High-Q resonant cavities for terahertz quantum cascade lasers

We report on the realization and characterization of two different designs for resonant THz cavities, based on wire-grid polarizers as input/output couplers, and injected by a continuous-wave quantum cascade laser (QCL) emitting at 2.55 THz. A comparison between the measured resonators parameters and the expected theoretical values is reported. With achieved quality factor Q ≈ 2.5× 105, these cavities show resonant peaks as narrow as few MHz, comparable with the typical Doppler linewidth of THz molecular transitions and slightly broader than the free-running QCL emission spectrum. The effects of the optical feedback from one cavity to the QCL are examined by using the other cavity as a frequency reference. © 2015 Optical Society of America OCIS codes: (140.4780) Optical resonators; (140.5965) Semiconductor lasers, quantum cascade; (300.6495) Spectroscopy, terahertz. References and links 1. S. 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Introduction
Optical resonators are well-established tools commonly used in spectroscopy [1,2].They have widespread applications over the whole electromagnetic spectrum, from microwaves [3] to UV [4], while record-level optical finesse were also achieved in the visible/near-IR [5], especially thanks to the advent of whispering gallery mode resonators [6].In this context, the portion of the electromagnetic spectrum ranging from 0.1 to 10 THz, better known as Terahertz, is still lacking of such tools.One reason is certainly that, for many years the THz range has been an underexploited region.However, recent advances in generation and detection of THz radiation, as well as the advent of novel THz-emitting laser sources, such as quantum cascade lasers (QCLs) [7], and the constantly evolving technology of new materials, are now making THz light emerge as a new promising frontier for interdisciplinary research areas, such as as bio-medical diagnostics, communication technology, security and defence.
Among the number of different applications of THz radiation, a central role is played by molecular spectroscopy.Indeed, many chemical species have very strong rotational and rovibrational transitions in the THz range, with line-strengths much stronger than typical microwave transitions, and comparable with the strongest fundamental ro-vibrational lines lying in the mid IR.For this reason, Terahertz spectrum can well represent a novel "molecular fingerprint region", once provided that sensitivity and resolution of newly developed THz spectroscopic techniques are improved to the levels reached in other spectral regions.
Among the different sources of THz radiation (multiplied frequency chains [8,9], tunable far-IR lasers [10,11], difference-frequency-generation processes [12]), in recent years THz QCLs are emerging as very promising sources not only for a practical exploitation of THz technology, but also for fundamental research, e.g. in the field of THz metrology.Indeed, they combine an inherently high spectral purity (with intrinsic linewidths as low as 100 Hz [13,14]) with mW-level output powers, a mix that makes them ideal candidates for high-resolution and high-sensitivity spectroscopy [15] as well as for local oscillators in astronomical THz spectrometers [16].Another recent achievement has been the extension to the THz region of optical frequency comb synthesizers [17][18][19], enabling direct and broadband phase/frequency referencing for any THz source and providing a new tool for high-precision measurements of THz frequencies.The combination of the absolute referencing provided by THz comb with the mW-level power of THz QCLs recently allowed for a metrological-grade QCL-based THz spectroscopy with an unprecedented level of accuracy (4 × 10 −9 in the determination of a THz transition frequency) [20], only limited by Doppler broadening of molecular spectra.In fact, even with very good signal-to-noise ratios, the MHz-level linewidth of the acquired line profiles did not allow to achieve the nominal precision of the THz spectrometer (about 5 × 10 −11 ).Fortunately, the high output power provided by THz QCLs can enable sub-Doppler spectroscopic techniques based on non-linear saturation of molecular transition [21] in analogy to what happened in the past years with mid-IR QCLs [22].
In this regard, cavity resonators represent an attractive tool to further increase the sensitivity of a spectroscopic system, as they give access to much longer interaction lengths between light and absorbing medium.Along with this enhancement capabilities, high-finesse resonant cavities could also provide a narrow reference for a QCL, allowing a reduction of its freerunning linewidth, with further benefit for high-precision spectroscopy.In other words, the development of THz resonant cavities could represent an invaluable tool for metrological-grade ultra-sensitive QCL-based spectroscopy, enabling the deployment of the most advanced cavityenhanced techniques, such as cavity-ring-down spectroscopy [23][24][25][26], to this region of the electromagnetic spectrum.
However, design and fabrication of cavities efficiently resonating at THz frequencies is challenging, due to the technological gap of THz materials and optical components, compared to other spectral regions.As concerns cavity mirrors, highly reflective dielectric coatings are scarcely developed at THz frequencies, and at present only metallic coatings can be used, with maximum reflectivity limited to 99.6% for gold.In addition, metallic mirrors are not suitable as input/output couplers, and also the solutions commonly adopted at microwave frequencies (hole output coupling) have proven to be quite unsuitable for THz [27].
An alternative approach consists in using a wire-grid polarizer (WGP) as input/output coupler: if the electric field component is parallel to the metal wires, electrons are free to flow along the wires, and the incoming field experiences an almost complete reflection.However, a small amount of radiation leaks through the grid, allowing for the coupling of light in and out of the cavity.This approach has been adopted in a few early experiments in far-IR spectroscopy [28,29], where finesses of about 14 and 3 were achieved at 690 GHz and 1.5 THz frequencies, respectively (corresponding to Q-factors of about 7000 and 1500, respectively).More recently, Braakman et al. demonstrated that, in the sub-THz range (around 300 GHz), resonant cavities based on WGPs can achieve Q-factors as large as 10 5 [30], sufficient for a relevant enhancement.
In this work, we report on the set up of WGP-based THz resonators coupled with radiation from a 2.55-THz QCL.We propose, and experimentally demonstrate, two different cavity configurations: a V-shaped and a ring-shaped geometry.Each cavity is characterized, and its relevant parameters (Q-factor, enhancement factor, optical coupling) are compared with the prediction of the theoretical model for the corresponding geometry.Finally, by simultaneously coupling the QCL to both cavities, the effect of optical feedback (OF) from the V-shaped cavity to the laser is investigated.This gives the possibility of optically locking a THz QCL to a cavity, with considerable benefits in terms of frequency stability and emission narrowing.

Cavity designs
We can consider the beam emitted by a QCL as an elliptical Gaussian beam with different propagation parameters in the (x, z) plane, containing the growth axis x of the laser gain medium, and in the (y, z) plane orthogonal to it.Given the propagation axis z, the Gaussian beam, at wavelength λ , is described by a set of parameters: the beam waists w 0i , the Rayleigh ranges z Ri , the M 2 i factors and the beam divergences θ i , related by the following equations: The Gaussian beam intensity is given by: where P is the beam power and where z 0i are the beam waist positions.
In order to satisfy the mode-matching condition, the QCL beam waist impinging on the input coupler must equal the calculated waist of the cavity mode.For our elliptic mode, with large M 2 x and M 2 y values, a trade-off condition must be found to satisfy mode-matching as good as possible in both x and y directions.Furthermore, stable linear polarization is a crucial factor to optimize the coupling of the QCL to a resonant cavity with polarization-sensitive elements, such as the free-standing tungsten WGP used as input/output coupler.
The performances of the cavity are affected both by input/output mirror losses (reflectance, transmittance and absorption/scattering losses, R, T , A respectively) and by internal losses per round-trip (due to absorption from air, additional mirrors, etc.), and are described by either the Finesse (F ) or the quality factor (Q) [31].
The absorption coefficient from air, due to THz transitions in ambient water vapour, is experimentally measured to be ∼ 0.0038 cm −1 .Therefore, in order to reduce these losses, the cavities must be enclosed in boxes purged with nitrogen gas.Furthermore, internal losses depend on wavelength, angles of incidence and fundamental physical properties of each cavity element, such as the conductivity of mirror metals, spacing and diameter of the wires of the WGP.
The V-shaped cavity, shown in Fig. 1 has a round-trip length l V = 480 mm and is composed by a WGP and two concave gold coated mirrors with the same effective focal length f mV = 200 mm, protected by a 150-nm-thick SiO 2 layer.We have measured the reflectance of these mirrors at λ = 117.4µm as R mV = (97.0± 0.3)%, and we performed measurements aimed at estimating R p , T p and A p for the WGP.The resulting values are: (R p , T p , A p ) ≈ (99.2%, 0.4%, 0.4%).For a WPG the absorption losses due to the metal resistivity and the transmittance are expected to have the same value [30] and they can be expressed as: where g, d, ρ are the wire spacing, diameter and resistivity, respectively.Considering our values g = 20 µm, d = 10 µm, ρ = 52.8nΩ, λ = 117.4µm, we can calculate A p = T p = 0.49%, very close to the measured values A p ≈ T p ≈ 0.4%.In absence of absorption from air, the finesse for this cavity geometry can be estimated as: Given its geometrical configuration, the V-shaped cavity (when in resonance condition) will feedback the QCL.Hence, in order to verify this possibility, we studied a different cavity with a ring-shaped configuration.In such a geometry the beam travels on a square optical path, with round-trip length l R = 480 mm defined by the polarizer, a plane mirror and two off-axis parabolic mirrors with the same effective focal length f mR = 101.6mm, as shown in Fig. 1.As desired, the light travels only in one direction and, due to the cavity geometry, there is no OF to the laser.The mirrors used in this ring-cavity setup are, like in the V-shaped cavity case, protected by a 150-nm-thick SiO 2 layer, and and their reflectance is therefore R mR = (97.0± 0.3)%.In absence of absorption from air, the finesse for this cavity geometry is expressed as: Main parameters of both cavities are reported in Table 1.
Table 1.Main parameters calculated for the V-shaped and ring cavities.All parameters are calculated in vacuum (without absorption from air).The column F air reports the finesse values calculated by taking into account an absorption coefficient of ∼ 0.0038 cm −1 .
Cavity l (mm) FSR (MHz) in the CNR-NEST laboratories, is based on a bound-to-continuum design, with emission frequency close to 2.55 THz, and is mounted on the cold finger of a liquid helium cryostat.It is driven in continuous-wave mode at a fixed heat sink temperature T ≈ 20.0 K.Under these experimental conditions the QCL threshold current is I th = 340 mA, and the operating current is around 380 mA, supplied by a home-made low noise current driver (< 1 nA/Hz 1/2 ).The divergent beam emitted by the QCL is collected by means of an off-axis parabolic gold coated mirror (with an effective focal length of 25.4 mm), and it is guided through a half waveplate (HWP -realized at the CNR-INO optics workshop from a quartz substrate) and a polarizing beam-splitter (PBS -QMC Instruments, mod.P10).This latter is a photolithographic polarizer, placed at 45 • angle of incidence and with the wires fixed at vertical orientation.In our case, the native QCL polarization, which is always linear and orthogonal to the epitaxial growth axis, is horizontal.The HWP/PBS system allows to finely tune the amount of radiation sent to each cavity, as the HWP allows to rotate the linear QCL polarization of the desired amount, while PBS splits the beam in two parts, with horizontal and vertical polarizations, respectively, and complementary powers.
As described above, the input couplers of both cavities are WGPs (QMC Instruments, mod.QWG/RT).Since they must act as mirrors (with very low losses), the orientation of their wires is chosen parallel to the polarization of the incoming beams, so it is vertical for the ring-shaped cavity, and horizontal for the V-shaped cavity (see Fig. 1 and Fig. 2).The distance between both the input couplers and the QCL is about 500 mm.Indeed, since the parabolic mirror in front of the cryostat was moved slightly away from the perfect collimation distance, the beam waist falls at that distance, and placing the input couplers there ensures a good mode-matching with both cavities.
In this work the QCL wavelength is fixed by keeping both the heat sink temperature and the driving current constant, while the resonance frequency of both cavities is tuned by changing their lengths.This is done, as shown in Fig. 1, by moving one of the cavity mirrors, that is mounted on a motorized translation stage (ThorLabs, mod.MTS25) controlled by a LabVIEW program.Moreover, the software allows to select the scanning speed (typical value 1.5 µm/s), the total scan length (typically 200 µm), the total scan time and the acquisition rate.
In both cases, a pyroelectric detector (Gentec-EO, mod.SPH-62 THZ) is aligned on the beam reflected by the input coupler.The detected power P r equals the total incoming power P 0 when off-resonance, whereas a power dip is expected in resonance condition, since a fraction of the incoming light is coupled to the cavity.In order to make a zero-offset acquisition, a beam chopper (driven at 172 Hz) is placed inside the cavities, and a lock-in detection is implemented.This allows to retrieve the power dip (P 0 − P r ) as a zero-background, positive signal.

Measurements and discussion
In this section we will first discuss about the recording of the resonance peaks of successive cavity modes during the cavity scan.We will show how the absorption from air of our THz radiation affects the peak amplitude and width, and therefore the cavity finesse.We will discuss OF from the V-shaped cavity to the laser, how it induces a frequency-lock of to the cavity resonance, and how it is possible to tune the laser emission frequency by scanning the V-shaped cavity around its resonances.

Coupling to cavities
The first step is the analysis and optimization of the beam shape and waist, that must be adjusted in order to match the theoretical cavity mode.For this reason, we implemented an iterative procedure that consists in acquiring beam sections at different propagating distances along the optical path, estimating the beam waist in both directions x and y (Fig. 3) and finely optimizing the beam waist until it reaches the best match with the calculated cavity mode.The retrieved values of M 2 x and M 2 y are far from unity, suggesting that the beam is not Gaussian; this will significantly affect the laser coupling to the cavities.
After this optimization procedure, the cavities can be singularly injected and their resonance signals can be maximized by fine adjustments in the alignment.The typical spectrum is obtained by scanning the cavity length in order to acquire two or more resonance peaks.
The resonance spectrum obtained by the V-shaped cavity is reported in Fig. 4 (black plot).The measured finesse value of 16 is far away from the theoretical one, but, as already said, this Fig. 4. Effect of the absorption from air on the V-shaped cavity spectrum, as evidenced by comparing two spectra acquired with the cavity either in ambient air (black) or under N 2 purging (red).In this latter case, the lower losses determine narrower and higher resonance peaks, due to the expected increase of the cavity finesse.can be explained by the absorption from the water vapour contained in the ambient air filling the cavity.This is confirmed by the good agreement with the cavity finesse value calculated in presence of absorption from air and presented in Table 1.In order to overcome this limitation, the cavities are placed in closed boxes purged with nitrogen.This strongly suppresses absorption from water vapour inside the cavities, and the resulting cavity spectrum is shown in Fig. 4 (red plot).The intensity of the modes rises by a factor of three, as expected, while the finesse only increases by a factor of two, up to a value of 25.
This apparent degradation of the finesse with respect to the expected value, is due to another issue hindering the measurement.According to the V-shaped geometrical configuration, when this cavity is resonant, a small fraction of the incoming radiation leaks back towards the laser.This radiation is expected to perturb the laser emission, through OF.In particular, the laser frequency is expected, within a given range, to follow the cavity resonance.This phenomenon is clearly shown in Fig. 5, as it can be studied by varying the amount of radiation feeding back to the laser.This is done in our apparatus by rotating the HWP before the PBS of Fig. 2, i.e.Fig. 5.The effect of OF from the V-shaped cavity to the QCL is quantitatively studied by analysing the width of the cavity peak as a function of the incoming power (a), and thus of the feedback level (normalized to its maximum value).The beam level is controlled by rotating the HWP (see Fig. 2).From the peak width it is possible to retrieve the dependence of the apparent cavity finesse on the feedback level (b).The plot clearly shows that the presence of OF results in a lower measured finesse value, suggesting that the QCL frequency is perturbed by OF and follows the cavity mode frequency.
controlling the power of the beam injecting the V-shaped cavity.Fig. 5(a) reports the comparison among several acquisitions of the cavity resonance peak, taken at different feedback levels; it is clear that the higher the beam power is, the larger the peak resonance becomes, and the apparent cavity finesse will change accordingly, as shown in Fig. 5(b).As a consequence, a realistic measurement of the V-shaped cavity finesse can be performed only at very low beam intensity.On the contrary, when performing the same analysis on the ring cavity, no changes can be noted while measuring the finesse at different laser powers, thus confirming once more that the ring-shape configuration is completely free from OF.
The typical spectrum obtained by the V-shaped cavity (at low laser power) is reported in Fig. 6(a).The achieved finesse is F V = 58, corresponding to Q = 2.4 × 10 5 .This value is significantly lower than the expected one (83) as even a small amount of OF to the laser will strongly affect the experimentally measured finesse (see Fig. 5).The presence of a transverse mode reveals that the mode matching between the laser beam and the longitudinal cavity mode is not perfect.The typical ring cavity spectrum is shown in Fig. 6(b).
Since this configuration does not produce any OF to the QCL, the optimization can be carried out at the maximum available power.This explains the very high signal-to-noise ratio of the acquired trace.The achieved finesse is F R = 63, corresponding to Q = 2.6 × 10 5 .The more complex cavity geometry and mirror shape result in a larger number of transverse modes, that are partially populated due to the non perfect mode-matching between the laser beam and the longitudinal cavity mode.

Optical feedback for V and Ring shaped cavities
Given the results shown in Fig. 5, we investigated the possibility of optically locking the QCL frequency to the V-shaped cavity resonance.In order to demonstrate this effect, we injected both resonators at the same time.The V-shaped cavity is swept across its resonances, while the ring cavity is kept fixed, at a resonance half-height.In this conditions any shift on the laser frequency will result in a variation of the signal retrieved from the ring cavity.Fig. 7 shows two V-shaped cavity scans (black plot), and the ring-cavity signals (red plot), in two opposite situations: a) with strong OF to the QCL laser( 1% of the V-shaped cavity incoming radiation), b) with almost no OF to the laser, i.e. while strongly attenuating the beam that feeds the V-shaped cavity ( 0.001% of the V-shaped cavity incoming radiation).Fig. 7.The effect of V-shaped cavity OF on the QCL can be studied by using the ring cavity as a monitor of the laser frequency fluctuations.The ring cavity is tuned at resonance half-height, so that the peak slope converts any frequency drift in a detectable amplitude variation.The V-shaped cavity is then scanned, and the signals from both cavities are simultaneously acquired.The measurement is performed in presence (a) and in absence (b) of OF to the QCL.Slow changes in the red signal are due to QCL laser temperature drifts, amplified by the signal slope.
The signal of the ring cavity (red, a) explains the reason of the apparent V-shaped cavity finesse degradation and peaks widening in presence of OF (black, a): as the V-shaped cavity gets closer to the resonance with the QCL, the QCL frequency is first pulled towards the cavity resonance, and then sticks to it for a while, until it is released again and restores to its original value.On the contrary, when the OF from the V-shaped cavity is suppressed, no effect on the QCL frequency is detected by the ring cavity signal (red, b) and the V-shaped cavity spectrum shows a higher finesse and sharper peaks (black, b).
When present, the frequency pulling effect is still quite small, in the range of 1 MHz or less, and this is probably due to two different reasons.First, the OF level to the QCL, in these experimental conditions, is estimated to be around 1%, and even less if a small misalignment of the optical paths is taken into account; this feedback level cannot be enough to ensure a large optical locking bandwidth.Second, no control of the phase of the OF is implemented at present, and this can explain a non-optimized efficiency of the optical locking mechanism.Nevertheless, the presented results are a clear evidence that, for the first time, an external high-Q THz cavity can have an influence on the frequency of a QCL.

Conclusions
In this work two different geometries of THz resonant cavities, a V-shaped and a ring-shaped cavity, are presented and tested with a THz QCL.They are based on Au-coated mirrors and free-standing wire-grid polarizers acting as input/output couplers.A complete characterization is reported, and the experimentally retrieved parameters are compared with the calculated ones, showing a good agreement.With finesses F ≈ 60 these cavities prove to be the first resonators with Q > 10 5 at frequencies well above 1 THz (in our case 2.55 THz).Moreover, further improvements are expected by using metallic mirrors with larger reflectivity (e.g.unprotected gold coated mirrors), with respect to the ones used in this work, leading to Q > 10 6 .THz cavities with such performances will be powerful tools for the next generation of high-sensitivity and high-resolution THz spectroscopic experiment based on QCLs, providing not only a dramatic enhancement of the available optical power, but also a narrow reference for the QCL frequency.To this regard, the present work also demonstrates the first experimental evidence of influence of the QCL frequency by means of OF from an external resonator (the V-shaped cavity).The validation of this effect has been made possible by using the second cavity (the ring-shaped one) as transducer of the QCL frequency fluctuation under OF condition.This first evidence opens up interesting perspectives on the narrowing and control of the emission frequency of a QCL by means of THz resonant cavities.

Fig. 1 .
Fig. 1.The two cavity configurations adopted in the present work.(a) The V-shaped cavity consists of two Au-coated spherical mirrors (SM) and one wire-grid polarizer (WGP) acting as planar input/output coupler.(b) For the ring-shaped cavity we use two parabolic mirrors (PM), one plane mirror (M), and one WPG, placed at the vertices of a square.The twosided arrows indicate the translating mirrors.The chosen lengths ensure, in both cases, an operation close to the confocal condition, while avoiding the degeneracy of transverse modes with longitudinal ones.

Fig. 2 .
Fig.2.The experimental setup includes both the developed cavities.The half-wave plate (HWP) and the polarizing beam-splitter (PBS) allow to choose the fraction of the QCL light to be send to each cavity.In this way it is possible to use one cavity at a time or both simultaneously.The mirrors placed after the PBS allows for an independent alignment of each cavity.By placing the chopper wheels inside the cavities it is possible to detect the amount of coupled radiation as a dip in the power of the beam reflected by the input coupler, occurring at resonance.

Fig. 3 .
Fig. 3. (a) Measurement of the beam waist dimensions and position is carried out by taking several images of the beam section (b,example) at different propagation distances, and by fitting them with Eq. 2. The laser collimation is adjusted in order to optimize the modematching with the cavities modes.

Fig. 6 .
Fig. 6.(a) Optimized spectrum of the V-shaped cavity in N 2 -purged atmosphere.The suppression of OF is obtained by attenuating the incoming beam and, consequently, the backreflected beam.(b) Optimized spectrum of the ring cavity in N 2 -purged atmosphere.