© 2008 OSA / CLEO/QELS 2008 a1696_1.pdf CFV4.pdf
Enhanced Terahertz Pulses Emission From InAs Surface By Femtosecond Laser Pulses With Tilted Intensity Front Yu. Avetisyan, K. Khachatryan Microwave Eng. Dept., Yerevan State University, Yerevan, 1 Alex Manoogian, 375025, Armenia,
[email protected]
R. Beigang Fraunhofer IPM, THz Measurement and Systems c/o University of Kaiserslautern, E. Schroedinger-Str. 67663 Kaiserslautern
Abstract: It is shown that using femtosecond laser pulses with tilted intensity front allows controlling the direction of terahertz emission from InAs surface and by that way achieving significant increase in the generated power.
©2008 Optical Society of America
OCIS codes: (260.3090) Infrared, far; (320.7080) Ultrafast devices.
The excitation of semiconductor surfaces by femtosecond laser pulses is one of the typical methods for generating ultrashort terahertz (THz) radiation pulses. When semiconductor wafer is illuminated by optical beam, a large number of electron–hole pairs are produced in thin layer below the surface. The fast free-carriers separation leads to formation of the transient electric dipole, which radiate an ultrashort THz pulse. The direction of THz emission is determined by radiation patterns of both the elementary dipole (~ sin2θ ) and assembly of dipoles which in turn is determined by temporal sequence of the photoexcitation of the dipoles. The latter factor is dominant if the waist of the excitation laser beam is much larger than the radiated wavelength. For this reason, the THz generation from a large-area photoconductive emitter occurs in the same direction as the reflected laser beam. However, the efficiency of generation is not high. The angle of THz emission in semiconductor (usually having high refractive index) is close to the normal to its surface and therefore only small part of the dipole’s power distribution sin2θ is involved in generation. For example, in case of 45° pump-incidence on the InAs-sample (nTHz = 3.78) the angle inside material is θ ≈ 11° and therefore the factor sin2θ ≈ 0.036. So it is highly beneficial either to reorient the dipoles or to change the directivity pattern of dipoles assembly [1], in order to increase the sin2θ factor. The Lorentz force associated with magnetic field may deflect transient dipole (current) into direction parallel to the emitting surface [2]. Another way to solve this problem is to use a tilted output surface when InAs emitter is attached to the base of a GaAs prism [3]. In the case of a prism with the 90° vertex angle, the THz dipole becomes oriented at the angle 45° with respect to the output surface. In both cases a significant improvement of the output power (more than by one order of magnitude) has been demonstrated. However, in the first case the large (3-8 T) magnetic field is required, in the second case there is a need for prism which would be transparent for both the optical (pump) and THz waves. In this report we suggest to use fs-laser pulses with tilted intensity front to introduce temporal delay between photoexcitation of the dipoles arranged at the surface of InAs surface. It results in an increase of the angle of THz emission in semiconductor material and therefore a more favorable part of the radiation pattern of the elementary dipole (~ sin2θ ) is involved in THz generation. The technique of pulse front tilting with respect to the phase front is presently well developed [4]. To extract THz waves generating at large angles in material, a thin slab with an output coupler (prism or grating) should be attached to an InAs wafer (Fig. 1).
θa
Output coupler
θi O
β
A B
θ
THz
Cover InAs
d Fig. 1. Schematic view of THz photoconductive emitter illuminated by fs-laser pulses with intensity front tilted at angle β with respect to phase front
Y X
© 2008 OSA / CLEO/QELS 2008 a1696_1.pdf CFV4.pdf
Before considering the directional diagram of THz emission we assume for simplicity that refractive indexes of the cover and InAs are nearly same and the intensity profile of the laser beam has a square form distribution with sizes significantly larger than emitted wavelength λTHz. The last results in the formation of thin dipoles sheet of the rectangular form inside the photoconductive material. As is seen from Fig. 1, the elementary dipoles separated at the distance x (along X-axis) oscillate with temporal delay equal to x(sinθi + cosθi sinβ)ng /c, where ng is the group index of the slab material at laser frequency, θi is the angle of incidence on the InAs surface, β is the tilt angle of the intensity front with respect to the phase front, c is the speed of light in vacuum. Using this one can easy obtain that direction of the radiation maximum is given by
θ m = sin −1 [(sin θ i + cos θ i sin β )n g / nTHz ] .
(1)
Therefore, all frequency components of the THz pulse are radiated at the same direction if the material dispersion in the THz region is neglected. Also it is follows from (1) that in a special case of the normal pumpincidence (θi = 0) the direction of THz emission departs from the normal at angle approximately equal to pulse front tilt angle β. In the case of InAs emitter (nTHz = ng = 3.78) the dependences of radiation angle θm on pulse front tilt angle β for θi = 0 and θi = 11° (it corresponds to θa = 45° pump-incidence in air) are presented in Fig. 2. It can be seen that the increase in the tilt angle β results in approach of θm to 90º, which is a favorite direction of the dipole emission. In Fig. 3, we plot the radiation patterns P(θ) from THz emitter (with beam spot size at the InAs surface d = 6λTHz) for different tilt angles β = 0º, 40° in case of the 45° pump-incidence (θi = 11°) and for β = 65º in case of normal incidence θi = 0. It is worth to note that presently the femtosecond pulses with front tilt angle β ≈ 65º are widely used for efficient THz emission from nonlinear crystals [4]. In fact, the radiation maximum P(θm) increases with the emitting angle θm approximately as sin2θm. Angular divergence of the THz beam depends on radiated wavelength and it is changed as Δθ ∝ λTHz/dcosθm .
θm
90
deg.
75
P(θ), a. u.
60
1 0.8 0.6
45 0.4
30
0.2
15 0
0
45
90
tilting angle β, deg. Fig.2. Dependence of maximum radiation direction θm on angle of pulse front tilting β.for oblique θa = 45° (solid) and normal (dotted) pump-incidence at emitter.
0
x 1/3
0
22.5
45
θ, deg.
67.5
90
Fig.3. Radiation pattern in case of oblique pump-incidence θa = 45° for different angles of pulse front tilting β = 0 (red line), β = 40º (blue) and in case of normal incidence θa = 0° for β = 65º (green); the calculated values of P(θ) without front tilting (β=0) are increased by 3 times.
By integrating radiation patterns we can estimate the enhancement factor η = PβTHz / P0THz, where PβTHz and P0THz are power generated in cases of β ≠ 0º and β = 0º. The 45° pump incidence at InAs surface is usually used without pulse front tilting. With sufficiently large tilting angle β = 65°, the normal pump incidence θi = 0 is mostly suitable. By calculating powers in mentioned cases, the enhancement factor is estimated as η ≈ 220. Thus, THz power radiated from InAs surface can be increased by more than two orders of the magnitude, due to the pulse front tilting. In conclusion, we show that femtosecond pulse front tilting improves greatly the THz pulse power generated at an optically excited InAs surface. The direction of THz emission is controllable by changing the pulse front tilting angle. [1] X.-C. Zhang, D. H. Auston, “Generation of steerable submillimeter waves from semiconductor surfaces by spatial light modulators,” Appl. Phys. Lett. 59, 768-780 (1991). [2] J. Shan, C. Weiss, R. Wallenstein, R. Beigang, T. F. Heinz “Origin of magnetic field enhancement in the generation of terahertz radiation from semiconductor surfaces,” Opt. Lett. 26, 849-851 (2001). [3] M. B. Johnston, D. Whittaker, A. Dowd, A. G. Davies, E. H. Linfield, X. Li, D. A. Ritchie, “Generation of high-power terahertz pulses in a prism,” Opt. Lett. 27, 1935-1937 (2002). [4] A. G. Stepanov, J. Hebling, J. Kuhlb, “Efficient generation of subpicosecond terahertz radiation by phase-matched optical rectification using ultrashort laser pulses with tilted pulse fronts,” Appl. Phys. Lett. 83, 3000-3002 (2003).
