354 IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 14, NO. 2, MARCH/APRIL 2008
Terahertz Sources Based on Intracavity ParametricDown-Conversion in Quasi-Phase-Matched
Gallium ArsenideJoseph E. Schaar, Konstantin L. Vodopyanov, Paulina S. Kuo, Martin M. Fejer, Member, IEEE, Xiaojun Yu,
Angie Lin, James S. Harris, Fellow, IEEE, David Bliss, Candace Lynch, Vladimir G. Kozlov, and Walter Hurlbut
Abstract—We have efficiently generated tunable terahertz (THz)radiation using intracavity parametric down-conversion in gal-lium arsenide (GaAs). We used three types of microstructuredGaAs to quasi-phase-match the interaction: optically contacted,orientation-patterned, and diffusion-bonded GaAs. The GaAs wasplaced in an optical parametric oscillator (OPO) cavity, and theTHz wave was generated by difference-frequency mixing betweenthe OPO signal and idler waves. The OPO used type-II phase-matched periodically poled lithium niobate as a gain medium andwas synchronously pumped by a mode-locked laser at 1064 nm(7 ps and 200 nJ at 50 MHz). With center frequencies spanning 0.4–3.5 THz, 250-GHz bandwidth radiation was generated. We mea-sured two orders of optical cascading generated by the mixingof optical and THz waves. In a doubly resonant oscillator (DRO)configuration, the efficiency increased by 21× over the singly res-onant oscillator performance with an optical-to-THz efficiency of10−4 and average THz power of 1 mW. The GaAs stabilized theDRO by a thermooptic feedback mechanism that created a quasi-continuous-wave train of THz pulses.
Index Terms—Difference-frequency mixing, doubly resonant,gallium arsenide (GaAs), nearly degenerate, optical paramet-ric oscillator (OPO), parametric down-conversion, self-stabilized,terahertz (THz), tunable.
I. INTRODUCTION
T ERAHERTZ (THz) waves are potentially useful for nu-merous applications including real-time imaging and
rotational–vibrational spectroscopy, both in condensed andgaseous phases [1], [2]. Parametric down-conversion of opticalpulses is an established, but so far inefficient, method for gener-ating THz radiation. Potentially, it enables compact tunable THz
Manuscript received September 22, 2007; revised November 9, 2007. Thiswork was supported by the Defense Advanced Research Projects Agency(DARPA) under Grant FA9550-04-01-0465.
J. E. Schaar, K. L. Vodopyanov, P. S. Kuo, and M. M. Fejer are with theEdward L. Ginzton Laboratory, Stanford University, Stanford, CA 94305 USA(e-mail: [emailprotected]; [emailprotected]; [emailprotected];[emailprotected]).
X. Yu, A. Lin, and J. S. Harris are with the Solid State Photonics Labora-tory, Stanford University, Stanford, CA 94305 USA (e-mail: [emailprotected];[emailprotected]; [emailprotected]).
D. Bliss and C. Lynch are with the Air Force Research Laboratory, HanscomAir Force Base, Bedford, MA 01731 USA (e-mail: [emailprotected];[emailprotected]).
V. G. Kozlov and W. Hurlbut are with Microtech Instruments, Inc., Eu-gene, OR 97401 USA (e-mail: [emailprotected]; [emailprotected]).
Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/JSTQE.2008.917957
emitters working at room temperature, by using efficient solidstate or fiber laser sources with different temporal formats: fromcontinuous wave (CW) to femtosecond pulses. This techniquecan generate THz radiation using difference frequency gener-ation (DFG) with two laser input beams [3]–[8] or throughTHz wave parametric oscillation [9]–[11] with a single fixed-frequency optical pump. Alternatively, broadband THz tran-sients can be generated by means of optical rectification (OR)of ultrashort (typically femtosecond) laser pulses [12]–[15].
There are three significant factors that limit THz conver-sion efficiency in both OR and DFG, namely: 1) conventionalcrystals used for THz generation (e.g., LiNbO3 and ZnTe)have large absorption at THz frequencies (characteristically 10–100 cm−1 [16], [17], 2) there is a mismatch between propaga-tion velocities of the THz wave and the optical pulse that limits(especially for OR) the useful length of the crystal, and 3) alarge quantum defect. Optical-to-THz conversion efficienciesachieved so far are low [18], typically 10−6–10−9 , even withfemtosecond pump pulse energies as high as 10 mJ [19]. Away to solve the problem of propagation velocity mismatchand increase the interaction length is to use tilted pulse frontexcitation. A conversion efficiency of 5 × 10−4 and a THz av-erage power of 240 µW was reported in [15] using bulk lithiumniobate pumped by optical pulses from a 1 kHz Ti:Sapphireoscillator–regenerative amplifier system with 500 mW of aver-age power. Another approach to increase the efficiency of ORis to use quasi-phase-matched (QPM) nonlinear materials, aswas first demonstrated with periodically poled lithium niobate(PPLN) [13], [20]. The effective mixing length is increased dueto quasi-phase-matching allowing for looser pump focusing, re-ducing the magnitude of parasitic nonlinear effects for a givenpump pulse energy. The authors of [13] and [20] used fem-tosecond pulses at 800 nm and a PPLN crystal with multipleQPM periods and achieved a conversion efficiency ∼10−5 . ThePPLN crystal was cryogenically cooled (T = 18 K) to reduceTHz absorption.
More recently, THz wave generation was demonstrated inQPM-GaP [8] and QPM gallium arsenide (GaAs) [21], [22].III–V semiconductors are attractive for QPM THz wave gener-ation because of several properties, including: 1) a small THzabsorption coefficient [smaller by more than one order of mag-nitude than commonly used electrooptic (EO) crystals: LiNbO3 ,ZnTe, CdTe, and ZnSe] [16], [17], [23], [24], 2) a large nonlin-ear coefficient, and 3) a large coherence length due to a smallmismatch between the optical group and THz phase velocities.
1077-260X/$25.00 © 2008 IEEE
SCHAAR et al.: TERAHERTZ SOURCES BASED ON INTRACAVITY PARAMETRIC DOWN-CONVERSION IN QUASI-PHASE-MATCHED GaAs 355
In [8], THz waves were generated by DFG in a periodicallyinverted GaP wafer stack, which was pumped with 10 ns pulsesnear 1.55 µm. The authors of [21] produced THz radiation viaOR using femtosecond laser pulses and two different QPM-GaAs structures: 1) diffusion-bonded GaAs (DB-GaAs) [25]and 2) orientation-patterned GaAs (OP-GaAs) [26]. By chang-ing the GaAs QPM period (504–1277 µm), or the pump wave-length (2–4.4 µm), tunable (0.9–3 THz) output was achievedwith up to 3.3% quantum conversion efficiency with 2.3 µJof pump pulse energy. With a Tm-fiber laser pump source atλ ≈ 2 µm, 3 µW of average THz power was generated in anOP-GaAs crystal at 1.8 and 2.5 THz [22].
Here we report THz generation using intracavity DFG ina picosecond pulse optical parametric oscillator (OPO). Thispaper focuses on experimental results. A detailed theoreticalanalysis will be given in a subsequent paper.
II. THZ WAVE GENERATION USING PICOSECOND OPO PULSES
A. Picosecond Pulse DFG in QPM-GaAs
Detailed analysis of the generation of THz pulses by planewave QPM-DFG [27] with transform-limited pump pulsesshows that, for a given crystal length, QPM period, and pumppulse energy, there is a characteristic pulse duration τnom belowwhich the efficiency reaches an asymptotic value, and abovewhich the efficiency decreases monotonically. This characteris-tic pulse duration corresponds to a bandwidth that matches theacceptance bandwidth of the DFG process, and the conversionefficiency for this pulse length is 70% of the asymptotic valuereached for shorter pulses.
For Gaussian pump beams, the efficiency rises only slowlyfor focusing tighter than confocal for THz radiation [27]. Forthis focusing condition and a pulse duration of τnom , the band-width of the THz radiation decreases with crystal length, whilethe efficiency for a fixed pulse energy does not change (untilthe crystal length becomes comparable to the THz absorptionlength). As peak pump intensities are often limited by para-sitic nonlinear effects (two- and three-photon absorption, non-linear refraction), the lower intensities associated with the looserfocusing in longer crystals can be advantageous in practicalimplementations.
Under these pulse length and focusing conditions, the THzpulse energy scales with the product of the energies of the pi-cosecond optical pulses, UTHz = η U1U2 . As a numerical ex-ample of generating 1.5 THz radiation using DFG of 2.1 µmpulses in a 1-cm-long GaAs crystal (τ1,2 = τnom = 3.4 ps), theefficiency η is 3.4 × 10−4 per microjoule of optical pulse en-ergy. For 200 nJ pulse energies in both optical waves (10 Weach, 50 MHz), this corresponds to a THz pulse energy of13.5 pJ (0.67 mW).
Using picosecond pulses, which match the bandwidth inQPM-GaAs for crystals of length equal to a THz absorptionlength, at optical frequencies to pump QPM-GaAs in a single-pass DFG process can create a milliwatt-level THz source witha large optical-to-THz conversion per microjoule of pump pulseenergy while limiting higher order nonlinear effects that wouldbecome increasingly important at shorter pulse widths.
Fig. 1. Frequency-domain schematic of the four waves involved in THz gen-eration (pump, signal, idler, and THz, not drawn to scale). The pump wavelengthis near 1 µm, and the signal and idler wavelengths are near 2 µm.
B. Picosecond Pulse OPO
Our approach in generating THz radiation is based on theDFG inside a QPM GaAs crystal between the picosecond sig-nal and idler pulses of a low-loss synchronously pumped OPO.Either extra- or intracavity mixing in GaAs can be performed.A low-loss OPO cavity has large circulating peak powers thatcan significantly increase the optical-to-THz conversion effi-ciency for intracavity experiments. This intracavity enhance-ment scheme has previously been used for intracavity sum-frequency generation and DFG in the visible and mid-infraredfrequency ranges [28], [29].
In our experiments, the OPO gain crystal, PPLN, is pumpedby a mode-locked ∼7 ps pulse width laser with a wavelengthnear 1 µm. In the PPLN crystal (see Fig. 1), energy is transferredfrom the pump to the signal and idler waves (ωi < ωs < ωp
where i, s, and p refer to the idler, signal, and pump, respec-tively) that have frequencies symmetrically split about the de-generate frequency, ωp/2 (λ ∼ 2 µm). By changing the temper-ature of the PPLN crystal, the signal and idler frequencies canbe tuned symmetrically about degeneracy. The frequency spac-ing between the signal and idler is equal to the THz frequencythat will be generated in a DFG process (ωTHz = ωs − ωi).The OPO uses type-II (o–oe) phase-matching that allows nar-row OPO signal and idler spectral widths while operating neardegeneracy, and consequently, generating a THz wave with afull-width at half-maximum (FWHM) bandwidth ∼200 GHz.The signal and idler fields are linearly orthogonally polarized.In the QPM-GaAs crystal, energy flows from the signal wave tothe idler and THz waves. Changing the center frequency of theTHz wave involves: 1) changing the temperature of the PPLNcrystal to tune ωTHz and 2) using the correct GaAs gratingperiod to provide the necessary phase-matching between thesignal, idler, and THz waves.
C. QPM-GaAs Samples
GaAs has many attractive properties for THz generation suchas a small THz absorption coefficient, small mismatch betweenthe optical group index (ng ,opt ≈ 3.41 [30]) and THz phaseindex (nTHz ≈ 3.6 [31]), large thermal conductivity, large non-linear coefficient, and well-established QPM fabrication tech-niques. The absorption in GaAs is <4.5 cm−1 for ν < 3 THz,and ∼1 cm−1 at 1.5 THz [32]. The large thermal conductivity ofGaAs, 52 W/m·K [33], reduces temperature changes and ther-mooptic index perturbations at large average pump powers. The
356 IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 14, NO. 2, MARCH/APRIL 2008
Fig. 2. (a) DB-GaAs with dimensions 10 mm×10 mm×6.05 mm and QPMperiod of 504 µm. (b) OC-GaAs with diameters of 5.08 cm and QPM periodsof 2 mm. (c) OP-GaAs with thickness of ∼800 µm, width of 6 mm, length of5 mm, and QPM period of 704 µm.
nonlinear coefficient for THz generation from DFG betweentwo optical waves is d14 = 47 pm/V [27].
The periodic structure needed for quasi-phase-matching can-not be achieved in GaAs by ferroelectric poling, as is com-monly done in ferroelectric crystals such as LiNbO3 . GaAs isa cubic crystal with 43m symmetry, whose linear properties areisotropic, and in which 90 rotations around the 〈100〉 axes re-sult in a crystallographic inversion, and hence, a sign change ofthe nonlinear susceptibility. The nonzero elements of the GaAsnonlinear coefficient tensor are dxyz and its permutations.
We used three different types of microstructured GaAs:DB-GaAs [25], optically contacted GaAs (OC-GaAs), andOP-GaAs [26]. DB-GaAs samples are made of N individualGaAs plates by rotating every other plate by 180 about [110]to create a sample with N/2 QPM periods. The GaAs platesare brought together under pressure and high temperature thatallows diffusion to occur across the interface creating a nearlymonolithic structure. The DB-GaAs sample we used for THzgeneration had an aperture of 10 mm × 10 mm, length of6.05 mm, QPM period of 504 µm, and was constructed of24 GaAs plates [see Fig. 2(a)].
OC-GaAs construction also involves separate [110] wafersof GaAs that are brought together with a 180 rotation about[110] between neighboring wafers. The wafers, however, arenot heated to create a monolithic crystalline structure. They arecontacted creating an interface that is maintained by van derWaals interactions [see Fig. 2(b)]. The thickness of the GaAswafers used to fabricate the stacks used in these experimentsranged from 0.5 to 1.0 mm. The OC-GaAs samples have lowerinfrared losses over larger useful apertures than the DB-GaAssample.
OP-GaAs is the third type of microstructured QPM-GaAs [seeFig. 2(c)]. OP-GaAs is manufactured using photolithographyand molecular beam epitaxy to grow a thin-film template withperiodic crystal inversions. A thick film (∼1 mm) is then grownon the template by hydride vapor phase epitaxy (HVPE) toproduce bulk OP-GaAs [26]. The QPM period of OP-GaAsis easily controlled down to tens of microns, and it can bemaintained with good long-range order for lengths greater thanthe 1-cm-long samples required for THz generation since theyare fabricated with a photolithographic process.
Recently, 15-wafer-thick OC-GaAs samples have been pro-duced with a useful aperture of 3 mm × 3 mm and infraredlosses of ∼0.01 cm−1 . OP-GaAs samples now grown in a singleHVPE step are ∼1 mm in thickness [34] with 2 µm absorption<0.005 cm−1 [35].
Fig. 3. Schematic of SRO and extracavity DFG experiment. The signal andidler were outcoupled from the SRO and focused into various QPM-GaAssamples. L1 was a focusing lens for the signal and idler, and L2 was a Picarinlens that focused the THz beam onto the liquid-helium-cooled silicon bolometer.Inset 1: signal TEM00 resonating spatial mode profile with M 2 = 1.2. Inset 2:type-II PPLN temperature-tuning curves for both the o–wave signal and e–waveidler (measured data points and solid-line polynomial fits).
III. SRO EXTRACAVITY THZ GENERATION
Fig. 3 shows the experimental setup for THz generationoutside the cavity of the synchronously pumped singly res-onant OPO [singly resonant oscillator (SRO)]. The OPOpump laser was a Nd:YVO4 CW-mode-locked solid-state laser(picoTRAIN, High Q Laser) with a 50 MHz pulse repetitionrate, 7 ps Gaussian FWHM intensity pulse width, 1064 nmwavelength, and 10 W average output power. The linear SROcavity was 3 m long with a round-trip time equal to the period be-tween pump laser pulses. For the OPO gain medium, we used anantireflection (AR) coated (for pump, signal, and idler) MgO-doped type-II PPLN crystal, with a QPM period of 14.1 µmand length of 10 mm. The nonlinear optical coefficient for type-II quasi-phase-matching at 2.1 µm, d31,eff = (2/π)d31 = 2.35pm/V calculated from [36] at 1.06 µm and scaled using Miller’srule [37] to 2.1 µm, was 6.2× smaller than the coefficient for typ-ical type-0 (e-ee) quasi-phase-matching (d33,eff ), which resultedin an OPO parametric gain reduced by a factor of 38.4 com-pared to the usual type-0 configuration. The focused 1 µm laserspot size (1/e2 intensity radius) at the center of the PPLN was30 µm. Mirrors M1 and M2 were end mirrors for the resonatingsignal wave. Mirrors M3 and M4 were separated by 21.3 cmand had 20 cm radii of curvature that created a signal spot sizeof 57 µm in the center of the PPLN. A second position forfocused signal and idler beams (140 µm beam waist) was cre-ated using mirrors M5 and M6, which were separated by 50 cmand had 50 cm radii of curvature. This second focus is impor-tant for intracavity THz generation and will be discussed inSection IV. The distance between mirrors M4 and M5 was30 cm, and the remaining cavity length of ∼200 cm was di-vided evenly into the two end lengths (M6–M1 = M3–M2).All mirrors were AR-coated for the pump and high-reflectivity(HR) coated for the signal and idler waves with a reflectionloss <0.1%. The front surface of the thin-film polarizer, TFP1,was AR-coated for signal (p-polarization) transmission andHR-coated for idler (s-polarization) reflection (p-polarization
SCHAAR et al.: TERAHERTZ SOURCES BASED ON INTRACAVITY PARAMETRIC DOWN-CONVERSION IN QUASI-PHASE-MATCHED GaAs 357
incident on the polarizer is equivalent to an o-wave in the PPLNcrystal). Fig. 3 (inset 1) shows the signal’s TEM00 spatial modemeasured by a pyroelectric-array camera. The beam M 2 pa-rameter was 1.2 as measured by focusing the 2.1 µm beamoutside the cavity. The type-II QPM temperature-tuning curvefor the signal and idler wavelengths is shown in Fig. 3 (inset 2)[38].
Large powers at both signal and idler wavelengths are re-quired for extracavity THz DFG. The nominal polarizer angleof incidence of 55 minimized the signal-SRO threshold but didnot outcouple the signal wave for extracavity experiments. Wechose the polarizer angle of 51.5 to increase the signal outcou-pling without greatly reducing the OPO quantum conversionefficiency. The signal and idler reflectivities at the polarizerwere 2% and 99.2%, respectively. The cavity mirrors and PPLNsurfaces created 2.4% round-trip loss, and the round-trip lossesof the polarizer were 4% (total OPO round-trip loss of 6.4%).We measured a signal autocorrelation width of 8.5 ps corre-sponding to a signal pulse width of 6 ps, assuming a transform-limited Gaussian pulse. A longpass filter (λ > 1.9 µm) blockedthe unwanted near-infrared and visible-wavelength light. At aPPLN temperature of 86C, the signal and idler average pow-ers were 620 and 180 mW, respectively. The powers variedonly slightly with the temperature of the PPLN crystal. L1 fo-cused the signal and idler beams down to 80 µm at the centerof the QPM-GaAs crystal. The signal field was linearly polar-ized along the GaAs [001] direction, and the idler and THzfields were polarized along [110]. All beams propagated along[110]. THz radiation was generated via picosecond DFG insidethe QPM-GaAs sample. The optical beams were blocked by asmall metal wire located directly after the GaAs crystal. Themajority of the THz wave propagated beyond the metal wire,because the THz diffraction cone was ∼100× larger than thatof the optical beam. The THz radiation was focused by a Pi-carin lens (L2, THz transmission ∼40%) onto a cryogenicallycooled silicon bolometer (T = 4 K). A black polyethylene filter(0.8 mm thick) was placed directly before the bolometer andblocked any remaining IR and visible light.
Fig. 4 shows measured THz center frequencies νTHz versusQPM period for several OP-, OC-, and DB-GaAs crystals [39].They are in good agreement with νTHz = c/(∆nΛg ), whereΛg is the QPM-grating period and ∆n = nTHz − ng ,opt [27].Dispersion information from [30] and [31] was used for GaAsat near-IR and THz frequencies, respectively. Typical generatedTHz average powers were between 0.1 and 1 µW.
IV. SRO INTRACAVITY THZ GENERATION
A. SRO Intracavity THz Generation
The QPM-GaAs samples were placed inside the SRO cavityto increase the generated THz average powers. The angle of inci-dence on the intracavity polarizer was set to 55 which reducedthe polarizer losses to 0.1%. We expect the GaAs nonlinearrefraction, and consequently, Kerr lensing to place an upperlimit on the circulating intensity in the OPO. The Gaussian spa-tial intensity profile of the signal and idler beams will createa Gaussian transverse phase, and the quadratic component will
Fig. 4. THz center frequencies versus GaAs QPM period (data points) forOC-, OP-, and DB-GaAs samples in good agreement with theory (dashed line)using dispersion information from [30] and [31] for GaAs at near-IR and THzfrequencies, respectively.
Fig. 5. Schematic of measurements of THz average powers generated viaintracavity DFG in the SRO configuration. The THz beam was outcoupledby M7, focused by Picarin lens L2, and measured with a DTGS pyroelectricdetector.
cause signal and idler focusing in the GaAs. An effective focallength can be calculated from the curvature of the transversephase profile including both self- and cross-phase modulationterms, and the GaAs can be modeled as a dynamic nonlinearlens with a lens strength proportional to intracavity intensity. Itis possible to design the OPO cavity with minimum sensitivityto the Kerr lensing at the location of the GaAs crystal, to al-low oscillation at large intracavity powers. Similar designs havebeen applied to mode-locked laser cavities that have a thermallyloaded diode-pumped gain element.
We designed the cavity to produce a focused 140 µm spotsize for the signal and idler beams at a position roughly halfwaybetween M5 and M6 (see Fig. 5). Following a design approachsimilar to that in [40], we placed the GaAs in this focus where thesignal and idler intensities as well as optical-to-THz conversionefficiency were large. For this spot size and GaAs-crystal lengthof 1 cm, the 3-m-long OPO can maintain oscillation from startupdown to focal lengths of fKerr ≈ 2–4 cm. When fKerr ∼ LGaAs ,the GaAs thin lens approximation breaks down, and a moregeneral analysis is required.
The THz wave was extracted from the SRO by mirror M7,which was a gold-coated 90-off-axis parabolic mirror with afocal length of 5 cm placed ∼5 cm after the QPM-GaAs crystal,which created a well-collimated THz beam. A 3-mm-diameter
358 IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 14, NO. 2, MARCH/APRIL 2008
Fig. 6. (a) Collimated THz beam intensity profile reconstructed from scanningknife-edge measurements just before lens L2. (b) Focused (f = 5 cm) THzbeam intensity profile measured by a pyroelectric camera (1 pixel = 100 µm× 100 µm) 5 cm after L2.
hole was drilled through M7 to fully transmit the resonatingsignal wave. The visible and IR radiation was blocked by twopolyethylene filters that transmitted >45% for ν < 3 THz. Fora 100 µm THz spot size generated in the GaAs (product ofsignal and idler Gaussian 140 µm spots), the 1 inch aperturegold parabolic mirror collected >90% of the incident power atfrequencies >2.8 THz.
The DB-GaAs sample (6 mm long and QPM period of504 µm) generated THz radiation with a center frequencyof 2.8 THz and FWHM spectral bandwidth estimated to be∼250 GHz from the convolution of the measured 200 GHzbandwidths of the signal and idler waves [38] and limited to250 GHz by the QPM-GaAs acceptance bandwidth [27]. Themeasured THz average power was 50 µW (after M7), and themeasured intracavity powers of the signal and idler were 11.1 Wand 2.2 W, respectively, with a large signal power enhance-ment compared to 690 mW in the previous section (before thelongpass filter). For a given pump depletion, the signal powerenhancement A is
A =aext
aintR(1)
where aext = 6.4% was the round-trip loss for extracavity exper-iments with signal output coupling R = 2% and aint = 14.4%was the round-trip loss for the intracavity experiments. TheDB-GaAs roundtrip loss was 12%. The calculated enhancementof A = 22 is close to the measured value of 11.1 W/0.69 W =16. The idler power of 2.2 W agreed with the quantum de-fect of 0.5 (pump to idler) and the measured 50% depletion of8.9 W of pump power. The undepleted pump power was mea-sured after M4 (see Fig. 5). The optical-to-THz conversion effi-ciency was 5.6 × 10−6 (quantum efficiency of 5.6 × 10−4).
Fig. 6(a) shows the THz beam intensity profile after collimat-ing mirror M7, reconstructed from scanning knife-edge mea-surements. The horizontal and vertical 1/e2 spot sizes were 7.8and 13.3 mm, respectively. The THz beam 5 cm after THz lensL2 (f = 5 cm) was captured [see Fig. 6(b)] by a pyroelectric-array camera [38] and was∼2 pixels in width (1 pixel = 100 µm× 100 µm). Taking the input beam size from the knife-edgemeasurements, the focused spot size agreed with the theoreticaldiffraction-limited spot size of 160 µm. The polarization of theTHz beam was along the [110] GaAs crystalline direction, inagreement with the symmetry of the GaAs χ(2) tensor [41], andfor signal and idler fields polarized along the [001] and [110]directions, respectively.
Fig. 7. First-, third-, and fifth-order QPM with a 4-mm-long OC-GaAs crystalwith Λg = 2 mm allowing generation of three different THz center frequencies(0.62, 2.24, and 3.32 THz, respectively) with a single QPM-GaAs sample.
B. Higher Order QPM THz Generation
The two-step down-conversion process (1 µm → 2 µm →200 µm) by which we generate THz radiation requires oper-ating the OPO very close to degeneracy. For generating 2.8 THzradiation, the signal and idler wavelength separation is 42 nm atan average wavelength of 2128 nm. This tuning behavior also al-lowed generation of other THz frequencies by taking advantageof higher order QPM peaks in the GaAs sample.
Modeling the QPM crystal as having a fundamental spatialfrequency of kg = 2π/Λg , and equal length positive and nega-tive half-periods, the mth spatial harmonic of the grating enablesquasi-phase-matching when the wavevector mismatch
∆k = ks − ki − kTHz − mkg (m odd) (2)
is zero [42]. Here, kj = 2πnjνj /c is the wavevector magnitude,nj is the index of refraction, and νj is the frequency. The max-imum DFG efficiency occurs for ∆k = 0. Assuming perfectphase-matching (∆k = 0), nearly degenerate signal and idler(νs ≈ νi νTHz), and negligible THz dispersion (nTHz ≈constant), the THz center frequency scales linearly with m:
νTHz = m
(c
∆nΛg
). (3)
We measured the higher order QPM tuning curves for a 4-mm-long OC-GaAs crystal with Λg = 2 mm. Fig. 7 shows thefirst-, third-, and fifth-order QPM tuning curves with centerfrequencies of 0.62, 2.24, and 3.32 THz, respectively. The centerfrequencies do not scale exactly with m because of the GaAsdispersion between 0.5 and 4.0 THz.
C. Cascading
In a DFG process within the GaAs crystal, the largest energyphoton (OPO signal) is destroyed, and two lower energy photons(OPO idler and THz) are generated, i.e., the GaAs crystal para-metrically amplifies the OPO idler, depleting the OPO signaland generating a THz photon. Since the ratio of the THz to theoptical frequency is ∼1%, 100% depletion of the signal energywould correspond to an optical-to-THz conversion efficiency ofonly 1%. In order to improve this efficiency, it may be possibleto take advantage of a cascading scheme, to generate more than
SCHAAR et al.: TERAHERTZ SOURCES BASED ON INTRACAVITY PARAMETRIC DOWN-CONVERSION IN QUASI-PHASE-MATCHED GaAs 359
Fig. 8. Parametric down-conversion and cascading illustrating amplificationof the THz wave after each cascading process, ωs > ωi ωTHz .
Fig. 9. Measured output spectrum of the SRO with idler wave resonant. Thetwo satellite peaks are generated by cascading of the THz-DFG process. Peaksare labeled with their polarization, referenced to the axes of the GaAs crystal.
one THz photon for each signal photon destroyed [43], [44].Fig. 8 illustrates this process. Similar to the parametric ampli-fication mentioned earlier, the OPO idler will amplify the THzwave and generate a down-shifted satellite ωsat,1 . This processcan be iterated up to a limit set by the phase-matching band-width of the QPM-GaAs crystal ∆Ωaccept,GaAs . Therefore, thenumber N can be N ≈ ∆Ωaccept,GaAs/ωTHz .
To explore these effects experimentally, we slightly modi-fied the apparatus shown in Fig. 5. By rotating the polarizerby 90, the idler rather than the signal was resonant in theSRO. Resonating the idler rather than the signal wave increasedthe efficiency of generating the first satellite. The temperatureof the PPLN crystal was set to 82.3C to generate signal andidler waves separated by 2.8 THz. A small amount of powerin each optical wave leaked out SRO mirror M1 (see Fig. 5)and was characterized with a grating monochromator. The OPOsignal, idler, and two satellites were observed around 2100–2240 nm (see Fig. 9). The generated THz output (not shown)was measured by the deuterated triglycine sulfate (DTGS) detec-tor. The grating monochromator was not calibrated for relativepower measurements of the four waves shown in Fig. 9; therelative heights of the peaks shown are arbitrary, but indicatethe ordering of the strengths of the waves. Consistent with ex-pectations, the separation between adjacent peaks was 2.8 THz,and adjacent fields were orthogonally polarized. The measured
Fig. 10. Schematic of the linear DRO with an “offset” cavity design. M1–M8 were cavity mirrors, and M9 was an off-axis parabolic mirror for THzoutcoupling.
spectra proved that two cascading events occurred; however,the optical-to-THz conversion efficiency was not significantlyimproved since the average powers of the two satellites werevery small. Having satellite waves with powers comparable tothe signal and idler will require all 2 µm waves (signal, idler,and satellites) to be resonant in the optical cavity. A dispersion-compensated cavity designed to obtain such multiply resonantoperation is currently under construction.
V. DRO INTRACAVITY THZ GENERATION
A. DRO Operation
The THz average power can be increased in a doubly reso-nant OPO [doubly resonant oscillator (DRO)], in which boththe signal and idler are resonant. Fig. 10 shows the DRO setupwith the addition of two mirrors, M3 and M4, and a second po-larizer, TFP2, to the SRO configuration of Fig. 5. To avoid backconversion of the signal and idler on the return pass throughthe PPLN [45], we made distances TFP1–M1 and TFP1–M3unequal. In order to keep the round-trip times for the signal andidler waves equal, the paths TFP2–M2 and TFP2–M4 were cor-respondingly adjusted. In this “offset” cavity design, the signaland idler pulses overlapped in time during their forward passthrough the PPLN; however, they did not overlap on the re-turn pass. Another challenge for DRO operation is the requiredsimultaneous resonance of the signal and idler waves [46], re-quiring precise control of both cavity lengths.
Both polarizers were set to an angle of 51 that equalized theround-trip losses for the signal and idler waves. The total round-trip loss including DB-GaAs was 22.4% (2.4% from mirrorsand PPLN, 12% from DB-GaAs, and 8% from two polariz-ers). In a first experiment, rather than servo-locking the DRO,we simply scanned one of the cavity mirrors through multiplecavity resonances at a 100 Hz rate and measured bursts of os-cillation with a duty cycle of 30%. During these DRO bursts,we generated 1 mW of THz average power at 2.8 THz from8.5 W with an optical-to-THz efficiency of 1.2 × 10−4 (quan-tum efficiency of 1.2%) [38], which was an increase of 21×over the SRO results with the DB-GaAs crystal. We foundthat the generated 1 mW of THz output power was within±10% of theoretical predictions for intracavity signal and idler
360 IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 14, NO. 2, MARCH/APRIL 2008
powers of 10.2 and 17 W, respectively, and efficiency followingthe theory described in Section II-A. The resonant enhance-ment for both waves was low, because the round-trip losseswere >20%. Later, we achieved quasi-CW DRO operation us-ing electronic feedback (piezoelectric stack attached to one endmirror) or a passive thermooptic feedback mechanism describedin the next section.
B. Thermooptic DRO Self-Stabilization
An electronic dither-and-lock control system was developedand successfully locked the synchronously pumped DRO topeak resonance where Pmax = Ps + Pi (peak of the cavity res-onance). With a single 1-mm-thick GaAs wafer in the cavity, theDRO was electronically stabilized with 90 W of average intra-cavity 2.1 µm power and 84% pump depletion for >30 minutes.Without electronic control but with an 8-mm-long OC-GaAssample, we observed a self-stabilizing effect that maintainedDRO operation for >30 minutes (only terminated due to expan-sion of the optical table due to temperature changes in the room).This passive thermooptic feedback mechanism provides length–noise suppression, as has been demonstrated in other parametricoscillators using AgGaS2 as the stabilizing element [47].
To understand the origin of the thermooptic stabilization,consider the case where the length of the DRO cavity is slightlylonger than the optimum that maximizes Pmax , so that a de-crease in cavity length increases the circulating power. In thepresence of a perturbation that decreases the cavity length, therewill be an increase in the temperature of the GaAs crystaldue to the increase in absorbed power, a positive thermoop-tic response (dn/dT > 0) due to the temperature rise, and acompensating increase in the optical path length. Such a mech-anism provides negative feedback with respect to length pertur-bations. The thermally loaded DRO remains self-stabilized aslong as the bandwidth of the length perturbations falls within theunity-gain bandwidth of the thermal self-stabilization process.The thermal bandwidth scales inversely with the thermal diffu-sion time across the 2.1 µm wavelength beam spot in the GaAscrystal [47]. For the 140 µm spot used in these experiments, thiscondition corresponds to a bandwidth of 1.8 kHz. The passivefeedback does not lock to peak resonance as the dither-and-locksystem does. It requires an initial length adjustment to operatenear Pmax . A more detailed theoretical description will appearsubsequently.
Fig. 11 shows the 1.5 THz power measured by the DTGS de-tector (chopped at 10 Hz). The DRO cavity contained an 8-mm-long OC-GaAs sample (Λg = 1.07 mm) that simultaneouslygenerated THz power and stabilized the DRO. Additional elec-tronic feedback can be used in conjunction with the thermoopticself-stabilization to further suppress length perturbations and tolock to a set THz power level.
VI. CONCLUSION AND FUTURE WORK
We demonstrate a novel source of frequency-tunable THzradiation based on intracavity parametric down-conversion inthree types of room-temperature QPM-GaAs (OC-, OP-, andDB-GaAs). As a pump for THz generation, we used the sig-
Fig. 11. Passively self-stabilized DRO signal (2.116 µm), idler (2.14 µm), andsignal–idler DFG (1.5 THz radiation chopped at 10 Hz) measured waveformsfor a duration of 90 s.
nal and idler waves of picosecond-pulse near-degenerate type-IIsingly and doubly resonant OPOs. Type-II QPM enabled near-transform-limited pulses with wavelengths near 2.1 µm to begenerated close to degeneracy, and the THz center frequencywas tunable from 0.4 to 3.5 THz. In both cases of active (elec-tronic feedback) and passive (GaAs thermooptic feedback) sta-bilization, the DRO operated for >30 minutes with only smallfluctuations in output power. Two orders of optical cascadingwere measured during intracavity THz generation. We havegenerated 1 mW of THz average power from 180 nJ pumplaser pulses with an optical-to-THz conversion efficiency of1.2 × 10−4 (quantum efficiency of 1.2%).
With total cavity losses of 4%, it should be possible to reach20 mW of average THz power with a 2.1 µm wavelength spotsize of ∼350 µm in the GaAs. Experiments are underway withimproved polarizers with round-trip losses of 10−3 and GaAssamples with losses of 2% to demonstrate this performance.Ring cavity designs offer an approach to a further, reduction ofcavity losses.
The output power is potentially scalable to >50 mW by im-plementing a design with multiple orders of resonant cascading.Such a system would require dispersion compensation, to main-tain resonance across the broader infrared spectrum of such adevice, and further, reduction of intracavity loss.
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Joseph E. Schaar received the B.S. degree in electrical engineering from theUniversity of Arizona, Tucson, in 2003, the M.S. degree in electrical engineer-ing from Stanford University, Stanford, CA, in 2005, where he is currentlyworking toward the Ph.D. degree in electrical engineering at the E. L. GinztonLaboratory.
His current research interests include terahertz-wave generation in quasi-phase-matched GaAs using intracavity parametric down-conversion, doubly res-onant optical parametric oscillator stabilization techniques, and synchronouslypumped OPO modeling.
Mr. Schaar is a member of the Optical Society of America (OSA).
362 IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 14, NO. 2, MARCH/APRIL 2008
Konstantin L. Vodopyanov received the Master’s degree from Moscow Phys-Tech, Moscow, Russia, in 1976, the Ph.D. degree from the Oscillations Lab-oratory, Lebedev Physical Institute, Moscow, in 1983, and the D.Sc. degree(Habilitation) from the General Physics Institute, Moscow, in 1993.
During 1985–1990, he was an Assistant Professor at Moscow Phys-Tech,during 1990–1992, a Alexander-von-Humboldt Fellow at the University ofBayreuth, Germany, and during 1992–1998, a Lecturer at the Imperial Col-lege, London, U.K. During 1998–2000, he was the Head of the Laser Group,Inrad, Inc., NJ, and later, during 2000–2003, the Director of mid-IR systems atPicarro, Inc., CA. In 2003, he returned to Academia and is now at the EdwardL. Ginzton Laboratory, Stanford University, Stanford, CA. His current researchinterests include laser interaction with matter, laser spectroscopy, nonlinear op-tics, mid-IR and terahertz-wave generation using micro- and nanostructuredmaterials, as well as spectrally resolved atomic force microscopy.
Dr. Vodopyanov was a Fellow of the Royal Society during 1992–1998. Hewas elected as a Fellow of the U.K. Institute of Physics in 1997 and OpticalSociety of America in 1998. He is a member of program committees for sev-eral major laser conferences and has been elected as the Program Chair for theConference on Lasers and Electro-Optics (CLEO) 2008 and the General Chairfor CLEO 2010.
Paulina S. Kuo received the B.S. degrees in physics and materials science fromthe Massachusetts Institute of Technology, Cambridge, in 2000. She is currentlyworking toward the Ph.D. degree in applied physics from Stanford University,Stanford, CA.
Ms. Kuo is a member of the Optical Society of America (OSA) and theSociety of Photo-optical Instrumentation Engineers (SPIE).
Martin M. Fejer (M’93) received the B.A. degree in physics from Cornell Uni-versity, Ithaca, NY, in 1977, and the M.S. and Ph.D. degrees in applied physicsfrom Stanford University, Stanford, CA, in 1979 and 1986, respectively.
In 1986, he joined the faculty at Stanford, where he is currently a Professorof Applied Physics. He is the author or coauthor of more than 200 techni-cal publications. He holds 20 patents. His current research interests includenonlinear optical materials and devices, guided wave optics, microstructuredferroelectrics and semiconductors, nonlinear devices for telecommunicationsapplications, low dissipation materials, and precision measurements.
Prof. Fejer is a Fellow of the Optical Society of America (OSA) and amember of the IEEE LEOS Board of Governors. He is also a member of theAmerican Association for Crystal Growth (AACG) and the Society of Photo-optical Instrumentation Engineers (SPIE).
In 1998, he was the recipient of the Optical Society of America (OSA) R.W.Wood Prize.
Xiaojun Yu received the B.S. and M.S. degrees in materials science andengineering from Tsinghua University, Beijing, China, in 1998 and 2000, re-spectively, and the second M.S. degree in electrical engineering and the Ph.D.degree in materials science and engineering from Stanford University, Stanford,CA, in 2004 and 2006, respectively.
He was engaged in research in the area of molecular beam epitaxy andthe applications in nonlinear optics. From 2005 to 2006, he was with MicronTechnology, where he was engaged in research on nonvolatile NOT–AND circuit(NAND) flash memory design. In 2006, he joined IBM Semiconductor Researchand Development Center, East Fishkill, NY.
Angie Lin is currently working toward the Ph.D. degree in materials scienceand engineering at Stanford University, Stanford, CA.
Her current research interests include molecular beam epitaxial growth oftwo different materials systems, GaAs-Ge and GaP-Si, and development oforientation-patterned GaP structures for nonlinear optical applications.
James S. Harris, photograph and biography not available at time of publication.
David Bliss received the B.A. degree in economics from Case-Western ReserveUniversity, Clevend, OH, in 1968 the S.M. degree in engineering (materialsscience) from the Massachusetts Institute of Technology, Cambridge, in 1981,and the Ph.D. degree in materials science from State University of New York(SUNY) Stony Brook, in 2000.
He is a Program Manager of substrate engineering and crystal growth inthe Optoelectronic Technology Branch of the Air Force Research Laboratory atHanscom Air Force Base, MA.
Dr. Bliss is a member, Executive Committee Member, and President of theAmerican Associtaion for Crystal Growth. He is a member of the Crystal GrowthCommission and the International Union of Crystallography.
Candace Lynch received the S.B. degree from the Massachusetts Institute ofTechnology, Cambridge, in 1999, and the Ph.D. degree from Brown University,Providence, RI, in 2004, both in engineering (materials science).
She was engaged in research on in situ measurement of strain relaxationduring lattice mismatched epitaxial growth of III-arsenides. From January 2005to February 2007, she was a National Research Council Postdoctoral ResearchAssociate at the Air Force Research Laboratory (AFRL), Hanscom Air ForceBase, Bedford, MA. Since February 2007, she has been a Research Physicistwith the AFRL. Her current research interests include hydride vapor phaseepitaxial growth of thick layers for nonlinear optical frequency conversion.
Vladimir G. Kozlov received the M.S. degree in physics from Moscow StateUniversity, Moscow, Russia, in 1992, and the Ph.D. degree in physics fromBrown University, Providence, RI, in 1997.
He held research positions at Lucent Technologies and Princeton University.He is the Vice President of Microtech Instruments, Inc., Eugene, OR. He hasmore than 20 years of experience in research and development of optoelectronicsystems, including terahertz (THz) devices.
Walter Hurlbut, photograph and biography not available at time of publication.
