1

CHAPTER 1

INTRODUCTION

An electromagnetic radiation exhibits transverse wave nature having mutually perpendicular

electric field vector E

, magnetic field vector B

and propagating vector k

(Figure 1.1) [1]. This

radiation can transport energy from the radiation source to an undetermined final destination even

through vacuum. It can transfer momentum (through absorption) to matter with which it interacts.

A standard measure of all electromagnetic radiation is the magnitude of the wavelength (in a

vacuum).

Figure1.1 Electromagnetic wave representations

The wavelength is defined as the distance between two successive peaks (or valleys) of the

waveform (Figure 1.1). The corresponding frequency of the radiated wave (the number of

sinusoidal cycles or oscillations that pass through a given point per second) is proportional to the

reciprocal of the wavelength. The electromagnetic spectrum extends from low frequencies

(higher wavelength), used for modern radio communication, to gamma radiation at the high

2

frequency (short wavelength) end (Figure 1.2). So, the spectrum covers wavelengths from

thousands of kilometers down to a fraction of the size of an atom.

In the past two decades, the Terahertz (THz) frequency region, which was difficult accessible

frequency region in the electromagnetic spectrum, has been researched extensively in science.

The THz region is defined as borderline of electronics (i.e. high frequency region of the

microwave band) and photonics (i.e. long wavelength region of far infrared light). Radiation at 1

THz has a period of sp1 , wavelength m300 , wave number -1cm33 and photon energy

meV1.4h [2-4].

Figure1.2: Electromagnetic spectra based on frequency and wavelength

Both neighboring frequency (microwave and infra-red) have been extensively investigated and

developed, but, the THz region remained the least explored region, commonly known as THz

gap. The THz technology has also emerged the immense potential interest for its applications in

many areas due to following properties: (i) most fundamental molecules (e.g. water, oxygen and

3

carbon monoxide) and chemical substances have their rotational and vibrational absorption lines

in the THz range [5], (ii) THz radiation can penetrate through many non-polar and non- metallic

materials such as paper, textiles, woods and plastics, (iii) THz radiation is reflected by metals,

(iv) it can be absorbed by polar molecules such as water [2] and (v) THz radiation is non-ionizing

and is not harmful for living cells [6]. Such characteristic features attract the rising interest for

THz applications in basic science [7-10], manufacturing [11], security [12], medicine [6] and

broadband THz communications [13].

1.1. Generation of THz radiation

Since the early nineties, the Terahertz region of the spectrum has been explored intensively. THz

radiations were generated by using various new techniques such as solid state electronic devices

[14], quantum cascade laser [15], optical THz generation [16, 17], accelerator based sources [18]

[19], optical rectification [20, 21], and sources based on laser plasma interaction [22-25]. Solid

state electronic based devices can produce THz radiations near or below 1 THz. In low frequency

microwave regime, fabrication of electronic devices operating at frequencies above a few

hundred GHz has been difficult [26] due to its inherent need for very short carrier transit times in

the active regions. The output of such sources can be harmonically multiplied to the THz range

[27]. In higher frequency optical regime, it is quite difficult to generalize the concept of interband

diode lasers working at visible and near-infrared frequencies into mid-infrared regime because of

non availability of appropriate semiconductors.

Recent improvement in the field of quantum cascade lasers, laser emission is achieved through

the use of inter-sub-band transitions in a periodic repetition of layers of two different

compositions, or super-lattice structure. A super-lattice is a periodic structure of quantum wells

and barriers. The photon emitted by the super-lattice is due to the inter-sub-band transition in the

4

super-lattice. Such transitions can be specified by the thickness of the coupled wells and barriers.

Therefore, by toiloring the periodicity of the super-lattice to specific well-barrier thickness, THz

radiations of specified energy range can be generated. Although the idea of inter-band emission

was known since 1971 [28, 29] , the crystal growth technology for creating quantum cascade

lasers is relatively new and expensive.

The optical THz generation can be divided into two categories: (i) THz radiation generation in

nonlinear media and (ii) THz radiation generation from accelerating electrons. In nonlinear

media, the incident electromagnetic waves undergo nonlinear frequency conversion, which is

based on the second order nonlinear properties of the materials [30]. Many nonlinear media have

been proved to have the ability to generate THz radiation through optical excitation, such as

GaAs, GaSe, GaP, ZnTe, CdTe, DAST, and LiNbO3. Two types of second order nonlinear

processes are involved in the THz generation in the nonlinear media. One is the optical

rectification, which is limited to femtosecond laser excitation. Femtosecond laser pulses have a

broad spectrum, which via optical rectification in nonlinear media can generate THz pulses with

the shape of the optical pulse envelope [20]. Several different approaches of optical rectification,

with different non-linear materials, have been investigated [21]. This has led to single cycle THz

pulses having energies ranging up to ( J10~ ), with roughly a frequency bandwidth of (0.1-3.0

THz). Another second order nonlinear process is difference frequency generation by laser

beating. Two continues wave (CW) optical beams with a frequency difference in THz range can

generate (CW) THz radiation via difference frequency generation in nonlinear media. THz

radiation can also be generated from accelerating electrons. The time varying current produced

by accelerating electrons radiate electromagnetic waves. The most popular THz radiation device

based on the accelerating electrons is photoconductive antennas excited by laser beams. A laser

5

beam illuminates the gap between two electrodes on the photoconductive antenna surface and

generates photo carriers. The photo carriers can be accelerated by the dc bias field between two

electrodes and produce the photocurrent. This photocurrent varying in time is proportional to the

laser beam intensity. Therefore, THz pulses can be generated by femto-second laser pulses, and

CW THz radiation can be produced by mixing of two laser beams with different frequencies to

form an optical beat [11, 31].

Currently, the most powerful sources of THz radiation are large accelerator based sources. These

sources generate THz radiation using ultra-relativistic electron bunches via various schemes, e.g.,

coherent undulator radiation (CUR) [32, 33], coherent synchrotron radiation (CSR) [34, 35], and

free electron laser (FEL) [36]. The free electron laser employs a strong dc magnetic wiggler and a

highly relativistic electron beam. The device is useful for producing high powers and is tunable

between 0.1 THz to 10 THz. For moderate powers, Liu and Tripathi [23] have proposed an

alternative scheme of radiation generation in which a relativistic electron beam is propagated

through a waveguide filled with a space periodic dielectric. An electron beam propagating

through the dielectric, along with an electromagnetic wave perturbation, drives a space charge

field. The space charge field couples with the periodic permittivity, producing a displacement

current which drives the original electromagnetic perturbation.

However, most of these methods are not efficient enough to achieve high energy pulses of THz

radiation due to their lower damage limit. To achieve this objective, plasma is utilized as a

nonlinear medium in various schemes because plasma can handle very high power lasers and it

has an added advantage of not having damage limit [22, 24, 25, 37-51]. Lasers impart their

energy to the oscillating electrons of the medium and in turn, these oscillating electrons constitute

a time dependent current, responsible for the THz radiation generation. In order to achieve phase

6

matching condition between the nonlinear ponderomotive force and the oscillatory current,

researchers have utilized corrugated plasma, amplitude modulated pump wave, etc. The present

research work also focuses on the THz radiation generation by laser plasma interaction. A brief

introduction of THz radiation generation by laser plasma interaction is given in the next section.

1.2. Schemes based on laser plasma interaction

THz radiation generation utilizing plasma as a nonlinear medium is widely used in literature. The

following two schemes based on nonlinear laser plasma interaction are given below:-

1.2.1. Wakefield THz schemes

The laser wakefield can be considered as a conical emission in the forward direction by laser

pulse induced oscillating electrons involving Cerenkov mechanism. The wakefield excitation is

reported by several authors utilizing different means, where the large amplitude wave is desirable

[11, 52, 53]. This scheme relies on the interaction of an intense laser beam with a plasma; in this

case, the accelerator is referred to as the laser wakefield accelerator (LWFA) [19, 54]. This

configuration was first proposed by Tajima and Dawson [55]. Through the laser ponderomotive

force, the rising edge of the laser pulse envelope pushes away the background plasma electrons.

Once the laser pulse is gone, the force resulting from the charge separation initiates a density

oscillation. The phase velocity of the electro-static density oscillation is roughly equal to the

group velocity of the laser. This charge oscillation is referred as wake or plasma wave. In the

most basic scheme, the electron bunch is produced through self-trapping of background plasma

electrons in the wake. Since, most pump-probe experiments rely on a laser beam (either as a

pump or probe beam), the availability of a synchronized laser pulse is a strong advantage of the

LWFA. The minimal laser intensity that is needed to drive a suitable plasma wave is the order of

21810 Wcm . Up until 1985, the damage threshold for laser amplifying crystals did not allow for

7

the production of such intense laser pulses using compact laser systems. The realization of the

Chirped Pulse Amplification (CPA) technique, reported in 1985 by Strickland et al. [56], led to

the production of laser pulses with intensities in excess of 22018 1010 Wcm . The experimental

implementation of CPA provided the start for significant experimental progress towards laser-

driven plasma-based accelerators. In generic LWFA experiments, these intense laser pulses are

focused onto a plasma from a gas jet or other plasma source, leading to the production of

relativistic electron bunches. Ladouceur et al. [57] were among the first to observe broadband

THz radiation employing the plasma filaments (electron density 31610~ m at 0.9 THz plasma

frequency) formed through multi-photon ionization by a 100 fs laser pulse propagating in air and

achieved power conversion efficiency of 910~ . Zhang et al. [58] have reported a powerful

coherent emission of broadband few THz radiation from a laser wake field in non-magnetized

and magnetized plasmas by linear mode conversion. Since laser field can be excited at amplitudes

as high as 100 GV/m even at the plasma density of 31810 cm , the field strength of the mode

converted emission in this scheme could easily reach a few GV/m. Tripathi et al. [59]

investigated terahertz radiation generation in air via bi-filamentation of two co-propagating

femtosecond laser pulses with suitable time delay. For a time delay of less than 2 ns, the

amplitude of 0.1 THz frequency radiation was found to be ten times higher than the one due to a

single pulse. However, for other frequencies, it could be greater or less than 10. When a

femtosecond laser pulse propagates through air, it undergoes filamentation and self-focusing and

forms the plasma channel which, attains strong dipole moment and emits electromagnetic

radiation. The radiation frequency can be controlled and maintained in the terahertz range by

choosing suitable plasma parameters. Loffler et al. [60] reported a large enhancement of the

intensity of THz radiation emitted by ionized air in the presence of a static field. They observed a

8

current surge following photo-ionization of the air with an applied bias field of cmKV /6.10

leading to the emission of THz pulses with an intensity which can be almost as high as that of

THz pulses radiated from a large-area intrinsic-field GaAs emitter. Recently, Houard et al. [61]

observed a three order magnitude enhancement of the THz energy radiated by a femtosecond

pulse undergoing filamentation in the air in the presence of a static electric field. The emitted

THz wave was found to be linearly polarized in the plane containing the static electric field. They

also provided a theoretical model which predicts the same enhancement of the THz generation

should be observed if the static field is replaced by a THz or a microwave pulse of the same

electric field (several kV/cm). Indeed, if the period of the applied field is much longer than the

time during which ionization occurs ( iont ≈ 50 fs), this field appears static by the ionization front.

Thus, by selecting a microwave pulse which is not absorbed by air and focusing it on the

filament, one should be able to remotely enhance the THz emission of the plasma string. Bhasin

and Tripathi [24] also studied the THz radiation generation from the laser filament in the

presence of a static electric field in a plasma. They observed an enhancement in coupling in the

presence of the static electric field. The ratio of the THz amplitude to that of filament amplitude

is the order of 510 at laser intensities

214 /10~ cmW . Cook et al. [62] demonstrated another

method to introduce the required transverse bias by using a superposition of both fundamental

and second harmonic pulse fields, which people called ac-biased method. As the frequency of the

ac-bias is well above the plasma frequency, this mechanism does not suffer from strong screening

effects as encountered in the dc-biased method.

9

1.2.2. Beat wave schemes

Recently, various experiments based on lasers beating in a corrugated plasma have reported

generation of efficient THz radiation at different frequencies. Out of various schemes based on

laser plasma interaction, THz radiation generation by beating of two lasers of different

frequencies and wave numbers in plasmas has shown tremendous potential in terms of amplitude,

tunability, efficiency and directionality. THz sources based on beating can also be scaled to high

peak powers. The basic mechanism to generate THz radiation by beating of two co-propagating

laser beams is as follows:

Consider two laser beams co-propagating in a corrugated plasma having electric field profiles

)(

00ˆ

xkti

jjjeEyE

, where 2,1j and2/122 )1()( jpjj ck . Here, menp

2

04 is

the electron plasma frequency; me and are the electronic charge and mass, respectively. Lasers

impart oscillatory velocity miEev j

to plasma electrons which is obtained by solving

equation of motion Eedtvdm

. Lasers beat together and exert a ponderomotive force

BvBvcevvvvmFp

** Re2..Re2

on plasma electrons at frequency

21 and wave vector 21 kkk

(the ponderomotive force will be discussed in more

details in Sec 1.3). The ponderomotive force drives space charge oscillations at 21 and

wave vector 21 kkk

. Assuming the potential of space charge mode to be , the oscillatory

velocity of electron due to space charge mode along with ponderomotive force can be expressed

as follows:

pxx Fem

iv

1.1

10

The nonlinear velocity given by Eq. (1.1) along with the continuity equation provides density

perturbationNLL nnn . Here, e

L ken 241 , px

NL Fmknn 2

0 and

22 p . Substituting NLL nnn into the Poisson’s equation ne 42 , we obtain the

characteristic equation for beating mode, given by NLnke 24 where e 1 .

Electrons, oscillating at ),( 21 kk

in the presence of density ripples zien

0 , excite nonlinear

current at ),( 21

kk which can be written as ziNL evenJ

0)2/1( . This oscillatory

current is the source for the emission of THz radiation at the beating frequency (which is the

same ( 21 ) as that of the ponderomotive force) and wave number (

21 kkk ).

For strong THz radiation, plasma density ripples should be periodic, otherwise )( 21

kkk

will exhibit non-periodic behavior; resonance condition will not be achieved and maximum

energy transfer will not take place and consequently, a weak THz radiation will be generated.

Hamster et al. [63] proposed a scheme of high power terahertz radiation from plasma short pulse

lasers, employing 1 TW, 100 fs laser pulse focused on gas and solid targets. They observed

terahertz radiation in a laser induced plasma channel where ponderomotive force drives

radiations. Antonsen et al. [64] have reported the excitation of terahertz radiation by laser pulses

propagating in miniature plasma channels. Generation of radiation by laser pulses in uniform

plasmas is generally minimal. However, if one considers propagation in corrugated plasma

channels, conditions for radiation generation can be achieved due to the inhomogeneity of the

channel and the presence of guided waves with subluminal phase velocities. It is found that, for

channels and laser pulses with parameters that can be realized today, energy conversion rates of a

fraction of a joule per centimeter can be achieved. Miniature corrugated channels can also be

11

used for excitation of THz radiation by bunching electron beams. Xie et al. [65] observed that the

properties of emitted THz radiation are consistent with four wave mixing in a plasma, and

terahertz emission is maximized when the polarization of the laser beams and the terahertz are

aligned. The wave vector of the density ripple controls the direction of the emission. Ladouceur

et al. [57] experimentally observed broadband THz radiation employing the plasma filaments

(electron density 31610 m at 0.9 THz plasma frequency) formed through multi-photon ionization

by a 100 fs laser pulse propagating in air and achieved power conversion efficiency of 910~ .

Loffler et al. [60] presented an experimental demonstration of the generation of far-infrared ~

(THz) pulses by photo-ionization of electrically biased air with amplified laser pulses. The

current surge following photo-ionization of the air with an applied bias field of 10.6 kV/cm leads

to the emission of THz pulses with an intensity which can be almost as high as that of THz pulses

radiated from a large-area intrinsic-field GaAs emitter. The spectra peaks at higher frequency

than those of biased large-area GaAs emitters.

Liu and Tripathi [23] have proposed a scheme of producing tunable THz radiation using a short

pulse laser to tunnel ionize a gas jet immersed in a magnetic field. In this scheme, an ultrashort

pulse laser emerging through a circular grating-axicon assembly is envisaged to line focus on a

gas jet immersed in a dc magnetic field, producing a thin plasma cylinder with axially periodic

density. The residual momentum left with the electrons, after the passage of the pulse, sets in

transverse oscillations of the thin plasma cylinder at two distinct Eigen frequencies: the right

circular polarization having a frequency greater than 2p and the left polarization with

frequency less than 2p . The wave vector of the density ripple controls the direction of

emission. The oscillating electron cylinder emits coherent terahertz radiation with the ambient

12

magnetic field providing the frequency tunability. The presence of an axial density ripple controls

the angular orientation of the emitted radiation. Singh et al. [66] proposed a model of terahertz

radiation generation by the nonlinear interaction of circularly polarized laser beams in a low

density rippled magnetized plasma. Self focusing (filamentation) of a circularly polarized beam

propagating along the direction of static magnetic field in the plasma is included in numerical

modeling utilizing extended-paraxial ray approximation. The laser beam gets focused when the

initial power of the laser beam is greater than its critical power. The resulting localized beam

couples with the pre-existing density ripple to produce a nonlinear current driving the THz

radiation. By changing the strength of the magnetic field, one can enhance or suppress the

amplitude of THz emission. For incident laser intensity 214 /10~ cmW , laser beam radius (0r ) ~

50μm, laser frequency (0 ) = sec/108848.1 14 rad , plasma density (

0n ) = 31710025.5 cm and

normalized ripple density amplitude ~ 0.1, the produced THz emission can achieve the level of

Giga watt (GW) in power. Lalita et al. [24] investigated terahertz radiation generation by laser

beating in a rippled density clustered plasma, having self-generated an azimuthal magnetic field.

The generated terahertz radiation field turns out to have ring shaped distribution and its amplitude

is enhanced by the cluster plasma resonance when }/{)}3/)(3/4{( 2

0

223

00 nnrn peecc .

Manish et al. [38] investigated a scheme of THz radiation by the nonlinear mixing of two

Gaussian laser beams in a magnetized plasma channel. The axial magnetic field enhances the

nonlinear coupling (between pump and THz radiation) via cyclotron resonance. The THz power

scales with the square of density ripple amplitude and inversely with the square of laser

frequencies. Monika et al. [49] suggested a scheme of terahertz (THz) generation by the cross-

focusing of two collinear Gaussian lasers at the frequency difference in a spatially periodic

13

density plasma. Various laser and plasma parameters were optimized and an efficiency 3108~

was reported. Ramkishor et al. [50] presents a theoretical model for terahertz (THz) radiation

generation by two cross-focused Gaussian laser beams in a collision less magneto plasma. The

enhanced cross focusing of two laser beams in the presence of static magnetic field resulted in the

THz yield ~10 kW.

Different types of laser profiles were utilized by various researchers to enhance amplitude and

power of THz radiation in various beat wave schemes in plasmas. Malik et al. [22, 40-44] utilized

the Gaussian profile with a frequency difference for obtaining more collimated terahertz (THz)

radiation at a desired position. The efficiency is enhanced by realizing stronger transient

transverse current due to the spatial variation of their fields. For the laser intensity 214 /10~ cmW ,

an efficiency ~ 310 is achieved. The efficiency is further improved by using a super Gaussian

laser beam. Spatial super Gaussian laser beams of higher index and smaller beam width resulted

in more focus, tunable and strong THz radiation compared to the case of Gaussian lasers. Malik

et al. [67] realized an efficiency ~10-3

and field amplitude 710~ V/cm by utilizing spatial

triangular laser beams. The consequences of any deviation from the triangular profile of lasers are

also discussed Monika et al. [25] presented a scheme to achieve THz radiation by the beating of

cosh-Gaussian lasers in spatially periodic density plasma (ripple density). Here, the lasers exert a

nonlinear ponderomotive force along the transverse direction which imparts an oscillatory

velocity of electrons that couples with the density ripple to generate a stronger transient

transverse current due to the spatial variation of their fields, driving THz radiation. The

importance of laser-beam width parameters, decentred parameter, amplitude and periodicity of

the density structure are discussed for THz emission. By changing the decentred parameter the

14

peak intensity of lasers can be shifted in the transverse direction and a notable change is found in

the magnitude of THz field amplitude and its conversion efficiency.

1.3. Ponderomotive force

Ponderomotive force is a non linear force expressed by the charged particles in an

inhomogeneous oscillating electromagnetic field. Ponderomotive force arises by combining

Lorentz force and the convective term in the equation of motion [68]. It is assumed that the laser

is propagating along the z- direction in a plasma, whose electric field profile is )(

0

kztieEE

,

where 0E is the amplitude of the laser field. The equation of motion for the plasma electrons in

the presence of an electromagnetic wave of electric field E

and magnetic field B

Bvc

eEevv

t

vm

. (1.1)

It contains two nonlinear terms, vvm

. on the left side and cve /)B(

on the right side, which

are generally ignored in the linearization approximation if wave amplitude is small. However, for

large amplitude wave, they become important and can be clubbed together to constitute the

ponderomotive force,

Bvc

evvmFp

. (1.2)

Here, v and B

are real parts of their complex representations. The time average ponderomotive

force can be written as

Bv

c

evvmFp

Re.Re (1.3)

where, Re refers to the real parts of the quantity. Using the complex number identity

15

BABABA

..Re2

1Re.Re *

we can write

BvBvc

evvvv

mFp

** Re

2..Re

2 (1.4)

First, we ignore the nonlinear terms in Eq. (1.1), and linearized equation of motion (by replacing

it ) and obtained the oscillatory velocity of plasma electrons as follows:

mi

Eev

(1.5)

Using the Maxwell’s third equation tB-

E , we have

i

EB

(1.6)

Substituting, Eqs. (1.5) and (1.6) into Eq. (1.4), we obtain

****

2

2

..Re2

EEEEEEEEm

eFp

(1.7)

For an electromagnetic wave of non-uniform intensity distribution in an unmagnetized plasma,

the ponderomotive force on plasma electrons turn out to be

pp eF

(1.8)

where

2

24E

m

ep

(1.9)

From Eq. (1.9), it is clear that the ponderomotive force always acts away from the high intensity

region. This force modifies the plasma density profile leading to modification in the plasma

refractive index. The refractive index also changes due to the relativistic mass effect, and non-

16

uniform ohmic heating. Boot and Harvie [69] calculated a force on charged particles in an

inhomogeneous electric field originating from the equations for the electromagnetic Lorentz

force. It was soon realized that this ponderomotive force could be used to trap and control the

electrons. This force has been exploited in particle accelerators and inertial confinement fusion

devices.

Mori and Katsouleas [70] had described a ponderomotive force associated with a uniform

electromagnetic wave propagating in a medium with time varying dielectric properties [e.g.

)( 0tvx ] (where 0v is phase velocity). They found that, when a laser ionizes a gas through

which it propagates, a force is exerted on the medium at the ionization front that is proportional

to2)( E

rather than the usual

2)1( E

. This force excites a wake in the plasma medium

behind the ionization front.

1.4. Rippled Density Plasma

Plasma is a dispersive medium, in which THz radiation (electromagnetic in nature) cannot be

directly excited by the beating of two lasers ( 11,k

and 22 ,k

) having frequency difference

( 21 ) in THz range because 21 kkk

; this phase matching conditions can be achived if

some extra momentum is provided. A corrugated plasma having density ripples with periodicity (

) equal to mismatch in phase may turn the process into a resonant one. The density ripple can

be produced by various ways, one of the simplest methods is the laser machining, which

generates the ripple of much longer wavelength. Kuo et al. [71] and Pai et al. [72] split the main

laser beam into two beams. One with 80% energy served as a longitudinal probe beam, and the

other with 20% energy was used as the machining pulse. When a machining laser pulse of

spatially varying laser intensity pattern is projected transversely onto a neutral gas jet, a plasma is

17

formed in the bright regions. Several nanoseconds after the passage of the machining pulse, the

plasma undergo hydrodynamic expansion into the dark regions. This leads to the creation of a

longitudinal distribution of interlacing layers of high-density neutral gas and low-density plasma.

Subsequently, when probing laser pulse propagates through such a structure in the direction of

the ripple wave number, the front foot of the pulse pre-ionizes the gas so that the peak encounters

a plasma with longitudinal plasma density variation. The other method to generate density ripple

is circular grating axicon assembly. Durfee and Milchberg [73] have seen that when a laser after

passing through the transparent portion of the grating falls on the axicon lens, it ionizes the gas,

giving a bright line segments separated in the dark regions.

1.5. Detection of THz radiations

The detection of THz frequency signals is another important area, where research is going on.

The low output power of THz sources coupled with relatively high levels of thermal background

radiation in this spectral range has necessitated highly sensitive detection methods [74-78]. THz

detection method is based on the thermal absorption. Helium cooled silicon, germanium, and

InSb bolometer are the most common systems based on the thermal absorption. Although, they

provide high sensitivity for THz detection, compared to the time domain THz detection method,

bolometer lack for the frequency spectrum detection ability. The Interferometer is often used to

extract the spectral information for bolometer detection. Several thermal detectors such as Golay

cells, which are based of induced thermal expansion of gas and pyro-electric devices which are

based on spontaneous polarization change are also commonly used. The most important THz

detection method is the electro-optic sampling technique which is based on the Pockels effect in

electro-optic crystals. The electro-optic sampling technique is a time domain THz detection

method. Due to its time domain detection characteristic, it offers ultra wideband spectrum

18

detection ability. Many materials have been used for electro-optic sampling, such as ZnTe and

BBO crystals [79-81]. The electro-optic sampling measures the electric field induced

birefringence in a nonlinear crystal which is proportional to the applied field amplitude. The

photoconductive antennas can also be used for time domain THz detection.

1.6. Applications of THz Radiations

Few potential applications of THz radiation like imaging, tomography, THz spectroscopy,

biomaterials, medical imaging, etc. are briefly discussed below:

1.6.1. Security

In airport terminal, it is difficult to detect explosive material by x-ray detection. The distinct

absorption signatures of narcotics and explosives are in the THz region allows their identification

by THz spectroscopy [82, 83]. Due to the high electrical conductivity, metallic substances show

high reflectivity at THz frequencies, which is vital in detecting and tracing the exact shapes of

hidden guns, ammunitions, and sharp instruments such as knives. THz can penetrate through

paper, ceramics, wood and clothing. Materials hidden under clothes can be identified using THz

multispectral imaging and those in envelopes can be identified by component spatial-pattern

analysis without opening the envelopes [84-87]. THz may be the alternate to detect drug

trafficking and terrorism.

1.6.2. Material Characterization

Determination of the carrier concentration and mobility of semiconductors can be achieved by

THz spectroscopy [88, 89]. Superconducting thin film parameters such as magnetic penetration

depth and the superconducting energy gap may also be determined by THz spectroscopy [90, 91].

Tonouchi et al. [92] has recently been used THz-TDS to study MgB2, a new material which is

superconducting with a transition temperature of 39 K. They measured superconducting gap

19

energy threshold of approximately 5 meV, which corresponds to half the value predicted by

current theory and points to the existence of complex material interactions [93].

1.6.3. THz Imaging and Tomography

Hu et al. [94] demonstrated Since then, it has been used for imaging a variety of targets including

semiconductors [11, 95], cancer tissue [96, 97] and flames [98]. THz imaging attracted this

scientific community due phase sensitive spectroscopic images of material for identification

purpose. THz systems are suitable for imaging dry dielectric substances (including paper, plastics

and ceramics), which are relatively non-absorbing in THz range, other materials may also be

easily discriminated on the basis of their refractive index, which can be extracted from the THz

phase information. In the context of security screening and manufacturing quality control, THz

imaging system has an important goal to the development of three-dimensional (3D) tomography

T-ray imaging systems [99-101].

1.6.4. Biological and pharmaceutical sciences

Current fields of scientific research are ranging from cancer detection to genetic analysis. The

occurrence of collective and vibrational modes of DNA molecules are proteins in THz range,

facilitates the application of THz spectroscopy in biomedical field. The complex refractive index

of pressed pellets consisting of DNA and other biomolecule’s has been determined, which shows

absorption consistent with a large density of low frequency infrared-active modes [102-105]. THz

radiations are non-invasive, and hence these can be a good substitute for X-rays in imaging live

cells. As mentioned earlier, the scattering of electromagnetic radiation in heterogeneous

biological system, (which may be more complex than a simple Rayleigh treatment), is many

orders of magnitude less for the THz band than for the neighboring infrared or visible regions of

the EM spectrum, which, is also an added advantage for medical imaging. Various examples of

20

applications based on THz radiation in the biomedical field include dermatology in the

characterization of the hydration-level of the stratum corneum, dentistry to detect dental cavities,

oncology (skin cancer) by distinguishing base cell carcinomas from other normal cells [106]. In

pharmaceutical industries, THz imaging is used to check the integrity of tablet coatings and the

performance of tablet cores [107-109].

1.7. Motivation & Objectives

As mentioned earlier, the generation of THz radiation is of great practical and theoretical interest

now days because of its non-ionizing character and penetrating power comparable to the

microwaves. In medical imaging, because of its nonionizing character, these radiations are not

expected to damage tissues and DNA, unlike X-rays. Some frequencies of the THz radiations can

be used for 3D imaging of the teeth and may be more accurate and safer than conventional X-ray

imaging in dentistry. Similarly, because, it can penetrate fabrics and plastics, it can be used in

surveillance, such as security screening to uncover concealed weapons on a person remotely. In

scientific fields, THz radiation can provide novel information in chemistry and biochemistry also.

In manufacturing, many uses are possible like in quality control and monitoring. Three key

performance factors are the peak THz electric field strength (or pulse energy), THz bandwidth,

and efficiency of conversion. The enhancement of these parameters is an active area of current

research in order to realize many of the envisioned THz experiments. Most of the above

mentioned applications are under theoretical as well as experimental development. Although,

efforts have been made for THz generation in view of these applications, still, there remain the

challenging tasks of creating a proper THz radiation source that could be quite useful in these

fields. For example, tunability of the radiation source, proper power of the source and

directionality (collimation) of radiation are the areas where new concepts and efforts are needed,

21

to meet the demanding applications talked before. Therefore, in the present thesis, we have

proposed some new schemes based on laser beating in plasmas. One of the advantages of the

proposed schemes is that we have been able to tune the frequency, amplitude and efficiency of

emitted THz radiation. Not only this, we have given special attention to the control of the

direction of emitted radiations. Our schemes supersede several other mechanisms of THz

radiation generation, explored by the other researchers.

1.8. Focus of the present thesis

The proposed thesis focuses on terahertz generation by beating of two laser beams in magnetized

plasma. The whole work of the thesis has been divided into seven chapters and a chapter wise

summary is given below:

Chapter 2

A scheme of terahertz radiation generation is proposed by beating of two extra-ordinary

lasers having frequencies and wave numbers ),( 11 k and ),( 22 k , respectively in a

magnetized plasma. Terahertz wave is resonantly excited at a frequency )( 21 and

wave vector )( 21

kk , where is the mismatch factor introduced by the periodicity

of plasma density ripples. In this process, the laser exerts a beat ponderomotive force on

plasma electrons and imparts them an oscillatory velocity with both transverse and

longitudinal components in the presence of a transverse static magnetic field. The

oscillatory velocity couples with density ripples and produces a nonlinear current that

resonantly excites the terahertz radiation. Effects of periodicity of density ripples and

applied magnetic field are analyzed for a strong THz radiation generation. The terahertz

radiation generation efficiency is found to be directly proportional to the square of density

ripple amplitude and rises with the magnetic field strength. With the optimization of these

22

parameters, the efficiency 310

is achieved in the present scheme. The frequency and

power of generated THz radiation can be better tuned with the help of parameters like

density ripple amplitude, periodicity and applied magnetic field strength in the present

scheme.

Chapter 3

A scheme of terahertz (THz) radiation generation is investigated by photo-mixing of two

super Gaussian laser beams having different frequencies ( 21, ) and wave numbers

),( 21 kk

in a performed corrugated plasma embedded with the transverse dc magnetic

field. Lasers exert a nonlinear ponderomotive force, imparting an oscillatory velocity to

plasma electrons that couples with the density corrugations (zienn

0

' ) to generate a

strong transient nonlinear current, that resonantly derives THz radiation of frequency ~

h (upper hybrid frequency). The periodicity of density corrugations is suitably chosen to

transfer maximum momentum from lasers to THz radiation at phase matching conditions

2121 and , kkk . The efficiency, power, beam quality and tunaibility of

the present scheme exhibit high dependency upon the applied transverse dc magnetic field

along with q-indices and beam width parameters ( 0a ) of super Gaussian lasers. In the

present scheme, efficiency ~10-2

is achieved with the optimization of all these parameters.

Chapter 4

A model to achieve the strong THz radiation is developed by the photo-mixing of two

cosh- Gaussian lasers pulses of different frequencies ),( 21 and wave numbers ),( 21 kk

and same electrical field amplitude in a corrugated plasma embedded with the transverse

23

static magnetic field. Cosh-Gaussian laser pulses having steep gradient in intensity profile

along with wider cross-section which exert a stronger nonlinear ponderomotive force at

21 and 21 kk

on plasma electrons which imparts a nonlinear oscillatory velocity to

plasma electrons. Oscillatory plasma electrons couples with the density ripple xienn

0

to produce a nonlinear current which is responsible for resonant THz radiation at

frequency 2/122~ pc . The amplitude, efficiency and beam quality of THz radiation

can be optimized by choosing proper corrugation factor ( of the plasma), applied

magnetic field ( c ), decentred parameter (b) and beam width parameter ( 0a ) of cosh-

Gaussian lasers. An efficiency12 1010~ is achieved for the laser electric field

cmVE 9102.3 .

Chapter 5

Resonant THz radiation generation is proposed by beating of two spatial-triangular laser

pulses of different frequencies ),( 21 and wave numbers ),( 21 kk

in a plasma having an

external static magnetic field. Laser pulses copropagating perpendicular to a dc magnetic

field exert a nonlinear ponderomotive force on plasma electrons, imparting them an

oscillatory velocity with finite transverse and longitudinal components. Oscillatory

plasma electrons couple with periodic density ripples zienn 0

' to produce a nonlinear

current, i.e. responsible for resonantly driving terahertz radiation at

),( 2121

kkk . Effects of terahertz wave frequency, laser beam width,

density ripples and applied magnetic field are studied for the efficient THz radiation

generation. The frequency and amplitude of THz radiation were observed to be better

24

tuned by varying dc magnetic field strength and parameters of density ripples (amplitude

and periodicity). An efficiency ~0.02 is achieved for laser intensity of 215 /102 cmW in a

plasma having density ripples ~30%, plasma frequency ~1THz and magnetic field

~100kG.

Chapter 6

Resonant excitation of terahertz radiation by nonlinear coupling of two filamented spatial-

Gaussian laser beams of different frequencies and wave numbers is studied in a plasma

having transverse static electric field. The static ponderomotive force due to filamented

lasers is balanced by the pressure gradient force which gives rise to transverse density

ripple, while, the nonlinear ponderomotive force at frequency difference of beating lasers

couples with density ripple giving rise to stronger transverse nonlinear current which

results into the excitation of THz radiation at resonance. The coupling is further enhanced

by the presence of a static electric field and spatial-Gaussian nature of laser beams. An

increase of six fold in the normalized amplitude of terahertz is observed by applying a dc

field cmKV /50~ . Effects of frequency, laser beam width and the periodicity factor of

modulated laser amplitude are studied for the efficient THz radiation generation. These

results can be utilized for generating controlled tunable THz sources for medical

applications using low filament intensities (214 /10~ cmW ) of beating lasers.

Chapter 7

This chapter concludes the results obtained on the basis of our analytical investigations on

the THz radiation generation and its tunaibility by beating of two lasers in a magnetized

plasma.