METHOD AND APPARATUS FOR GENERATING THZ RADIATION

Abstract

A method of generating THz radiation includes the steps of generating optical input radiation with an input radiation source device (10), irradiating a first conversion crystal device (30) with the optical input radiation, wherein the first conversion crystal device (30) is arranged in a single pass configuration, and generating the THz radiation having a THz frequency in the first conversion crystal device (30) in response to the optical input radiation by an optical-to-THz-conversion process, wherein a multi-line frequency spectrum is provided by the optical input radiation in the first conversion crystal device (30), and the optical-to-THz-conversion process includes cascaded difference frequency generation using the multi-line frequency spectrum. Furthermore, a THz source apparatus being configured for generating THz radiation and applications thereof are described.

Claims

1. A method of generating THz radiation, comprising the steps of: generating optical input radiation with an input radiation source device, irradiating a first conversion crystal device with the optical input radiation, wherein the first conversion crystal device is arranged in a single pass configuration, and generating the THz radiation having a THz frequency in the first conversion crystal device in response to the optical input radiation by an optical-to-THz-conversion process, wherein a multi-line frequency spectrum is provided by the optical input radiation in the first conversion crystal device, and the optical-to-THz-conversion process includes cascaded difference frequency generation using the multi-line frequency spectrum.

2. The method according to claim 1, wherein the optical input radiation generated with the input radiation source device comprises a first radiation component and a second radiation component including optical frequencies separated by the THz frequency of the THz radiation to be generated, wherein the first radiation component and the second radiation component irradiate the first conversion crystal device with a mutual spatial and temporal overlap along a beam path through the first conversion crystal device and the multi-line frequency spectrum is provided by beating frequencies derived from the optical frequencies of the first and second radiation components.

3. The method according to claim 1, wherein the optical input radiation generated with the input radiation source device comprises a first radiation component including an optical frequency and a second radiation component including the THz frequency of the THz radiation to be generated, wherein the first radiation component and the second radiation component irradiate the first conversion crystal device with a mutual spatial and temporal overlap along a beam path through the first conversion crystal device and the multi-line frequency spectrum is provided by beating frequencies derived from the optical frequency of the first radiation component and the THz frequency of the second radiation component.

4. The method according to claim 2, wherein the first radiation component and the second radiation component irradiate the first conversion crystal device with a collinear geometry.

5. The method according to claim 2, wherein the input radiation source device has two laser sources being locked to each other and generating the first radiation component and the second radiation component, respectively, the laser sources including: two continuous wave laser sources, two quasi-continuous wave laser sources emitting pulses having a duration in a range from 100 ps to 10 ns, one continuous wave laser source and one quasi-continuous wave laser source, two pulse laser sources emitting pulses having a transform limited duration in a range from 10 fs to 100 ps, one broadband chirped pulse laser source, combined with a pulse stretcher, and one pulse laser source, combined with a relative delay unit, or two broadband chirped pulse laser sources, combined with a relative delay unit.

6. The method according to claim 5, wherein the laser sources generate the first radiation component and the second radiation component with different output power, wherein a fraction of a weaker output power to a stronger output power is larger than 0.01% and smaller than 50%.

7. The method according to claim 3, wherein the second radiation component having the THz frequency is generated by optical rectification of a single ultrashort optical pulse in a pump conversion crystal device, cascaded parametric amplification using the first and second radiation components, or optical rectification of a sequence of multiple pulses in a pump first conversion crystal device.

8. The method according to claim 1, wherein the optical input radiation generated with the input radiation source device comprises a sequence of optical laser pulses having a temporal separation (Δt) equal to an integer multiple of a reciprocal of the THz frequency of the THz radiation to be generated (Δt=N.Math.1/f.sub.THz, N=1, 2, . . . ) and the multi-line frequency spectrum is directly provided by the optical input radiation.

9. The method according to claim 8, wherein the first conversion crystal device comprises a periodically poled nonlinear crystal comprising a sequence of alternatingly poled crystal domains, and a domain period of the periodically poled nonlinear crystal is equal to an integer multiple of Λ=c/(f.sub.THzΔn), wherein f.sub.THz is the frequency of the THz radiation to be generated and Δn is an absolute value of a difference between the group refractive index of the optical input and THz refractive index, Δn=|n.sub.THz−n.sub.g|.

10. The method according to claim 8, wherein the input radiation source device comprises one of an ultrashort pulse laser oscillator having a pulse repetition rate at the THz frequency of the THz radiation to be generated, an ultrafast laser oscillator and a sequence of pulses is generated by a multi pulse generator splitting and stacking incoming optical pulses, or an optical pulse inter-leaver, or pulse shaper based on chirp and delaying an optical pulse.

11. The method according to claim 1, wherein the first conversion crystal device has at least one of the features the first conversion crystal device is configured for quasi phase matching by bonding of wafers with periodically inverted crystal device axes or by stacking several smaller periodically poled crystal devices, the first conversion crystal device is configured for quasi phase matching with gradually varying quasi phase matching period along a beam path, the first conversion crystal device is configured for regular phase matching being phase-matched for the THz frequency of the THz radiation to be generated, the first conversion crystal device comprises a plurality of crystal layers being arranged at Brewsters's angle relative to the optical input radiation, the first conversion crystal device comprises a bulk crystal or a periodically poled crystal, the first conversion crystal device comprises congruent Lithium Niobate (cLN), Stoichiometric Lithium Niobate (sLN), Congruent Lithium Tantalate (cLT), Stoichiometric Lithium Tantalate (sLT), Potassium Titanyl Phosphate (KTP), potassium titanyl arsenate, Zinc Germanium Phosphide (ZGP), Cadmium Silicon Phosphide (CdSiP.sub.2), or Gallium Phosphide (GaP), the first conversion crystal device includes at least one dopant, and the first conversion crystal device has a beam path length of at least one of at least 5 mm and at most 10 cm.

12. The method according to claim 1, wherein irradiating at least one further conversion crystal device arranged at an output side of the first conversion crystal device with at least one of the optical input radiation and the THz radiation, and generating THz radiation in the at least one further conversion crystal device in response to the optical input radiation by the optical-to-THz-conversion process.

13. The method according to claim 12, wherein the first conversion crystal device and the at least one further conversion crystal device are configured for quasi phase matching, wherein the first conversion crystal device and the at least one further conversion crystal device have different quasi phase matching periods.

14. The method according to claim 1, wherein each conversion crystal device is cooled with a cooling device.

15. A THz source apparatus, being configured for generating THz radiation, comprising an input radiation source device being arranged for generating optical input radiation, and a first conversion crystal device being arranged to be irradiated with the optical input radiation, wherein the first conversion crystal device is arranged in a single pass configuration and for generating the THz radiation having a THz frequency in response to the optical input radiation by an optical-to-THz-conversion process, wherein the input radiation source device and the first conversion crystal device are configured such that a multi-line frequency spectrum is provided by the optical input radiation in the first conversion crystal device and the optical-to-THz-conversion process includes cascaded difference frequency generation of the optical input radiation using the multi-line frequency spectrum.

16. The THz source apparatus according to claim 15, wherein the input radiation source device is arranged for generating a first radiation component including an optical frequency and a second radiation component including an optical frequency separated from the first radiation component optical frequency by the THz frequency of the THz radiation to be generated or including the THz frequency of the THz radiation to be generated, wherein the first radiation component and the second radiation component irradiate the first conversion crystal device with a mutual spatial and temporal overlap along a beam path through the first conversion crystal device.

17. The THz source apparatus according to claim 16, wherein the input radiation source device has two laser sources locked to each other and configured to generate the first radiation component and the second radiation component, respectively, the laser sources including two continuous wave laser sources, two quasi-continuous wave laser sources configured to emit pulses having a duration in a range from 100 ps to 10 ns, one continuous wave laser source and one quasi-continuous wave laser source, two pulse laser sources configured to emit pulses having a duration in a range from 10 fs to 100 ps. one broadband chirped pulse laser source, combined with a pulse stretcher, and one pulse laser source, combined with a relative delay unit, or two broadband chirped pulse laser sources, combined with a relative delay unit.

18. The THz source apparatus according to claim 16, wherein the input radiation source device is configured for generating the second radiation component having the THz frequency by optical rectification of a single ultrashort optical pulse in a pump conversion crystal device, cascaded parametric amplification using the first and second radiation components, or optical rectification of a sequence of multiple pulses in a pump first conversion crystal device.

19. The THz source apparatus according to claim 15, wherein the input radiation source device is arranged for generating a sequence of optical laser pulses having a temporal separation (Δt) equal to an integer multiple of a reciprocal of the THz frequency of the THz radiation to be generated (Δt=N.Math.1/f.sub.THz, N=1, 2, . . . ).

20. The THz source apparatus according to claim 15, wherein the input radiation source device comprises one of an ultrashort pulse laser oscillator having a pulse repetition rate at the THz frequency of the THz radiation to be generated, an ultrafast laser oscillator and a sequence of pulses is generated by a multi pulse generator splitting and stacking incoming optical pulses, and an optical pulse inter-leaver, or pulse shaper based on chirp and delaying an optical pulse.

21. The THz source apparatus according to claim 15, comprising at least one further conversion crystal device being arranged at an output side of the first conversion crystal device to be irradiated with at least one of the optical input radiation and the THz radiation, wherein the at least one further conversion crystal device is arranged for generating THz radiation in response to the optical input radiation by the optical-to-THz-conversion process.

22. The method of claim 1, wherein the THz radiation is used for driving high energy terahertz guns and electron accelerators for coherent X-ray generation or for imaging and medical therapy, imaging, coherent diffractive imaging, spectroscopy, detecting explosives, small angle X-ray scattering, THz or Optical pump and X-ray probe time resolved spectroscopy, X-ray pump and X-ray probe time resolved spectroscopy, directional wireless communication, radar technique, driving of highly correlated quantum systems into new phases, driving of quantum information devices with transitions in the THz range, and an electromagnetic undulator.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Further details and advantages of the invention are described in the following with reference to the attached drawings, which show in:

[0069] FIG. 1: a schematic illustration of the first embodiment of creating THz radiation according to the invention, including two optical sources;

[0070] FIG. 2: a schematic illustration of a multi-stage variant of the first embodiment according to FIG. 1;

[0071] FIG. 3: further details of an input radiation source device;

[0072] FIGS. 4 to 6: practical results obtained with the inventive THz source apparatus 100 of FIG. 1;

[0073] FIG. 7: a schematic illustration of the first embodiment of creating THz radiation according to the invention, including an optical source and a THz source;

[0074] FIG. 8: a schematic illustration of a multi-stage variant of the first embodiment according to FIG. 7;

[0075] FIGS. 9 to 13: simulation results obtained with the inventive THz source apparatus 100 of FIG. 1;

[0076] FIG. 14: a schematic illustration of the second embodiment of creating THz radiation according to the invention, employing multi-pulse input radiation;

[0077] FIG. 15: graphical illustrations of the multi-pulse input radiation in frequency (A) and time (B) domain;

[0078] FIG. 16: schematic illustrations of input radiation source devices used in the second embodiment of FIG. 14;

[0079] FIG. 17: a schematic illustration of a multi-stage variant of the second embodiment according to FIG. 14;

[0080] FIGS. 18 to 22 simulation results obtained with the inventive THz source apparatus 100 of FIG. 14;

[0081] FIGS. 23 to 25: schematic illustrations of conversion crystal devices used for creating THz radiation according to the invention; and

[0082] FIGS. 26 and 27: schematic illustrations of conventional techniques of creating THz radiation (prior art).

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

[0083] The invention is described with reference to the first and second embodiments of providing the multi-line frequency spectrum by the optical input radiation in the first conversion crystal device. As the physics of the optical-to-THz-conversion process using cascaded difference frequency generation using the multi-line frequency spectrum is equal in both embodiments, features described with reference to the first embodiment can be used with the second embodiment and vice versa.

[0084] Details, e.g., of the input radiation source device, the optical input radiation, the imaging system and the first or further conversion crystal device(s) can be selected on the basis of practical tests or numerical simulations as described below. In particular, the results of the numerical simulations can be directly used for designing the inventive THz source apparatus. It is emphasized that the practical implementation of the invention is not restricted to the described examples, but rather possible with modified features.

[0085] The invention is described in particular with regard to the provision of the optical radiation field having the multi-line frequency spectrum in the conversion crystal(s) and the cascaded THz generation. Details of the invention, like e.g., details of phase-matching, are not described if they are known as such from prior art.

First Embodiment of the Invention

[0086] Features of the first embodiment of the invention are described with reference to FIGS. 1 to 13.

[0087] FIG. 1 shows a schematic of the THz source apparatus 100 comprising an input radiation source device 10 for generating optical input radiation, an imaging system 20 and a first conversion crystal device 30 for THz generation. The input radiation source device 10 comprises of a pump system with an optical pump source 11 creating a first radiation component and an optical seed source 12 creating a second radiation component. In this case, the THz source apparatus 100 is called Type O THz-COPA. In an alternative case (see FIG. 7), a THz seed source 13 is employed, and the THz source apparatus 100 is called Type T THz-COPA. Various possible implementations for the optical pump source 11 and optical seed source 12 are described below.

[0088] The imaging system 20 (details not shown) comprises refractive and/or reflective optics as well as a beam combiner unit, e.g., based on a dichroic beam combiner, which are configured for superimposing the first and second radiation components and collimating, focusing or diverging them into the first conversion crystal device 30. Preferably, the imaging system 20 contains a vacuum based imaging system to eliminate aberrations from the beam.

[0089] The first conversion crystal device 30 comprises e.g., a nonlinear crystal 31, which is a quasi-phase-matched (QPM) crystal, for example periodically poled Lithium Niobate (PPLN) or a regular phase matched crystal with favorable nonlinear parameters, phase-matched for the requisite THz frequency. For Joule level optical input radiation which is available in the about 800 nm/1 μm wavelength region, congruent/stoichiometric lithium niobate and congruent/stoichiometric lithium tantalate with dopants are suitable for high efficiency THz generation. In addition, Potassium Titanyl Phosphate (KTP) available with periodic poling (PPKTP) and Potassium Titanyl Arsenate (PPKTA) with Rubidium dopants are also viable solutions at these frequency ranges. Furthermore, when longer wavelength Joule class lasers used, the nonlinear crystal 31 can be made of other materials, such as Zinc Germanium Phosphide (ZGP) and Cadmium Silicon Phosphide (CdSiP.sub.2). Further details of manufacturing quasi-phase-matched (QPM) crystals are described below with reference to FIGS. 23 to 25.

[0090] A number of methods exist for the implementation of the input radiation source device 10. As a first example, two continuous wave lasers 11, 12, one of high power and the other of significantly lower power, separated by the desired THz frequency can be locked to each other. As a second example, quasi-CW waves with pulse durations ranging from some 100 ps to nanoseconds, with center frequencies separated by the THz frequency may be used. As a third example, the input radiation source device 10 comprises broadband pulses (transform limited durations of 10 fs to 100 ps) optical pump and seed sources 11, 13. Within this variant of the invention, there exists a number of approaches, like (i) generation of transform limited pulses (with their center frequencies separated by the desired THz frequencies; (ii) generation of chirped broadband pulses with center frequencies separated by the desired THz frequency, which can also be overlapped to mimic the situation of using two transform limited narrowband pulses (chirp and no-delay approach, CANDy); or (iii) generation of chirped broadband pulses with the appropriate amount of relative delay such that one of them is of much weaker intensity than the other can also be used. This is similar to a chirp and delay approach (see FIG. 3) but differs significantly in that one of the pulses is of significantly low energy.

[0091] The THz source apparatus 100 can be provided with a multistage configuration as shown in FIG. 2. The first stage including the input radiation source device 10, the imaging system 20 and the first conversion crystal device 30 is structured as described above with reference to FIG. 1. A second stage comprises the first stage as input radiation source device 10A, a second imaging system 20A and a second conversion crystal device 30A. Every further stage, e.g., the third stage as shown, comprises the preceding stage as input radiation source device, e.g., 10B, a further imaging system, e.g., 20B, and a further conversion crystal device, e.g., 30B. The imaging systems and the conversion crystal devices can be configured as described above with reference to FIG. 1. The THz radiation output at each stage is combined for providing the THz output of the multistage THz source apparatus 100. Alternatively, THz radiation output at each stage is used in another channel. Advantageously, the multistage configuration can be used to boost the conversion efficiencies to high levels.

[0092] Alternatively, both the generated THz radiation and optical pump radiation can be re-phased by delaying them with respect to each other and injected into a second and each further stage. The process can be repeated and terahertz can be extracted in the Nth stage as shown in FIG. 8.

[0093] During the cascading cycles, the optical spectrum downshifts significantly and due to material dispersion the phase matching conditions change which limits the number of cascading cycles and, therefore, limits the achievable THz conversion efficiency. Therefore, THz generation can be dispersion limited at very high conversion efficiencies. This can be circumvented by gradually varying the period of the QPM crystals 30, 30A, 30B, . . . along the propagation length. Alternatively, when the multiple stages are employed, each stage can contain a crystal with a different optimal QPM periods.

[0094] The above variant of providing the optical input radiation with the input radiation source device 10 based on a chirp and delay approach is illustrated with an example in FIG. 3. The input radiation source device 10 includes a fs laser source 11.1, a grating stretcher 11.2, and a set of partially reflecting mirrors, in particular an etalon 11.3. For instances two pulses with very short pulse durations, e.g., 30 fs, can be first stretched with the grating compressor 11.2 by adding a chirp to long durations. These chirped pulses can be relatively delayed with the etalon 11.3, resulting in the formation of a chirped pulse including multiple frequency lines, which is input to the nonlinear crystal 31. In addition, one may also use two chirped pulses with their center frequencies separated by the requisite THz frequency. In this case, there is no mandatory need for a delay (CANDy). The setup of FIG. 3 represents an example only. It can be modified, e.g., by using beam splitters.

[0095] FIGS. 4 to 6 illustrate exemplary practical results obtained from the inventive THz source apparatus 100, wherein FIG. 4 shows the experimental optical pump and seed spectra, FIG. 5 shows phase-matching diagrams for various non-collinear phase-matching possibilities, and FIG. 6 shows experimental evidence of forward and backward phase-matched THz waves due to amplification of optical spectra at two different frequencies corresponding to different phase-matched conditions.

[0096] THz source apparatus 100 used for obtaining the results of FIGS. 4 to 6 includes an optical pump source 11 comprising a laser emitting pump pulses (first radiation component) with a pulse duration of 0.25 to 0.3 ns, a center wavelength of 1029.5 nm, an energy of 15 mJ and a repetition rate of 0.1 kHz, and an optical seed source 12 comprising a laser emitting seed pulses (second radiation component) with a pulse duration of 0.25 to 0.3 ns, an effective center wavelength of 1031.25 nm, an energy of 200 ρJ and a repetition rate of 0.1 kHz. Both of the optical pump source 11 and the optical seed source 12 are synchronized so that the pump and seed pulses are overlapped in the nonlinear crystal 31. The nonlinear crystal 31 is a 1 cm long QPM structure based on periodic poling of lithium niobate with a grating period 212 μm at 300 K.

[0097] In a first test an optical seed is launched at an angle θ=0.42 degrees with respect to the pump. The non-collinearly phase-matched THz frequency can be generated as either backward propagating or forward propagating as depicted in the various phase-matching diagrams in FIG. 5. Two distinct THz generation frequencies will be phase-matched depending on whether the condition satisfies class 1 or class 2 phase-matching in FIG. 5. The fact that two possible THz frequencies can be generated is experimentally observed in FIG. 6, where different delays produce two different phase-matched THz generation frequencies. In a further test, both optical seed and pump are launched into a quasi-phase-matched crystal 31 collinearly, again resulting in THz generation.

[0098] According to FIG. 7, the THz source apparatus 100 comprising the input radiation source device 10 for generating optical input radiation, the imaging system 20 and the first conversion crystal device 30 for THz generation. Deviating from FIG. 1, the input radiation source device 10 includes a THz seed source 13, emitting THz pulses with a frequency equal to the frequency of the THz radiation to be created.

[0099] With a practical example, the optical pump source 11 and the THz seed source 13 locked to each other comprise a quasi-CW pump laser and a quasi-CW THz source. The optical pump source 11 creates quasi-CW optical pulses, 100 ps to several nanosecond long, and the THz seed source 13 creates multi-cycle THz pulses. The optical source maybe a CW, a transform-limited (or compressed) pulsed, a broadband stretched pulse, a sequence of pulses separated by multiples of the inverse of the THz frequency (obtained through chirp and delay, multiple lines or pulse trains), or quasi-CW source. The THz may be a CW, quasi-CW, multi-cycle (10's of cycles obtained by optical rectification of an ultrashort laser pulse) or obtained from the first or second embodiment.

[0100] The THz source apparatus 100 of FIG. 7 also can be provided with a multistage configuration as shown in FIG. 8. In this case, both of the optical and THz radiation from a preceding stage are input to a subsequent stage. As described above with reference to FIG. 2, the first stage with the input radiation source device 10, the imaging system 20 and the first conversion crystal device 30 provides the input radiation source device 10A of the second stage etc.

Numerical Simulations of the First Embodiment

[0101] Numerical simulations of the first embodiment have been conducted using the following model formulation. In general, the electric field of an optical longitudinal mode at frequency ω.sub.m=ω.sub.0+mΩ.sub.0, where ω.sub.0 is the central optical angular frequency and Ω.sub.0 is the generated THz angular frequency is given by E.sub.m=A.sub.me.sup.−jk.sup.m.sup.z. Here, A.sub.m is the envelope of the m.sup.th longitudinal mode and k.sub.m is the wave number of the m.sup.th longitudinal mode in the nonlinear medium. The evolution of the envelop A.sub.m is m given by Eq. (1).

[00003]$\begin{array}{cc}\frac{{\mathrm{dA}}_m}{\mathrm{dz}}=\frac{-j.Math..Math.{\omega }_m}{2.Math.\mathrm{cn}\left({\omega }_m\right)}.Math.\hspace{1em}\left[A_{m-1}.Math.A_{\mathrm{THz}}.Math.e^{-j\left(k_{m-1}+k_{\mathrm{THz}}-k_m\right).Math.z}+A_{m+1}.Math.A_{\mathrm{THz}}^{*}.Math.e^{-j\left(k_{m+1}-k_{\mathrm{THz}}-k_m\right).Math.z}\right]& \left(1\right)\end{array}$

[0102] The first term on the RHS of Eq. (1) is sum frequency generation between the red-shifted optical frequency component A.sub.m−1 and the THz field. The second term on the RHS of Eq. (2) is due to difference frequency generation between the blue-shifted optical frequency component A.sub.m+1 and the THz field.

[0103] Similarly, Eq. (2) describes the evolution of the THz field envelope A.sub.THz.

[00004]$\begin{array}{cc}\frac{{\mathrm{dA}}_{\mathrm{THz}}}{\mathrm{dz}}=-\frac{\alpha }{2}.Math.A_{\mathrm{THz}}-\frac{j.Math..Math.{\Omega }_0}{2.Math.{\mathrm{cn}}_{\mathrm{THz}}}.Math.\underset{m=1}{\overset{N}{.Math.}}.Math..Math.A_{m+1}.Math.A_m^{*}.Math.e^{-j\left(k_{m+1}-k_m-k_{\mathrm{THz}}\right).Math.z}& \left(2\right)\end{array}$

[0104] The first term on the RHS of Eq. (2) corresponds to THz absorption and the second term corresponds to an aggregate of all difference frequency generation processes between optical frequency components.

[0105] Numerical simulations of the conversion efficiency of a THz source apparatus 100 according to FIG. 1 have been done as illustrated in FIGS. 9 to 12, assuming center wavelengths of the input radiation source device 10 around 1 μm, a QPM Lithium Niobate crystal 31, and continuous pump, seed and THz waves. A second order nonlinear coefficient of

[00005]${\chi }^{\left(2\right)}=\frac{2}{\pi }.Math.336$

pm/V is assumed, with the factor of 2/π resulting from the QPM structure's periodicity. The refractive index data for the materials accounting for full dispersion of THz and optical waves is based on literature data.

[0106] Simulations of the embodiment of FIG. 1 (Type O THz-COPA) are illustrated in FIGS. 9 and 10. For these simulations, a strong optical pump pulse has been assumed centered at 1030 nm, and the injected optical seed is down-shifted in frequency by the desired THz generation frequency. The crystal 31 is phase matched for that THz frequency and optical pump frequency. The percentage of energy in the seed is varied and is limited to be no larger than 10% of the pump energy. Thus, if 1 J of energy is used as an optical pump, then at most 100 mJ of seed is assumed. Such a system is within the realm of feasible laser technology. The pump fluence is limited to be a factor of 2 smaller than the damage fluence, i.e. about 1.5 J/cm.sup.2. The crystal 31 is assumed to be at cryogenic temperatures of 100 K. The crystal length is restricted to be no longer than 5 cm.

[0107] FIG. 9 shows a peak conversion efficiency as a function of THz frequency for various initial optical seed energies, wherein the seed energy is represented as a fraction of the energy in the pump. FIG. 10A shows the conversion efficiency as a function of length for various THz frequencies, assuming only 0.1% of the energy in the seed, wherein the drop in conversion efficiency beyond a certain length is attributed to phase-mismatch caused by dispersion. FIG. 10B shows the optimal crystal lengths as a function of THz frequency for various seed levels.

[0108] From FIG. 9, it is seen that the initial seed value does not influence the peak conversion efficiency much. This is because cascading of the optical spectrum occurs, at which point the initial conditions are no longer relevant. The peak conversion efficiencies increase with frequency but show an eventual saturation. The saturation of conversion efficiency is owed mostly due to dispersion. At high conversion efficiencies, the broadened optical spectrum is no longer well phase-matched to the generated THz radiation, leading to a decline in conversion efficiency beyond a certain length as shown in the plot of conversion efficiency as a function of length for a seed ratio of 0.1% in FIG. 10A. The maximum conversion efficiency occurs at shorter lengths for higher frequencies, which is in agreement with the understanding of conventional OPA's. The optimal crystal lengths as a function of frequency and initial seed energy are plotted in FIG. 10B. Here, it is shown how higher seed energies and THz generation frequencies reduce the required crystal length. Furthermore, using these calculations, it is shown how conversion efficiencies of >5% can also be achieved using a relatively easily accessible 1 J quasi-CW pulse as a pump. If damage constraints are relaxed, then even higher conversion efficiencies, approximately scaling with the fluences are achieved.

[0109] Simulations of the embodiment of FIG. 7 (Type T THz-COPA) are illustrated in FIGS. 11 and 12. For these simulations, a strong optical pump pulse and a weak THz seed instead of an optical seed are assumed. The THz seed can be generated in numerous ways as outlined above. With further examples, optical rectification of a single ultrashort pulse, chirp and delay approaches, multi-pulse approaches (second embodiment of the invention) and also a Type O THz-COPA may be used to generate the initial THz radiation.

[0110] FIG. 11 shows a peak conversion efficiency as a function of THz frequency for various initial THz seed energies, wherein the seed energy is represented as a fraction of the energy in the pump. FIG. 12A shows the conversion efficiency as a function of length for various THz frequencies, assuming only 0.1% of the energy in the seed, wherein the drop in conversion efficiency beyond a certain length is attributed to phase-mismatch caused by dispersion. In FIG. 12A, for a 1 J of optical pump, a seed of 0.1% corresponds to a mJ of THz seed. FIG. 12B shows optimal crystal lengths as a function of THz frequency for various seed levels. The crystal length was also limited to 5 cm.

[0111] The behaviors depicted in FIGS. 11 and 12 are similar to the case of using an optical seed depicted in FIGS. 9 and 10. However, it may be practically more challenging to seed large amounts of THz energy straightaway since obtaining mJ's of THz seed is a challenging prospect. Therefore, the Type O THz-COPA is more preferred. A type T COPA starting with a weak seed, may be implemented with multiple stages.

[0112] As shown in FIGS. 2 and 8, multi-stage THz-COPA apparatuses can be provided, involving the recycling of either only the optical radiation (FIG. 2) or using both the optical and THz radiation (FIG. 8). The experimentally simplest approach is to simply recycle the optical radiation as depicted in FIG. 2 due to challenges in THz beam transportation and manipulation.

[0113] Simulations of the multi-stage configuration are illustrated in FIGS. 13A and 13B, wherein FIG. 13B shows the conversion efficiency for a Type O THz-COPA with two stages and FIG. 13A shows a three stage structure leading to about 8% conversion efficiency. These are exemplary simulations and do not reflect the limit of possibilities. For example, inclusion of further stages, can lead to conversion efficiencies surpassing 10%. According to FIG. 13A, the crystal length for the first stage is set to be the optimal length, e.g. 5 cm, and the optical radiation from the first stage is basically recycled for the second stage. The QPM period of the structure is optimized (see FIG. 13B) in order to achieve the best conversion efficiency. The sensitivity of the conversion efficiency to the QPM period in FIG. 13B shows that the process is dispersion limited. The reason is that as the optical spectrum cascades, the group velocity changes and consequently a different QPM period is required to optimally phase-match the THz radiation. On the same vein, it is also possible to gradually change the grating period even within a single crystal.

Second Embodiment of the Invention

[0114] Features of the second embodiment of the invention are described with reference to FIGS. 14 to 17.

[0115] FIG. 14 shows a schematic illustration of the THz source apparatus 100 comprising an input radiation source device 10 for generating multi-pulse optical input radiation, an imaging system 20 and a first conversion crystal device 30 for THz generation. The input radiation source device 10 is adapted for creating a sequence of ultrashort pulses having a temporal separation (Δt) equal to an integer multiple of a reciprocal of the THz frequency of the THz radiation to be generated (Δt=N.Math.1/f.sub.THz, N=1, 2, . . . ). With this embodiment, the multi-line frequency spectrum is provided by the optical input radiation in the first conversion crystal device 30.

[0116] The temporal pulse format and corresponding spectrum of the optical input radiation in frequency domain is illustrated in FIG. 15. The temporal pulse format (FIG. 15B) is a sequence of ultrashort pulses in which the temporal separation equals the period (or an integer multiple) of the generated THz radiation. Correspondingly, the pulse sequence includes the frequency lines separated by the THz frequency, as shown in FIG. 15A.

[0117] Each ultrashort laser pulse of the pulse sequence (FIG. 15B) generates a THz wave in the first conversion crystal device 30. Since the delay between the pulses parallels the terahertz field oscillations in time, consecutive ultrafast pulses coherently boost the THz field. In this way, the THz conversion efficiency is enhanced and a high degree of monochromacity is ensured. The amount of energy that can be packed into a single pulse is limited by the damage fluence as determined by F.sub.damage=400τ.sup.1/2 mJ/cm.sup.2. Here, the use of multiple pulses allows us to circumvent this limitation and pack a large amount of energy cumulatively into the sequence. Thus, the gains of going from a single to multiple-pulses is particularly evident for Joule-class pump lasers.

[0118] The imaging system 20 (details not shown) comprises refractive and/or reflective optics which are configured for focusing the optical input radiation into the first conversion crystal device 30.

[0119] The first conversion crystal device 30 preferably comprises a nonlinear crystal 31, which is a quasi-phase-matched (QPM) crystal, for example periodically poled Lithium Niobate (PPLN) or Potassium Titanyl Phosphate (KTP) with periodic poling (PPKTP) or Potassium Titanyl Arsenate (KTA) with periodic poling (PPKTA).

[0120] For Joule level pumping, depending on the pulse format, large apertures of the nonlinear crystal 31, larger than 10 mm*10 mm can be provided. Commercially available quasi phase matched Lithium Niobate, Lithium Tantalate structures are produced by periodically inverting domains using a periodically applied voltage. This approach however can result in apertures only as large as 1.5 to 2 cm.sup.2 at best currently. If larger apertures are needed since the damage fluence of lithium niobate empirically scales according to F.sub.damage, in particular at a repetition rate of 1 kHz, the nonlinear crystal 31 can be constructed as described below with reference to FIG. 25. At lower repetition rates, the damage threshold is higher.

[0121] A number of methods exist for the implementation of the input radiation source device 10, which are illustrated in FIGS. 16A to 16D. According to FIG. 16A, the input radiation source device 10 comprises a multi pulse laser source 14 and a laser amplifier 15. The multi pulse laser source 14 is a high repetition rate master oscillator, with the feature of emission of a pulse train at several GHz, such as fundamentally mode-locked lasers minimizing the cavity length such as mode-locked integrated external-cavity surface emitting laser (MIXSEL) that generate currently pulse repetition rates up to around 100 GHz or by using intra-cavity interferometers enabling repetition rates 7 to 1100 GHz, or harmonically mode-locked lasers. The repetition rate corresponds to the desired terahertz frequency to be generated.

[0122] With the modified version of FIG. 16B, the input radiation source device 10 comprises the multi pulse laser source 14, a pulse picker unit 16 and the laser amplifier 15. The pulse picker unit 16 comprises e.g., an electro-optical modulator or acousto-optical modulator that selects a sequence of the high repetition rate pulses created by the multi pulse laser source 14. This burst of pulses is amplified with the laser amplifier 15 to ultra-high energies. In this way, the burst can contain higher pulse energies after amplification in a power amplifier. The repetition rate from burst to burst is typically several Hz or kHz. The pulse picker unit 16 also allows for shaping of the burst envelope.

[0123] According to FIG. 16C, the input radiation source device 10 comprises a master oscillator 17, a multi pulse generator 18 and a laser amplifier 15. The master oscillator 17 comprises an ultrashort pulsed laser oscillator emitting pulses at a repetition rate much lower than the desired terahertz frequency. Particularly for ultrashort lasers emitting pulses of several μJ to mJ the repetition rate are typically in the range of MHz to kHz. The multi-pulse generator 18 is adapted for a division of the laser pulse of the master oscillator 17 into several pulses that are separated by the inverse of the terahertz frequency or one of its harmonics. For example, the multi-pulse generator 18 several options exist a stack of birefringent crystals, semi-reflective surfaces, Gires-Tournois Interferometer mirrors, 4-f pulse shapers with phase-gratings in the Fourier-plane, acousto-optical pulse shapers or Death-star pulse shapers [8]. If the pulse-shaper provided by the multi-pulse generator 18 shows loss then it may be useful to place the pulse-shaper before the power amplifier otherwise the device can also be externally attached to the output of the laser.

[0124] Alternatively, a multi pulse generator 18 can be a device that chirps a broadband pulse and split into two parts which are overlapped with each other after an appropriate delay. The delay and the chirp may be tuned to yield the desired THz frequency.

[0125] FIG. 16D illustrates another variant, wherein the input radiation source device 10 comprises a source 19 creating and mixing multiple quasi-continuous, long duration pulses or frequency lines and a laser amplifier 15 amplifying the frequency lines. Source 19 comprises e.g., two cw single-frequency lasers that are phase-locked. Long pulses from these cw lasers can be generated by controlling the current of the laser diodes inside the lasers or alternatively the optical signal output by an external optical modulator, which can be a Pockels cell, acousto-optical or electro-optical modulators.

[0126] The THz source apparatus 100 of the second embodiment of the invention can be provided in a multistage configuration as shown in FIG. 17. A first stage comprises an input radiation source device 10 for generating multi-pulse optical input radiation and a first conversion crystal device 30 for THz generation as described above. The first stage provides the input radiation source device 10A of the second stage, further including a second conversion crystal device 30A. Further stages can follow.

[0127] The multistage configuration provides a recycling of the optical input radiation for subsequent stages of THz generation. Here, the pump laser system can refer to the multi-pulse laser system or any other pump laser system. Contrary to the use of the recycling the pump to generate further THz radiation proposed [7], the recycling of pump in the case of lithium niobate at the high conversion efficiency obtained with the invention is unique. The reason is that when conversion efficiencies reach the percent level, there is a repeated down conversion of the optical frequency. The fact that this distorted spectrum can still be used to generate THz radiation in subsequent stages is unprecedented. Therefore, recycling at low conversion efficiencies is quite different from recycling at large conversion efficiencies.

Numerical Simulations of the Second Embodiment

[0128] Numerical simulations of the second embodiment have been conducted using the following model formulation. The generated terahertz field at the angular frequency Ω can be calculated based on the formula presented below.

[00006]$\begin{array}{cc}A\left(\Omega ,z\right)=\frac{-j.Math..Math.{\mathrm{\Omega \chi }}^{\left(2\right)}.Math.F\left(|E_{\mathrm{op}}\left(t\right).Math.{|}^2\right)}{2.Math.n\left(\Omega \right).Math.c}.Math.\left(\frac{e^{-j.Math..Math.\Delta .Math..Math.\mathrm{kz}}-e^{-\frac{\alpha .Math..Math.z}{2}}}{\frac{\alpha }{2}+j.Math..Math.\Delta .Math..Math.k}\right)& \left(3\right)\end{array}$

[0129] Here, A(Ω,z) is the terahertz electric field, χ.sup.(2) is the effective second order nonlinearity, n(Ω) is the terahertz refractive index, α is the terahertz absorption coefficient, Δk is the phase-mismatch between the optical pump laser and the generated terahertz and c is the speed of light in vacuum. F(|E.sub.op(t)|.sup.2) is the Fourier transform of the optical pump laser pump intensity.

[0130] The optical to terahertz conversion efficiency is then readily evaluated as follows.

[00007]$\begin{array}{cc}\eta \left(z\right)=\frac{{\mathrm{\pi .Math.}}_0.Math.c.Math.{\int }_0^{\infty }|A\left(\Omega ,z\right).Math.{|}^2.Math.d.Math..Math.\Omega }{F_{\mathrm{pump}}}& \left(4\right)\end{array}$

[0131] Based on the formulae (3) and (4) presented above, the optical-to-terahertz conversion efficiencies for pulse formats given by E.sub.op.sup.(t) can be calculated. Calculations are provided for the case of lithium niobate and 1030 nm optical pump wavelengths. The lists of relevant parameters are tabulated below.

TABLE-US-00001 Parameter Value Second order nonlinear susceptibility χ.sup.(2) (2/π) *336 pm/V F.sub.pump = 50% of maximum damage Fluence 50% of F.sub.damage Crystal temperature T 100 K

[0132] In order to model the nonlinear conversion process numerically, the following 1-D equations were used.

[00008]$\begin{array}{cc}\frac{{\mathrm{dA}}_{\mathrm{THz}}\left(\Omega ,z\right)}{\mathrm{dz}}=-\frac{\alpha \left(\Omega \right)}{2}.Math.A_{\mathrm{THz}}\left(\Omega ,z\right)-\frac{j.Math..Math.{\Omega }^2.Math.{\chi }_{\mathrm{eff}}^{\left(2\right)}\left(z\right)}{2.Math.k_{\mathrm{THz}}\left(\Omega \right).Math.c^2}.Math.e^{\mathrm{jk}\left(\Omega \right).Math.z}.Math.\underset{-\infty }{\overset{\infty }{\int }}.Math.E_{\mathrm{IR}}\left(\omega +\Omega ,z\right).Math.E_{\mathrm{IR}}^{*}\left(\omega ,z\right).Math.d.Math..Math.\omega & \left(5\right)\\ \frac{{\mathrm{dA}}_{\mathrm{IR}}\left(\Omega ,z\right)}{\mathrm{dz}}=-\frac{j.Math..Math.{\omega }^2.Math.{\chi }_{\mathrm{eff}}^{\left(2\right)}\left(z\right)}{2.Math.k_{\mathrm{IR}}\left(\Omega \right).Math.c^2}.Math.e^{\mathrm{jk}\left(\omega \right).Math.z}.Math.\underset{-\infty }{\overset{\infty }{\int }}.Math.E_{\mathrm{IR}}\left(\omega +\Omega ,z\right).Math.E_{\mathrm{THz}}^{*}\left(\Omega ,z\right).Math.\mathrm{d\Omega }-\frac{j.Math..Math.{\mathrm{.Math.}}_0.Math.{\omega }_0.Math.n_{\mathrm{IR}}^2\left({\omega }_0\right).Math.n_2\left(z\right)}{2}.Math.F.Math.\left\{|E_{\mathrm{IR}}\left(t,z\right).Math.{|}^2.Math.A_{\mathrm{IR}}\left(t,z\right)\right\}& \left(6\right)\end{array}$

[0133] Equation (5) considers the evolution of the terahertz electric field envelope A.sub.THz(Ω) at angular frequency Ω. The first term is the absorption of the terahertz radiation. The second term corresponds to the optical rectification process which is a sum of all possible difference frequency generation processes between various optical spectral components.

[0134] Equation (6) considers the evolution of the optical electric field envelope A.sub.IR(ω) at angular frequency ω. The first term corresponds to the terahertz induced spectral broadening of the optical spectrum. The second term corresponds to the self-phase-modulation term.

[0135] FIG. 18A shows a sequence of pulses in time separated by a time interval corresponding to the generated terahertz frequency, FIG. 18B shows a conversion efficiency optimized over length using Eq. (3) for various transform limited pulse durations at various terahertz frequencies for a sequence of (solid), 10 (dashed) and 30 (dotted) pulses for cryogenically cooled lithium niobate, and FIG. 18C shows a conversion efficiency as a function of the number of pulses in the sequence (N) for 0.3 and 0.1 THz respectively.

[0136] Ideally, the terahertz field would grow linearly with the number of pump pulses. Since the terahertz energy is proportional to the square of the electric field, the total conversion efficiency will also scale linearly with the number of pulses. However, when optical damage is taken into consideration, this growth ceases to be linear beyond a certain value of N. In FIG. 18A, a particular case of a sequence of pulses is illustrated, wherein the intensity of each pulse in the sequence is identical. In FIG. 18B, the total fluence is maintained constant at half the damage fluence value given by F.sub.damage. As can be seen in FIG. 18B, compared to the single pulse case, the conversion efficiency continues to grow as the number of pulses is increased. Calculations illustrated in FIG. 18C reveal that conversion efficiencies in excess of 10% can be achieved at 0.3 THz and approximately 2% at 0.1 THz can be achieved.

[0137] In the case of FIG. 18, the intensity of each pump pulse in the sequence is equal. However, as the initially generated terahertz radiation is absorbed the most, and the terahertz that is generated the last, exits the crystal first and consequently has the least overlap with the subsequent pulses in the sequence, the conversion efficiency can be increased if the intensity of the pump pulse in the sequence are varied as follows. For maximum efficiency gains, the pulse sequence is provided such that the THz pulses experience both the maximum coherent growth from the pulse sequence and also the least absorption. Preferably, the pulse sequence have an envelope with a Gaussian shape. Advantageously, this provides higher conversion efficiency in relation to a flat envelope over the pulse sequence.

[0138] The pulse sequences have an envelope with a Gaussian profile can be generated by several methods. Firstly, a pulse splitter and stacker for ultrashort laser pulses device can be used for shaping the pulse sequence, e.g., as described in [8]. Secondly, the pulse sequence can be shaped by mixing two or more frequency lines, each corresponding to a long, quasi-continuous pulse as illustrated with reference to FIG. 19.

[0139] FIG. 19A shows a sequence of pulses separated by a time interval corresponding to the generated terahertz frequency with a Gaussian envelope. Such an intensity pattern is produced with a pair of frequency lines or quasi-continuous wave pulses of 150 ps duration each. FIG. 19C shows the conversion efficiency optimized over length for various quasi-continuous pulse durations at various terahertz frequencies for cryogenically cooled lithium niobate (100 K). FIG. 19B shows the conversion efficiency as a function of the number frequency lines N for 0.3 and 0.1 THz for cryogenically cooled lithium niobate.

[0140] Calculation of the conversion efficiency as a function of the transform limited pulse duration of each frequency line for exactly a pair of lines shown in FIG. 19C shows that conversion efficiencies as high as about 6% can be achieved using a pair of 300 ps pulses separated by 0.3 THz. In the intensity pattern of the pair of lines in FIG. 19A, they appear approximately as a train of pulses separated exactly by (f.sub.THz).sup.−1=Δt=3.33 ps with a Gaussian envelope. Note, due to the redistribution of the fluences within the sequence of pulses, higher conversion efficiencies compared to the case of just N pulses may be achieved. For example, for 0.3 THz, conversion efficiencies on the order of 20% and 5% for 0.1 THz are calculated as seen in FIG. 19B

[0141] Thirdly, an alternative variant employs pulse shaping to an ultrashort pulse. Specifically, the ultrashort pulse is chirped, split and the copies are delayed with respect to each other, e.g., with the arrangement of FIG. 3. The order of the chirping, splitting and delay can be changed. This method is particularly applicable to broadband optical pump pulses, such as commercially available 800 nm Ti:Sapphire pulses. In this approach, a large bandwidth pulse is chirped, split into two and interfered with the appropriate delay to generate terahertz at the desired frequency.

[0142] In FIGS. 20A and 20B, the optimized conversion efficiency is shown as a function of the chirped pulse duration for 0.3 and 0.1 THz respectively in cryogenically cooled lithium niobate (100 K). FIG. 20A shows the conversion efficiency at 0.3 THz optimized over length as a function of the chirped pulse duration τ2 for various transform limited durations (30 fs, 330 fs, 600 fs and 1 ps) using the chirp and delay approach. FIG. 20B shows the conversion efficiency at 0.1 THz optimized over length as a function of the chirped pulse duration τ2 for various transform limited durations (30 fs, 330 fs, 600 fs and 1 ps) using the chirp and delay approach in cryogenically cooled lithium niobate (100 K).

[0143] FIG. 21A shows the conversion efficiency as a function of length for a train of 32 pulses of 500 fs each passing through 5 crystals with identical QPM periods Λ, phase-matched for 0.1 THz. Each, time the efficiency is about 1% or more. Therefore the cumulative efficiency is around 5%. This can be further increased by adding further stages and/or optimizing the QPM period for each stage and/or by having a single crystal with an appropriately varying value of Λ along its length. Thus, several stages of recycling the optical pump pulse can be employed as shown in FIG. 17 to yield very high cumulative conversion efficiencies. The optical spectra at the end of the fifth stage is plotted in FIG. 21B.

[0144] FIG. 22A shows the conversion efficiencies as a function of length for three stages of optical pulse recycling through a quasi-phase-matched crystal phase-matched for 0.3 THz, with identical QPM period value Λ in each stage. The original input optical field comprises of a train of 32 pulses of 500 fs each. In the first stage, a conversion efficiency close to 6% was achieved. In the second stage, a conversion efficiency of 2% was achieved and in the third stage, conversion efficiency close to 1% was achieved. Cumulatively, this corresponds to conversion efficiencies on the order of 9%. Once again, this does not represent a limit since further optimization of QPM periods Λ in each stage and/or addition of stages can be employed. The broadened spectrum at the end of the third stage is plotted in FIG. 22B. Thus, the approach of recycling the optical pulse can result in very high cumulative conversion efficiencies.

Configuration of the Conversion Crystal Device

[0145] Preferred configurations of the first or further conversion crystal device(s), which can be used with the first or second embodiment of the invention are illustrated in FIGS. 23 to 25. Exemplary reference is made to periodically poled lithium niobate (PPLN) crystals. Periodically poled nonlinear crystals made of other materials as cited above can be provided correspondingly.

[0146] According to FIG. 23A, commercially available PPLN crystals with apertures of up to 1.5 to 2 cm.sup.2 can be used. Alternatively, large area PPLN crystals can be made from wafers bonded to each other as shown in FIGS. 23B and 25. As a further alternative, structures formed by stacking of several smaller PPLN crystals can be used as shown in FIG. 23C.

[0147] The period of the QPM can vary along the propagation length or remain constant, and/or or multiple crystals with different but uniform periods can be used for different stages of THz generation to provide increased conversion efficiencies. Besides, collinear geometries, non-collinear geometries may also be adopted.

[0148] Non-collinear geometries may be advantageous with regard to the fabrication of structures. For instance several wafers maybe rotated by the appropriate angles and merely placed at distances smaller than the THz wavelength as shown in FIG. 24. The optical pulse can be incident at Brewster's angle α, so that all reflections for the optical beam are circumvented. The THz wave does not see interfaces much smaller than the wavelength and passes through as if there were no interfaces. This embodiment advantageously circumvents the need to adopt an expensive wafer bonding process to fabricate the QPM structures.

[0149] FIG. 25 further illustrates the structure of FIG. 23B, wherein the nonlinear crystal 31 is made of multiple wafers. The wafers are rotated to each other such that the appropriate QPM is obtained by nonlinear crystal 31. Subsequently, the wafers are bonded to each other. This structure may be referred to as wafer bonded QPM (WB-QPM) structures. In this way large aperture periodically poled crystals can be produced. The nonlinear susceptibility is a function of the relative angle between the crystal axis and incident electric field. Therefore alternate rotation of the crystal axes results in an alternating sign of the second order susceptibility. In the case of lithium niobate, the electric field along the z axis of the crystal produces maximum terahertz energy. With a practical example, a prototype of nonlinear crystal 31 has been produced with eight, 0.5 mm thick 5% Magnesium Oxide Doped Congruent lithium niobate wafers with alternating z axes diffusion bonded to each other, having an aperture of 15-20 cm.sup.2. With alternative examples, the nonlinear crystal 31 can be made of stoichiometric Lithium Niobate, Congruent/Stoichiometric Lithium Tantalate, Gallium Phosphide, Potassium Titanyl Phosphate and Potassium Titanyl Arsenate wafers, with various dopants such as Magnesium Oxide or Iron or Chromium or Rubidium.

[0150] The features of the invention disclosed in the above description, the drawings and the claims can be of significance both individually as well as in combination or sub-combination for the realization of the invention in its various embodiments.