Abstract:
The invention relates to a broadband Terahertz (THz) radiation generation and detection system and method. THz radiation is generated by optical rectification of an ultrashort pump pulse of a first wavelength having a duration in the picosecond- or sub-picosecond range in a first nonlinear optical crystal. The THz radiation is detected by electro-optic sampling or another appropriate method of a probe beam having a second wavelength in a second nonlinear optical crystal. According to the invention, at least one of the following conditions is fulfilled: a) the first wavelength is different from the second wavelength; b) the material of the first nonlinear optical crystal is different from the material of the second nonlinear optical crystal. This makes it possible to choose for the generation and for the detection process—independent of one another—the combination of wavelengths and nonlinear material and possibly other features of the pump/probe pulses like polarization with the highest efficiency for generation and detection of Terahertz pulses, respectively.

Description:
[0001]    This application claims priority from U.S. provisional patent application No. 60/794,013 filed Apr. 21, 2006. For the United States of America, this is a regular patent application based on this U.S. provisional No. 60/794,013. 
     
    
     BACKGROUND OF THE INVENTION 
       [0002]    1. Field of the Invention 
         [0003]    The invention relates to the generation and detection of Terahertz (THz) radiation, and more specifically to the generation and detection of pulsed Terahertz (THz) radiation in nonlinear optical crystals pumped by ultrashort optical pulses. 
         [0004]    2. Description of Related Art 
         [0005]    In the past decade, the science and technology on electromagnetic radiation with a spectral content in the 0.1 to 10 THz range (Terahertz or THz radiation, 1 THz=10 12  s −1 ) have attracted widespread interest and evolved into a useful tool for a number of applications (see Ref. [1] for a review). Many materials are transparent for electromagnetic radiation in the THz range, but unlike X-rays the THz radiation does not have an ionizing effect on the material due to the low energy of its photons. This makes it possible to apply THz radiation in different areas such as imaging of biological tissue and the measurement of fundamental solid-state processes in semiconductor physics. 
         [0006]    For some applications, namely THz absorption spectroscopy or spectroscopic imaging, tunable narrow-band THz pulses with nanosecond duration may be favorable due to their better spectral resolution. Such systems for generating narrow-band THz radiation with a well defined THz frequency by means of difference frequency generation in a nonlinear optical crystal are known, e.g. from U.S. Pat. No. 7,054,339. A pair of fiber lasers generates single-frequency outputs at frequencies ω 1  and ω 2 . The nonlinear interaction process in the nonlinear optical crystal generates THz radiation at Ω=ω 1 −ω 2  (difference frequency generation, DFG). These systems are complicated because they need two lasers that have to be synchronized and combined. 
         [0007]    For some applications it is desirable to have shorter THz pulses, e.g. in the picosecond (10 −12  s) or sub-picosecond range. Such broadband THz pulses on a picosecond time scale offer additional benefits that are unique to this technique. The excellence of such broadband THz pulses is the possibility of a phase-coherent detection technique that provides the inherent advantage of a time-resolution that may be as short as a few tens of femtoseconds (10 −15  s). 
         [0008]    Broadband THz pulses may be generated by several methods which all employ femtosecond laser pulses, namely using photoconductive switches, semiconductor surfaces, and optical rectification (OR) in nonlinear optical crystals. A pump pulse in the picosecond or sub-picosecond range contains frequencies in a frequency band Δω around the central frequency ω. Such an ultrashort pulse may produce broadband electromagnetic radiation at THz frequencies in a nonlinear optical material if certain phase matching and velocity matching conditions are fulfilled. This process is known as optical rectification. 
         [0009]    A frequently used technique for the coherent detection of THz pulses is electro-optic (EO) sampling, a process that is based on the interaction of an optical pulse with the THz wave in a nonlinear material. A THz pulse traveling through the crystal is able to change the polarization of a co-propagating probe pulse in the optical range. This change of polarization is a measure for the electric field of the THz pulse and can be detected by appropriate means, e.g. a polarization beam splitter in combination with two photodetectors. EO sampling enables coherent detection of the THz pulse. 
         [0010]    Among different approaches to generate and coherently detect THz pulses, which all require femtosecond lasers, those based on nonlinear optical effects (optical rectification (OR) and electro-optic (EO) sampling, respectively [2]) are advantageous since they use optical pulses at wavelengths outside the material&#39;s absorption range. Therefore the emitted THz field scales with both optical pulse energy and source crystal thickness up to the coherence length (see Eq. (2)), whereas the THz emission from processes that involve the excitation of free charge carriers (e.g. in photoconductive switches) is limited to the optical absorption length of the optical radiation; furthermore there is a risk of damaging the source through high optical power in the latter case. 
         [0011]    Two prerequisites are given for a nonlinear optical material to be useful for THz applications, especially THz generation via OR and detection via EO sampling. First is a sufficient nonlinear optical susceptibility X (2)  and electro-optic (EO) coefficient r. Second is velocity-matching between the optical and the THz pulse, i.e. the THz and the optical pulse have to propagate through the crystal with the same velocity. Velocity-matching is characterized by the coherence length l c ; the latter ought to be at least the crystal thickness, typically 0.1 to 1 mm. Due to dispersion, l c  is a function of both the optical wavelength λ and the THz frequency v. Hence, the material of choice depends on the desired range of v and the available laser source. 
         [0012]    Velocity-matching with THz pulses is achieved e.g. within the inorganic semiconductor ZnTe (zinc telluride) when one uses laser pulses at a wavelength of, for example, 822 nm, i.e., within the tuning range of the widely used Ti:sapphire femtosecond lasers. This factor made ZnTe the material of choice for the generation of pulses with a broadband spectrum below a frequency of 3 THz. ZnTe has an electro-optic coefficient r=4 pm/V and good velocity-matching between optical pulses from Ti:Sapphire lasers also at λ&lt;800 nm [3]. Ti:Sapphire lasers, however, are still very complex, require a given space and maintenance and are costly. 
         [0013]    Among inorganic semiconductors, GaAs with an optimum velocity-matching wavelength of 1.4 μm [3] is the most promising candidate for generation and detection with “telecommunication” wavelengths (around 1.5 μm) and has been demonstrated as a source and detection material with 1.56 μm pulses from a fiber laser [4]. However, its electro-optic (EO) coefficient is about a factor of two lower than that of ZnTe. 
         [0014]    Generally, organic nonlinear optical materials offer several advantages for THz applications, namely their high nonlinear optical susceptibilites, low dielectric constants, and the almost unlimited possibility to design molecules for a specific application [5]. These molecules can be incorporated in either organic crystals or polymers. Although polymers may be efficient emitters and detectors of THz radiation [6], they suffer from fast degradation and limited thickness; disadvantages that apply for organic crystals to a much lesser extent. 
         [0015]    A known organic nonlinear optical material suited for the generation of THz pulses is the crystal DAST (4-N,N-dimethylamino-4′-N′-methyl stilbazolium tosylate). The EO coefficient of DAST (r 111 =47 pm/V at λ=1535 nm [7]) is more than an order of magnitude higher than that of ZnTe or GaAs. Velocity-matching between THz pulses and optical pulses with a wavelength λ around 1300 nm in DAST has been observed [8],[20]. Therefore, THz generation with a high conversion efficiency in DAST is possible. However, the coherent detection by EO sampling in DAST is problematic as DAST has a high birefringence and is thus not suited for EO sampling. 
         [0016]    Ref. [20] proposes to employ another effect, namely the focusing of the probe beam (“Terahertz induced lensing”, TIL) by a spatial variation of the refractive index of the DAST crystal caused by a co-propagating THz pulse. The change in the beam profile can be detected, e.g. by measuring the intensity at a certain location of a screen onto which the optical probe beam is directed. The detection via TIL, however, may have a reduced sensitivity as compared to EO sampling in ZnTe if the relevant electro-optical coefficients are the same. 
         [0017]    It is, therefore, an objective of the invention to provide a system and a method for broadband THz generation and detection that has an increased conversion efficiency in the generation step and an increased sensitivity in the detection step. 
         [0018]    It is a further objective of the invention to provide a system and a method for broadband THz generation and detection that has a reduced complexity, does not require permanent maintenance and attention and is thus suited for commercial use, e.g. as a THz spectrometer and/or imaging device. 
       BRIEF SUMMARY OF THE INVENTION 
       [0019]    These and other objects are achieved by a broadband Terahertz radiation generation and detection system. Preferred embodiments are described in the dependent claims and in the following description. 
         [0020]    The inventive system includes a light source for generating a pump beam and a probe beam, each including light pulses in the optical range (including UV, visible and infrared light) having a pulse duration in the picosecond- or sub-picosecond range, wherein said pump beam has a first wavelength (λ 1 ) and said probe beam has a second wavelength (λ 2 ), that may be identical to the first wavelength or different therefrom. The system further includes a first nonlinear optical crystal arranged in the path traveled by the pump beam (pump beam path). The optical properties of the first nonlinear optical crystal are chosen such that Terahertz pulses forming a Terahertz beam are generated when the pump beam travels through the first nonlinear optical crystal, e.g. by optical rectification. The Terahertz beam travels along a Terahertz beam path. The system further includes a second nonlinear optical crystal arranged in the path traveled by the probe beam (probe beam path). The optical properties of the second nonlinear optical crystal are chosen such that optical properties of the probe beam are altered, e.g. by EO sampling or TIL, when the second nonlinear optical crystal is exposed with the probe beam and the Terahertz beam. In the region of the second nonlinear optical crystal, the beam paths of the probe beam and the Terahertz beam are, thus,partially aligned. The system further includes detection means for detecting predetermined optical parameters of the probe beam, e.g. its polarization and/or intensity. According to the invention, at least one of the following conditions is fulfilled: a) the first wavelength (wavelength of the pump beam) is different from the second wavelength (wavelength of the probe beam); b) the material of the first nonlinear optical crystal used for the generation of THz pulses is different from the material of the second nonlinear optical crystal used for the detection of THz pulses. 
         [0021]    The ultrashort probe and THz pulses enable coherent detection of the THz radiation. This makes it possible to gain time-resolved and/or spectral information on a sample. 
         [0022]    The system may further include beam path shaping means, e.g. normal or dichroic mirrors, normal or polarization beam splitters, lenses and the like, to shape the beam paths in the desired way. A sample is preferably arranged in the Terahertz beam path at a location before the second nonlinear optical crystal. 
         [0023]    The light source can include a single light emitting element, preferably a laser, in combination with adequate means, e.g. beam splitters, frequency doubling, for generating the probe beam and the pump beam at different wavelengths or the same wavelength. As an alternative, the light source can include multiple light emitting elements, e.g. two synchronized lasers, that generate the pump beam and the probe beam, respecitvely. 
         [0024]    The light source is preferably able to generate pairs of ultrashort pulses at first and second wavelengths that may be the same or different from one another. The light source preferably includes a laser. The light source is, for example, a laser having an output at the first wavelength—used as pump beam—in combination with a frequency doubling means, e.g. a nonlinear crystal like BBO, LiNbO 3 , KNbO 3 , for generating the second harmonic of the first wavelength that is then used as a probe beam. This embodiment will be described in more detail below. The light source may also be an optical parametric amplifier (OPA) or optical parametric oscillator (OPO) generating a signal and idler beam with constant sum-of-frequencies. The signal beam may be used as pump beam, and the idler beam as probe beam, or vice versa. Other nonlinear processes may be employed as well, e.g. third harmonic generation and the like. It is also possible that pump beam and probe beam have the same wavelength; in this case, the light source may simply be a laser with a beam splitter to split the probe beam from the pump beam. 
         [0025]    As the pump and probe pulses have a duration in the picosecond or sub-picosecond range, they have a certain bandwidth of wavelengths. This bandwidth determines the upper frequency of the achievable THz spectrum. In the context of the present invention, the first and second wavelengths are the central wavelengths of the pump and probe pulses. 
         [0026]    The system may also include a delay arranged in one of the beam paths. This delay serves to adapt the lengths of the respective beam paths to one another and ensures that the Terahertz pulse and the probe pulse overlap (in time domain) within the second nonlinear crystal, such that the Terahertz pulse affects the probe pulse and coherent detection is possible. Furthermore, the shape of the Terahertz pulse can be probed by varying the delay, thus enabling coherent detection and access to spectral information of the Terahertz pulse. 
         [0027]    The inventive method for broadband Terahertz generation and detection, includes the following steps:
       generating a pump beam and a probe beam each including light pulses in the optical range having a pulse duration in the picosecond- or sub-picosecond range, wherein said pump beam has a first wavelength (λ 1 ) and said probe beam has a second wavelength (λ 2 );   exposing a first nonlinear optical crystal with the pump beam in order to generate a Terahertz beam;   directing the Terahertz beam onto a sample;   exposing a second nonlinear optical crystal with the probe beam and the Terahertz beam in order to alter optical properties of the probe beam in presence of the Terahertz beam;   detecting predetermined optical parameters of the probe beam,   wherein at least one of the following conditions is fulfilled: a) the first wavelength (λ 1 ) is different from the second wavelength (λ 2 ); b) the material of the first nonlinear optical crystal is different from the material of the second nonlinear optical crystal.       
 
         [0034]    The invention makes it possible to chose for the generation and for the detection—independent of one another—the combination of wavelengths and nonlinear material and possibly other features of the pump/probe pulses like polarization with the highest efficiency for generation and detection of Terahertz pulses, respectively. By using pairs of pump/probe pulses that originate from the same source (or from two very precisely synchronized sources) coherent detection is possible. Ultrashort pump pulses enable generation of broadband Terahertz pulses that contain a continous spectrum from 1.3 to 4.8 THz (in DAST), for example. The spectral content of these pulses, after passing a sample, can be resolved by coherent detection, giving a kind of fingerprint of the sample. Furthermore, time resolution as short as a few tens of femtoseconds is possible. 
         [0035]    Generally, materials with a high nonlinear optical susceptibility in which velocity-matching between the generated Terahertz pulse and the pump pulse is given are suited for the generation of Terahertz pulses. Similarly, materials with a high nonlinear electro-optical coefficient or a high nonlinear optical susceptibility in which velocity-matching between the Terahertz pulse and the probe pulse is given are suited for the detection of Terahertz pulses. 
         [0036]    The invention may be implemented by using already known and/or newly developed components. The combination of these components in the claimed way enables one to achieve an enhanced output that exceeds that of the Terahertz systems known so far. In particular, the invention makes it possible to use the high conversion efficiency achievable with organic nonlinear crystals in a first wavelength region, for example infrared, with the well established electro-optic sampling detection method in a different, second wavelength region, for example in the visible or infrared region. 
         [0037]    Preferably, THz generation is achieved using a stilbazolium salt crystal. DAST (4-N,N-dimethylamino-4′-N′-methyl stilbazolium tosylate) has been described in the introductory portion of this application. Organic crystals, e.g. DAST derivatives like DSMOS (4-N,N-dimethylamino-4′-N′-methyl stilbazolium p-methoxybenzenesulfonate) [23] or DSTMS (4-N,N-dimethylamino-4′-N′-methyl stilbazolium 2,4,6 trimethylbenzenesulfonate) [22] or DSNS (4-N,N-dimethylamino-4′-N′-methyl-stilbazolium 2-naphthalenesulfonate) [24] with also very high nonlinear optical coefficients may be used as well. 
         [0038]    Stilbazolium salt crystals, especially DAST, are effectively pumped with lasers emitting in the infrared range, e.g. between 1.0 and 1.7 μm, preferably between 1.3 and 1.6 μm, especially at telecommunication wavelengths from 1.5 to 1.56 μm. Effective THz generation in DAST is possible if the pump beam has a first wavelength between 1.4 and 1.7 μm and wherein the pump beam is directed onto the first nonlinear optical crystal such that its polarization is oriented along the main (a-) axis of the DAST crystal and the beam propagates in a direction in the b-c-plane. In this case, velocity-matching is achieved. Other orientations of the polarization vector with respect to the crystal axes are possible and lead to other pump wavelengths where velocity-matching is achieved. 
         [0039]    It is further preferred that the THz detection is performed by electro-optic sampling in a second nonlinear optical crystal, e.g. ZnTe. Depending on the spectrum of the THz pulse, the preferred wavelength for the probe beam is, thus, around 800 nm. Other nonlinear detection materials like GaAs or GaP can be used as well. It is also possible to use a detection material in which Terahertz induced lensing (TIL) is observed, e.g. DAST. 
         [0040]    Due to the progress in the telecommunications industry, compact and reliable and cost efficient femtosecond lasers, e.g. fiber lasers, emitting in the infrared wavelength range, e.g. from 1.5 to 1.56 μm, are becoming readily available. According to the invention, the detection process is independent of the generation process. The invention makes it, thus, possible to use these lasers to pump a nonlinear optical crystal, preferably DAST or a DAST derivative, for THz generation. The added value is that the wavelength range of these lasers allows an optimum efficiency of THz pulse generation in DAST crystals. Moreover, the variation of using a probe beam at another wavelength, in particular a frequency-doubled probe beam, allows the use of the well established and widely used material ZnTe also with optimum efficiency; additionally, electro-optic sampling is often more versatile than THz-induced lensing that had to be used before for detection when THz radiation was generated in DAST. 
         [0041]    In a preferred embodiment, lasers emitting in the infrared range, in particular at telecom wavelengths, are used to generate THz radiation in DAST crystals, and the frequency doubled beam is used to coherently detect the THz radiation in a standard material like ZnTe. 
         [0042]    The invention thus makes it possible to provide efficient, comparably compact, stable and cost-effective THz systems. 
         [0043]    The invention is applicable, in particular, to systems using ultrashort THz pulses, namely for spectroscopic and imaging applications, e.g. for the security inspection of explosives, biothreats or materials testing, but not limited to these applications. Imaging applications have the appealing feature that besides the absorption also the sample thickness or the composition of a layered structure may be measured due to the coherent detection of the pulses. 
         [0044]    When the variation of the delay is correlated with the measured THz amplitude, spectral information of the THz pulse—and indirectly also of a sample—can be retrieved. 
         [0045]    In a preferred embodiment of the invention, few-cycle THz pulses are generated in the organic crystal DAST (4-N,N-dimethylamino-4′-N′-methyl stilbazolium tosylate) using a telecommunication wavelength in the range of 1.5 to 1.56 μm. A continuous spectrum from 1.3 to 4.8 THz was generated with a very high conversion efficiency (E THz,max &lt;50 kV/cm at an optical pump pulse energy of 25 μJ in a 0.6 mm thick crystal) using the high nonlinear optical susceptibility of DAST (X (2)   111 =490 pm/V at λ=1535 nm) and velocity-matching observed in this material. Using a frequency-doubled probe beam at λ=750 nm, nearly velocity-matched detection can also be realized in ZnTe crystals, resulting in a continuous spectrum from 1.3 to 4 THz. 
         [0046]    For an orientation of the polarization such that the polarization vector has a component in the same direction as the b-axis of the crystal, in DAST also velocity-matching for other pump wavelengths is achievable, e.g. a first wavelength between 680 and 780 nm, preferably between 700 and 740 nm. Similar results can be expected for DAST derivatives. Further crystal orientations lead to other preferred pump wavelengths, e.g. a pump wavelength of 1000 and 1200 nm and orientation of the polarization vector in the ab-plane under 45° with respect to the a- and b-axis. Setups with such arrangements, e.g. as described in claims  10 ,  11 ,  27 , and  28 , have benefits also for efficient THz generation in general and may be used independent of the present invention. In the present invention, the THz generation in DAST or a DAST derivative with a first wavelength between 700 and 740 nm may be combined with detection in ZnTe at the same wavelength, for example, without the need for frequency doubling. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0047]      FIG. 1  shows a contour plot of the coherence length l c  or THz generation and/or detection in DAST. The numbers indicate the value of the contour in millimeters; 
           [0048]      FIG. 2  shows a contour plot of the coherence length l c  for THz generation and/or detection in ZnTe. The numbers indicate the value of the contour in millimeters; 
           [0049]      FIG. 3  shows a contour plot of the harmonic mean of the coherence lengths l c  of DAST and ZnTe; the harmonic mean may serve as a measure for the efficiency of a THz system that combines two materials, one material for the generation and the other for the detection of the THz radiation; 
           [0050]      FIG. 4  shows the experimental setup using a pump beam at ω and a frequency-doubled probe beam at 2ω. EM: Ellipsoidal mirror; PBS: Polarizing Beam Splitter; 
           [0051]      FIG. 5   a+b  show a THz pulse generated through optical rectification in a 0.60 mm thick DAST crystal and detected using THz-induced lensing [20] in a 0.69 mm thick DAST crystal, at an optical wavelength of 1.50 μm.  FIG. 5   a : Signal in time-domain. The indicated modulation is in first order proportional to the THz electric field, limited by nonlinear effects (see text for details).  FIG. 5   b : Fourier transform of the same THz pulse. Absorption by the residual ambient water vapor leads in time-domain to the oscillation that persists for t&gt;1 ps, in frequency-domain to the numerous dips; thus the effectively emitted THz spectrum is given by the envelope; 
           [0052]      FIG. 6   a+b  show a THz pulse generated through optical rectification of 1.5 μm pulses in a 0.60 mm thick DAST crystal and detected by electro-optic sampling in a 0.5 mm thick ZnTe crystal using a frequency-doubled probe beam (λ=0.75 μm).  FIG. 6   a : Time-domain.  FIG. 6   b : Frequency-domain. The effect of water vapor absorption is the same as in  FIG. 5 . 
           [0053]      FIG. 7  gives an overview of different processes for THz pulse generation and detection 
           [0054]      FIG. 8  shows an inventive system using a pump beam at ω and a probe beam at ω with generation and detection in DAST 
           [0055]      FIG. 9  shows an inventive system with a sample located within the THz beam path; 
           [0056]      FIG. 10  shows an alternative method to detect THz radiation by THz induced lensing; 
           [0057]      FIG. 11   a+b  show a contour plot of L max , the maximum of the effective generation length L gen (ω,λ,z) when the actual crystal length z is varied, for DAST using  X OR111 or r111, respectively, for THz frequencies of 0-1 THz ( FIG. 11   a ) and more than 1 THz ( FIG. 11   b ). The thick line represents 0.5 mm, the line spacing equals 0.1 mm throughout. 
           [0058]      FIG. 12   a+b  show a contour plot of L max , the maximum of the effective generation length L gen (ω,λ,z) when the actual crystal length z is varied, for DAST using  X OR122 or r221, respectively, for THz frequencies of 0-1 THz ( FIG. 12   a ) and more than 1 THz ( FIG. 12   b ). 
       
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Introduction 
       [0059]    The velocity-matched generation and detection of THz pulses with 1.5 μm laser pulses in the organic nonlinear crystal DAST (4-N,N-dimethylamino-4′-N′-methyl stilbazolium tosylate) with an EO coefficient (r 111 =47 pm/V at λ=1535 nm [7]) that is more than an order of magnitude higher than that of ZnTe or GaAs is demonstrated theoretically and experimentally. A THz-induced modulation of up to 140% using a nominally linear technique is achieved (see section 4.1). Additionally, it is shown that DAST and ZnTe can be combined in a single THz system if one of the optical beams is frequency-doubled, which allows more versatile detection schemes. 
         [0060]    Optimal wavelength range for generation/detection of THz pulses Optical rectification is a second-order nonlinear optical process, where two optical waves with angular frequency ω interact with each other in a noncentrosymmetric crystal to generate a dc polarisation P OR  through the nonlinear susceptibility X (2) (Ω=0; ω,−ω). If P OR  is induced by a short laser pulse, i.e., with a typical duration of 200 fs or less, it contains components at angular frequencies Ω≠0 that act as a source for radiation in the THz frequency range. This process may also be interpreted as the generation of the difference-frequency between the frequency components of the input pulse, thus using X (2) (Ω; ω,−ω−Ω). An upper limit for Ω is given approximately by the bandwidth Δω of the optical pulse. 
         [0061]    The efficiency of the THz pulse generation depends on the phase-matching between the optical and the THz wave. It can be characterized by a function f (l, v, λ) that contains the complete dependence of the emitted THz electric field E THZ  on the length l of the nonlinear crystal in the non-depleted pump approximation and in the absence of absorption [8]: 
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         [0000]    v=Ω/(2π) is the THz frequency, λ=2π/ω the optical wavelength, and l c (v, λ) the coherence length for THz generation. It has been pointed out that in the case of THz pulse generation, the optical group index n g (λ) rather than the refractive index n(λ) determines the coherence length [2, 3, 9], in contrast to other nonlinear conversion processes such as second-harmonic generation (SHG). Thus l c (v, λ) is given by [2] 
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         [0062]    The coherent detection of the transient THz electric field E THz (t) through electro-optic sampling (EOS) [3, 10] is a prerequisite for the unique applications of these pulses. In standard EOS, E THz alters the polarisation state of a copropagating optical probe pulse through the linear electro-optic effect (Pockels effect). A measurement of this polarisation change as a function of the delay time between THz and probe pulse reveals the THz electric field E THz (t). The measured probe beam modulation also depends on the phase-matching conditions; for unequal propagation velocities of THz and probe pulse, the measured waveform gets distorted [9]. In the frequency-domain, the modulation amplitude is proportional to the same factor f (l, v, λ) from Eq. (1) as the generation efficiency. 
         [0063]    Maximizing f for a given THz frequency range by choosing the optical wavelength λ and the crystal length l properly is thus necessary to obtain an optimal THz signal, in terms of both generation and detection. However, not all electro-optic materials are equally well suited for electro-optic sampling as for THz generation, since EOS in its standard configuration requires a material that is not or only weakly birefringent, which excludes e.g. DAST (n a −n b =0.53 at λ=1.5 μm). One possibility to overcome this restriction is a double-pass scheme [11], another is to use a variation of EOS that is not inhibited by the birefringence, namely THz-induced lensing (TIL) [8]. Nevertheless, standard EOS is more versatile since it allows extensions such as two-dimensional real-time imaging [12] or single-shot measurements [13]. According to the invention, a high-efficiency THz source using DAST is combined with the standard EOS detection in ZnTe in order to profit from the respective advantages. 
         [0064]    2.1 DAST 
         [0000]    In the following, we determine the THz frequency range where a long coherence length l c  (Eq. (2)) allows efficient THz generation or detection for a given optical wavelength λ in DAST in the X (2)   111  configuration, i.e., both optical and THz waves are polarized along the crystal a-axis. 
         [0065]    Walther et al. measured the refractive index n 1 (v) using THz time-domain spectroscopy from 0 to 3 THz [14]. We extended this range up to 4.2 THz using the same method [15]. Above a phonon resonance at 1.1 THz, n 1  (v) increases up to about 3 THz where it shows a small kink; above this frequency, it remains nearly constant. From 1.8 to 4.2 THz, it ranges between 2.2 and 2.3. These values match approximately the optical group index n g,1 (λ) between 1.4 and 1.8 μm that was calculated analytically from the Sellmeier function determined by Pan et al. [7].  FIG. 1  shows a contour plot of the coherence length l c (v, λ) according to Eq. (2). 
         [0066]    Broadband velocity-matching, i.e., a value of l c (v, λ) that is larger than a typical crystal thickness of 1 mm in a wide frequency range, is achieved for wavelengths λ between 1.3 and 1.6 μm, with corresponding frequencies from 1.5 to above 4 THz. From these data it can be expected that telecommunication wavelengths (&lt;1.50 to 1.56 μm) are well suited for pulsed THz systems that use DAST as the emitter material. 
       2.2 ZnTe  
       [0067]    By comparing the THz transients measured with two ZnTe crystals of a different thickness, Wu et al. [3] found experimentally that broadband THz pulses with a frequency content below 2 THz are velocity-matched to optical pulses with λ=822 nm. Due to THz dispersion, this wavelength changes with the center frequency of the THz pulse. 
         [0068]    For a quantitative analysis, we calculated the coherence length l c (v, λ) also for ZnTe. The result is shown in  FIG. 2 . The index data in the THz range are taken from references [16] and [17], those in the optical range are calculated with a Sellmeier fit to the data from Sliker et al. [18]; a more elaborate function for the optical dispersion of ZnTe presented by Sato et al. [19] does not agree better with the measured values in the 600-900 nm range and was therefore not used. 
         [0069]    In the 2 to 3 THz range, the largest values of l c (v, λ) are obtained for wavelengths A between 750 and 850 nm (see  FIG. 2 ), i.e., frequency-doubled pulses from lasers at telecom wavelengths may be used for velocity-matched electro-optic sampling in ZnTe. 
         [0070]    Taking the results of the paragraphs 2.1 and 2.2, one finds that a THz spectroscopy or imaging system combining the advantages of highly efficient generation in DAST and velocity-matched EOS in ZnTe may be built using a telecom laser if the probe pulse is frequency-doubled.  FIG. 3  resumes the data of  FIG. 1  and  FIG. 2  to show which combinations of THz frequency and optical wavelength are expected to give the highest detectable THz signal in a setup using DAST at the fundamental wavelength as the source and ZnTe at the frequency-doubled wavelength for the detection. One finds that the broadest THz frequency range is accessible with a fundamental wavelength near 1500 nm. 
       Experiments 
       [0071]    The laser source in our experiment was an amplified Ti:Sapphire laser that generated pulses with a duration of 160 fs (full width at half maximum, FWHM) and a repetition rate of 1 kHz. Pulses in the desired wavelength range were obtained by means of an optical parametric generator/amplifier (OPG/OPA) whose signal wave was tunable from 1100 to 1600 nm, with a typical pulse energy of several tens of microjoules, depending on the wavelength. The signal wave with the angular frequency ω was separated from the idler wave and the fundamental Ti:Sapphire wave by dichroic mirrors and appropriate filters. 
         [0072]    The setup that was used with a frequency-doubled probe beam is shown in  FIG. 4 . The light source  1  comprises a pulsed laser  2  and means  3  for generating a pump beam  5  and a probe beam  7  from the laser pulses. The incoming laser pulses at ω pass a nonlinear optical crystal  3 , here BBO, in which a fraction of the pulse energy is converted to the second-harmonic frequency 2ω. The two frequencies are then split by a dichroic mirror  4  into a pump pulse at the fundamental frequency ω and a probe pulse at 2ω. Note that the energy of the probe pulse may be two to three orders of magnitude lower than that of the pump pulse since it only has to lead to an ample signal on the photodetectors  16 ,  17 . Thus a high SHG conversion efficiency is not required, or even not desired, since a reduction of the pump pulse energy at the frequency ω would decrease the emitted THz field. 
         [0073]    The pump pulse or pump beam  5  travels a pump beam path  6 , passing a delay line  18  with a variable delay (indicated by the arrows). The delay  18  may comprise one or more mirrors or may be an optical element that is able to induce a variable phase shift, e.g. a rotating plate with variable thickness. They then hit a first nonlinear optical crystal  9 , here DAST, acting as source crystal for the THz radiation. The emitted THz beam  19  travels along a THz beam path  20 . It is focused by a mirror  11  onto a second nonlinear optical crystal  13 , here ZnTe, acting as detection crystal for the THz radiation. The pump beam  5  is blocked by an absorber  10  arranged behind the first nonlinear optical crystal  9  in the pump beam path  6 . 
         [0074]    The probe pulse or probe beam  7  travels along a probe beam path  8  to the second nonlinear optical crystal  13  and further to a detector  14 . To combine the probe beam path  8  and the THz beam path  20 , a pellicle  12  is used. As an alternative, other elements reflective for the optical beam and transmissive for THz radiation, or vice versa, can be used. The delay line  18  may be arranged in the probe beam path  8  instead of in the pump beam path  6 . 
         [0075]    The polarisation change that the electric field E of the THz pulse induced on the probe pulse in the electro-optic detection crystal  13  (ZnTe) is high enough to be measured directly by taking the ratio of the two polarisation components, split by a polarization beam splitter  15 , by detecting their intensities with two photodiodes  16 ,  17 , without the need of lock-in detection (which is also possible). 
         [0076]    In the measurements with the probe beam at the fundamental frequency ω, the dichroic mirror  4  in  FIG. 4  was replaced by a conventional beamsplitter  4 ′. The THz pulses were detected by THz-induced lensing in DAST as second nonlinear optical crystal  13  with the necessary changes in the detection setup  14  described in Ref. [20] and shown in  FIG. 8 . 
         [0077]    As shown in  FIG. 8 , the probe beam  7  is projected onto a screen  21 . A multimode fiber  22  is coupled to the center of the screen  21  and enables measurement of the intensity of the probe beam in its center by a first photodiode  16 ′ arranged at the other end of the fiber  22 . A second photodiode  17 ′ measures the overall intensity of the probe beam  7  on the screen  21  and acts as a reference. The ratio of the signals of the two photodiodes  16 ,  17  is a measure for the THz-induced lensing and, thus, the amplitude of the THz beam  19 . 
         [0078]    Results 
       4.1. Detection in DAST Crystals 
       [0079]    In  FIG. 5   a+b,  we show a THz pulse generated and detected in DAST crystals with 150 fs laser pulses at a wavelength of 1.50 μm and a pulse energy of 25 μJ, e.g. with a setup according to  FIG. 8 . The time-domain signal  FIG. 5   a , measured by varying the delay  18 , is the relative intensity modulation m(t)=Δl(t)/I 0  in the center of the probe beam caused by the lensing effect that the THz electric field E THz (t) exerts on the probe beam profile in the far-field after the electro-optic detection crystal  13  (THz-induced lensing [20]). The relation between m(t) and E THz (t) is intrinsically linear for a relative modulation well below unity; the signal presented in  FIG. 5   a+b  however exceeds the linearity range. As an estimation, we calculated the maximum electric field of the THz pulse in the linear regime using Ref. [20] and obtained a value of 50 kV/cm. 
         [0080]    A direct comparison of this value with those obtained by other groups in different materials is difficult, since absolute values of the transient THz electric field are often not published. However, the ratio between the induced modulation per pump pulse energy and crystal thickness may serve as a measure for the conversion efficiency. Nagai et al. reported 12(mm mJ) −1  for their experiment with 1.56 μm pulses in GaAs (ΔI/I 0 =2·10 −5 , pulse energy 3.4 nJ, 0.5 mm crystal [4]), compared to 93(mm mJ) −1  in our experiment. Considering that the negative effect of two-photon absorption on the THz amplitude is stronger for the higher energy optical pulses in our setup, one can conclude that the THz generation efficiency using DAST crystals at telecommunication wavelengths is an order of magnitude higher than that using GaAs at comparable wavelengths. 
         [0081]    The Fourier spectrum of the THz pulse in  FIG. 5   b  extends from 0 to 6.5 THz, where the upper frequency limit is mainly determined by the duration of the optical probe pulse. Absorption of the THz wave in the DAST crystals reduces the amplitude at the resonance frequencies 1.1 THz [14], 3.1 THz, and 5.2 THz [21]. However, the second resonance at 3.1 THz is weak enough not to reduce the amplitude to the noise level, such that a continuous spectrum without gaps is obtained in the central part of the spectrum from 1.3 to 4.8 THz. 
         [0082]    Detection in ZnTe Using a Frequency-Doubled Probe Beam 
         [0083]    In  FIG. 6   a+b  we present a measurement of the same THz pulse in time and frequency-domain, detected by EO sampling in a ZnTe crystal with a frequency-doubled probe beam (λ=0.75 μm). The spectrum extends from 0 to 4 THz, again with a gap at 1.1 THz due to the phonon resonance in DAST. Here, the upper frequency limit is given by the properties of the detection material, on the one hand since the coherence length becomes shorter than the crystal thickness above 3.5 THz (see  FIG. 2 ), on the other hand due to the THz absorption in ZnTe that strongly increases above 4 THz [16]. The residual velocity-mismatch in ZnTe for the major part of the spectrum leads to a reduction of the maximum THz amplitude compared to that in  FIG. 5 , such that the linearity range of the detection is not exceeded. 
         [0084]    It is remarkable that the observed upper frequency limit of 4 THz lies higher than that measured with e.g., 800 nm probe pulses [2], even though the optimum probe wavelength for ZnTe was considered to be 822 nm so far [3]. This can be explained by the increased coherence length for frequencies above 3 THz at λ=750 nm compared to 800 nm (see  FIG. 2 ). 
       CONCLUSIONS  
       [0085]    In conclusion, we demonstrated a highly efficient generation and detection of few-cycle THz pulses using optical pulses at a wavelength of 1.5 μm and the nonlinear optical crystal DAST. Its large nonlinear optical susceptiblity can be fully exploited due to a coherence length l c  above 1 mm from 1.5 to 4.5 THz at this wavelength. Alternatively, nearly velocity-matched detection in ZnTe crystals was achieved for a frequency-doubled probe beam, resulting in a continuous spectrum from 1.3 to 4 THz. This is important since the detection by conventional electro-optic sampling in ZnTe is more versatile than by THz-induced lensing as it was used with DAST. 
         [0086]    Together with compact and stable femtosecond lasers originally built for the telecommunications industry, DAST-based systems are an efficient and cost-effective alternative for any application of short THz pulses. 
       6. Further Embodiments 
       [0087]      FIG. 7  gives an overview over different methods for THz generation and detection with their advantages and drawbacks. 
         [0088]      FIG. 9  shows a system for measuring properties of a sample  23  by THz radiation. The basic setup corresponds to  FIG. 4  or  8 , for example, with the difference that the delay is arranged in the probe beam path. By a first mirror  11 , the Terahertz beam  19  is directed and focused onto the sample  23 . A second mirror  11 ′ serves for directing and focusing the Terahertz beam  19  onto the detection crystal  13 . The sample  23  may be moved with respect to the Terahertz beam  19  (indicated by the arrows) in order to scan the sample in space, e.g. along a line or in two dimensions. It is also possible to vary the Terahertz beam path  20 , e.g. by adjusting the mirrors  11 ,  11 ′, in order to scan the Terahertz beam  19  over the sample. Additionally or alternatively, the delay  18  may be varied and a delay-dependent signal acquired. This signal corresponds to the amplitude of the Terahertz beam as a function of time, and yields the Terahertz spectrum after Fourier transformation. Consequently, spectral information, optionally spatially resolved, may be retrieved. 
         [0089]      FIG. 10  shows an alternative method to detect THz radiation by THz induced lensing in a nonlinear optical crystal  13 , e.g. in a DAST crystal. The method is based on two-photon absorption of a probe pulse in a standard photodiode  16 ″, e.g. a silicon photodiode or any other detection material with no or reduced sensitivity at the probe wavelength. The change in the spatial probe pulse profile caused by terahertz-induced lensing leads to a variation of the diode signal that is induced by two-photon absorption even though the total pulse energy has remained constant. This variation is proportional to the terahertz electric field. 
         [0090]    The experimental setup for the coherent detection of terahertz pulses (the Terahertz beam path  20  is indicated by a shade of gray) generally corresponds to  FIG. 8  (with the exception of the location of the delay line). The THz pulses are generated by optical rectification in a first nonlinear optical crystal  9 , e.g. DAST, here pumped by a 1.5 μm, 150 fs pump beam  5  for example. The thin line represents the beam path  7  of the probe pulse that is focused by the THz electric field in the second nonlinear crystal  13 , e.g. also DAST, through Terahertz-induced lensing (TIL). The different intensity distribution on the Si diode  16 ′ leads to a change in the two-photon absorption within the Si photodiode that is proportional to the THz field. The further photodiode  17 ″, e.g. a InGaAs photodiode or any other photosensitive material with normal sensitivity at the pump wavelength, is used as a reference to correct for pulse energy fluctuations. 
         [0091]    The method is simple and robust and is suited for the measurement of the terahertz-induced lensing effect, also in other materials than DAST, and may also be used for the coherent detection of few-cycle terahertz pulses in general. 
         [0092]      FIG. 11   a+b  show a contour plot of the maximum effective length L max  for DAST using  X OR111 or r111, respectively, for THz frequencies of 0-1 THz ( FIG. 11   a ) and more than 1 THz ( FIG. 11   b ). L max  is a generalization of the coherence length l c  that incorporates additionally absorption effects within the material [15]. The thick line in  FIG. 11   b  represents 0.5 mm, the line spacing equals 0.1 mm throughout. 
         [0093]      FIG. 12   a+b  is analog to  FIG. 11   a+b , but showing L max  for DAST using  X OR122 or r 221 , respectively, i.e., the polarization of the optical wave is parallel to the crystal b-(or 2-)axis, whereas the THz field is still polarized along the a-(or 1-)axis. 
         [0094]    One finds that the emitted THz field E varies with the real crystal length z proportional to the following factor L gen (ω,λ,z) which may thus be regarded as an effective crystal length for the generation of terahertz pulses. Since the optical absorption coefficient α 0  is negligibly small, the same proportionality applies to the coherent detection by electro-optic sampling in the same material. 
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         [0095]    For nonzero absorption coefficient α(ω).≠0 and a dispersive material, where the indices n and n g  vary with the angular terahertz frequency ω and optical wavelength λ, respectively, L gen  reaches a maximum as a function of the crystal thickness z for fixed values of ω and λ. 
         [0096]      FIGS. 11   a+b  and  12   a+b  present calculations of these maximum values of Lgen for DAST for two different combinations of polarisations of the electric fields of the THz wave and the optical, respectively.  FIG. 11   a+b:  Both fields are polarized along the crystal a-axis (or 1-axis).  FIG. 12   a+b : The THz field is polarized along the a (or 1)-axis, the optical field along the b (or 2)-axis. 
         [0097]    The graphs may be interpreted as follows. The larger the plotted value, the more efficient the THz generation process can be (respectively the more sensitive the detection) for the given combination of ω and λ. However, the crystal length must be chosen adequately. As a rule of thumb, it ought to be 1.6 to 2.2 times larger than the plotted maximum value of L gen (ω,λ,z). 
         [0098]    If the crystal is shorter, its potential is not fully used, if it is longer, the emitted amplitude might already decrease. 
         [0099]    Example: One is interested in a THz amplitude between, say, 2.0 and 2.5 THz. The plotted value in  FIG. 11   a+b  is about constant and at maximum for λ˜1400 nm: L gen ˜0.5 mm. Thus it is favorable to use a 0.8-1.1 mm thick crystal and an optical wavelength of 1400 nm. 
         [0100]    Several combinations of the optical wavelength λ and THz frequency v with enhanced THz emission could be identified. Within the tuning range of Ti:Sapphire lasers, velocity-matched THz generation is achieved using the nonlinear coefficient  X (2) 122  and a pump wavelength of 700 to 740 nm (see  FIG. 12   a+b ). Of primary technological importance is that telecom wavelengths λ around 1500 nm are velocity-matched to frequencies between 1.5 THz and 2.7 THz if the largest nonlinear coefficient  X (2)  111  is used ( FIG. 11   a+b ). 
         [0101]    Using DAST crystals of less than 0.7 mm thickness for generation and detection, we have demonstrated a THz-induced modulation of 140 percent in a nominally linear regime (see  FIG. 5   a ). With the advent of compact and stable femtosecond lasers at 1.5 to 1.56 μm (e.g. Erbium-doped fiber lasers), highly efficient and cost-effective THz systems may be developed using DAST as the THz emitter. Higher frequencies (3.3 THz to 6.7 THz) are most efficiently generated using λ near 1350 nm. These results demonstrate the considerable potential of DAST for THz applications in general and how it can be fully exploited. 
       REFERENCE AND LINKS  
       [0000]    
       
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