Cascaded Stimulated Polariton Scattering (SPS) to the fourth-Stokes order is observed experimentally in an intracavity THz polariton laser utilising Mg:LiNbO3. The performance of the cascaded laser is presented, the origin of the cascaded fields is explained and compared to theory, and the potential consequences for using cascading to enhance the THz output from this type of device are discussed.
© 2015 Optical Society of America
With rising interest in THz radiation and its applications, there has been a surge of activity around the development of compact THz sources [1–6]. One of the most practical and efficient approaches is based on intracavity nonlinear conversion within conventional neodymium (Nd) lasers, with the nonlinear process employed being difference frequency generation [7,8], optical parametric oscillation  or stimulated polariton scattering (SPS) [5,6,10–18]. Of these Nd-based sources, polariton lasers utilising SPS have been shown to generate frequency tunable output, and operate in either pulsed [5,6,10–17] or continuous-wave  modalities, with extracavity [12–15] or intracavity [5,6,17,18] configurations.
THz polariton lasers can deliver reasonably high THz output powers, for example in the pulsed regime, average powers in the 1 μW-100 µW range have been demonstrated [5,14,17], along with peak powers exceeding 1 kW . Also, CW powers of up to 2.3 µW have been demonstrated . However, the conversion efficiencies are relatively low, of the order of 1 × 10-4% (pump diode to measured THz power in the case of intracavity sources). To a large extent, this is due to the Manley-Rowe limit, which is determined by the relative photon energies of the excitation photons and the resultant THz photons. In the case where an Nd-laser operating at 1 µm generates a THz photon at 1 THz, the Manly-Rowe limit will be ~0.4%. Another significant factor affecting the efficiency of this type of THz laser is the high absorption losses (with absorption coefficients exceeding 20 cm−1 [14,17] at the THz frequencies within the SPS-active material, typically Mg:LiNbO3. Despite this significant drawback, Mg:LiNbO3 remains the crystal of choice for THz generation via SPS due to its high non-linearity, high optical damage threshold and transparency in the near-infrared (NIR).
The process of cascading fields within a THz polariton laser (or equivalently a THz parametric oscillator) has been studied theoretically in the collinear regime using periodically-polled lithium niobate [19,20]. It has also been observed experimentally in the non-collinear regime, in extracavity , and intracavity configurations using bulk lithium niobate by Yao et. al. , and more recently by Thomson et. al. . In both experimental studies, a secondary beam, described as a second-order Stokes line in , and a secondary idler beam in  was generated from their respective systems. Both publications suggested that the role of this secondary beam would impact THz generation within the system, in  it was suggested that such cascading offered an approach to improving the efficiency of their device, by “overcoming” the Manley-Rowe limit, or effectively, increasing the overall THz-to-pump photon yield.
Here we report an investigation of cascading in an intracavity THz laser employing SPS. Despite the similarity of architectures here and in [16,22], the nature of the cascading is completely different in the two systems, with the cascaded idler being non-resonant in [16,22], but resonated in the present work. We have observed four Stokes lines, and show that the wavelengths corresponding to each cascaded Stokes order tune with the angle between fundamental and Stokes resonators. Clear threshold behaviour is observed between successive cascaded orders, and we anticipate that in a fully optimised setup, cascading will offer an approach to improving the efficiency with which THz output is generated.
2. Experimental details
The experimental layout is shown schematically in Fig. 1. The fundamental (1064 nm) resonator comprises two mirrors, M1 and M2; the input surface of M1 was coated anti-reflection (AR) at 808 nm, and the other surface high reflecting (HR) from 1064 −1090 nm with R>99.99%. M2 had a radius of curvature of 1 m and was HR coated from 1064 to 1090 nm (R = 99%). The length of the fundamental resonator was 190 mm. The laser gain material was a 1 a.t. % Nd:YAG crystal with 5 mm diameter and 7 mm length; both surfaces were AR coated for 808 nm (R<0.1%) and 1064-1173 nm (R<0.1%). An intracavity acousto-optic Q-switch (NEOS, part number 33027-25-2-i) was used to achieve pulsed laser operation at a repetition rate of 3 kHz. The laser resonator was pumped using a 10 W, 808 nm, fiber-coupled laser diode (400 µm core diameter, 0.22 NA), with its output focussed to a 400 µm diameter spot, incident on the Nd:YAG crystal.
SPS was achieved within an x-cut, congruent, 5 a.t. %Mg:LiNbO3 crystal (HC Photonics Corp.) with dimensions 5 × 5 × 25 mm, and end-faces AR coated from 1064 to 1090 nm (R<0.1%). High resistivity Si prisms were bonded (using liquid-mediated adhesion) to a polished surface of the Mg:LiNbO3 crystal, perpendicular to the crystal y-axis. The Stokes resonator was formed using mirrors M3 and M4, which were mounted on a rotation stage to enable rotation about the z-axis of the Mg:LiNbO3 crystal, thereby changing the angle about the axis of the fundamental resonator (external angles from 0 to 5 degrees could be achieved). The length of the Stokes resonator was 75 mm. Both M3 and M4 were flat and coated HR from 1064 nm-1090 nm, M3 with R>99.99% and M4 with R = 99%.
D-shaped mirrors were used to pick-off the emission from the Stokes resonator (leaking through M4) to monitor power and spectral content. The THz emission was collected using a 50 mm focal length lens (fabricated from polymethylpentene-tpx), and focussed onto a Golay cell (Tydex, GC-1P). The spectral content of the output emitted from the fundamental and Stokes resonators were monitored using a calibrated Ocean Optics spectrometer (HR4000).
3. Observation of cascaded Stokes emission
Up to four Stokes orders were observed when the laser was pumped with up to 8.5 W incident diode pump power. We observed that the fundamental, second-Stokes and fourth-Stokes wavelengths were generated within the fundamental resonator (M1-M2), whilst the first- and third-Stokes wavelengths were generated within the Stokes resonator (M3-M4). For each interaction, the THz frequency could be calculated from the measured fundamental and Stokes wavelengths, by conservation of energy. Each cascaded Stokes line was generated spontaneously from noise as the intensity of the prior line increased with incident pump power, akin to the onset of cascaded lines within a laser utilizing Stimulated Raman Scattering (SRS). The constraint here is that these lines are forces to oscillate within the bounds of the fundamental and Stokes field resonators as shown in Fig. 1. Figure 2(a) shows the spectral output from the fundamental resonator, while Fig. 2(b) shows the spectral output from the Stokes resonator, for the case where the internal angle of between the fundamental and Stokes fields (Θ) was 0.70 degrees. The internal angle was derived by applying the cosine rule, as required to satisfy conservation of momentum between the fundamental and first-Stokes wavelengths. The refractive index of the Mg:LiNbO3 crystal at each NIR wavelength, and THz frequency, were determined from Sellmeier equations and coefficients published in [23,24]. It should be noted that the strength of the fourth-Stokes order was significantly lower than that of the other cascaded orders.
Next we consider the angles at which the cascaded Stokes fields are generated, and the resultant angles at which the THz fields are produced, in order to satisfy phase matching. As mentioned, the resonator configuration forces the Stokes cascades to take place along the axes of the fundamental and Stokes resonators. Given a fixed angle of Θ between the fundamental and Stokes resonators, the wave-vectors of the fields involved can be represented as shown in Fig. 3, where each wave-vector diagram shows the phase-matched interactions for generating the 1st, 2nd, 3rd and 4th Stokes respectively. Note that the angle between the wave vectors in the Fig. is exaggerated for clarity. The actual angles between the fundamental and Stokes wave vectors investigated in this work were in the range 0.5 – 1.2 degrees, and the resultant difference in length of the fundamental and Stokes wave vectors only ~0.5 – 0.6%.
The wave vector diagrams in Fig. 3 illustrate the directions of oscillation of the fundamental and cascaded Stokes fields, and show that the fundamental, second-Stokes and fourth-Stokes lines oscillate within the fundamental field resonator (M1-M2). The first-Stokes and third-Stokes fields oscillate within the Stokes resonator (M3-M4). From the wave vectors, it is apparent that the THz fields generated with the first- and third-Stokes fields are generated in a similar direction (in this case down the page), while the THz field generated with the second- and fourth-Stokes fields are generated in the opposite direction (up the page).
It was found experimentally that the wavelength of each cascaded Stokes field changed smoothly as the angle between the fundamental and Stokes resonators was changed, as shown in Fig. 4(a). When operating at an incident pump power of 8.5 W (just above threshold for the fourth-Stokes line), the wavelength tuning range of the first Stokes was the broadest, while that of the fourth Stokes was narrowest. The tuning range of the higher order Stokes fields decreased as the effective SPS threshold increased with interaction angle (Θ), due to factors of lower effective SPS gain (the effective gain changes with THz frequency [13,14]), smaller interaction length and increasing off-axis reflection losses from the faces of the Mg:LiNbO3 crystal.
The measured wavelength of the cascaded Stokes orders were compared to wavelengths predicted theoretically through simultaneous solution of the dispersion relation for Mg:LiNbO3, along with the phase matching condition, assuming fixed angles between the fundamental and subsequent cascaded Stokes orders. The frequencies, oscillator strengths and linewidths of the A1-symmetry modes used to solve the dispersion relation for Mg:LiNbO3 were taken from [11,13], and the Sellmeier equations and coefficients for Mg:LiNbO3 were taken from [23,24]. In our simulation, we made use of the Raman oscillator data for the 252 cm−1 mode published by Shikata et.al , which was determined specifically for 5% a.t. Mg:LiNbO3, as used in our work. The dispersion curve corresponding to the 252 cm−1 polariton mode was calculated using the method in , and the phase matching conditions for the fundamental, Stokes and polariton fields were determined through solution of the cosine rule, along with and conservation of energy, where νfundamental = νStokes + νpolariton. The simultaneous solution of the dispersion curve and phase matching condition yielded the wavelength of the Stokes field, and the frequency of the polariton field. This was done for a range of angles (ϴ) from 0 to 2 degrees. The wavelength of the Stokes field was then used effectively as the “fundamental” field, and the calculation was repeated to determine the wavelength of the next cascaded Stokes field and frequency of the corresponding polariton field; this process was repeated to the fourth-Stokes order. The computationally modelled Stokes wavelengths are shown as a function of internal angle in Fig. 4(a). While such calculations have been reported previously for first Stokes frequencies , this is the first time to our knowledge for the wavelengths for cascaded wavelengths have been presented. Figure 4(a) shows excellent agreement between the measured and predicted Stokes wavelengths as a function of angle (ϴ), testifying to the accuracy of refractive index data, and Raman oscillator data used to simulate the dispersion curve for the Mg:LiNbO3 used in this work.
The THz frequencies that were generated with each Stokes line were calculated based on conservation of energy, and the theoretical values also determined through solution of the dispersion curve and phase matching angles; these are plotted in Fig. 4(b). The experimentally determined THz frequencies carry an uncertainty of 0.03 THz, based on the resolution limit of the spectrometer (0.09 nm) used to determine the wavelengths of the NIR fields. Also shown in the inset of Fig. 4(b) is the predicted angle (φ) between the generated THz field and the stimulating field (refer to Fig. 3); these values were calculated using the cosine rule, and using the measured wavelengths of the fundamental and cascaded Stokes fields.
The experimentally-determined frequency of the THz field was not observed to vary in any systematic way with cascading order of the interaction, nor was the angle at which the THz exited the Mg:LiNbO3 crystal. As depicted by the solid lines in Fig. 4(b), theory predicts that the frequency of the polariton generated with each cascaded Stokes order is slightly lower than that of the polariton generated with the preceding Stokes order for a given angle (Θ). Also, this difference gets slightly larger as the interaction angle (Θ) increases. This difference in THz frequency with each cascaded Stokes order could not be resolved experimentally due to the experimental uncertainty arising from the resolution of our spectrometer.
4. Performance of cascaded and non-cascaded lasers
The terahertz laser could be operated in two regimes, either without any cascading of the Stokes field, or with cascading of the Stokes fields occurring. Switching between regimes of operation was achieved through slight adjustment of Stokes resonator alignment. In both cases, threshold for oscillation of the fundamental field was achieved at ~1 W incident pump power, and threshold for the SPS was reached at ~3.5 W. At this point, both first-Stokes and THz fields were generated.
The temporal characteristics of the emission from the fundamental and Stokes resonators when pumping at an incident power of 7.5 W, are shown respectively in Figs. 5(a) and 5(b), for the non-cascaded and cascaded regimes respectively. In the absence of SPS, which is easily achieved by blocking the Stokes resonator, the fundamental pulse duration was ~74 ns and this provides a means by which the depletion of the fundamental field can be quantified. A maximum fundamental field depletion of ~60% is achieved, for both non-cascaded and cascaded regimes, with the fundamental pulse being narrowed to ~52 ns (FWHM). The first-Stokes pulse duration was ~15 ns (FWHM). In Fig. 5(b), additional features are seen in the tail of the pulse from the fundamental and Stokes cavities, and these correspond to the second- and third-Stokes fields (indicated on the Fig.). The presence of these features correlate with the presence of the second and third cascaded Stokes wavelengths respectively, as observed on the spectrometer. Note that the temporal feature corresponding to the fourth-Stokes could not be resolved due to its significantly lower power than the fundamental and second-Stokes fields. The temporal properties of each field could not be examined in isolation due to spatial overlapping and small spectral separation between the fundamental and cascaded Stokes fields.
The power scaling curves of each field (determined from the output of mirrors M2 and M4), both without and with cascade are shown in Figs. 6(a) and 6(b) respectively. The Stokes resonator was angled so as to generate THz emission at 1.6 THz. As each field could not be spatially separated, the spectrally calibrated spectrometer was instead used to determine the respective amount of power in each spectral line. Power scaling is shown up to a maximum incident pump power of 7.5 W, and does not show data for the fourth-Stokes line. This is due to frequent damage that would occur to the Mg:LiNbO3 anti-reflection coating at pump powers exceeding 7.5 W. The threshold for onset of the fourth-Stokes line was at ~8.5 W incident pump power, and while we could undertake study of the Stokes wavelength-tuning characteristics at this incident pump power, reliable power scaling data could not be obtained.
In the non-cascaded regime of Fig. 6(a), the THz output increases rapidly and then rolls over for incident pump powers greater than 6.5 W. The Stokes field also exhibits a rapid increase in power, and this rate decreases as the incident pump power increases. As noted in our prior publication , we speculate that the decrease in THz and Stokes output, and increase in fundamental power may be due to two effects: back-conversion of the THz and Stokes fields to the fundamental and a change in mode shapes and overlap between the three fields. Even in the non-collinear geometry of this system, back-conversion may still occur due to the high intensity of the oscillating fields within the cavity, and the high fundamental-field depletion at high pump powers. We have confirmed that for incident pump powers above 6 W, the Stokes field retains a Gaussian profile, but the fundamental field experiences slight elongation which we believe is driven by thermal lensing within the Nd:YAG crystal [25,26].
The threshold behaviour of the successive Stokes orders in the cascaded regime is clearly seen in Fig. 6(b). The second Stokes line reaches threshold for an incident pump power of ~5 W, and there is a corresponding decrease in output at the first-Stokes wavelength. The third Stokes reaches threshold at an incident pump power of ~5.7 W, and there is a corresponding decrease in the output at the second Stokes wavelength indicating power transfer between fields. The third Stokes wavelength continues to increase with incident pump power. The THz power in this regime also increases rapidly but instead of rolling-over, maintains a steady output. We believe this is due to additional THz photons generated with the third-Stokes field, contributing to the total detected THz power. The steady THz power at pump powers greater than ~6 W, clearly correlates with the onset of the third Stokes field.
The THz output tuned continuously across the range 1.4 – 2.7 THz, and tuning behaviour for the cascaded regimes is shown in Fig. 7 for an incident pump power of 7 W. Note the presence of a water absorption feature at ~1.7 THz. The tuning range was limited by clipping of the Stokes fields by the Mg:LiNbO3 crystal and the change in overlap/interaction region as the angle between Stokes and fundamental resonators is increased.
In this paper we have described our observations of cascading to the fourth Stokes order and presented our explanation of how it arises. In this section we consider the potential for cascading to usefully enhance the terahertz output from an optimised THz polariton laser. We note that there are some subtitles to this process. With each Stokes cascade, the THz photon which is also generated, has a slightly lower THz frequency than that generated with the prior Stokes field. For a fixed interaction angle between the fundamental and Stokes fields (Θ), this difference amounts to at most 0.1 THz when comparing the THz photons accompanying the first-Stokes and that generated with accompanying the fourth-Stokes. As such, there will be some broadening of the overall THz field that is generated in a cascaded system. The implication here is that for applications where high spectral purity is required, for example in high-resolution THz spectroscopy, additional THz photons generated through the cascade process may not be particularly beneficial, because the boost in power is offset by a broader spectrum. This is in contrast to applications such as imaging, where gross THz power is of primary concern. The following discussion focusses on the potential to increase THz output power.
The cascading process can increase the terahertz output power, simply by increasing the overall THz photon to pump photon yield. In a non-cascading SPS laser, at best, a single THz photon is generated for each fundamental photon. In this work, by cascading to the fourth-Stokes, this THz to fundamental photon yield can be increased up to four times, and we have seen some early evidence of this improvement in this work. The small increase in the overall THz output that was observed for pump powers above 6 W in this work was limited due to the geometrical constraints of the system and the lack of temporal coherence/overlap of the THz fields generated with each cascade. With our THz collection geometry, we were only able to observe additional THz photons generated with cascade to the third-Stokes. THz photons accompanying the second and fourth Stokes were generated in the opposite direction. We anticipate that a different geometry where a thin Mg:LiNbO3 crystal is used, would enable collection of the THz beam from both sides of the crystal (ie. including the side opposite that with the Si prisms in Fig. 1) would be beneficial. Significantly, we anticipate that the cascaded process will improve the efficiency of SPS THz lasers which operate in the continuous-wave regime. Here the temporal coherence/overlap between THz fields generated with each cascade will be significantly better than that achieved in the pulsed case.
In addition to considering resonator and crystal geometries which will enable us to better capture the enhanced THz field, we are investigating means by which thermal load and consequent distortion of the fundamental field can be better managed at high incident pump powers. One approach that we will investigate is the use of direct-band-gap-pumping  of the Nd laser crystal. We will also investigate the use of better quality coatings (for example ion beam sputtered) to improve damage tolerance of the system, to facilitate pumping with higher powers, and enable generation of a stronger third-Stokes and THz field. With such improvements, we anticipate significant enhancement of the overall THz photon to pump photon yield from a cascaded SPS THz laser.
We have demonstrated cascaded Stokes generation to the fourth Stokes line within an SPS THz laser operating on the 252 cm−1 A1 polariton mode in Mg:LiNbO3. The cascaded Stokes fields continuously tune with angle between the fundamental and Stokes resonators. We have shown evidence of enhancement of the detected THz field with cascade to the third-Stokes line, and potential for significantly increasing the THz photon-to-pump photon yield.
This research was supported under Australian Research Council’s Discovery Projects funding scheme (project number DP110103748).
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