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SPATIAL-TIME PATTERN OF ELECTRICAL FIELD OF TERAHERTZ PULSE IN THE FAR FIELD
M.S. Kulya1, Ya.V. Grachev1, V.G. Bespalov1, V.P. Kujanpaa2
:St. Petersburg National Research University of Information Technologies, Mechanics and Optics, Saint Petersburg, Russia 2VTT Technical Research Centre of Finland, Finland
[email protected], [email protected], [email protected], [email protected]
The spatial and temporal dependence of the electric field amplitude of a terahertz (THz) pulse of several oscillations in the far field near the focal plane of a parabolic mirror was experimentally obtained. During experimentation a space-time anomaly was discovered in the diffraction patterns. In the wave front of the field the amplitude decreases to zero, and going through this spatial plane, the phase of oscillations changes, while in the integrated intensity, there is a dip in the curve. The results can be applied in pulsed terahertz optics and spectroscopy. Keywords: THz electric field pulsed THz radiation, diffraction, pulses of a few electromagnetic field oscillation.
1. Introduction
Terahertz (THz) radiation lies in the frequency range 0.1-10 THz, which corresponds to wavelengths between the infrared and millimeter/submillimeter range from 0.03-3 mm. The physics and technology of THz radiation is not new [1], however, the development of femtosecond optics and microelectronics has permitted significant progress in this field. Correspondingly, interest in basic and applied research has increased, and recent monographs have been published [2,3]. Methods for obtaining and detecting THz radiation were established using femtosecond pulses of light when excited charge carriers of semiconductors and superconductors [2-5], with optical detection in x(2) nonlinear media [6], in optical breakdown of gases and radiation of first and second harmonic of a femtosecond laser [7,8] .
One of the fundamental phenomena of optics is the diffraction of light, but experimental studies of the spatial and temporal structure of ultra short broadband pulses, which have a complex amplitude-phase structure, have not been sufficiently carried out [9-12]. Experimentally, it is difficult to study the diffraction of a few electromagnetic field oscillation pulses for the wavelengths of visible and infrared ranges of the spectrum. This is because there is practically no possibility for the direct detection of the amplitude and phase, and only iterative calculation procedures can be used to recover the original temporal or spatial profile [13].
The experimental study of the diffraction of an ultra short pulse with a complex amplitude-phase structure became possible only with the advent of methods for recording temporal forms of an electric field pulse of broadband THz radiation. The THz wave front usually has only a few oscillations of the electromagnetic field. The wave front also has a complex amplitude-phase structure, which is connected with the process of its generation, further diffraction on the formed aperture, and with the influence of the medium's dispersion [14,15].
The aim of this work was to obtain the spectral and temporal shape of the electric field of a THz pulse from a few oscillations with a broadband spectrum and of picoseconds duration. The particular feature of this research is the direct detection of the spatial-time form of extremely short pulses, which was difficult in the optics of long pulses, as the photodetectors measure only field intensity. This study may be useful in interpreting the results of measurements in pulsed THz optics and spectroscopy.
2. Experimental Setup
The scheme of experimental arrangement is shown in Fig. 1. A femtosecond laser beam Yb:KYW laser FL-1 (wavelength Ap = 1040 nm, beam diameter d = 2 mm, the pulse width at half-width t > 120 fs, repetition rate of 80 MHz, average power W =1.2 W) with use of a beam splitter BS is divided into a probe beam and a pump beam. The pump beam passes through an optical delay line (Delay). It falls on a semiconductor crystal InAs, placed in a constant magnetic field M, where THz radiation is generated [5]. The plane of the crystal coincides with the focal plane of a parabolic mirror PM1 with focal length of 90 mm and an optical aperture of 60 mm. THz radiation is collimated by a parabolic mirror PM1 behind which there is a teflon filter F, transmitting THz radiation and scattering powerful femtosecond laser infra-red radiation. In addition, horizontal polarization is separated by a polarizer P. After passing along the optical path in the air L = 25 cm, THz radiation is focused by a parabolic second mirror PM2 on the electro-optical crystal CdTe, with an area of 10 x 10 mm2 and a thickness of 2 mm. This crystal is most suitable for electro-optic detection of THz radiation due to its dispersion properties [16,17].
Fig. 1. The experimental scheme: Yb: KYW laser FL-1 (A
1040 nm,
t « 200 fs, repetition rate of 80 MHz, W = 1.2 W); BS -beam splitter; G — Glan prism; M —magnet; CL —cylindrical lens; T —telescopic system; D — diaphragm; L - lens; PM -parabolic mirror; OMM -optical-mechanical modulator; P — Teflon filter; V — Wollaston prism; BD — balanced detector. Solid lines — femtosecond laser infra-red radiation; dot lines — THz radiation
After the femtosecond laser probe beam passes a Glan prism G, its radiation obtains horizontal linear polarization with an accuracy of 10-4. Then, the telescope T increases the diameter of the beam to about 5 mm, and the cylindrical lens CL focuses the radiation on the central region of the crystal CdTe. Thus a rectangular shaped spot of the probe radiation is formed on the crystal, the larger being directed dimension towards the horizontal axis x. When the probe beam propagates through the electro-optical crystal CdTe, it is influenced by the constant electric field of collinearly propagating THz pulse, which affects the linear polarization of the probe beam and change it to elliptical polarization. A quarter-wave plate A/4 transforms
the probe beam polarization to near-circular polarization. The beams with different polarization states are separated by a Wollaston prism V and they fall on the balanced detector BD. Since the magnitude of the birefringence is directly proportional to the electric field, the intensity difference on the balanced circuit photodiodes is also proportional to the field of THz radiation. The signal from the balanced detector enters the lock-in amplifier, consistent with the optical modulator OMM and then the signal goes to an analog-to-digital converter built into the PC.
The optical delay line Delay changes the crossing time of THz radiation and the probe beam in the crystal. Thus, by measuring the effect of birefringence for various delays, the dependence of the amplitude of the electric field of the terahertz pulse on time ETHz (t) can be recorded.
A firmly fixed aperture with a diameter of 1 mm was placed after the crystal CdTe, in order to study the spatial and temporal form of the THz pulse, Fig. 2. With movement of the recording system in the horizontal x and vertical y directions the point-to-point detection of the THz field in the focal plane of the cylindrical lens ETHz(x,y,t) was provided.
x
Fig. 2. Scheme of point-to-point measurement of THz field. Solid lines — femtosecond laser infra-red radiation; dot lines — THz radiation
The optical system of two parabolic mirrors (PM1, PM2) transfers the image (size d) illuminated by the beam of femtosecond laser on the crystal InAs into the plane of the electro-optical crystal CdTe. As THz radiation is formed only in the illuminated region [2,3], a far field THz radiation is formed in the focal plane of a parabolic mirror PM2 (electro-optical detector plane of CdTe). The dimensions of the far field THz radiation are defined by the size of the generation region and THz wavelength range. The spectrum covered by the THz generator includes 0.1 - 1.7 THz (wavelengths 3,000-176 ^m) [18], with a maximum of intensity at 0.6-0.7 THz (A ~ 500 ^m < d). The maximum size of the diffraction pattern of THz radiation in the plane of the electro-optical detector CdTe can be estimated to be equal to d. As the spectrum contains wavelengths larger than d, the size of the area will increase accordingly.
The measurements of the spatial-time pattern of the diffraction were made with different pump beam geometries, illuminating the InAs crystal generating the THz radiation. Fig. 3 shows the spatial profiles with different apertures. Fig. 3a describes the pump beam profiles of the femtosecond laser of aperture d =2 mm and Fig. 3b shows a focused laser beam with aperture value d = 1 mm. Fig. 3c and d show the rectangular beams created by the introduction of a cylindrical lens in the scheme of the laser beam. It should be noted that by focusing with the cylindrical lens, the generated area on the x-coordinate is a sub-wavelength for THz radiation, which affects the distribution of the far field.
Fig. 3. Spatial profile of the pump beam incident on the crystal InAs generating THz radiation: a femtosecond laser source aperture d = 2 mm (a), a focused laser beam diameter of 1 mm (b), beams of quasi-rectangular forms created by the introduction of a cylindrical lens in the scheme of the laser beam (c, d)
3. Experimental Results
By moving the mobile measurement system, Fig. 2, the point where the value of the THz field was in its maximum max[ETHz(x,y,t)] was found. The vertical coordinates of the given maximum point was taken as y = 0. The zero horizontal coordinates as x = 0 when the system was put into the edge position. Fig. 4 and Fig. 5 show the time dependence of the THz electric field ETHz (x =1 cm, y = 0,t) and ETHz(x = 2 cm, y = 0,t), respectively. Fig. 6 depicts a two-dimensional spatial-time picture of the distribution of the amplitudes of THz field ETHz (x,y = 0,t) using the spatial profile of the pump beam incident on the generating InAs crystal with d =2 mm (Fig. 3a).
From Fig. 6, it can be seen that the wave front of THz radiation has a spatial-time anomaly. In the time plane ETHz (x = 1.7 cm, y = 0,t) there is a reduction of the field amplitude to zero. In addition, there is a transition point where the phase of the oscillation changes. For visual demonstration, Fig. 7 shows the normalized integrated intensity of THz radiation pattern of the coordinate x:
Ithz (x,y = 0) = y |Ethz (x,y = 0,t)|2 dt. (1)
A similar spatial-temporal anomaly was observed in the case of the excitation by focused laser beam with diameter value of d = 1 mm (Fig. 8 on the right), and a beam of quasi-rectangular form (Fig. 8 on the left).
It should be noted that when decreasing the size of the excitation spot of THz radiation the wave front curvature is increased, and the area of maximum intensity of the THz field in the x axis decreases. When comparing the measured energy in a variety of fields of spots illuminating the crystal InAs it was found that the highest values of the electric field for THz radiation were achieved by focusing of the pump beam into a circular aperture with a diameter of 1 mm, which corresponds approximately to the maximum power density of the femtosecond
Fig. 4. Temporary form of the THz field in the focal plane of the spatial point
Ethz (x = 1 cm, y = 0, t)
Fig. 5. Temporary form of the THz field in the focal plane of the spatial point
Ethz (x = 2 cm, y = 0, t)
radiation. Thus, it is also the maximum efficiency of the energy transform from IR to the THz [2,3].
The presence of the spatial-time anomaly in the diffraction pattern can be explained by the appearance of the phase shift larger than n/2 in the plane of the beam of THz radiation, which leads to an intensity dip in the far field [19]. A spatial phase shift can be caused by localized heating of the Teflon filter (P in Fig. 1), due to the powerful absorption of high intensity femtosecond laser beam. Additional studies are needed for explanation of this phenomenon.
2,8 5,6 8,3 11,1
t, ps
Fig. 6. Spatial-time picture of the amplitude distribution of THz field ETHz (x,y = 0,t)
0,0
0,0 0,4 0,8 1,2 1,5 1,9 2,3 2,7 x, mm
Fig. 7. Integrated picture of the intensity of THz radiation to the coordinate x
Ithz (x, y = 0)
4. Conclusion
The scheme was proposed for an experimental setup, which was then assembled for measurements of the spatial and temporal patterns of the electric field amplitudes of THz radiation near a parabolic mirror focal plane. In these experiments different pump beam geometries of a femtosecond laser were used. Experimentally a spatial-time anomaly was observed in the diffraction patterns. In the wave front of the field the amplitude decreased to zero, and after going through this spatial plane, the phase of the oscillations changed. On the other hand, there was a dip in the integrated intensity curve. A spherical wave front in the observed diffraction patterns was observed, and by reducing the diameter of the excitation spot, the curvature of
Fig. 8. Spatial-time picture of the amplitude distribution of THz field ETHz (x, y = 0, t) in the case of the excitation laser focused beam with diameter d =1 mm (right), and a beam of quasi-rectangular form 5 x 0.1 mm (left)
the THz wave front increased. So, the experiments show that the spatial non-uniformity of the THz field must be taken into consideration for correct spectroscopic measurements. It is also important to scan the THz pulse through the central peak of the diffraction pattern and the center of the sphere of the wave front, otherwise, the shape of the measured pulse will undergo a temporary distortion and the corresponding spectrum will be changed.
Acknowledgments
This work was supported by grant from the Ministry of Education and Science of the Russian Federation (projects No. 14.512.11.0020).
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