terahertz generation by the beating of two laser beams in collisional plasmas ram kishor singh and...

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Terahertz generation by the beating of two laser beams in collisional plasmas Ram Kishor Singh and R. P. Sharma Centre for Energy Studies, Indian Institute of Technology Delhi, . Considering the solution as follows The spatial profile of intensity distribution of laser beams can be written as, The dielectric function can be written as, In the steady state: the thermal pressure induced by the laser beams is balanced by the space charge force. j j 2 2 E .E c t c t j j0 j j j j ˆ E r,z xA r,zexpikz t ikS r,z 2 2 2 j0 ' j0 j 2 j0 j j E r A r,z exp 2K z rf f 2 j j j df r S r,z z 2f dz eff j0 j j ij E.E i * 0 1 . e j j j j T T A A 2 2 2 0 3 j e B j e M m k T 1 2 0 0 0 2 s e e T n n T T 2'2' 2'2' 22 1101220211012202 3 224242 22 24 0110220 12 0 11 exp2exp2exp2exp2 1 22 exp 22 jp j jj jjj ss EK zEK zEK zEK z dff d z frfr ff k r f j ij ' j j0 k 1 K 2 From the equation of motion The energy balance equation The electron temperature at beat wave frequency The THz wave propagation equation The nonlinear current density THz amplitude variation with respect to propagation direction ' e e dv m eE m v dt B e e B e 0 0 d 3 3 k Tn J.E k T T n dt 2 2 2 2 e 1 2 1 2 2 2 0 e 1 B 0 e 2 B 0 T e e E .E E .E T 6m k T 6m k T l nl T T T T T . . 2 J J 1 E 4 2 E E 2 2 2 t c t c 2 q p ' dc 1 10 20 2 10 20 T T0 2 T 0 1 2 1 2 2 ' ' 1 2 2 2 2 2 10 1 20 2 n iE s E .E E .E K E z 4k n c 2 ff ff r 1 1 exp K K z 2 rf rf nl iqz 0 d T q 1 1 2 2 1 2 s ve J 1 n e E .E E .E t 2 2 , , , , j j0 j j 2 j0 r ikz t 2r E xE exp s 2 j e j j0 0 0 T k , c T dc d e 0 eE v m T T T T0 ik z t x E E e 1 0 1 ns 1 0.5 dc E kVcm 1 1 dc E kVcm 1 0 1 ns 1 0.5 dc E kVcm 1 1 dc E kVcm 1 0 1.3 ps Abstract The role of two cross-focused spatial-Gaussian laser beams has been studied for the high power and efficient terahertz (THz) radiation generation in the collisional plasma. The nonlinear current at THz frequency arises on account of temperature dependent collision frequency of electrons with ions in the plasma and the presence of a static electric field (applied externally in the plasma) and density ripple. Optimisation of laser-plasma parameters gives the radiated THz power of the order of 4 0 10 P. Conclusions: The cross focused laser beams in collisional plasmas are able to enhance the generation of THz radiation in the presence of external transverse static electric field. The maximum amplitude of THz radiation generation can be achieved by the suitable phase matching condition with the employment of ripple density. Amplitude of the generated THz radiation increased by factor of two to three in the case of cross-focusing of two Gaussian beams as compared to the case without cross-focusing. Acknowledgement: University Grant Commission (UGC), India. 14 1 1.96 10 rad/s 14 2 1.78 10 rad/s 13 p 1.7 10 rad/s q 0 n 0.3n 9 2 1 2 I I 1 10W /cm 10 20 r r 40 m s 3 1 2 2 p T 2 T q 1 1 c 1 2 2 T P T 2 T k 1 c 2 p ' 0 T 2 T T K 2 ck T 1 2 k k k q References: R. P. Sharma and R. K. Singh, Phys. Plasmas, 21, 073101 (2014). A. Houard, Y. Liu, B. Prade, V. T. Tikhonchuk, and A. Mysyrowicz, Phys. Rev. Lett., 100, 255006 (2008). M. S. Sodha, A. K. Ghatak, and V. K. Tripathi, Prog. Opt., 13, 169 (1976) S. A. Akhmanov, A. P. Sukhorukov, and R. V. Khokhlov, Sov. Phys. Usp., 10, 609(1968). 1 0 1.3 ps 1 0 1 ns

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Page 1: Terahertz generation by the beating of two laser beams in collisional plasmas Ram Kishor Singh and R. P. Sharma Centre for Energy Studies, Indian Institute

Terahertz generation by the beating of two laser beams in collisional plasmas

Ram Kishor Singh and R. P. SharmaCentre for Energy Studies, Indian Institute of Technology Delhi, India

...

The wave equations for the laser beams can be written as

Considering the solution as follows

The spatial profile of intensity distribution of laser beams can be written as,

The dielectric function can be written as,

In the steady state:the thermal pressure induced by the laser beams is balanced by the space charge force.

j j2j j 2 2

J E4 1E .E

c t c t

j j0 j j j jˆE r, z xA r, z exp i k z t ik S r, z

22

2 j0 'j0 j2

j0 jj

E rA r, z exp 2K z

r ff

2

jj

j

dfrS r, z z

2f dz

eff j0 j j ijE .E i

*0 1 .e j j j

j

T T A A

2

2 203j

e B j

e M

m k T

12

00

0

2s

ee

Tn n

T T

2 ' 2 ' 2 ' 2 '2 21 10 1 2 20 2 1 10 1 2 20 2

32 2 4 2 4 2 2 22 40 1 10 2 20 1 20

1 1exp 2 exp 2 exp 2 exp 21 2 2exp

2 2j p j

j jj j j

s sE K z E K z E K z E K zd f f

dz f r f r f fk r f

j ij'j

j0

k1K

2

From the equation of motion

The energy balance equation

The electron temperature at beat wave frequency

The THz wave propagation equation

The nonlinear current density

THz amplitude variation with respect to propagation direction

'e e

dvm eE m v

dt

B e e B e 0 0

d 3 3k T n J.E k T T n

dt 2 2

2 2e

1 2 1 22 20 e 1 B 0 e 2 B 0

T e eE .E E .E

T 6m k T 6m k T

l nlT T

TT T. .

2 J J1 E 42E E2 2 2 tc t c

2q p' dc 1 10 20 2 10 20

T T0 2T 0 1 2 1 2

2' '1 22 2 2 2

10 1 20 2

ni E s E .E E .EK E

z 4k n c 2 f f f f

r 1 1exp K K z

2 r f r f

nl

iqz 0 dTq 1 1 2 2 1 2

s v eJ 1n e E .E E .E

t 2 2

,

,

,

,

2

j j0 j j2j0

ri k z t

2rE x E exp

s

2j ej j0 0

0

Tk ,

c T

dc

de 0

eEv

m

iqzn n n eq0

T TT T0

i k z txE E e

10 1ns

10.5dcE kVcm

11dcE kVcm

10 1ns

10.5dcE kVcm

11dcE kVcm

10 1.3ps

AbstractThe role of two cross-focused spatial-Gaussian laser beams has been studied for the high power and efficient terahertz (THz) radiation generation in the collisional plasma. The nonlinear current at THz frequency arises on account of temperature dependent collision frequency of electrons with ions in the plasma and the presence of a static electric field (applied externally in the plasma) and density ripple. Optimisation of laser-plasma parameters gives the radiated THz power of the order of 4

010 P .

Conclusions:

The cross focused laser beams in collisional plasmas are able to enhance the generation of THz radiation in the presence of external transverse static electric field. The maximum amplitude of THz radiation generation can be achieved by the suitable phase matching condition with the employment of ripple density. Amplitude of the generated THz radiation increased by factor of two to three in the case of cross-focusing of two Gaussian beams as compared to the case without cross-focusing.

Acknowledgement: University Grant Commission (UGC), India.

141 1.96 10 rad / s

142 1.78 10 rad / s

13p 1.7 10 rad / s q 0n 0.3n

9 21 2I I 1 10 W / cm

10 20r r 40 m

s 3

12 2pT2T

q 1 1c

12 2

T PT 2

T

k 1c

2p' 0

T 2T T

K2 c k

T 1 2k k k q

References:R. P. Sharma and R. K. Singh, Phys. Plasmas, 21, 073101 (2014).A. Houard, Y. Liu, B. Prade, V. T. Tikhonchuk, and A. Mysyrowicz, Phys. Rev. Lett., 100, 255006 (2008).M. S. Sodha, A. K. Ghatak, and V. K. Tripathi, Prog. Opt., 13, 169 (1976)S. A. Akhmanov, A. P. Sukhorukov, and R. V. Khokhlov, Sov. Phys. Usp., 10, 609(1968).

10 1.3ps

10 1ns