We report the use of quasi-phase-matching techniques based on periodically-poled MgO:LiNbO3 for the generation of nanosecond duration pulses of terahertz radiation in intracavity optical parametric oscillators. Multiple idler-waves are generated with temporal studies indicating that the initiating process is the expected parametric down-conversion, but followed by cascaded difference frequency generation. A number of grating geometries have been explored, revealing the presence of dual solutions for the quasi-phase-matching process in the general case. Choice of grating parameters so as to minimize oscillation threshold while simultaneously ensuring effective extraction of the THz radiation is considered.
©2010 Optical Society of America
The generation of electromagnetic radiation in the terahertz (THz) frequency range (0.3-10THz) continues to attract world-wide research interest; not least because of potential applications in areas extending from the medical and biological to homeland security and defence, and involving spectroscopic, tomographic and hyperspectral imaging techniques. Generation schemes based on the use of optical lasers play an important role in this regard; for a critical overview of the range of techniques involved, see the recent (2008) review paper by Kitaeva . Optical parametric generation (OPG) of terahertz radiation, the subject of this communication, is one of these techniques, now well established. The early work of Puthoff & Pantell [2–4], has subsequently been extensively developed by Kawase and others over a period of years [5–11], leading to the emergence of practical sources based on nanosecond-pulse lasers. More recently we have demonstrated the benefits of using the intracavity approach for the optical parametric generation of terahertz radiation [12–14]. In this approach the nonlinear medium is located within the cavity of the pump laser used to pump the optical parametric oscillator (OPO) as well as within the cavity used to resonate the down-converted idler-wave, thereby providing compact, low-threshold sources of THz radiation.
All of the aforementioned sources have used conventional phase-matching techniques based on bulk lithium niobate as the nonlinear gain medium, and have involved non-collinear phase-matching in which the pump-wave (near infrared), the idler-wave (near infrared), and the signal-wave (THz)* are all non-parallel with each other.
In recent years periodically-poled lithium niobate has been widely investigated for generating terahertz radiation, but mainly confined to techniques other than optical parametric generation, namely optical rectification techniques based on excitation with femtosecond pulses [15–18], and difference frequency generation (DFG) [19–21]; aspects that are reviewed by Kitaeva .
The first report, to our knowledge, of periodically-poled lithium niobate (PPLN) being used for the optical parametric generation of terahertz radiation, involving in this case nanosecond-pulse lasers, is that of Molter et al . In this scheme, for which our interpretation is shown in Fig. 1(a) , the grating vector describing the periodic-poling is arranged perpendicular to the pump-wave propagation direction, thereby allowing parallel (collinear) propagation of the pump and idler waves while still retaining the rapid (non-collinear) exiting of the signal (THz) wave through the side facet of the crystal; the latter being an essential feature because of the high absorption of this wave by lithium niobate.
Molter et al  used this phase-matching scheme within a pump-enhancement cavity. This configuration was essential in order to circumvent difficulties encountered with standard dielectric mirrors in the case where the pump and idler waves share a common cavity, as here, and are close in wavelength (1064 and 1070 nm respectively), as arises for a signal-wave in the THz spectral range. In addition, a pump-enhancement cavity also reduces the external power/energy required to bring the device to oscillation threshold.
In the present communication we report a quasi-phase-matching scheme for the generation of THz radiation based on using intracavity optical parametric oscillators [23,24]. The intracavity approach also provides a practical solution to the afore-mentioned difficulties associated with the common cavity for idler- and pump-waves, in this case through including the gain medium of the pump laser along with the nonlinear medium within this common cavity. It also confers the benefit of much reduced oscillation thresholds as a consequence of the high intensity of the intracavity pump field to which the nonlinear medium is now subjected. Importantly it also exhibits additional practical advantages over the previously-reported pump-enhanced geometry in that the need for a single-frequency pump source, injection seeding, and inter-cavity frequency locking schemes is avoided, thereby significantly simplifying the overall optical set-up, so resulting in robust and compact devices.
As well as the use of an orthogonal grating vector as previously reported by Molter et al , we have also explored a number of other periodically-poled geometries of a more general type as illustrated in Fig. 1(b). In so doing we have gained further insights into the underlying processes associated with the quasi-phase matching approach. In the next section (section 2) we first describe our experimental investigation of an intracavity device based on the orthogonal grating geometry. In section 3 we report on an extended investigation of the use of periodically-poled geometries, thereby enabling us to draw wider conclusions on both the limitations and the optimization of the approach.
[*We here define the wave that provides the required output frequency, namely the THz wave, as the signal-wave, despite this wave having a much lower frequency than the other down-converted wave that is close in frequency to the pump-wave and is referred to as the idler-wave.]
2. Intracavity configuration for THz generation based on periodically-poled materials
The intracavity OPO, see Fig. 2 , was similar to that described by us previously in relation to our demonstration of the intracavity configuration as applied to the non-collinear phase-matching scheme (often referred to as the Cherenkov scheme ), but with two important modifications to be discussed in more detail shortly after a brief summary of common features.
The gain medium (LG) of the pump laser is a Nd:YAG crystal, 7mm long by 4mm diameter doped with Nd at a level of 1.3%. It is optically excited by a fiber-coupled AlGaAs pulsed laser diode delivering 250μs duration pulses with peak powers up to 100W at repetition rates around 15Hz and at a wavelength of 804.7nm. The radiant output from the fiber is imaged by suitable lenses to provide a pumped volume in the Nd:YAG crystal with a cross-sectional diameter of 1mm, closely matching the pump-wave mode size at this location. A standard electro-optic configuration based on a Pockels cell, zero-order quarter-wave plate and linear polariser is incorporated in the cavity for the purpose of Q-switching (QS). The generated terahertz radiation is extracted from the nonlinear crystal using an array of silicon prisms (SPA) as previously described by Kawasi et al .
In the present configuration the pump-wave cavity now also serves as the idler-wave cavity since this latter wave is now collinear with the former wave (see Fig. 1). No separate off-axis idler-wave cavity is hence required, in contrast to the case with the non-collinear phase-matching scheme. In particular the same mirrors (M1 and M2) serve for both the pump- and the idler-waves; the closeness of the wavelengths of these two waves means that both now experience similar cavity finesses. In this regard mirror M1 has a reflectivity >99%, and mirror M2 has a reflectivity of 97% for both waves, this latter being chosen so as to allow external temporal monitoring of both waves. The nonlinear lithium niobate crystal (PPLN) was poled with a grating vector orthogonal (i.e. along the y-axis) to the common propagation direction (along the x–axis) of the pump and idler waves and with a period of 42.4μm, predicted to phase match for a THz wavelength of ~200μm with the THz radiation then propagating at an angle of 65% to the common propagation direction of the pump- and idler-waves. The length (along the x-axis) of the crystal is 30mm, with a cross-section of 5mm x 1mm, the latter dimension corresponding to the poling direction (z-axis). All three waves are linearly polarized parallel to the z-axis of the crystal.
The cavity geometry associated with our earlier non-collinear device was such that the diameter of the pump-wave in the bulk lithium niobate nonlinear crystal was of the order of 1mm (full-width at 1/e2), advantageous with regard to enhancing the overlapping of the three non-collinear waves (pump, signal and idler) in the nonlinear medium, thereby reducing the oscillation threshold. In the present case, however, the limited aperture (~1mm) of the periodically-poled lithium niobate crystal along its poling direction requires the mode diameter to be significantly reduced below 1mm in order to avoid deleterious clipping losses. This was brought about by the inclusion of the intracavity lens L of focal length + 200mm. With mirrors M1 and M2 as plane mirrors, this results in a beam waist of measured radius ~100μm (1/e2) located on the mirror M2 itself, and with the beam radius within the nonlinear crystal not exceeding 200μm throughout the length of the crystal (the range being from ~150μm at face B, to ~200μm at face A). The present cavity geometry also ensured reasonable matching of the pump wave mode size to the cross-sectional area of the pumped volume in the Nd:YAG. The physical length of the cavity is ~35cm.
In order to determine the temporal evolution of pump-wave and idler-wave(s) pulses separately, the collinear output beams emerging through mirror M2 were spatially dispersed using a diffraction grating (1050lines/mm), and then monitored with a number of separate high-speed (<1ns rise time) photodiodes appropriately located. In addition, an optical spectrum analyzer was used for the determination of the wavelengths of these beams.
In agreement with the earlier findings of Molter et al  for the case of the pump-enhanced geometry, multiple idler-waves were observed to be generated within a single pulse, see Fig. 3(a) , resulting in a cascade of down-converted frequencies. Each idler-wave was found to be separated from the previous idler-wave in the sequence by the same frequency; this frequency corresponding to the frequency of the generated THz radiation, which was measured using standard techniques based on a Fabry-Perot interferometer designed for the THz spectral range.
In addition, as shown in Fig. 3(b), an up-converted wave was also found to be present, separated from the pump-wave by a frequency also corresponding to the frequency of the THz radiation, indicative of the sum-frequency mixing of the pump wave with the generated THz wave. This wave was also reported by Molter et al . [Note that due to the manner in which the results shown in Fig. 3 were taken, namely using the optical spectrum analyzer in peak-hold mode, neither the peak heights nor the areas under the peaks can be taken as a measure of the relative energies of the different spectral components.]
Figure 4 shows the energy characteristics of the device in which the Q-switched laser pulse energy (in units of μJ), the energies of two of the idler pulses (also in units of μJ), and the THz pulse energy (in units of pJ) are plotted as a function of the excitation energy per pulse applied to the Nd:YAG by the laser diode (in arbitrary units but normalized to the excitation energy required to reach laser threshold). In the case of the idler-wave, two idler pulse energies are plotted, corresponding to idler A and idler B as defined in Fig. 3. It should be noted that the pump-pulse and idler-pulse energies are as emitted through mirror M2, and the THz pulse energy is that emitted in only one of the four possible emission directions (see section 4 for a fuller discussion of these issues). A calibrated composite silicon bolometer (QMC Instruments Ltd. model QSIB/2) was used to give absolute terahertz energy measurements, whereas the pump energy was inferred by splitting it from the idlers using a diffraction grating (and correcting for the loss) and measuring the average power on a thermopile. The idler energies were too low to detect on the thermopile, so relative energies were found by focusing the pump and then each idler in turn on to a fast (<1nS rise time) InGaAs photodiode (after attenuation with calibrated ND filters) and integrating the pulse areas.
Two important features are to be noted in Fig. 4. Firstly in the case of both the idler-waves and the THz wave a distinct oscillation threshold is to be observed, and this threshold is the same in all three cases. Secondly, the energy of the pump-wave pulse shows no evidence of any reduction due to depletion by the down-conversion processes taking place above the OPO threshold, in that the linear dependence of the pump-wave pulse energy on the excitation energy continues beyond this threshold. In other words only a small fraction of the pump pulse energy is being down-converted; this conclusion will be discussed more fully later in section 4.
A key question that needs to be addressed relates to the processes responsible for the generation of the multiple idler-waves. Mechanisms potentially causing this effect include: (i) repeated parametric processes, in which, for example, idler A becomes the effective pump-wave leading to the generation of idler B from noise with an associated build-up time, and so on, (ii) Idler B being generated by another nonlinear process conforming to the same phase-matching conditions as are associated with the generation of the primary idler-wave, for example difference frequency generation, and (iii) Higher order grating effects in the poled nonlinear medium generating multiple idler waves. Similar observations may also be expected due to a cascaded Raman process, however no Raman shift consistent with the frequency spacing observed (~1.5THz) can be identified. Indeed the lowest frequency Raman shift in this configuration would be ~7.6THz, due to the lowest order A1 polariton resonance.
In order to gain further insight into these issues the temporal profiles of the pump-pulse and the first three of the down-converted idler-pulses (idlers A, B, and C) have been monitored, using a fast photodiode following separation by the diffraction grating. The results are shown in Fig. 5 , which is made up by overlaying multiple pulses for each of the wavelengths being monitored. Although there is significant variation in pulse amplitudes from pulse to pulse, the reproducibility of the starting times of the optical pulses within each set of pulses corresponding to a particular spectral component is apparent. The first observation to be made is that the onset of the principal idler-wave (idler A) is delayed relative to the leading edge of the pump pulse, as is to be expected on the basis of the time required for the idler-wave pulse to build up from noise in the presence of the parametric gain associated with the presence of the pump-wave pulse, a time in this case of the order of 50ns. Contrastingly, idlers B and C exhibit only small delays (<5ns) relative to idler A and B respectively; all three idler-waves building up close to simultaneously and hence being approximately equally delayed relative to the pump-wave pulse. The absence of any observable depletion of the pump-wave pulse contemporaneously with the temporal growth of the idler pulse is again indicative of low down-conversion efficiency.
These observations are contrary to expectation on the basis of the latter down-conversion processes being of the cascaded parametric type, where idler A acts as the pump-wave leading to the generation of idler B, and so on. If such were the case then each additional idler would have to grow from noise hence experiencing the same characteristic delay relative to its effective pump-wave (namely the nearest neighbour idler on the high frequency side) as experienced by the growth of the primary idler from the original pump-wave. However, the important difference with regard to all idler-waves after the primary idler is that a signal-wave is also present in the nonlinear medium, namely the terahertz wave itself generated as the signal-wave along with the primary idler-wave. So, simultaneously present in the nonlinear medium (along with the pump-wave) after the observed build up time is the primary idler-wave and the terahertz (signal) wave. These two waves may readily be shown to be phase-matched for the nonlinear process of difference frequency generation in which the terahertz wave mixes with the primary idler-wave to generate a wave at their difference frequency, this being the next idler-wave down in frequency from the primary idler-wave (i.e. idler-wave B), along with enhancement of the terahertz wave thereby increasing the total terahertz power generated at the original frequency of the THz wave. The process of difference frequency generation then proceeds in a cascade fashion so that idler-wave B generates idler-wave C, with further enhancement of the terahertz wave, and so on. Since the required (two) fields for the process of difference frequency generation are simultaneously present and do not need to build up from noise (through parametric gain), all idler-waves are generated simultaneously (at least to a reasonable approximation), and a significant build up time is required only for the case of the primary idler-wave (idler A). The observation of a common oscillation threshold for the generation of idler A and idler B, see Fig. 4, is also consistent with the above interpretation based on parametric generation of idler A combined with difference frequency generation of idler B. If parametric generation had been the case for both, then idler B would have exhibited a higher oscillation threshold than idler A.
A further possibility that needs to be considered in relation to the appearance of a sequence of idler-waves is that the different idlers are a result of higher order grating vectors (overtones) than the fundamental associated with the periodic-poling. This explanation implies that the accompanying terahertz radiation associated with each of the idler-waves would be generated at a different frequency depending on the idler concerned. However, this process is unable to account for idler-wave B since the first overtone of the grating period does not give rise to net parametric gain. In the case of idler C the expected frequency would be close to but not exactly triple the frequency associated with idler A, differing from the integer ratio as a result of the known changes in refractive index with wavelength experienced by the terahertz radiation in the lithium niobate. As a result the frequency spacings of the idler-waves would significantly (and observably) differ from the uniformity observed in practice. Finally, since in third order the effective length of the grating is reduced by a factor of three, a significant increase in the pulse energy required to reach oscillation threshold for idler C is to be expected, but this was not observed to be the case in practice. As well as measuring the frequencies of the idler waves, we have also directly measured the wavelength of the generated terahertz radiation using a Fabry-Perot interferometer specifically designed for the terahertz spectral range. The measured terahertz wavelength of 192.9μm corresponds to a terahertz frequency of 1.56THz ± 20GHz, to be compared to the measured frequency spacing between adjacent idler waves obtained using the optical spectrum analyser of 1.584THz ± 12GHz.
Finally, additional evidence for a difference frequency generation process lies in the quadratic characteristic of the Idler B wave as shown in Fig. 4. Above the common generation threshold of the Idler A and terahertz waves both can be seen to grow linearly with pump laser energy. As the energy of the generated difference frequency (Idler B) is proportional to the product of the input wave energies, it then follows that Idler B should grow quadratically with pump laser energy above downconversion threshold.
3. Further investigation of grating geometries
We have investigated a number of other grating geometries in addition to the orthogonal grating. It is important to realize at the start that as a consequence of the grating vector being a bipolar vector there are two possible solutions for the frequency and wave normal direction of each of the down converted waves associated with any particular grating geometry(this does not appear to have been recognized previously). In the case of the orthogonal grating vector these two solutions become degenerate in terms of frequency and angle of propagation of the THz radiation relative to the common propagation direction of the pump- and idler-waves.
These situations are illustrated in Fig. 1(b) for the general case, and in Fig. 1(a) for the degenerate case. It will be appreciated that for case (b), the general case, of the two possible solutions the one for which the terahertz (signal) wave exhibits the smaller angle of propagation relative to the collinear idler- and pump-waves (kTHz(2)) will be the solution expected to reach oscillation threshold first in that it is the one with the greater spatial overlap of the three waves, thereby experiencing the greater gain. This is what we have observed to be the case in practice for the grating geometries we have explored as described in Table 1 . The predicted solutions in Table 1 were calculated using the Sellmeier equation from Zelmon et al.  for the pump/idler-waves, and an empirical fit to the terahertz refractive index data compiled in . The angles θ and ϕ are the angles that the THz wave normal makes with the common optical axis of the pump/idler-waves and the normal to the crystal face through which the radiation exits, respectively; note that these angles are hence complementary angles (These angles are also further defined in Fig. 7 .). The table contains the experimentally measured wavelengths of the idler-waves actually observed to oscillate with predicted values for all possible idler-waves.
It is seen from the table both in the case of crystal I and crystal II that the solution with the lower walk-off angle (θ), is the one that reaches oscillation threshold first, in line with our predictions.
As also may be seen from Table 1 in neither of the two crystals has it been possible to reach oscillation threshold for the solutions with the greater walk-off angles, and hence lower gain (I(1), II(1)) despite further increasing the pump power. This is possibly due to cross-saturation of the nonlinear gain associated with these higher oscillation thresholds, which arises from the presence of the down-converted radiation associated with the lower oscillation threshold that is already present in the nonlinear medium. In the case of the orthogonal grating (III) the two solutions are degenerate, and so cross-saturation is no longer an issue, hence allowing oscillation as indicated.
The issue that now arises is that of the extraction of the terahertz radiation from the nonlinear crystal. In the case where no special arrangements are put in place to assist this extraction process, the terahertz wave must meet the lithium niobate-air interface at an angle less than the critical angle, which in this case is ~11°. By using silicon prisms in contact with the lithium niobate crystal face, as proposed by Kawasi  and as is the case here, the critical angle can be increased to ~41°. In the present case it can be seen that, even with silicon prisms incorporated, the lower-threshold solutions for which parametric oscillation is observed to occur have associated emission angles such that the terahertz radiation meets the interface at an angle greater than the above critical angle, and so the generated terahertz radiation cannot be extracted by the current means. (Although we are of course able to ascertain that it is being generated by monitoring the presence of the associated idler wave.) On the other hand the terahertz radiation potentially generated by the higher threshold solution in case II(1) could be extracted if it were to be generated, since it meets the lithium niobate-silicon interface at less than the critical angle. However in case I neither the lower nor higher threshold THz radiation can be extracted since in both cases the terahertz radiation meets the interface at greater than the critical angle. In the degenerate case (case III) the angle is such that THz extraction is possible and does occur, as discussed previously. It is to be noted that in the case of a standing-wave cavity geometry, as here, the THz generation and emission associated with any particular non-degenerate solution takes place in two distinct directions, as may readily be seen by reversing the direction of the pump and idler wave vectors in Fig. 1 while still retaining phase matching. In the case of degeneracy four distinct directions are now associated with the emission of the THz radiation.
It is therefore vital in designing devices that crystal geometries employed are such that the lower threshold (smaller walk-off/higher overlap) solution generates terahertz radiation that meets the extraction interface at less than the critical angle, and obviously from the point of view of lowering the threshold, as close to this critical angle as is deemed comfortable. Such a requirement limits the degree of overlap that can be attained, and hence the degree to which oscillation thresholds may be reduced by this means. A useful rule of thumb is therefore to choose a geometry such that the terahertz radiation emitted at the smaller of the two angles to the pump- idler-wave axis is incident on the interface at just less than the critical angle, thus maximizing the overlap and hence gain while still allowing useful extraction of the generated terahertz radiation. This condition is not necessarily reached through the use of an orthogonal grating geometry as has previously been claimed ; indeed the use of an orthogonal grating reduces the THz output by a further factor of 2 as generation takes place into 4, rather than 2, directions, as pointed out above. Further, in the case of an orthogonal grating vector the pump- and idler-waves are then propagating parallel to the interfaces between the poled domains, see Fig. 1(a). We have observed that under these conditions side-lobes can appear on the main beams due to diffraction effects, probably arising from residual strain fields or static electric-fields at the interfaces within the material. It should also be noted that lithium niobate is highly absorbing of the terahertz radiation generated, and increasing the path length of this radiation within the crystal in order to attain greater overlap will thereby reduce extraction efficiency. Clearly compromises need to be made in designing a practical device between lowering thresholds and improving extraction efficiency.
Given the ability to change both the period and the orientation of the grating, it is possible to design, for any particular terahertz frequency, a grating that both phase-matches for such a frequency and generates the terahertz radiation with a minimum walk-off angle to the optical axis while avoiding total internal reflection. Solution 2 as defined above in Fig. 1(b) is the one resulting in the smaller of the two possible walk-off angles for the terahertz radiation for any given grating geometry. This is illustrated in Fig. 6 where for the case of a grating of period 42.4μm, the walk-off angles and associated terahertz wavelengths corresponding to the two solutions are plotted as a function of the angle of the grating vector to the common propagation direction of the pump and idler.
The geometry associated with the higher overlap Solution 2 is shown in more detail in Fig. 7. From this it is possible to derive expressions for the grating properties required to produce a specific terahertz frequency in a given direction.
By solving for the geometry of the two right angle triangles in Fig. 7, Eq. (6) and Eq. (7) are obtained that define the grating required for the THz radiation generated to propagate at the angle θ to the optical axis [Note that these equations are valid for the angles and θ as defined in Fig. 7 being in the range 0° to 180°].Eq. (6) above then the value of the angle θ corresponding to this other solution associated with the above chosen bipolar grating-vector can be determined from the quadratic equation (for ) that results, and in the present case this may readily seen to be 83.5°, clearly indicating that this solution is the one with the higher threshold. [This latter calculation assumes that the ratio of the refractive indices is the same as in the original case, which is a reasonable approximation, although of course the frequency of the THz radiation generated will differ from that in the original case. This frequency can be determined from Eq. (7), on the assumption that the refractive index has the same value as previously, when we obtain 1.5THz].
4. Thresholds and down-conversion efficiencies
We now consider power and energy characteristics of the intracavity parametric oscillator in particular as they relate to thresholds and down-conversion efficiencies. As can be seen in Fig. 3 the pump pulse energy extracted through M2 at OPO oscillation threshold was ~18μJ. The measured pump pulse duration was ~60ns (FWHM), hence indicating a peak pulse power, external to the cavity, of ~300W. In so far as mirror M2 is 3% transmitting, the peak intracavity power associated with the pump pulse is hence ~10kW, corresponding to an enhancement factor of 33. On the basis of the measured radius of the pump beam within the nonlinear crystal being ~200μm (giving an area of approximately 1.3 × 10−7m2), this implies a peak pump pulse intensity within the nonlinear medium at oscillation threshold of 8MWcm−2. These latter two values are comparable to those reported in , although in our system injection seeding was not implemented.
The device was operated at pump pulse energies corresponding to up to 1.4 × oscillation threshold. At this upper limit and when allowance is made for all output losses (14%) associated with the pump cavity (and not just the 3% associated with mirror M2) the estimated total energy of a typical pump pulse is ~120μJ/pulse. The total energy of the associated down-converted idler wave pulse under such conditions is then estimated to be 1.6μJ/pulse. This latter estimate is based on the measured idler pulse output energy through mirror M2, with allowance being made as before for all output losses from the idler wave cavity, these being similar in magnitude to those associated with the pump wave cavity. It may readily be seen that the above characteristics imply a slope-efficiency for parametric down-conversion of ~4.5% at 1.4 × oscillation threshold.
The quantum efficiency associated with the accompanying terahertz wave (signal wave) is of the order of 0.5%, implying that the terahertz pulse energy (at point of generation) is of the order of 8nJ. We have directly measured the extracted terahertz pulse energy under the above conditions using a cryogenically-cooled bolometer calibrated for use in the terahertz spectral range, obtaining a value of ~5pJ/pulse. The bolometer accesses only one of the four directions into which the total terahertz radiation is emitted, and if allowance is made for this the above implies a remaining extraction efficiency of the order 2-3 parts in 103. Such a value is quite consistent with previous observations where prism arrays are used, and where serious absorption losses within the lithium niobate itself, the prisms and at interfaces are encountered .
The intracavity geometry is ideally suited to the parametric generation of terahertz radiation based on periodically-poled nonlinear material where pump and idler waves propagate collinearly. As well as alleviating optical coupling issues, significant benefits include reduced pump power/energy to reach oscillation threshold and a much simplified optical arrangement compared to the pump enhanced approach.
Through a study of the relative delays between the appearance of the various idler-wave pulses complemented by studies of their power characteristics we have demonstrated that the higher order idler-waves are due to difference frequency generation rather than parametric generation (from noise). Properly exploited this process is capable of significantly improving the conversion efficiency at THz frequencies.
Since in general two possible phase matching solutions are associated with any particular grating geometry, it is important to ensure that the solution providing the lower oscillation threshold of the two is also one that allows the generated terahertz radiation to be output coupled through the lithium niobate interface. We provide a useful rule of thumb along with a simple analysis for identifying the grating characteristics to ensure this, hence resulting in a practical device..
Unlike non-collinear devices which exhibit wide tuning ranges (multi-THz) the collinear scheme is limited to a tuning bandwidth of ~100GHz for any particular grating period, hence necessitating changes in grating period in order to provide wider spectral coverage.
At the present time limitations on the volume of nonlinear material that can be poled compromise both the efficiency and power/energy scaling of current devices. Improvements in poling techniques could in the future enable quasi-phase-matching geometries to reach their potential as practical sources of terahertz radiation.
We would like to thank the Engineering and Physical Sciences Research Council (EPSRC) and Scottish Enterprise for partial support of this work.
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