high-q resonant cavities for terahertz quantum cascade lasers · high-q resonant cavities for...

High-Q resonant cavities for terahertzquantum cascade lasers

A. Campa,1,2,∗ L. Consolino,1,2 M. Ravaro,1,2 D. Mazzotti,1,2M. S. Vitiello,3 S. Bartalini,1,2 and P. De Natale,1,2

1 INO, Istituto Nazionale di Ottica - CNR, Largo Fermi 6, 50125 Firenze, Italy2 LENS, European Laboratory for Non-Linear Spectroscopy, Via Carrara 1, 50019 Sesto

Fiorentino FI, Italy3 NEST, Istituto Nanoscienze - CNR and Scuola Normale Superiore, Piazza San Silvestro 12,

56127 Pisa, Italy∗[email protected]

Abstract: We report on the realization and characterization of twodifferent designs for resonant THz cavities, based on wire-grid polarizers asinput/output couplers, and injected by a continuous-wave quantum cascadelaser (QCL) emitting at 2.55 THz. A comparison between the measuredresonators parameters and the expected theoretical values is reported. Withachieved quality factor Q ≈ 2.5× 105, these cavities show resonant peaksas narrow as few MHz, comparable with the typical Doppler linewidth ofTHz molecular transitions and slightly broader than the free-running QCLemission spectrum. The effects of the optical feedback from one cavityto 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 cas-cade; (300.6495) Spectroscopy, terahertz.

References and links1. S. Haroche, “Nobel Lecture: Controlling photons in a box and exploring the quantum to classical boundary,” Rev.

Mod. Phys. 85, 1083–1102 (2013).2. G. Gagliardi and H.-P. Loock, eds., Cavity-Enhanced Spectroscopy and Sensing, vol. 179 of Springer Series in

Optical Sciences (Springer, 2014).3. S. Kuhr, S. Gleyzes, C. Guerlin, J. Bernu, U. B. Hoff, S. Deleglise, S. Osnaghi, M. Brune, J.-M. Raimond,

S. Haroche, E. Jacques, P. Bosland, and B. Visentin, “Ultrahigh finesse Fabry–Perot superconducting resonator,”Appl. Phys. Lett. 90, 164101 (2007).

4. G. A. Gary, E. A. West, D. Rees, J. A. McKay, M. Zukic, and P. Herman, “Solar CIV vacuum-ultraviolet Fabry–Perot interferometers,” Astron. Astrophys. 461, 707–722 (2007).

5. G. Rempe, R. J. Thompson, H. J. Kimble, and R. Lalezari, “Measurement of ultralow losses in an optical inter-ferometer,” Opt. Lett. 17, 363–365 (1992).

6. A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, and L. Maleki, “Optical resonators with ten million finesse,”Opt. Express 15, 6768–6773 (2007).

7. R. Kohler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, andF. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417, 156–159 (2002).

8. B. J. Drouin, F. W. Maiwald, and J. C. Pearson, “Application of cascaded frequency multiplication to molecularspectroscopy,” Rev. Sci. Instrum. 76, 093113 (2005).

9. J. C. Pearson, B. J. Drouin, A. Maestrini, I. Mehdi, J. Ward, R. H. Lin, S. Yu, J. J. Gill, B. Thomas, C. Lee,G. Chattopadhyay, E. Schlecht, F. W. Maiwald, P. F. Goldsmith, and P. Siegel, “Demonstration of a room tem-perature 2.48-2.75 THz coherent spectroscopy source,” Rev. Sci. Instrum. 82, 093105 (2011).

10. K. M. Evenson, D. A. Jennings, and F. R. Petersen, “Tunable far-infrared spectroscopy,” Appl. Phys. Lett. 44,576–578 (1984).

11. F. Matsushima, K. Kobayashi, and Y. Moriwaki, “Frequency measurement of pure rotational transitions of D2Ousing tunable terahertz spectrometer,” J. Phys.: Conf. Series 185, 012028 (2009).

#229141 - $15.00 USD Received 4 Dec 2014; revised 21 Jan 2015; accepted 21 Jan 2015; published 6 Feb 2015 © 2015 OSA 9 Feb 2015 | Vol. 23, No. 3 | DOI:10.1364/OE.23.003751 | OPTICS EXPRESS 3751

12. G. Mouret, F. Hindle, A. Cuisset, C. Yang, R. Bocquet, M. Lours, and D. Rovera, “THz photomixing synthesizerbased on a fiber frequency comb,” Opt. Express 17, 22031–22040 (2009).

13. M. S. Vitiello, L. Consolino, S. Bartalini, A. Taschin, A. Tredicucci, M. Inguscio, and P. De Natale, “Quantum-limited frequency fluctuations in a Terahertz laser,” Nat. Photon. 6, 525–528 (2012).

14. M. Ravaro, S. Barbieri, G. Santarelli, V. Jagtap, C. Manquest, C. Sirtori, S. P. Khanna, and E. H. Linfield,“Measurement of the intrinsic linewidth of terahertz quantum cascade lasers using a near-infrared frequencycomb,” Opt. Express 20, 25654–25661 (2012).

15. L. Consolino, S. Bartalini, H. E. Beere, D. A. Ritchie, M. S. Vitiello, and P. De Natale, “THz QCL-BasedCryogen-Free Spectrometer for in Situ Trace Gas Sensing,” Sensors 13, 3331–3340 (2013).

16. Y. Ren, J. N. Hovenier, R. Higgins, J. R. Gao, T. M. Klapwijk, S. C. Shi, B. Klein, T.-Y. Kao, Q. Hu, andJ. L. Reno, “High-resolution heterodyne spectroscopy using a tunable quantum cascade laser around 3.5 THz,”Applied Physics Letters 98, 231109 (2011).

17. S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. E. Beere, and D. A.Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat.Photon. 4, 636–640 (2010).

18. M. Ravaro, C. Manquest, C. Sirtori, S. Barbieri, G. Santarelli, K. Blary, J.-F. Lampin, S. P. Khanna, and E. H.Linfield, “Phase-locking of a 2.5 THz quantum cascade laser to a frequency comb using a GaAs photomixer,”Opt. Lett. 36, 3969–3971 (2011).

19. L. Consolino, A. Taschin, P. Bartolini, S. Bartalini, P. Cancio, A. Tredicucci, H. E. Beere, D. A. Ritchie, R. Torre,M. S. Vitiello, and P. De Natale, “Phase-locking to a free-space terahertz comb for metrological-grade terahertzlasers,” Nat. Commun. 3, 1040–1044 (2012).

20. S. Bartalini, L. Consolino, P. Cancio, P. De Natale, P. Bartolini, a. Taschin, M. De Pas, H. Beere, D. Ritchie, M. S.Vitiello, and R. Torre, “Frequency-comb-assisted Terahertz quantum cascade laser spectroscopy,” Phys. Rev. X4, 021006 (2014).

21. L. Consolino, A. Campa, M. Ravaro, D. Mazzotti, M. S. Vitiello, S. Bartalini, and P. De Natale, “Saturatedabsorption in a rotational molecular transition at 2.5 THz using a quantum cascade laser,” Appl. Phys. Lett. 106,021108 (2015).

22. S. Bartalini, M. S. Vitiello, and P. De Natale, “Quantum cascade lasers: a versatile source for precise measure-ments in the mid/far-infrared range,” Meas. Sci. Technol. 25, 012001 (2014).

23. A. O’Keefe and D. Deacon, “Cavity ringdown optical spectrometer for absorption measurements using pulsedlaser sources,” Rev. Sci. Instrum. 59, 2544–2554 (1988).

24. D. Romanini, A. A. Kachanov, N. Sadeghi, and F. Stoeckel, “CW cavity ring down spectroscopy,” Chem. Phys.Lett. 264, 316–322 (1997).

25. B. A. Paldus, C. C. Harb, T. G. Spence, R. N. Zare, C. F. Gmachl, F. Capasso, D. L. Sivco, J. N. Baillargeon,A. L. Hutchinson, and A. Y. Cho, “Cavity ringdown spectroscopy using mid-infrared quantum-cascade lasers,”Opt. Lett. 25, 666–668 (2000).

26. G. Giusfredi, S. Bartalini, S. Borri, P. Cancio, I. Galli, D. Mazzotti, and P. De Natale, “Saturated-absorptioncavity ring-down spectroscopy,” Phys. Rev. Lett. 104, 110801 (2010).

27. L. A. Surin, B. S. Dumesh, F. Lewen, D. a. Roth, V. P. Kostromin, F. S. Rusin, G. Winnewisser, and I. Pak,“Millimeter-wave intracavity-jet OROTRON-spectrometer for investigation of van der Waals complexes,” Rev.Sci. Instrum. 72, 2535–2542 (2001).

28. G. Cazzoli, L. Cludi, C. Degli Esposti, and L. Dore, “Lamb-dip absorption spectroscopy in the far infrared regionusing a laser sideband spectrometer,” J. Mol. Spectrosc. 151, 378–383 (1992).

29. M. Bellini, P. De Natale, and M. Inguscio, “Progress in the far-infrared pecision spetroscopy,” Laser Phys. 4,408–411 (1994).

30. R. Braakman and G. A. Blake, “Principles and promise of FabryPerot resonators at terahertz frequencies,” J.Appl. Phys. 109, 063102 (2011).

31. P. Maddaloni, M. Bellini, and P. De Natale, Laser-Based Measurements for Time and Frequency Domain Appli-cations: a Handbook, Series in Optics and Optoelectronics (CRC Press, 2013).

1. Introduction

Optical resonators are well-established tools commonly used in spectroscopy [1, 2]. They havewidespread applications over the whole electromagnetic spectrum, from microwaves [3] toUV [4], while record-level optical finesse were also achieved in the visible/near-IR [5], es-pecially thanks to the advent of whispering gallery mode resonators [6]. In this context, theportion of the electromagnetic spectrum ranging from 0.1 to 10 THz, better known as Tera-hertz, is still lacking of such tools. One reason is certainly that, for many years the THz rangehas been an underexploited region. However, recent advances in generation and detection ofTHz 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 nowmaking THz light emerge as a new promising frontier for interdisciplinary research areas, suchas as bio-medical diagnostics, communication technology, security and defence.

Among the number of different applications of THz radiation, a central role is played bymolecular spectroscopy. Indeed, many chemical species have very strong rotational and ro-vibrational transitions in the THz range, with line-strengths much stronger than typical mi-crowave transitions, and comparable with the strongest fundamental ro-vibrational lines lyingin the mid IR. For this reason, Terahertz spectrum can well represent a novel “molecular fin-gerprint region”, once provided that sensitivity and resolution of newly developed THz spec-troscopic techniques are improved to the levels reached in other spectral regions.

Among the different sources of THz radiation (multiplied frequency chains [8, 9], tunablefar-IR lasers [10, 11], difference-frequency-generation processes [12]), in recent years THzQCLs are emerging as very promising sources not only for a practical exploitation of THztechnology, but also for fundamental research, e.g. in the field of THz metrology. Indeed, theycombine 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 andhigh-sensitivity spectroscopy [15] as well as for local oscillators in astronomical THz spectrom-eters [16]. Another recent achievement has been the extension to the THz region of optical fre-quency comb synthesizers [17–19], enabling direct and broadband phase/frequency referencingfor any THz source and providing a new tool for high-precision measurements of THz frequen-cies. The combination of the absolute referencing provided by THz comb with the mW-levelpower of THz QCLs recently allowed for a metrological-grade QCL-based THz spectroscopywith an unprecedented level of accuracy (4×10−9 in the determination of a THz transition fre-quency) [20], only limited by Doppler broadening of molecular spectra. In fact, even with verygood signal-to-noise ratios, the MHz-level linewidth of the acquired line profiles did not allowto achieve the nominal precision of the THz spectrometer (about 5× 10−11). Fortunately, thehigh output power provided by THz QCLs can enable sub-Doppler spectroscopic techniquesbased on non-linear saturation of molecular transition [21] in analogy to what happened in thepast years with mid-IR QCLs [22].

In this regard, cavity resonators represent an attractive tool to further increase the sensitiv-ity of a spectroscopic system, as they give access to much longer interaction lengths betweenlight and absorbing medium. Along with this enhancement capabilities, high-finesse resonantcavities could also provide a narrow reference for a QCL, allowing a reduction of its free-running linewidth, with further benefit for high-precision spectroscopy. In other words, the de-velopment of THz resonant cavities could represent an invaluable tool for metrological-gradeultra-sensitive QCL-based spectroscopy, enabling the deployment of the most advanced cavity-enhanced techniques, such as cavity-ring-down spectroscopy [23–26], to this region of the elec-tromagnetic spectrum.

However, design and fabrication of cavities efficiently resonating at THz frequencies is chal-lenging, due to the technological gap of THz materials and optical components, comparedto other spectral regions. As concerns cavity mirrors, highly reflective dielectric coatings arescarcely developed at THz frequencies, and at present only metallic coatings can be used, withmaximum reflectivity limited to 99.6% for gold. In addition, metallic mirrors are not suitableas 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 cou-pler: if the electric field component is parallel to the metal wires, electrons are free to flowalong 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 spec-troscopy [28, 29], where finesses of about 14 and 3 were achieved at 690 GHz and 1.5 THzfrequencies, 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 105 [30], sufficient for arelevant enhancement.

In this work, we report on the set up of WGP-based THz resonators coupled with radia-tion from a 2.55-THz QCL. We propose, and experimentally demonstrate, two different cavityconfigurations: a V-shaped and a ring-shaped geometry. Each cavity is characterized, and itsrelevant parameters (Q-factor, enhancement factor, optical coupling) are compared with theprediction of the theoretical model for the corresponding geometry. Finally, by simultaneouslycoupling the QCL to both cavities, the effect of optical feedback (OF) from the V-shaped cavityto 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.

2. Cavity designs

We can consider the beam emitted by a QCL as an elliptical Gaussian beam with different prop-agation 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, atwavelength λ , is described by a set of parameters: the beam waists w0i, the Rayleigh ranges zRi,the M2

i factors and the beam divergences θi, related by the following equations:

w20i = λ zRi/π = (λM2

i /πθi)2 (i = x,y) (1)

The Gaussian beam intensity is given by:

I(x,y,z) =2P

πwx(z)wy(z)e−2[

x2

wx(z)2+ y2

wy(z)2

](2)

where P is the beam power and

wi(z) = w0i

√1+[

M2i (z− z0i)

zRi

]2

(i = x,y) (3)

where z0i 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 largeM2

x and M2y 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 factorto 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 perround-trip (due to absorption from air, additional mirrors, etc.), and are described by either theFinesse (F ) or the quality factor (Q) [31].

The absorption coefficient from air, due to THz transitions in ambient water vapour, is ex-perimentally measured to be ∼ 0.0038 cm−1. Therefore, in order to reduce these losses, thecavities must be enclosed in boxes purged with nitrogen gas. Furthermore, internal losses de-pend on wavelength, angles of incidence and fundamental physical properties of each cavityelement, such as the conductivity of mirror metals, spacing and diameter of the wires of theWGP.


The V-shaped cavity, shown in Fig. 1 has a round-trip length lV = 480 mm and is composedby a WGP and two concave gold coated mirrors with the same effective focal length fmV =200 mm, protected by a 150-nm-thick SiO2 layer.

Fig. 1. The two cavity configurations adopted in the present work. (a) The V-shaped cavityconsists of two Au-coated spherical mirrors (SM) and one wire-grid polarizer (WGP) actingas 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 two-sided arrows indicate the translating mirrors. The chosen lengths ensure, in both cases,an operation close to the confocal condition, while avoiding the degeneracy of transversemodes with longitudinal ones.

We have measured the reflectance of these mirrors at λ = 117.4 µm as RmV = (97.0±0.3)%,and we performed measurements aimed at estimating Rp, Tp and Ap for the WGP. The resultingvalues are: (Rp,Tp,Ap) ≈ (99.2%,0.4%,0.4%). For a WPG the absorption losses due to themetal resistivity and the transmittance are expected to have the same value [30] and they can beexpressed as:

Awg = Twg = 4

√2ρg

πµ0cλd(4)

where g, d, ρ are the wire spacing, diameter and resistivity, respectively. Considering our valuesg = 20 µm, d = 10 µm, ρ = 52.8 nΩ, λ = 117.4 µm, we can calculate Ap = Tp = 0.49%, veryclose to the measured values Ap ≈ Tp ≈ 0.4%. In absence of absorption from air, the finesse forthis cavity geometry can be estimated as:

FV ≈π

1−RpRmV≈ 83 (5)

Given its geometrical configuration, the V-shaped cavity (when in resonance condition) willfeedback the QCL. Hence, in order to verify this possibility, we studied a different cavity witha ring-shaped configuration. In such a geometry the beam travels on a square optical path,with round-trip length lR = 480 mm defined by the polarizer, a plane mirror and two off-axisparabolic mirrors with the same effective focal length fmR = 101.6 mm, as shown in Fig. 1.As desired, the light travels only in one direction and, due to the cavity geometry, there is noOF 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 SiO2 layer, and and their reflectance is therefore RmR = (97.0±


0.3)%. In absence of absorption from air, the finesse for this cavity geometry is expressed as:

FR ≈π

1−√

RpR3mR

≈ 65 (6)

Main parameters of both cavities are reported in Table 1.

Table 1. Main parameters calculated for the V-shaped and ring cavities. All parameters arecalculated in vacuum (without absorption from air). The column Fair reports the finessevalues calculated by taking into account an absorption coefficient of ∼ 0.0038 cm−1.

Cavity l (mm) FSR (MHz) Fair F δν (MHz) QV-shape 480 625 24 83 7.5 3.4×105

ring 480 625 22 65 9.6 2.7×105

3. Experimental setup

A sketch of the experimental setup is shown in Fig. 2. The QCL used in this work, fabricated

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 QCLlight to be send to each cavity. In this way it is possible to use one cavity at a time or bothsimultaneously. The mirrors placed after the PBS allows for an independent alignment ofeach cavity. By placing the chopper wheels inside the cavities it is possible to detect theamount of coupled radiation as a dip in the power of the beam reflected by the input coupler,occurring at resonance.

in the CNR-NEST laboratories, is based on a bound-to-continuum design, with emission fre-quency close to 2.55 THz, and is mounted on the cold finger of a liquid helium cryostat. Itis driven in continuous-wave mode at a fixed heat sink temperature T ≈ 20.0 K. Under theseexperimental conditions the QCL threshold current is Ith = 340 mA, and the operating currentis around 380 mA, supplied by a home-made low noise current driver (< 1 nA/Hz1/2). The


divergent beam emitted by the QCL is collected by means of an off-axis parabolic gold coatedmirror (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 polarizingbeam-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, thenative 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 eachcavity, as the HWP allows to rotate the linear QCL polarization of the desired amount, whilePBS splits the beam in two parts, with horizontal and vertical polarizations, respectively, andcomplementary 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 wiresis chosen parallel to the polarization of the incoming beams, so it is vertical for the ring-shapedcavity, and horizontal for the V-shaped cavity (see Fig. 1 and Fig. 2). The distance between boththe input couplers and the QCL is about 500 mm. Indeed, since the parabolic mirror in frontof the cryostat was moved slightly away from the perfect collimation distance, the beam waistfalls at that distance, and placing the input couplers there ensures a good mode-matching withboth cavities.

In this work the QCL wavelength is fixed by keeping both the heat sink temperature and thedriving current constant, while the resonance frequency of both cavities is tuned by changingtheir lengths. This is done, as shown in Fig. 1, by moving one of the cavity mirrors, that ismounted on a motorized translation stage (ThorLabs, mod. MTS25) controlled by a LabVIEWprogram. 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 thebeam reflected by the input coupler. The detected power Pr equals the total incoming power P0when off-resonance, whereas a power dip is expected in resonance condition, since a fractionof the incoming light is coupled to the cavity. In order to make a zero-offset acquisition, a beamchopper (driven at 172 Hz) is placed inside the cavities, and a lock-in detection is implemented.This allows to retrieve the power dip (P0−Pr) as a zero-background, positive signal.

4. Measurements and discussion

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

4.1. Coupling to cavities

The first step is the analysis and optimization of the beam shape and waist, that must be adjustedin order to match the theoretical cavity mode. For this reason, we implemented an iterativeprocedure that consists in acquiring beam sections at different propagating distances along theoptical path, estimating the beam waist in both directions x and y (Fig. 3) and finely optimizingthe beam waist until it reaches the best match with the calculated cavity mode. The retrievedvalues of M2

x and M2y 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


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

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 bycomparing two spectra acquired with the cavity either in ambient air (black) or under N2purging (red). In this latter case, the lower losses determine narrower and higher resonancepeaks, due to the expected increase of the cavity finesse.

can be explained by the absorption from the water vapour contained in the ambient air fillingthe cavity. This is confirmed by the good agreement with the cavity finesse value calculated inpresence 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 absorp-tion 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 finesseonly 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 anotherissue hindering the measurement. According to the V-shaped geometrical configuration, whenthis 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 fre-quency is expected, within a given range, to follow the cavity resonance. This phenomenon isclearly shown in Fig. 5, as it can be studied by varying the amount of radiation feeding backto 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 byanalysing the width of the cavity peak as a function of the incoming power (a), and thusof the feedback level (normalized to its maximum value). The beam level is controlled byrotating the HWP (see Fig. 2). From the peak width it is possible to retrieve the dependenceof the apparent cavity finesse on the feedback level (b). The plot clearly shows that the pres-ence of OF results in a lower measured finesse value, suggesting that the QCL frequency isperturbed by OF and follows the cavity mode frequency.

controlling the power of the beam injecting the V-shaped cavity. Fig. 5(a) reports the compari-son 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 theapparent cavity finesse will change accordingly, as shown in Fig. 5(b). As a consequence, arealistic measurement of the V-shaped cavity finesse can be performed only at very low beamintensity. On the contrary, when performing the same analysis on the ring cavity, no changescan be noted while measuring the finesse at different laser powers, thus confirming once morethat the ring-shape configuration is completely free from OF.

The typical spectrum obtained by the V-shaped cavity (at low laser power) is reported inFig. 6(a). The achieved finesse is FV = 58, corresponding to Q = 2.4× 105. This value issignificantly lower than the expected one (83) as even a small amount of OF to the laser willstrongly affect the experimentally measured finesse (see Fig. 5). The presence of a transversemode reveals that the mode matching between the laser beam and the longitudinal cavity modeis 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 carriedout at the maximum available power. This explains the very high signal-to-noise ratio of theacquired trace. The achieved finesse is FR = 63, corresponding to Q = 2.6× 105. The morecomplex cavity geometry and mirror shape result in a larger number of transverse modes, thatare partially populated due to the non perfect mode-matching between the laser beam and thelongitudinal cavity mode.


Fig. 6. (a) Optimized spectrum of the V-shaped cavity in N2-purged atmosphere. The sup-pression of OF is obtained by attenuating the incoming beam and, consequently, the back-reflected beam. (b) Optimized spectrum of the ring cavity in N2-purged atmosphere.

4.2. Optical feedback for V and Ring shaped cavities

Given the results shown in Fig. 5, we investigated the possibility of optically locking the QCLfrequency to the V-shaped cavity resonance. In order to demonstrate this effect, we injected bothresonators at the same time. The V-shaped cavity is swept across its resonances, while the ringcavity is kept fixed, at a resonance half-height. In this conditions any shift on the laser frequencywill result in a variation of the signal retrieved from the ring cavity. Fig. 7 shows two V-shapedcavity 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) withalmost no OF to the laser, i.e. while strongly attenuating the beam that feeds the V-shapedcavity (' 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 cav-ity as a monitor of the laser frequency fluctuations. The ring cavity is tuned at resonancehalf-height, so that the peak slope converts any frequency drift in a detectable amplitudevariation. The V-shaped cavity is then scanned, and the signals from both cavities are si-multaneously 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 cavitygets closer to the resonance with the QCL, the QCL frequency is first pulled towards the cavityresonance, and then sticks to it for a while, until it is released again and restores to its originalvalue. On the contrary, when the OF from the V-shaped cavity is suppressed, no effect on theQCL frequency is detected by the ring cavity signal (red, b) and the V-shaped cavity spectrumshows a higher finesse and sharper peaks (black, b).

When present, the frequency pulling effect is still quite small, in the range of ' 1 MHz orless, and this is probably due to two different reasons. First, the OF level to the QCL, in theseexperimental conditions, is estimated to be around 1%, and even less if a small misalignmentof the optical paths is taken into account; this feedback level cannot be enough to ensure a largeoptical 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 cavitycan have an influence on the frequency of a QCL.

5. Conclusions

In this work two different geometries of THz resonant cavities, a V-shaped and a ring-shapedcavity, are presented and tested with a THz QCL. They are based on Au-coated mirrors andfree-standing wire-grid polarizers acting as input/output couplers. A complete characterizationis 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 resonatorswith Q > 105 at frequencies well above 1 THz (in our case 2.55 THz). Moreover, further im-provements are expected by using metallic mirrors with larger reflectivity (e.g. unprotected goldcoated mirrors), with respect to the ones used in this work, leading to Q > 106. THz cavitieswith such performances will be powerful tools for the next generation of high-sensitivity andhigh-resolution THz spectroscopic experiment based on QCLs, providing not only a dramaticenhancement 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 influenceof the QCL frequency by means of OF from an external resonator (the V-shaped cavity). Thevalidation of this effect has been made possible by using the second cavity (the ring-shapedone) as transducer of the QCL frequency fluctuation under OF condition. This first evidenceopens up interesting perspectives on the narrowing and control of the emission frequency of aQCL by means of THz resonant cavities.

Acknowledgments

This work was partly supported by the Italian Ministry of Education, University, and Research(MIUR) through the program FIRB-Futuro in Ricerca 2010, RBFR10LULP; Laserlab-Europe,grant agreement no. 284464, EU 7th Framework Program; ESFRI Roadmap, Extreme LightInfrastructure (ELI) project.


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