High-speed all-optical terahertz polarization ... - Stanford University

APPLIED PHYSICS LETTERS 96, 161103 !2010"

High-speed all-optical terahertz polarization switching by a transient plasma phase modulator Haidan Wen,1,a! Dan Daranciang,2 and Aaron M. Lindenberg1,3 1

SLAC National Accelerator Laboratory, PULSE Institute, Menlo Park, California 94025, USA Department of Chemistry, Stanford University, Stanford, California 94305, USA 3 Department of Materials Science and Engineering, Stanford University, Stanford, California 94305, USA 2

!Received 4 February 2010; accepted 1 April 2010; published online 20 April 2010" We demonstrate high-speed all-optical polarization switching of broadband terahertz frequency electromagnetic fields with subpicosecond switch-on time. This is achieved through the use of a two-plasma configuration in an orthogonal geometry in which one plasma modulates the relative phase of a two-color optical pump field, enabling rapid terahertz polarization modulation at rates limited by the repetition-rate of the control pulse. © 2010 American Institute of Physics. #doi:10.1063/1.3407514$ Optical polarization modulators have been widely used to realize key functionalities in photonic devices, including fiber optic communication, polarization multiplexing, and optical polarimetry. In contrast to optical frequencies, where the fields are usually modulated during propagation through controlled media such as electro-optic crystals,1 the development of ultrafast modulators in the terahertz !THz" frequency range represents an important technological challenge.2,3 These challenges arise in part due to the lack of natural birefringent materials at THz frequencies, making manipulation and control of THz electromagnetic waves difficult to achieve. In addition, the wide bandwidth of ultrashort THz pulses, extending over several octaves, places significant constraints on the bandwidths of optical elements. Recent efforts have focused on engineering metamaterials with resonant response for THz frequency filtering, waveform modulation, and phase shifting.3–7 Nevertheless, devices enabling modulation of the THz polarization have not been extensively explored. Although narrow-band wave plates for THz polarization control have been made by carefully stacked quartz plates8 or by designed metamaterials,9 more practical schemes are required to enable high speed THz polarization modulation, for THz dichroism,10 THz polarization imaging11 and next generation THz photonic applications. In this letter, we demonstrate an all-optical method to modulate the THz polarization by an optically induced plasma in air, with high throughput and potential modulation speed up to megahertz frequencies with existing laser technology, limited by the repetition-rate of the optical modulation signal. THz generation through the ionization of air by a twocolor laser field12–14 has been widely adapted as a convenient and efficient way to generate intense THz pulses for nonlinear THz spectroscopy15–17 and remote THz sensing.18,19 The generation mechanism has been understood as the result of a transient current developed during the photoionization of air.20–22 Recently, it has been demonstrated that the THz polarization can be controlled by the relative phase of the two-color field through the coherent manipulation of electron trajectories within the plasma.23,24 However, the phase modulation rate was limited by mechanical manipulation of optics such as moving a beta barium borate !BBO" crystal23 a"

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or inserting a thin wedge.24,25 Without using any physical element, we create a transient “optic,” a laser induced plasma, to serve as a phase modulator that turns on within 1 ps and lasts only a few nanoseconds. The creation of this plasma in the pump beam path changes the relative phase of the two-color pump field and reversibly switches the THz polarization. A 5 mJ, 800 nm, 50 fs laser pulse is split by a 50/50 beam splitter in a Mach‑Zender interferometer. One of the laser pulses is focused by an f = 400 mm lens through a 100 !m thick, type-I, beta-BBO crystal in the air. The THz field radiating from the plasma is separated from the residual optical pulses by a silicon filter and collected by a pair of parabolic mirrors into an electro-optical !EO" sampling setup or an InSb-based, liquid helium cooled bolometer. The other laser pulse is focused by an f = 200 mm lens to generate an orthogonal plasma that intercepts the beam path of the pump laser field !Fig. 1". The relative delay and position of the two optical pulses are controlled by a delay stage and a steering mirror, respectively. A CCD camera is used to image the fluorescence of the plasma. The fluorescence image !Fig. 1" shows that the THz generation plasma !P1" is a 16 mm long filament with 0.14 mm width !full width half maximum" while the interception plasma !P2" is 4 mm long and 0.32 mm wide due to better focusing. P2 is placed at the position at which the intensity of the THz generation field just reaches the ionization threshold, i.e., upstream of P1 !z = 0, Fig. 1". The majority of THz field is generated downstream after P2 !z " 0, Fig. 1" by the phase-modulated two-color field. The polarization of the THz field is analyzed by recording the transmitted THz intensity as a function of the angle Lens t

0 BBO

z

Filter

Plasma (P2) THz

Plasma (P1)

To EO sampling or Bolometer 1mm

FIG. 1. !Color online" Schematic layout of the experiment: A time delayed laser pulse creates a plasma !P2" that intercepts the two-color pump field. As a result, the generated THz field’s polarization is switched, which is analyzed by rotating a THz polarizer while recording the transmitted THz intensity. The fluorescence image shows the filaments of the two plasmas.

96, 161103-1

© 2010 American Institute of Physics

Author complimentary copy. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp

Appl. Phys. Lett. 96, 161103 "2010!

Wen, Daranciang, and Lindenberg

θ 0 = 90o

(a)

(b)

θ 0 = 0o

t0=20ps

THz polarizer angle (degree)

Relative Delay (ps)

FIG. 2. !Color online" !a" Transmitted THz intensity I through a THz polarizer as a function of the polarizer angle $ before !blue, grayscale: dark" and after !red, grayscale: light gray" the creation of interception plasma. The solid lines are fits corresponding to I = I0 cos2!$ − $0". !b" The THz polarization as a function of the relative time delay. The blue !grayscale: dark" and red !grayscale: light gray" squares indicate the relative time delay at which the polarizer scans in !a" are taken. The solid line is the fit based on Eq. !1" with time constant t0 = 20 ps and 35° offset.

late the phase slippage induced by the transient plasma phase modulator. The spatial temporal profile of the intercepting plasma !P2" can be written as Ne!z , t" = Ne0!t"exp&−4 ln 2#z2 / a2!t"$'. In this simple model, we do not include the plasma recombination or nanosecond-timescale expansion effects.30 The time dependent full width half maximum a!t" = a0!1 + t / t0" and plasma density Ne0!t" = Ne0 / !1 + t / t0"2 at z = 0 reflect the ballisticlike transverse expansion of ionized electrons with velocity ve = a0 / 2t0 within the first hundred picoseconds as previously observed by electron deflectometry measurements.31,32 The optical beam diameter is used to approximate the initial plasma width a0 = 60 !m. The longitudinal expansion is negligible. 4

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40 60 80 Relative Delay (ps)

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-1 0 0.4 0.8 Relative Delay (ps)

EO Delay (ps)

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of a THz polarizer !contrast" 95: 1 up to 3 THz" that is placed in front of the bolometer. Optimization of the plasma density and the overlap of two plasmas yields an additional # / 2 relative phase within the two-color field when propagating through P2, resulting in 90° polarization switching of the THz field. The # / 2 phase shift of the polarizer scans #Fig. 2!a"$ confirms the orthogonal switching of the THz polarization. After the creation of P2, the orthogonally switched THz polarization is followed by a fast recovery with 20 ps time constant #Fig. 2!b"$. It suggests that the relative time delay can be used as a control parameter to obtain a desired THz polarization. The THz waveforms are recorded as a function of the relative time delay #Fig. 3!a"$ by electro-optically sampling the transmitted THz field. We detune the ZnTe crystal rotation angle in the EO sampling setup to avoid zero signal when the THz polarization switches 90°. It is observed that the EO signal flips its polarity #Fig. 3!c"$ when the THz field rotates 90° as expected from the EO signal dependence on the THz polarization angle.26 The trend of the waveform recovery is clearly seen in Fig. 3!a" after the creation of P2. To quantify the time scale of the waveform change, we fit the THz peak field as a function of the relative time delay with an 18 ps time constant #Fig. 3!d"$. This agrees with the polarization dynamics as shown in Fig. 2!b" well, as expected, as both originate in the phase slippage of the two-color fields. The turn-on time of the plasma effect is observed to occur within %500 fs #Fig. 3!b"$ which is partially a result of the geometrical propagation time associated with the intersection of the two-color field within the modulation plasmas !P2". At longer time scales, using bolometric detection with sensitivity independent of the THz polarization, we observe a recovery that lasts at least hundreds of picoseconds, corresponding to the lifetime of the plasma #Fig. 3!d", inset$. The reduction in the THz energy after time zero can be partly attributed to lower THz generation efficiency due to pump pulse distortion, broadening, and defocusing during the propagation through P2.27–29 This is also seen in the 50% peak intensity reduction in Fig. 2!a". To minimize the amplitude modulation during the THz polarization rotation, a nearly circular polarized 800 nm optical field needs to be obtained by tilting the BBO crystal along its vertical axis.23 To understand the short-time-scale dynamics of the THz polarization switching, we employ a Drude model to calcu-

EO Delay (ps)

1


Transmitted THz intensity (arb. unit)

161103-2

t0=18ps

Relative Delay (ps) FIG. 3. !Color online" !a" The THz waveforms recorded by EO sampling as a function of the relative time delay. !b" The zoomed-in plot of !a" around time zero. !c" The THz waveforms before and after the creation of interception plasma. !d" A line-out #the dashed line in !a"$ of the peak THz field as a function of the relative time delay. The solid line is a fit based on Eq. !1" with time constant t0 = 18 ps. The inset shows the THz pulse energy recorded by the bolometer as a function of the relative time delay. The fit is to an exponential decay with 305 ps time constant.


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Appl. Phys. Lett. 96, 161103 "2010!

Wen, Daranciang, and Lindenberg

After the two-color field passes through P2, the induced phase change is %& = %&plasma − %&air, where %&air ( 0 is the phase change during the propagation through the air over the plasma transverse diameter and %&plasma!t" ( = 2'800 / c)−( #n400!z , t" − n800!z , t"$dz. The refractive index nl 2 2 * = 1 − ' p / 'l is determined by the plasma frequency ' p and the laser angular frequency 'l. Considering ' p ) 'l for plasma density Ne0 * 1019 cm−3, in the first order approximation, the phase slippage of the two-color field takes the simple form, %&!t" = %&0/!1 + t/t0" with %&0 (

3*# ln!2" e2a0 Ne0 . 8 ln!2" +0me'800c

!1"

Thus, the fast THz polarization recovery #Fig. 2!b"$ reflects the rapid decrease in the plasma density, resulting from the expansion of the plasma and leading to a time-dependent relative phase shift with time constant t0 = 20 ps #Fig. 2!b"$, much shorter than the plasma recombination time as measured using holographic imaging33 or interferometric methods.34,35 The expansion velocity thus can be calculated to be ve = a0 / 2t0 = 1.5, 106 m / s. This time-resolved polarization measurement therefore provides an alternative means to visualize the expansion dynamics of a laser induced plasma, complementary to the electron deflectometry measurements.31,32 The fast polarization change in Fig. 2!b" corresponds to a plasma density at the center of the plasma Ne0 = 4.5, 1018 cm−3, in line with the estimation36,37 based on our experimental conditions. At lower modulation pulse energy, better focusing is needed to yield similar polarization modulation amplitude. We have observed 70° polarization change using 1 mJ modulation pulse. With higher power, high repetition rate laser systems,38 and stronger focusing, the modulation rate of the THz polarization should be potentially extendable to megahertz repetition rates. In conclusion, we have demonstrated that high-speed alloptical THz polarization switching can be achieved by a laser-induced plasma that modulates the relative phase of a two-color pump field for THz generation. The phase modulation only lasts for several nanoseconds, the lifetime of the plasma, and thus can potentially reach megahertz modulation rate, limited by the repetition rates of existing laser systems. The relative delay of the generation and modulation pulses provides a convenient control of the THz polarization. An ultrafast recovery time of the polarization occurring on timescales of 20 ps is naturally obtained as a result of the plasma volume expansion without the use of engineered materials.39 The presented all-optical polarization control utilizes the laser induced plasma as a phase modulator, adding a building block to the recent development of plasma photonics used for generating12–14 and detecting18,19 THz fields. Finally, we note that the methods described in this paper are not only limited to the control of the THz polarization but also can be employed to achieve fast relative phase modulation of a twocolor field for coherent control experiments involving, for example, photocurrents in semiconductors40,41 and high harmonic generation.42 This research is supported through the PULSE Institute at the SLAC National Accelerator Laboratory by the U.S. Department of Energy, Office of Basic Energy Sciences.

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