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Abstract
A new approach for dual-mode (namely broadband mode and narrowband mode) terahertz (THz) pulses generation in a single lithium niobate (LN) crystal excited by spatially shaped tilted-pulse-front femtosecond (fs) laser pulse was proposed and experimentally demonstrated. The two THz emission modes are generated simultaneously while spatially separated. Both central frequency and bandwidth of narrowband THz emission is controllable by in situ tuning the spatial modulation period and beam size of the fs-laser, and the broadband (0.1-1.5 THz) THz emission keeps almost unchanged while tuning the narrowband emission. Further optimization achieves the narrowband THz emission with energy spectral density up to 0.27 μJ/THz and with bandwidth narrowly down to 23 GHz. Such dual-mode THz source is useful for nonlinear THz optics, such as selected resonant THz excitation with broadband THz probe spectroscopy of crystalline matters.
© 2017 Optical Society of America
1. Introduction
The development of THz source has been drawn much attention due to its importance for all of the THz technology applications [1–3], and many researches have been promoted to develop different kinds of THz source. In some cases, broadband single-cycle THz pulses are generated [4,5], and such pulses are suitable for broadband spectroscopic applications. While in some other cases, narrowband multicycle THz pulses are preferred for some applications such as sensing techniques, communication, and imaging [6,7].
Optical rectification (OR) of fs-laser pulses in nonlinear optical crystals has emerged as one of the most powerful way to generate THz radiation [8–11]. OR with tilted-pulse-front pumping in LN crystal is of particular interest due to its compatibility and had produced sub-mJ broadband single-cycle THz pulses [12, 13]. Narrowband multicycle THz pulses also can be generated by OR pumped with temporally [14] or spatially [15] pre-shaped fs-laser. Recently, a simple, more effective scheme is proposed to generate tunable narrowband THz pulses, where a virtual quasi-phase-matching (QPM) structure is formed in LN crystal illuminated through a binary shadow mask (SM) or a phase mask (PM) [16–18].
The advance of high electrical field of broadband THz pulse enables the studies of nonlinear physics of crystalline condensed matters in the few-meV energy range [19]. However, selective excitation of vibrational mode in matter can resonantly drive the mode to non-equilibrium state by isolating the selected mode from other modes, which requires THz sources with both strong tunable narrowband as pump and broadband THz spectrum as probe. Simple, but inefficient, way is to split the femtosecond pulse into two, one of which is used to generate THz pump pulse in one nonlinear optical crystal while the other is to generate THz probe pulse in another crystal. Since THz generation from nonlinear optical crystal is second-order nonlinear process, splitting optical energy results quadratic decreasing of THz output power and consequently insufficient excitation THz field. A more comprehensive way might be generation of both high power narrowband and broad THz pulse by sending one femtosecond laser pulse into one single nonlinear crystal.
In this paper, we proposed a new configuration for dual-mode (broadband and narrowband) tunable THz pulses generation by OR in a single LN crystal which was illuminated by spatially shaped fs-laser beam. A grating and a 1-D binary SM were used to generate periodically modulated tilted-pulse-front pump beam. Non-collinear phase matching condition and QPM condition are satisfied simultaneously, and a broadband THz pulse and a narrowband THz pulse are generated simultaneously while spatially separated pumped by this spatially shaped laser. The central frequency and bandwidth of narrowband THz pulses can be easily tuned by in situ varying the SM period and pump beam spot size. The broadband THz pulses with 0.1~1.5 THz bandwidth and narrowband THz pulses with energy spectral density up to 0.27 μJ/THz were obtained, and such dual-mode THz source could be useful for many applications, especially for selected resonant THz pump-THz probe spectroscopy. The THz generation efficiency and beam properties were also demonstrated in this paper.
This paper is organized as follows. Section 2 describes the concept design and experimental setup in detail. In section 3 the experimental results are presented for dual-mode tunable terahertz generation, and detailed discussion is given. Conclusions are drawn in section 4.
2. Concept design and experimental setup
We consider a new scheme for broadband and narrowband THz pulses generation as shown in Fig. 1(a). A tilted-pulse-front laser is used as pump beam and incident on a SM-covered LN crystal. The SM is illustrated in Fig. 1(c), which is made of chromium on a 2.3 mm thick quartz substrate. As shown in Fig. 1(b), with tilted-pulse-front pumping, a broadband THz pulse can be emitted from the right surface of SM-covered LN crystal, since the non-collinear phase matching condition is still satisfied, and the angle θB is equal to the pulse front tilted angle and determined by the velocity matching condition, as shown in Fig. 1(d), that is θB = cos−1(VTHz/Vg) = cos−1(ng/nTHz)≈63°, where Vg and VTHz are the group and phase velocity of the optical pulse and the THz radiation, respectively, ng is the group refractive index at pump wavelength, and nTHz is the refractive index at the THz wavelength.
Fig. 1 (a) Scheme of dual-mode THz generation in SM-covered LN crystal with tilted-pulse-front pumping. NB: narrowband, BB: broadband. (b) Schematic illustration of broadband and narrowband THz generation with tilted-pulse-front pumping at two different time (t1<t2). (c) Binary shadow mask (SM). d: the SM period, Wy: pump beam spot size. (d) Broadband and narrowband THz generation phase matching condition.
On the left face of SM-covered LN crystal, the non-illuminated parts of crystal can be considered as a nonlinear medium having nonlinear coefficient d33 = 0. Thus, the THz generation can be considered as OR process in uniformly illuminated LN crystal having spatially modulated nonlinear coefficient d33. The periodical spatially modulated structure serves to obtain a constructive interference of THz fields radiated by illuminated parts of the LN crystal, and the THz emission angle θN = θB = cos−1(ng/nTHz) is determined by Cherenkov radiation angle. As shown in Fig. 1(d), the wave vector diagram of narrowband THz generation forms right-angled triangular and therefore the phase matching condition can be written as
where kTHz = ωTHznTHz/c is the wave number at angular frequency of THz generation ωTHz, c is the speed of light in vacuum, kg = k(ω + ωTHz)-k(ω)≈ωTHzng/c, k(ω + ωTHz) and k(ω) are the wave numbers of spectral components at ω + ωTHz and ω frequencies of the laser radiation. We note that the THz generation period with tilted-pulse-front pumping can be considered as twice period without tilted front pumping as shown in Fig. 1(b), thus, the spatial wave number kd should be written as kd = 2π/2d. Using Eq. (1) the central frequency of narrowband THz pulse fTHz = ωTHz /2π can be given byBecause each illuminated part of the LN crystal is responsible for one cycle of THz oscillation. Hence, the total duration of the multicycle THz generation tim is equal to the product of the oscillation period T = 1/fTHz and the number of SM’s slits N≈Wy/d illuminated by laser radiation [17]. Using Eq. (2), the total duration of the multicycle THz pulses tim can be given by
As the pump beam is gauss spatial distribution, the generated narrowband THz pulse can be considered as a pulse with gauss temporal envelope, therefore, the intensity full width at half maximum (FWHM) bandwidth of the narrowband THz radiation can be given by
From Eqs. (2) and (4), it can be found that the central frequency and bandwidth of the narrowband THz pulse are inversely proportional to the SM period d and the pump beam spot size Wy, respectively. Hence, one can easily tune the central frequency and bandwidth of the narrowband THz radiation by designing different periods SM and using different spot size pump beam.The dual-mode tunable terahertz generation setup we used in the experiment is shown in Fig. 2. A Ti:sapphire system was used as the pump laser with 1 mJ/pulse energy, 800 nm central wavelength, 1 kHz repetition rate, and 110 fs pulse duration. The intensity front of the pump pulse was tilted by a 1200-lines/mm grating, and a λ/2 plate in front of the grating was used to maximize the diffracted efficiency of the grating, while the other λ/2 plate was used to rotate the polarization of the pump laser diffracted from the grating to parallel to the optical axis of stoichiometric LN (sLN) crystal [20] which is perpendicular to the plane of Fig. 2. The telescope scheme which is more advantageous for THz generation than the single lens imaging [21] consists of one 175-mm focal-length, 50-mm diameter (magnification of 2/7) and one 50-mm focal-length, 25-mm diameter lenses in confocal arrangement. The sLN crystal is isosceles triangle with two 63° angle and 1.3% Mg-doped, and the entrance face of the crystal is 5 × 5 mm2. A SM illustrated in Fig. 1(c) was attached to the sLN crystal entrance face by using an adhesive tape on the bottom of the crystal and SM, and a periodically modulated tilted-pulse-front laser was generated and propagated through the crystal. Different SMs having period of d = 50 μm, 100 μm, and 150 μm were used in our experiment, respectively. The pump beam spot size on the SM surface was about 2.1 × 1.9 mm2 at 1/ e2 of its intensity, and the maximal pump beam energy behind the SM we used was about 0.28 mJ/pulse. A calibrated pyroelectric detector (Microtech Instruments) with 2 × 3 mm2 active area and a cone-shaped metallic input was used to measure the energy of the THz pulse. The generated THz pulses waveforms were measured by electro-optical (EO) sampling. One should note that although our experimental scheme is a little similar to the hybrid type scheme proposed in [22], the concept is very different that the contact grating in hybrid type scheme is used to generate tilted pulse front, and the grating period is on a level with pump laser wavelength, while in our scheme the SM is used to generate a periodical spatially modulated structure and to obtain a constructive interference of THz fields, and the SM period is much larger than that of contact grating.
3. Results and discussion
3.1 Dual-mode THz generation
In this subsection, we first tested the dual-mode THz generation from the proposed tilted-pulse-front pumping SM-covered LN crystal setup experimentally. Only a broadband THz radiation was emitted from the right surface of LN crystal without the SM, while both broadband and narrowband THz radiations were emitted respectively from the right and left surfaces of LN crystal with the SM. The spectrums of the THz pulses emitted from both sides of the 50-μm period SM-covered LN crystal with tilted-pulse-front pumping were measured by using the EO sampling method. The results measured with SM are shown in Fig. 3, and the multicycle THz pulse waveform is offset for clearness. As can be seen, a broadband and narrowband THz waveforms were achieved simultaneously. The single-cycle broadband THz pulse carries a spectrum that covers the full range between 0.1 THz and 1.5 THz. The measured central frequency of narrowband THz pulse with 50 μm period is 0.70 THz, agreeing well with that calculated by Eq. (2). The satellites around 1.40 THz are related to second-order quasi-phase-matching (QPM) process.
Fig. 3 The dual-mode THz waveforms with 50 μm period SM measured by EO sampling. The inset is the corresponding dual-mode THz pulses spectra.
3.2 Tunable spectrum
In this subsection, we demonstrate the tunable frequency and bandwidth of the narrowband THz pulse. By substituting in Eq. (2) ng = 2.23 (at 800 nm laser wavelength [23]) and nTHz from dispersion formula of the 1.5% Mg-doped LN crystal [24], we obtain that the central frequencies of narrowband THz pulse are 0.715 THz, 0.360 THz, 0.242 THz for SM periods of d = 50 μm, 100 μm, and 150 μm, respectively.
We measured the dual-mode THz waveforms with different SM periods. Figure 4 shows the measured dual-mode THz waveforms and corresponding spectra with the SM having periods of d = 50 μm, 100 μm, and 150 μm, respectively. As shown in Fig. 4(a), the durations of multicycle THz pulses are nearly the same and it is about 55 ps for all used different period SMs with same pump beam spot size, which is corresponding with the calculated results by using Eq. (4). By substituting the pump beam spot size Wy = 2.1 mm in Eq. (4), the pulse duration is estimated to be tim = 60 ps, agreeing with the measured value ~55 ps. Figure 4(b) shows the dependences of generated narrowband THz pulse frequency on SM period, and the 2nd-order QPM frequency and the calculated results with Eq. (2) are also shown in this figure. The frequencies of narrowband THz generation with 50, 100, 150 μm periods are respectively 0.70, 0.35, and 0.23 THz, agreeing well with the calculated results (0.715, 0.360, and 0.242 THz) by Eq. (2).
Fig. 4 (a) Narrowband THz waveforms, and (b) corresponding 1st-order and 2nd-order QPM frequency versus SM period, solid lines show the dependencies calculated with Eq. (2). (c) Broadband THz waveforms and (d) corresponding Fourier spectra with the SM having periods of d = 50, 100, and 150 μm, respectively.
The measured single-cycle THz waveforms and corresponding broadband spectra are shown in Figs. 4(c) and 4(d). As can be seen, the THz pulse amplitude increases a little and the spectrum bandwidth broadens slightly as the SM period increases. This may because larger SM period ensure larger pump beam size per slit and realize better phase matching. The spectra cover the range between 0.1 THz and larger than 1.5 THz and are peaked at around 0.36 THz for all used different period SMs.
We then changed the pump beam spot size by using a variable diaphragm before the grating, and the pump beam spot size on the SM surface was changed from 2.1 mm to 0.2 mm. The measured THz waveforms and corresponding spectra around 0.36 THz are shown in Fig. 5, and the results calculated with Eq. (4) are also shown in this figure. As can be seen, the duration of multicycle THz pulse decreases with the pump beam spot size, while the spectrum bandwidth increases with the pump beam spot size. The FWHM bandwidth is nearly inversely proportional to the pump beam spot size, and the bandwidths for different SM periods but same pump beam spot size are nearly the same, which is corresponding with the law of Eq. (4). The measured bandwidths with large pump beam size agree with the results calculated with Eq. (4), while the slight divergence of the measured and calculated bandwidth with small beam size may because that the diaphragm cuts the pump beam spot and breaks the gauss spatial distribution, and the measured error may be another reason. The minimal FWHM bandwidth is about 23 GHz with the maximal pump beam spot size of 2.1 mm. The amplitude of broadband THz waveforms decreases with the pump beam spot size, while the spectrum bandwidth changes little.
Fig. 5 (a) Narrowband THz waveforms and (b) corresponding FWHM bandwidth with different pump beam spot sizes. Blue triangle, red circle, black square shows the bandwidths with the SM having periods of d = 50, 100, and 150 μm, respectively. Black solid line shows the dependency calculated with Eq. (4). The inset is the corresponding Fourier spectra with different pump beam spot sizes.
3.3 THz pulse energy and generation efficiency
The dual-mode THz pulse energies and generation efficiencies were measured by using a pyroelectric detector. The results are shown in Fig. 6, and the broadband THz generations with 100 and 150 μm period SMs are not shown in this figure for clearness, since they are just a little larger, but have a similar relationship with 50 μm period SM. As can be seen from Fig. 6(a), the output narrowband and broadband THz pulse energies have a quadratic relationship with the pump fluence. The corresponding linear relationships between THz generation efficiency and pump fluence are shown in Fig. 6(b). Although our experimental setup was not optimized for broadband THz generation but for the narrowband THz generation, since it is difficult to optimize both of them synchronously, the broadband THz generation efficiency is still larger than the narrowband THz generation efficiency with same pump fluence. Interestingly, the narrowband THz generation efficiency with the SM period of 100 μm is larger than those of 50 and 150 μm, which means there exists optimal SM period for narrowband THz generation. This can be explained by following considerations. For large period SM, the constructive interference of THz fields is weaker than that of small period SM, while small period SM leads to higher frequency narrowband THz generation (e.g. 0.70 THz for 50 μm period SM), and the increase of THz absorption in LN crystal results in the decay of the generation efficiency. The maximal narrowband THz pulse energy we achieved is about 12 nJ only with 0.28 mJ pump energy.
Fig. 6 (a) The measured dual-mode THz generation energies with quadratic fits and (b) corresponding efficiencies with linear fits. The broadband THz generation is measured with 50 μm period SM.
The energy spectral density of broadband THz radiation generated with 50 μm period SM and 1st-order QPM narrowband THz radiation generated with different period SMs are shown in Fig. 7, which are calculated by using the THz pulse energy and the spectral bandwidth. As can be seen, the energy spectral densities of narrowband THz pulses are larger than that of broadband THz pulses at the same frequency, which may because that the constructive interference of the SM configuration enhances the energy spectral density of narrowband THz generation. Another reason is that in these experiments the scheme was not optimized for broadband THz generation but for the narrowband THz generation. The maximal narrowband energy spectral density we achieved is about 0.27 μJ/THz, which is sufficient for many applications, especially when taking into account its ability to easily in situ tune the central frequency and spectral bandwidth of generated THz radiation. Moreover, the energy spectral density can be increased additionally by using higher pump energy, larger pump beam spot size and cryogenic cooling the LN crystal.
Fig. 7 The energy spectral densities of broadband THz radiation generated with 50 μm period SM and 1st-order QPM narrowband THz radiation generated with different period SMs.
3.4 THz Beam properties
We finally measured the narrowband THz beam properties by scanning with the pyroelectric detector combining with a small diaphragm. Figure 8(a) and 8(b) shows the cross-section profiles of narrowband THz radiation with Gaussian fits and the measured spot sizes at FWHM as a function of propagation distance with linear fits, respectively. The THz intensity image is also shown in the inset of Fig. 8(b). As can be seen, the THz beam has a divergence of about 47 mrad and 68 mrad in horizontal and vertical direction, respectively. The diameter at FWHM in vertical direction is larger than that in horizontal direction, which is the inverse of the pump beam size (about 2.1 × 1.9 mm2 on the SM surface). This may because the triangular shape and THz absorption of the LN crystal leads to the decrease of THz beam size in horizontal direction, while the THz generation efficiency in vertical direction only relates to the pump beam intensity profile. The beam profile of the broadband THz radiation is similar to that of narrowband THz radiation, which also has a mrad-level divergence in horizontal and vertical directions [25].
Fig. 8 (a) The cross-section profiles of narrowband THz radiation at 20 mm from the LN output surface with Gaussian fits, and (b) the measured spot size as a function of propagation distance with linear fits. The inset is the THz intensity image.
4. Conclusion
In summary, a new approach for dual-mode (broadband and narrowband) tunable terahertz pulses generation in a single LN crystal excited by spatially shaped fs-laser pulses was proposed and experimentally demonstrated. Pumping with periodically modulated tilted-pulse-front fs-laser pulses generated by using a grating and a binary SM, a broadband THz pulse with 0.1~1.5 THz bandwidth and a narrowband THz pulse with energy spectral density up to 0.27 μJ/THz and with bandwidth narrowly down to 23 GHz were obtained simultaneously while spatially separated. Such dual-mode THz source should be useful for nonlinear THz optics, such as selected resonance, especially when taking into account its ability to easily in situ tune the central frequency and spectral bandwidth of generated THz radiation. Finally, the energy spectral density of generated THz radiation is expected to be increased additionally by using higher pump energy, larger pump beam spot size, cryogenic cooling the LN crystal and phase mask covered scheme.
Funding
National Key Basic Research Program of China (No. 2015CB755405), the National Key R&D Program (No. 2016YFC0101003), the National Natural Science Foundation of China (Nos. 61427814 and 11604316), and Foundation of President of China Academy of Engineering Physics (No. 201501033).
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