, inside the TGG crystal, vs. distance to the structure at the surface. The line has been taken below the cross indicated in the drawing. (b) Two dimensional spatial distribution of magnetic near-field after integration from z = 0 to z = -300 µm inside the crystal. The magnetic field distribution matches exactly to the distribution calculated at z = -20 µm distance, shown in fig.2.7

.

why we observe a magnetic field distribution at an effective depth of 10-20 microns, we plot in Fig.2.8(a), the calculated magnetic field component Hz as a function of depth z inside the crystal at the location indicated by the cross in the figure. The figure shows that as we move away from the surface the magnetic field decays rapidly over a distance of about 30 microns and becomes negligibly small at larger distances. The largest contribution to the signal, therefore, comes from a region of space less than about 30 microns away from the surface. In Fig.2.8(b), we plot the two-dimensional distribution of the field calculated by integrating the field along the length of the crystal at each point. Clearly, this calculation strongly resembles both the measured distribution and the calculated one for a depth of 20 microns.

2.4 Double Split Ring Resonator

Additionally, we have performed measurements on a double split ring resonator (dSRR). This sample, dSRR-1, is composed of two sSRRs sharing a middle arm; the dimensions are shown in Table. 2.1 and the drawing is shown in Fig.2.4(b). When the THz electric field is polarized parallel to the gaps along the ˆy-axis it generates at one moment in time, a clockwise running current in the left ring and a counterclockwise running current in the right ring. Some time later, the situation reverses since the currents oscillate in time. Due to the opposite directions of the currents, we have at a moment of time a magnetic-field component pointing down into the plane in the left ring, while in the right ring it is pointing up. This means that we have time-dependent magnetic fields of opposite direction in a deep

(34)

subwavelength sized region of space, which thus more or less cancel in the far-field. We note that only near-field measurements are capable of discerning these fields. 2.4.1 Single point measurements

Fig. 2.9(a) shows a measurement of the time-dependent magnetic near-field Hz(t) of the dSRR structure at two different locations indicated by two crosses in the insert of Fig. 2.9(a): one inside the left ring and the other inside the right ring. In both measurements, the presence of long-lasting temporal oscillations indicates that the structure has a well defined resonance. The two time traces of the mag-netic near-fields are opposite in sign for the two locations. This means that the component of the magnetic near-field Hz(t) points into the plane for the left ring, and out of plane for the right ring. The spectrum of |Hz|, calculated from the time-domain measurement is plotted in Fig. 2.9(b) and shows a strong peak at 0.17 THz. The resonance frequency was calculated again via FIT simulations, and was found to be 0.174 THz, in good agreement with the experiment.

The current in the dSRR in the central arm is larger than the current in a sSRR and distributed uniformly across its width, because the current is fed by two identical resonators rather than just one. The presence of the magnetic field is mainly due to this high current flowing in the middle arm, along the ˆy-direction as shown in Fig.2.9(c). This creates a magnetic near-field with field lines describing roughly circles around the arm as schematically shown in the insert of Fig.2.9(b).

2.4.2 Two dimensional distribution

The two-dimensional spatial distribution of the magnetic near-field component Hz, below the dSRR at the resonance frequency of 0.17 THz is shown in Fig.2.10. The total area covered is 140 µm by 140 µm. The measurement shows that there is little or no field Hz outside the structure and at the location of the middle arm. In contrast, a field Hz is present in the left and right ring and is strongest in the area of the dSRR near the middle arm. Due to the structure of the resonator, clockwise and anti-clockwise oscillating currents exist in the left and the right ring and therefore the magnetic fields Hz in both resonators are opposite in direction. The change of sign of the magnetic near-field component, from positive (red) to negative (blue) occurs within 10-15 µm, a distance two orders of magnitude smaller than the vacuum wavelength of 1.7 mm. This is also shown in Fig.2.9(d) and2.9(e) where we plot the calculated amplitude and phase of Hz in the plane below the dSRR structure at the resonance frequency.

As in the case of the sSRR, for DSRR also, measured 2D distribution of the magnetic near-field doesn’t match the 2D distribution calculated at z = 0. To understand this difference, Fig. 2.10 shows the calculated spatial distribution of the magnetic near-field inside the crystal at various distances from the crystal surface at z = 0 (at surface), -10, -20 and -30 µm. The calculated field distribution at z = 0, shows inside each ring a distribution resembling the one of the sSSR, and the field is mainly concentrated along the middle arm of the structure. As z increases, it gradually expands and fills up the resonator. The measurement resembles the calculation for a distance between 10 to 20 µm, confirming again

(35)

0.1 0.2 0.3 0.4 0.5 Frequency (THz) 0 0.2 0.4 0.6 0.8 1 |Hz | (arb. units) 0 5 10 15 20 25 Time (ps) |Hz | (arb. units) Right Side Left Side Current Distribution

at 174 GHz Amplitude of the Hat 174 GHz z field Phase of the Hat 174 GHz z field

0 180º 0º max c) d) e) a) b) y _z x X X

Figure 2.9: (a) Measurement of the time dependent magnetic near-field Hz at positions indicated by the crosses in the Fig. 2.9(a), induced by the electric field incident on the structure. The field is reversed in sign for the left and right part of the structure as shown in the inset. (b) Associated spectrum of the out of plane magnetic near-field (c) Calculated surface current density and (d) two dimensional spatial distribution of the calculated amplitude and (e) phase of Hz at the crystal surface z = 0, immediately below the structure for the resonance frequency of 174 GHz.

that we are probing the magnetic-field at an average distance of 10-20 µm from the structure, once again confirming that we are measuring the magnetic field in the near-field region. Moreover, as we move away from crystal surface, the magnitude of the magnetic near-field decreases. At z = 0, the magnetic near-field Hz is 155 times stronger than the incident magnetic field, while at 30 µm distance from the crystal surface, the strength of the calculated Hz is still 8 times stronger than the incident magnetic field.

2.5 Conclusion

While our MM/TGG magneto-active devices have enabled direct imaging of the magnetic field with a resolution of λ/200, numerous other possibilities are worthy of detailed exploration. This includes further optimization of the response to create compact devices such as dynamic Faraday isolators. In addition, SRRs

(36)

0 -10 -20 -30 z (µm) 0 155 -155 0 20 -20 0 8 -8 0 13 -13 140 µm 140 µm 140 µm 140 µm 140 µm 140 µm 140 µm

Figure 2.10: Measured (left) and calculated (right) two-dimensional spatial distri-butions of the magnetic near-field Hzat the resonance frequency of sample dSRR-1: for z = 0, -10, -20 and -30 µm. The 2D measurement agrees mostly with the cal-culated spatial distributions between 10 and 20 µm below the surface.

provide a unique pathway to locally excite magnetic materials with well-defined high frequency fields to interrogate, for example, magnetic field induced switching or control of ferromagnets initiated by an applied picosecond electric field - that is, creating dynamic magneto-electric materials. This is essentially what we have accomplished at a basic level with our MM/TGG. It is the incident electric field which induces the SRR magnetic dipole that, in turn, induces the TGG Faraday rotation at near-infrared frequencies.

Finally, recent advances in generating high-field THz pulses will be of interest for magnetic structures similar to what we have presented [70]. For example, an incident THz pulse with a peak electric field of 1 MV/cm has a corresponding peak magnetic field of 0.3 Tesla. A field enhancement of 200 suggested by our numerical calculation would correspond to a local magnetic field of 60 Tesla of picosecond duration in the plane of the SRRs, sufficient to interrogate the dynamic magnetic properties of numerous materials.

(37)

2.6 Complementary split ring resonators

A complementary split-ring resonator (CSRR) is the “negative” of the split-ring resonator (SRR). The CSRR can be realized by replacing the metal area of the SRR with nothing and filling the empty area with the metal. The schematic drawing of a CSRR is shown in the Fig. 2.11(a). Here, d and t represent the length and width of the arm of the CSRR and g represents the width of the metal region connecting the voids. The concept of CSRRs was introduced by Falcone in 2004 [71]. The origin of the word “complementary” of the CSRR derives from the fact that the electromagnetic behavior of a SRR and a CSRR are almost dual or complementary to each other. For example, if we measure the THz electric field transmission in the time domain, for a SRR, the transmission decreases and shows a dip at the resonant frequency. However, for a CSRR, the transmission is enhanced and shows a peak at the same resonance frequency [72]. Also, a SRR shows a negative permeability whereas a CSRR shows a negative permittivity [73].

a)

g

b)

c)

d THz E-field polarisation _{THz E-field} polarisation E H Gold Gold Void

d

t

Gold TGG

d

Bridge Gap E H

Figure 2.11: (a) The schematic drawing of the CSRR describing the parameters; d = length of the arm of the CSRR, t = width of the arm of the CSRR, g = width of the metal region connecting the voids. (b) The schematic drawing of a SRR. The incident THz electric field is parallel to the arm containing the gap and (c) In case of a CSRR, the incident THz electric field is perpendicular to the empty (no gold) arm containing the “bridge”.