Coherent electro-optical detection of terahertz radiation from an optical parametric oscillator

We report the realization of coherent electro-optical detection of nanosecond terahertz (THz) pulses from an optical parametric oscillator, which is pumped by a Q-switched nanosecond Nd:YVO4 laser at 1064 nm and emits at ∼ 1.5 THz. The beam profile and wavefront of the THz beam at focus are electro-optically characterized toward the realization of a real-time THz camera. A peak dynamic range of ∼ 37 dB/√Hz is achieved with single-pixel detection. © 2010 Optical Society of America OCIS codes: (230.5170) Photodiodes; (160.2100) Electro-optical materials; (110.6795) Terahertz imaging; (110.4280) Noise in imaging systems. References and links 1. D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, and M. Koch, “Recent advances in terahertz imaging,” Appl. Phys. B 68, 1085–1094 (1999). 2. W. L. Chan, J. Deibel, and D. M. Mittleman, “Imaging with terahertz radiation,” Rep. Prog. Phys. 70, 1325–1379 (2007). 3. B. B. Hu and M. C. Nuss, “Imaging with terahertz waves,” Opt. 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Introduction
THz radiation in the frequency range of ∼0.1 -3 THz is non-ionizing, harmless to biological tissue, and has the special property of penetrating various materials which are opaque in the visible spectral range, such as paper, cardboard, ceramics, wood, textiles, and plastics.This makes it useful in many industrial and security applications, including non-destructive inspection of sealed post packages, identification of defects in plastic pipes, security inspection of human bodies at airports, and distinguishing diseased skin tissue [1][2][3][4].Many THz imaging systems have been developed for such applications.Most of them obtain the image by raster scanning of the objects with a focused THz beam [5][6][7].Although a high dynamic range can be achieved [8], such measurement schemes are generally time-consuming.There are also THz imaging systems that can acquire simultaneously two-dimensional THz images by coherent electro-optical (EO) detection of THz radiation with a CCD camera in femtosecond-laser-based systems [9][10][11][12].However, such systems usually need an amplifier laser which is relatively expensive and delicate.One type of narrow-band THz source, -i.e. the THz optical parametric oscillator (OPO) pumped by a nanosecond (ns) laser at 1064 nm and using LiNbO 3 as the gain medium -should be a good candidate for making up the shortcomings of the forementioned systems.THz OPOs, which ordinarily employ Q-switched YAG or Nd:YVO 4 lasers that are relatively cheap and are avaliable with industry-grade design for use in harsh environments, have been developed by several groups [13][14][15][16][17].Among the reported applications of THz OPOs -for instance imaging and spectroscopy [14,15] -incoherent intensity detection (e.g. using a Si-bolometer or pyro-electric detector) is the most popular method.Although there have been reports [18,19] of coherent detection of ns-THz pulses, using a parametric optical process, the requirements of an intense near-IR pump beam and a long nonlinear crystal allow this method to work in a single-pixel regime only.In this paper, we report the realization of EO detection of the radiation from a ns THz OPO.The OPO is designed for collinear propagation of the pump and signal beams as reported by Molter et al. [17].EO detection provides a sensitive THz field measurement, enables the recovery of phase information, and allows one to realize a real-time THz camera based on multi-pixel EO detection.Given the nanosecond duration of both the THz and laser pulses, an imaging system with the THz OPO is very robust with regard to the synchronization of the THz-and optical probe-pulse arms.A fast temporal scan in the range of one THz wavelength can accomplish a phase identification [20].In this paper, the THz beam profile and wavefront at focus are electro-optically characterized as well.

The experimental setup
A sketch of the experimental setup is shown in Fig. 1.The THz OPO employs a novel collinear phase matching regime and uses periodically poled LiNbO 3 (PPLN) as the gain medium [17].
It is pumped by a 1064-nm Q-switched Nd:YVO 4 laser, which emits 33-ns pulses with a pulse energy of 0.7 mJ at a repetition rate of 10 kHz, and is seeded by a grating-stabilized diode laser which is tunable from 1064 nm to at least 1076 nm.The THz radiation is coupled out of the side surface of the PPLN crystal by a linear array of five Si prisms and propagates in a direction of 50°relative to the side surface.A frequency range of 1.45 ∼ 1.6 THz is attainable while tuning the seed laser.The THz beam is strongly divergent in the vertical plane (with a divergence angle of about 30°) but only weakly divergent in the horizontal plane.In our experiment, we use a cylindrical lens to correct the elliptical beam and subsequent paraboloidal mirrors to focus In front of the EO crystal, the THz and laser beams are combined collinearly with the aid of a piece of ITO-coated glass [21].The invisibility of the THz radiation and the lack of visible or NIR radiation copropagating with the emitted THz beam makes the alignment of the THz optics less straightforward than in other optoelectronic THz systems.
The correct alignment of these optics is important in order to minimize beam aberrations (such as astigmatism) which degrade the wavefront and focusability of the THz beam.In order to optimize the alignment (in particular, for the cylindrical lens), we employed a thorough procedure where the resultant THz beam profile was monitored using raster-scan measurements with a Golay cell.Representative THz beam profiles following this optimization procedure will be presented in Sec.3.4.
The THz OPO has a pump-enhancement cavity [17], which is an effective solution of building an oscillator for the signal laser while maintaining an efficient input coupling for the pump laser, with a simple linear cavity instead of employing a non-collinear-propagation phase matching configuration [13][14][15][16].The IR laser pulse coming out of the OPO is a mixture of the strongly depleted pump laser pulse, the generated signal laser pulse, and some other additional mixing products with negligible power [17].The total output power is about 250 mW.Herein the power of the pump laser is about 5 times that of the signal laser.For EO detection, one requires both pump and signal laser beams, whose temporal intensity modulation is coherent with the THz field.Although the signal laser pulse is generated from the pump laser pulse, their beams might not completely overlap spatially.In order to ensure optimal overlap, to remove any phase-front distortions, and to achieve a pure fundamental-lateral-mode beam profile, the two laser beams are guided through a short section of single-mode fibre (length 30 cm), before reaching the delay stage and EO detector.A coupling efficiency of 25 % can be achieved with a single-lens fibre input coupler (focal length 15.3 mm, numerical aperture 0.16).Temporally, the pulses of the two lasers are partially overlapped, as shown in Fig. 2. The impact of this on the EO detection will be discussed in detail in Sec.3.3.
For the EO detector, a crossed-polarizer-type configuration is used, in which a quarter-wave plate works as the compensator [22][23][24].This configuration will make the transition to multipixel detection straightforward.The lens groups F 1 and F 2 are a beam shrinker and expander, respectively.A collimated optical beam with a spot diameter smaller than 1 mm can be obtained with F 1, and a spot diameter of about 12 mm can be obtained with F 2. The second polarizer is in a rotational orientation close to that with maximal modulation depth for the EO signal [24].
For EO detection, relatively slow Ge photodiodes (Thorlabs, model no.PDA25K-EC, 8.75μs rise time; 40-kHz bandwidth) are used to avoid saturation of the detection electronics.For reducing the noise due to laser fluctuations and improving the signal-to-noise ratio (SNR), we use two photodiodes and perform differential detection with the lock-in amplifier.One photodiode (PD1) is fed with the laser beam going through the crossed-polarizer detector.Another photodiode (PD2) is fed by a small fraction (10 %) of the laser beam split off the main beam before the EO crystal and behind the first polarizer (see Fig. 1).In the measurement, the dominating noise source is still due to laser fluctuations (which are well above the shot noise level).In order to reduce their impact in future multi-pixel detection, where photodiode PD1 will be replaced by a multi-pixel detector array, the signal of photodiode PD2 will be used for the

The crossed-polarizer-type EO detector
We employ the crossed-polarizer-type configuration [22,25] in the EO detector.Assuming the intensity of the input probe-light is I 0 (t), in absence of the THz field, the intensity of the transmitted light through the detector can be expressed as: where η represents the fraction of transmitted light due to scattering from the polarizers and the EO crystal, Γ 0 is the residual birefringence of the EO crystal, and δ is the tilt angle of the second polarizer.When there is a THz field in the EO crystal, the intensity of the transmitted light is given by where Γ (t) is the phase retardation induced by THz field.Therefore, the difference between I T (t) and I b (t) is the intensity modulation ΔI (t) due to the THz field, i.e. the EO signal, which is a linear function of Γ (t) when Γ (t) (Γ 0 , δ ) 1,

The EO crystal CdTe (110)
CdTe ( 110) is used as the EO crystal in our measurements.It belongs to the same zinc blende class as ZnTe.For EO detection, its EO coefficient r 41 is one of the key factors.CdTe (110) used with 1064 nm lasers has an EO coefficient as high as that of ZnTe (110) crystals at 800 nm [26].
The expression for the THz field induced phase retardation Γ(t) in Eq. ( 3) is given by [25]: where E THz (t) = E T cos (Ω THz t − ϕ 1 ) is the temporal field of THz pulse, Ω THz is the THz frequency, λ opt is the laser wavelength, n opt is the refractive index of the crystal at the laser wavelength, r 41 is the electro-optical coefficient, and L is the thickness of the crystal.Besides the EO coefficient, the coherence length and the absorption of the crystal at IR optical and THz wavelengths are also important factors.The coherence length L c of CdTe at 1064 nm and 1.5 THz is about 1 mm [25].The absorption effects in CdTe for these conditions are dominated by the THz field absorption.One defines an absorption length L α = (α/2) −1 with α being the power absorption coefficient [25,27].Referring to Ref. [25], the indium-compensationdoped CdTe (110) shows a lower THz absorption coefficient than nominally undoped material, which gives an absorption length of L α > 1.3 mm at 1.5 THz.Based on these considerations, a CdTe crystal with a 1-mm thickness and 15 × 15 mm 2 size is used in our measurements.

Effect of imperfect temporal overlap of the laser pulses on EO detection
The strongly depleted pump laser pulse and the signal laser pulse overlap only partially in time.This reduces the relative modulation depth of the EO signal and raises the question whether measures should be taken to improve the pulses' overlap and hence EO signal-to-noise ratio (SNR).
The individual power and temporal shape of each pulse are measured by splitting off 10 % of the laser beam and separating each spectral component with a grating.The separated signal laser beam, whose power is proportional to that of the THz radiation, can also be used for monitoring the operation of the OPO.The measured waveforms of the laser pulses are shown in Fig. 2. The ratio of the peak intensity is I p : I s = 3.3 : 1.The FWHM-durations of the pulses are 18 ns (pump) and 12 ns (signal), respectively, such that the corresponding power ratio is 5:1.If their temporal intensities are assumed to be I s (t) and I p (t), the interference signal has an intensity I(t) which can be written as: where Ω d = Ω THz is the difference frequency.For EO detection, only the overlapping part of the superimposed pulses, which exhibits an intensity modulation at the difference frequency, produces a useful signal.The intensity of this contribution is given by the last term in Eq. ( 5).Then, refering to Eq. ( 3), the EO signal ΔI(t), when mixing the THz radiation E THz (t) with the laser radiation in the EO [CdTe (110)] crystal and neglecting dispersion effects in the crystal, is given by: The integrated signal from the photodetector is hence: with and where Δd is the relative path difference between the laser and the THz pulses, and c is the vacuum speed of light.Thus the modulation depth γ can be written as: Considering the partial temporal overlap and the power difference of the two laser beams, the modulation depth is calculated to be about γ = 0.23 Γ .As the two optical components are separated by a grating before coupling them into a single-mode fibre, it would be possible to manipulate both their relative intensity and time delay.From the data in Fig. 2, we have calculated the resultant peak modulation depth that could be achieved if the delay were optimised to be γ = 0.48 Γ .Hence a factor of two in modulation depth could be gained in principle.While this is not insignificant, we neglect this option of optimization in the following, and, for the sake of convenience, use the laser-pulse overlap and intensity ratio as given from the laser output.

Alignment of the THz beam
As stated above, we measured intensity profiles of the THz beam with a Golay cell to assist the beam alignment.In Fig. 3 were also performed in order to optimize the alignment of the first paraboloidal mirror.This procedure was decisive in achieving the subsequent focal beam quality at the EO crystal.

EO detection of THz radiation
The THz emission from the OPO corresponds to a tilted line source.When the THz beam is collimated and focused with common optical lenses and mirrors, minimizing the astigmatism at a focal spot is challenging [28].Since the beam profile and wavefront at a subsequent focus are of great importance for both single-pixel and multi-pixel imaging, here we investigate the beam properties using a single-pixel EO detector, as well as an optical geometry which corresponds to multi-pixel EO detection by raster-scanning a single optical detector and an expanded optical beam.
A collimated laser beam with a small width (diameter < 1 mm, formed with lens group F 1), and a power just below the saturation of the photodiode, is used for single-pixel EO detection.As shown in Fig. 1, mirror M 1 and optical-component group F 3 are put on two independent manual translation stages.The EO signals on a line across the focal THz beam spot are measured by scanning the small laser spot with M 1 through it with a step size of 0.4 mm.For each step, F 3 is moved to the corresponding position to detect.The amplitude of the measured EO signal versus the scan range is shown in Fig. 4(a).The range where a THz signal can be detected is more than 7 mm.The corresponding THz intensity is shown in Fig. 4(b).The main peak in the THz power has a full-width-at-half-maximum (FWHM) of ∼ 2 mm.The secondary peak to the left may well be due to a slight misalignment of one of the Si output prisms of the OPO crystal.
The temporal field signal at the beam maximum is shown in Fig. 5(a) as a function of relative time delay between the THz and probe laser arms.Here a maximum modulation depth of γ = 1.5 × 10 −6 is measured, which corresponds to a phase retardation of Γ = 1.88 × 10 −4 rad.With Eq. (4), Eq. ( 8), Eq. ( 9) and Eq. ( 10), the THz field on the EO crystal can be calculated to be 490 V/m, which is in fair agreement with the field value (1152 V/m) estimated by using an average THz power of 1.26 μW (measured by a Golay cell close to the source), a beam radius of 1 mm, and a pulse duration of 10 ns, if we take into account the propagation loss.The data  shown correspond to an average of 10 scans with a 50-ms lock-in time constant, which we take as the characteristic measurement time interval in the following.The rms signal fluctuations σ are the same as those obtained from a reference scan (i.e. with the THz beam blocked).Hence the signal noise is due to the residual noise from the balanced detection with no measurable contribution due to THz fluctuations.The time-domain noise level corresponds to a dynamic range (DR) vs peak amplitude of 37 dB/ √ Hz ( based on the average THz power of 1.26 μW for detection, this DR implies a noise equivalent power (NEP) of 250 pW/ √ Hz ).Also included in Fig. 5(a) is a sinusoidal fit to the data with a THz frequency of 1.50 THz.
The corresponding power spectrum of the averaged EO data is shown in Fig. 5(b) (the calculated rms noise floor is also included as a dashed line).Note that care was taken to truncate the time-domain data to an integer number of THz cycles to avoid artificial spreading of the spectral line.The observed peak at 1.5 THz for the averaged data is 51.9 dB above the noise floor.Accounting for the total measurement time of the data (10 scans × 50 ms × 256 points), this corresponds to a DR of 31 dB/ √ Hz.This apparent reduction of 6 dB/ √ Hz compared to the time-domain DR quoted above is due to the fact that (i) the average temporal signal power is half that of the maximum signal (-3 dB), and (ii) the spectral energy is divided between both the positive and negative frequencies of the complex Fourier transform (which is directly related to the additional determination of the temporal phase, which requires both signal quadratures, resulting in an addition -3 dB).The dominant noise source in the EO measurement is due to laser fluctuations arising in the OPO cavity, which are not completely compensated by the balanced detection (due to e.g.non-equal response of the two photodetectors).If the noise in the measurement could be reduced to the residual detector-noise level, which is still much higher than the shot noise level (greater than 130 dB/ √ Hz for the power levels used here), a DR of ∼ 52 dB/ √ Hz would be achievable.A uniform wavefront of the THz beam is highly desirable for multi-pixel imaging (e.g. in terms of establishing the spatial reference phase in the absence of a test object).With our experimental setup, it is not very clear whether the astigmatism will cause an irregular wavefront or not.An experimental arrangement which approaches multi-pixel EO detection was constructed for the purpose of investigating the wavefront of the THz beam at focus.We illuminated the focal spot of the THz beam with an expanded laser beam (diameter ∼ 12 mm, formed with lens group F 2), then applied a φ 1 mm pinhole behind the EO crystal and scan it together with F 3 over a 2 D area of 2.8 × 2.4 mm 2 with a 0.4 mm step size.6 (black curves) as a function of relative time delay between the THz and the probe laser arms.We fit all the time-domain THz signal traces using linear regression and a non-linear search for the optimum global THz frequency (in this case, 1.52 THz).The resultant fits are shown superposed on the data in Fig. 6 (gray curves).The linear regression yields both the amplitude and phase of each THz scan.This allows the THz wavefront to be extracted from the data, after removing a planar fit to the phase (due to a slight misalignment between the x-y translation stage axes and the THz beam).
The squared-amplitude (intensity) image is shown in Fig. 7(a).

Conclusion
In conclusion, we reported the realization of EO THz detection with a ns-laser-pumped OPO.The alignment of the THz beam was assisted by scanning the cross-section of the beam with a Golay cell at different positions along the optical axis.The use of relatively slow Ge photodiode for the EO detection provides good performance for the 10-kHz and ∼ 10-ns duration pulses in terms of saturation and signal duty cycle for the lock-in amplifier.At the highest signal position, a DR (which is limited by the laser fluctuations in our measurements) of 37 dB/ √ Hz can be achieved, and a THz field of 490 V/m is measured.The THz beam can be focused to a relatively small size (1.6 × 2.4 mm 2 ), where the wavefront of the THz beam is essentially flat.Two approaches would be possible for improving the dynamic range by suppressing the laser noise: 1. improvement of the common-mode rejection of the balanced detection; 2. use of a dichroic mirror (as opposed to the interferometric cavity) to couple the pump beam into the cavity.A Si-based CCD camera system is in preparation for multi-pixel read-out of the EO detector to realize a real-time THz camera.

#Fig. 1 .
Fig.1.The experimental setup for EO detection of THz radiation with the THz OPO.Lens groups F 1 and F 2 are a beam shrinker and expander, respectively.Mirror M 1 and opticalcomponent group F 3 are mounted on individual translation stages.The short green lines (a) to (c) mark the positions where raster scans of the THz beam profile using Golay cell are made (the corresponding images are shown in Fig.3).

#Fig. 2 .
Fig.2.The signal (solid red line) and the depleted pump (dashed blue line) laser pulses.The pulse durations are 12 ns and 18 ns, respectively, and the power ratio is 1 : 5 (power determined as intensity integrated over time).

Fig. 3 .
Fig. 3. Images of the THz beam profile at various distances d away from the cylindrical PE lens (focal length 60 mm): (a) d =200 mm, (b) d =280 mm, and (c) d =360 mm.

− 3 Fig. 4 .
Fig. 4. (a) Amplitudes of the measured EO signal in a line across the THz beam spot. 1 D EO scan of the THz beam spot at focus with a step of 0.4 mm.(b) Corresponding THz intensity.

Fig. 5 .
Fig. 5. (a) Measured EO signal as a function of relative time delay between the THz and probe laser arm, including sinusoidal fit (1.50 THz); (b) power spectrum of the data in (a).

#Fig. 6 .
Fig. 6.The measured time-domain signals (black curves) of EO signal attained by scanning optical-component-group F 3 together with a 1 mm pinhole over the expanded laser beam and the fitted spectra (gray curves).The scan step in both directions is 0.4 mm

#Fig. 7 .
Fig. 7. Square of amplitudes (intensity) (a) and the THz wavefront (b) extracted from global fit of the measured EO-signal spectra.