Osellame et al. Vol. 20, No. 7 /July 2003 /J. Opt. Soc. Am. B 1559
Femtosecond writing of active optical waveguideswith astigmatically shaped beams
Roberto Osellame, Stefano Taccheo, Marco Marangoni, Roberta Ramponi, and Paolo Laporta
Istituto di Fotonica e Nanotecnologie, Consiglio Nazionale delle Ricerche, Istituto Nazionale per la Fisica dellaMateria, Dipartimento di Fisica, Politecnico, Piazza L. da Vinci, 32, I-20133 Milano, Italy
Dario Polli, Sandro De Silvestri, and Giulio Cerullo
National Laboratory for Ultrafast and Ultraintense Optical Science, Istituto Nazionale per la Fisica della Materia,Dipartimento di Fisica, Politecnico, Piazza L. da Vinci, 32, I-20133 Milano, Italy
Received November 19, 2002; revised manuscript received February 7, 2003
1. INTRODUCTIONOptical waveguides and related photonic devices, such aswaveguide amplifiers and lasers, couplers, splitters, andinterleavers, are finding increasing applications in opticalcommunication systems. The realization of optical struc-tures in glass substrates can provide reliable and cheapdevices with the best match to optical fibers. Traditionalmanufacturing technologies include chemical vapor depo-sition with subsequent reactive ion etching or ionexchange.1,2 While these techniques are well estab-lished, they present some disadvantages, such as the needof a photolithographic step, limiting the flexibility of thedevice fabrication process, and the capability of producingonly structures in planar geometry close to the surface ofthe sample.
Recently, a novel technique for the direct writing ofwaveguides and photonic circuits, exploiting focused fem-tosecond pulses, has emerged.3–8 When a femtosecondpulse is tightly focused in a transparent material, energyis deposited in a small volume around the focus due to acombination of multiphoton absorption and avalancheionization.4,9 The photogenerated hot electron plasmarapidly transfers its energy to the lattice, giving rise tohigh temperatures and pressures; this produces, by amechanism still under investigation, a local material den-sification with an increase of refractive index over amicrometer-sized volume of the material.10,11 This indexgradient allows one to produce a wide variety of devices,both active and passive.12,13
Femtosecond micromachining shows, compared withtraditional techniques, a number of distinct advantages:(i) three-dimensional capabilities; (ii) rapid device proto-
typing, since the device pattern can be easily changed bysimple software control, with significant cost reductionwith respect to standard techniques requiring photolitho-graphic steps; and (iii) simpler and less expensive produc-tion plants.
Nonlinear absorption in glasses takes place for intensi-ties around 1 –5 3 1013 W/cm2; for a pulse duration of100 fs, this corresponds to a fluence of 1–5 J/cm2. Therequired pulse energy depends on the focusing condition:For ‘‘mild’’ focusing (1–3-mm beam waist), it is at the levelof a few microjoules, but it can be reduced to a few tens ofnanojoules by extremely tight focusing, of the order of ahalf-wavelength (diffraction limited). Two different re-gimes of femtosecond micromaching can be distinguished,depending on whether the pulse period is longer orshorter than the time required for heat to diffuse awayfrom the focal volume: the ‘‘low-frequency’’ regime, inwhich material modification is produced by the singlepulse, and the ‘‘high-frequency’’ regime, in which cumula-tive effects take place. Since the heat diffusion time outof the absorption volume in the glass can be estimated at;1 ms, the boundary between the two regimes is at fre-quencies around 1 MHz. Low-frequency systems use am-plified Ti:sapphire lasers (1–100-kHz frequency) with anenergy of a few microjoules, while high-frequency systemsuse stretched-cavity oscillators (5–20-MHz frequency)with energies of a few tens of nanojoules.14–16
High-frequency micromachining offers several advan-tages: (i) simplification of the experimental setup, be-cause of the lack of the amplification stage; (ii) muchgreater processing speeds, up to 1 cm/s; and (iii) the pos-sibility of controlling the waveguide size by changing the
2003 Optical Society of America
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writing speed, because of thermal accumulation effects.On the other hand, the small available intensity rangelimits the process flexibility, and the need of tight focus-ing enables formation of structures only in close proxim-ity to the surface, thus not allowing full exploitation of thethree-dimensional capabilities of the process.
For the low-frequency regime, two different writing ge-ometries are possible, longitudinal and transverse, inwhich the sample is translated, respectively, along andperpendicularly to the beam propagation direction. Inthe longitudinal geometry, the waveguides are intrinsi-cally symmetric, and their transverse size is determinedby the focal spot size; however, the waveguide length islimited by the focal length of the focusing objective, andtheir quality is degraded by spherical aberrations, whichdepend on the depth of the focus inside the glass sample.The transverse geometry provides a much greater flexibil-ity and allows one to write waveguides or waveguidestructures of arbitrary length; it has, however, the disad-vantage of producing a strong asymmetry in the wave-guide cross section.17 This asymmetry can be explainedas follows: perpendicularly to the beam propagation di-rection, the waveguide size is given approximately by thebeam focal diameter 2w0 , while along the propagation di-rection, it is given by the confocal parameter b5 2pw0
2/l. For focused diameters of the order of a fewmicrometers, this results in a large difference in wave-guide sizes in the two directions. This asymmetry be-comes particularly severe when the waveguide size is in-creased, as required for waveguiding at the opticalcommunication wavelength of 1.5 mm, thus greatly reduc-ing the efficiency of fiber butt coupling in conventionaltelecommunications setups. Recently, we introduced anovel focusing geometry in which the femtosecond writingbeam is astigmatically shaped by changing both the spotsizes in the tangential and sagittal planes and the rela-tive positions of the beam waists.18 This shaping allowsone to modify the interaction volume in such a way thatthe waveguide cross section can be made circular andwith arbitrary size.
In this paper we analyze this technique in detail, show-ing in particular the importance of controlling the offsetdistance between the focal planes in order to achieve a cir-cular waveguide cross section. We demonstrate experi-mentally that it is possible to control the size as well asthe symmetry of the waveguide. We then apply thismethod to the fabrication of active waveguides in Er:Yb-doped glasses. This paper is organized as follows: InSubsection 2.A, we introduce a simple model for nonlinearabsorption in transparent materials, which allows one topredict the shape of the material volume modified by thefemtosecond pulse and the ensuing waveguide transverseprofile. In Subsection 2.B, we analyze in detail the astig-matic beam-shaping technique, showing how it allows oneto obtain a symmetric waveguide profile of controllablesize. In Subsection 3.A, we describe the experimentalwaveguide fabrication setup and present results obtainedwith the astigmatic shaping of the writing beam. In Sub-section 3.B, we present the characterization, both activeand passive, of the manufactured waveguides. Finally,in Section 4 we draw conclusions and give perspectives forfuture work.
2. ASTIGMATIC BEAM SHAPINGA. Model for Nonlinear AbsorptionIn low-repetition-rate systems, the local index modifica-tion is produced by a single pulse; thus cumulative effectscan be neglected.19 Since the material modification isdue to energy transfer from the free electrons to the lat-tice, the size and the shape of the material volume modi-fied by the femtosecond pulse are correlated to those ofthe region in which free electrons are generated. It istherefore useful to calculate the electron-density profileinside the material. A simple model describing the evo-lution of the free-electron density n(t) in a medium ex-posed to an intense laser pulse is based on the followingrate equation20–22:
dn
dt5 aI~t !n~t ! 1 skIk~t !, (1)
where a is the avalanche coefficient, sk is the k-photonabsorption coefficient, and the pulse temporal profile isassumed Gaussian, I(t) 5 I0 exp b2(t/tp)2c. k is chosen asthe smallest integer such that k times the photon energyexceeds the bandgap of the material. This equation hasthe following solution:
n~t ! 5 h21~t !expFskE2`
t
h~t8!I~t8!dt8G , (2)
where
h~t ! 5 expF2aE2`
t
I~t8!dt8G . (3)
In the focal region of a symmetric Gaussian beam, thepeak intensity varies along both the radial (x, y) and thepropagation (z) directions; by solving Eq. (1) at differentpoints within the focal volume and plotting the photoge-nerated free-electron density n(`) as a function of x, y,and z, one can obtain the shape of the volume modified bythe femtosecond laser pulse. Figure 1(a) presents an ex-ample of such a calculation, showing a contour surface ofthe free-electron density for a circularly symmetricTEM00 Gaussian beam (l 5 0.8 mm) focused to a waistw0 5 2 mm. We assume a pulse energy of 0.5 mJ and du-ration of 150 fs and use the parameters for a barium alu-minum borosilicate glass (k 5 3, a 5 1.2 cm2/J, s3 5 73 1017 cm23 ps21 (cm2/TW)3).22 The shape of the vol-ume enclosed by this surface corresponds, to a first ap-proximation, to that of the material volume modified bythe femtosecond laser pulse. As expected, this volumehas an ellipsoidal shape, strongly elongated along thepropagation direction; in fact, the confocal parameter cor-responding to a focal diameter of 4 mm is 31 mm. If thesample is translated along the x direction, the ensuingwaveguide transverse profile is strongly asymmetric withan aspect ratio of nearly 10 to 1. Achievement of a sym-metric profile would require a tighter, nearly diffraction-limited focusing, so that w0 5 zR 5 pw0
2/l; in this case,however, the waveguide size shrinks to less than 1 mm.The situation is somewhat improved by considering, in-stead of an ideal Gaussian beam, a real laser beam with abeam-quality factor M2 . 1. In this case, in fact, the
Osellame et al. Vol. 20, No. 7 /July 2003 /J. Opt. Soc. Am. B 1561
confocal parameter of the beam is expressed by b5 2(pw0
2/M2l) and is therefore reduced, for a given focalspot size, with respect to the ideal case. This helps to de-
Fig. 1. Contour surfaces of photogenerated free-electron densityfor (a) a circularly symmetric Gaussian beam with waist w05 2 mm and (b) an astigmatic Gaussian beam with w0x5 1 mm, w0y 5 3 mm, z0 5 0. Contour plots in the xy and yzplanes are also shown.
crease the asymmetry of the waveguide profile, but, fortypical beam-quality factors for femtosecond laser beams(1.3 , M2 , 2), does not allow one to obtain a symmetricwaveguide.
B. Effect of Astigmatic Beam ShapingFrom the previous discussion, two limitations of thetransverse waveguide writing geometry are apparent: (i)The confocal parameter is much greater than the focalspot size, giving rise to strongly asymmetric waveguides.(ii) The asymmetry can be decreased by tighter focusing,but in this case the waveguide size becomes too small.Point (ii) becomes particularly important if thewaveguides must support a guided mode at 1.5 mm. It istherefore obvious that, in order to circularize the wave-guide cross section, it is necessary to decrease the depthof focus independently from the focal diameter. In thefollowing, we will show that astigmatic beam shaping canbe useful to this purpose.
The intensity profile of a focused astigmatic Gaussianbeam can be written as23
I0~x, y, z ! 5 I00
w0x
wx~z !
w0y
wy~z !
3 expH 22F x2
wx~z !2 1y2
wy~z !2G J , (4)
where
wx~z ! 5 w0xA1 1 S z
zRxD 2
,
wy~z ! 5 w0yA1 1 S z 2 z0
zRyD 2
, (5)
zRx,y 5 p(w0x,y2 /l) are the Rayleigh ranges for the x and y
directions, and z0 is the offset distance between the beamwaists, which we will call astigmatic difference in the fol-lowing. The basic idea behind astigmatic focusing isthat, in the transverse writing geometry, the size of thewaveguide is independent of the focal size in the directionalong which the sample is translated (the x direction inour writing geometry). We can exploit this fact to focusvery tightly in the x direction, thus decreasing the Ray-leigh range zRx ; the increased divergence in the xz planewill rapidly bring the intensity below the threshold fornonlinear absorption, thus decreasing the depth of focus.The focal spot size in the y direction can be chosen inde-pendently to optimize the transverse waveguide size. Toillustrate this concept, Fig. 1(b) shows a simulated con-tour plot of electron-density profile obtained with an as-tigmatic beam (w0x 5 1 mm, w0y 5 3 mm); for the mo-ment, the astigmatic difference z0 is set to zero. In thiscase, the shape of the modified volume is flattened alongthe x direction, but it is also decreased along the z direc-tion, resulting in a greatly reduced waveguide asymme-try. To achieve a round waveguide profile, the astigma-tism needs to be increased even more, requiring a ratio
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w0y /w0x close to 10. As an example, Fig. 2(a) shows asimulation performed with w0x 5 0.6 mm, w0y 5 4 mm,z0 5 0; the modified volume now has a lenticular shape,and the waveguide profile is almost circular. Such astrong difference in focal spot sizes requires a high(de)magnification cylindrical telescope, which may be dif-ficult to align and introduces aberrations; in addition, ex-perimental optimization of the waveguide symmetry re-
Fig. 2. Contour surfaces of photogenerated free-electron densityfor (a) an astigmatic Gaussian beam with w0x 5 0.6 mm, w0y5 4 mm, z0 5 0 and (b) an astigmatic Gaussian beam withw0x 5 1 mm, w0y 5 3 mm, z0 5 100 mm. Contour plots in thexy and yz planes are also shown.
quires changing the telescope magnification, which is atime-consuming operation and can only be accomplishedin discrete steps.
In the following, we show how the waveguide profilecan be circularized, even with smaller w0y /w0x ratios, ofthe order of 2 to 3, by controlling the astigmatic differencez0 between the focal planes. For a focused astigmaticbeam, the highest intensity is normally reached in theplane corresponding to the smallest focal spot (w0x in ourcase); the waveguide extent along the beam propagationdirection is therefore roughly given by 2zRx . By chang-ing the focal plane offset z0 , one can increase the beamsize wy , with respect to w0y , at the plane correspondingto the beam waist in the x direction; this allows one tocontinuously increase the size of the waveguide perpen-dicularly to the beam propagation direction, until thesymmetry of the waveguide profile is achieved. To illus-trate this concept, Fig. 3 shows the beam profiles of a fo-
Fig. 3. Beam profiles in the yz plane (solid curves) and the xzplane (dashed curves) of a focused astigmatic Gaussian beam(w0x 5 1 mm, w0y 5 3 mm) for (a) z0 5 0 and (b) z0 5 100 mm.The corresponding waveguide cross section in the yz plane isshown as a shaded area.
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cused astigmatic Gaussian beam (w0x 5 1 mm, w0y5 3 mm) for the two cases z0 5 0 [Fig. 3(a)] and z05 100 mm [Fig. 3(b)]. A simulation of the modified vol-ume for this last case is shown in Fig. 2(b): The resultsare similar to those obtained with a larger astigmatic ra-tio, resulting in a nearly circular waveguide cross section.Changing the astigmatic difference z0 therefore providesan experimental degree of freedom that allows optimiza-tion of the symmetry of the waveguide profile.
It is important to notice that the astigmatic writingtechnique allows one not only to obtain a circular wave-guide profile, but also to vary its size. To this purpose, itis sufficient to choose w0x so that the transverse wave-guide extent matches the required size along the z direc-tion, and then to vary the astigmatic difference untilwaveguide symmetry is achieved.
3. EXPERIMENTAL SETUP AND RESULTSA. Waveguide FabricationWaveguides were fabricated by a standard regenerativelyamplified Ti:sapphire laser (model CPA-1 from Clark In-strumentation), generating 150-fs, 500-mJ pulses at a1-kHz repetition rate at the wavelength of 790 nm. Thebeam had a nearly TEM00 transverse profile; the laserpulse energy used for waveguide writing, controlled by avariable attenuator, ranged from 0.5 to 10 mJ. A He–Nelaser, collinear with the Ti:sapphire, was used for align-ment purposes. The optical setup is depicted in Fig. 4;the beam, initially circular with a variable spot size (con-trolled by a spherical telescope), is passed through a cy-lindrical telescope ( f1 5 50 mm, f2 5 150 mm); provid-ing a demagnification by a factor 3 in the y direction.The distance between the cylindrical lenses is finely con-trolled by a translation stage so as to vary the position ofthe focal plane in the y direction and thus control the as-tigmatic difference z0 . The astigmatically shaped beamis focused by a long working distance microscope objec-tive; two different objectives were used, either a 20x (nu-merical aperture NA 5 0.3, focal length f 5 10 mm) or a50x (numerical aperture NA 5 0.6, focal length f5 4 mm). Typically, the focus is located ;200 mm belowthe surface of the sample, to minimize aberrations of thefocused beam by the glass path. The samples are movedperpendicularly to the beam propagation direction by aprecision translation stage (Physik Instrumente modelM-155.11); in these experiments, the samples were trans-lated at a speed of the order of 20 mm/s.
Waveguides were written in phosphate glass bases (Ki-gre, Inc.) doped with Er (1.1 3 1020 ions/cm3 concentra-tion) and Yb (1.5 3 1021 ions/cm3 concentration), result-ing in absorption coefficients of 15 dB/cm at 976 nm and 2dB/cm at 1534 nm. At first, waveguides were writtenwith the 20x objective with a circular beam, focused to aradius of w0 5 3 mm at the waist; a microscope image ofthe exit face of the waveguide is shown in Fig. 5(a). Thewaveguides show a strongly elliptical cross section ex-tending over 70 mm along the z direction and only 5 mmalong the y direction.17,18 This is in agreement withsimulations presented in Fig. 5(b). Next, we inserted thecylindrical telescope, decreasing the spot size in the y di-rection by a factor of 3. A variation of 1 mm in the tele-
Fig. 4. Schematic of the waveguide writing setup.
Fig. 5. (a) Optical microscope image of the exit face of a wave-guide written with a circularly symmetric beam (w0 5 3 mm).(b) Simulated electron-density profile for the same focusing con-ditions (see text for simulation parameters).
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scope lenses’ distance resulted in a 40-mm variation of theastigmatic difference. Figure 6 shows, in its left panel, aseries of microscope images of the exit faces of waveguideswritten with increasing values of z0 : As expected, in-creasing z0 , the asymmetry of the waveguide cross sec-tion changes. Indeed, it increases in the y direction whilekeeping the z size nearly constant. Initially, the wave-guide cross section is elongated along the z direction; thenit becomes symmetric, and, by further increasing z0 , itbecomes elongated along the y direction. The right panelof Fig. 6 shows simulated electron-density profiles for fo-cusing conditions corresponding to the experiments (spotsizes w0x 5 1.2 mm, w0y 5 3.6 mm); we can see an excel-
Fig. 6. Left column: optical microscope images of the exit faceof waveguides written with a focused astigmatic beam (w0x5 1.2 mm, w0y 5 3.6 mm) for increasing values of the astig-matic difference z0 . Right column: corresponding simulatedelectron-density profiles.
lent agreement with the experiments, showing that oursimple nonlinear absorption model is able to capture themain features of the waveguide writing process. Notethat in the experimental results the waveguide size alongthe z direction decreases for increasing z0 values; this canbe explained by considering that, by increasing z0 , we re-duce, for a given pulse energy, the peak intensity in thefocus; experimentally, we tried to compensate for this byincreasing the pulse energy; however, a different peak in-tensity can explain the variation of the waveguide sizealso in the z direction. With these focusing conditionsand an energy of 5 mJ, it was possible to obtain symmetricwaveguides with an 18-mm diameter (with z0 5 180 mm).Figure 7(a) shows an image of one of these waveguides inthe xy plane; the corresponding image of the exit face isshown in Fig. 7(b). It is worth noting that pulse energyis a critical fabrication parameter. As an example, animage of a waveguide written under identical focusingconditions but with a higher energy (10 mJ), clearly indi-cating optical damage, is shown for comparison in Fig. 8.
To obtain a smaller waveguide cross section, we usedthe 50x objective and decreased the beam-spot size beforethe cylindrical telescope; in this way, we obtained a fo-cused beam-spot size of w0y 5 2.85 mm and w0x5 0.95 mm, thus decreasing the Rayleigh range and thewaveguide dimension along the z axis; suitable adjust-ment of the astigmatic difference allowed obtaining asymmetric waveguide with smaller size. Figure 9(a)shows an image of the exit face of such a waveguide (withz0 5 80 mm), with 8-mm diameter, together with a simu-lated electron-density profile [Fig. 9(b)].
B. Active Waveguide CharacterizationThe refractive-index changes Dn in the waveguides wereestimated following the method proposed in Ref. 8, inwhich the refractive-index change was related to the nu-merical aperture (NA) of the waveguide by the expression(valid for a step-index waveguide) NA 5 A2nDn. Tomeasure the waveguide NA, we observed, on a screen inthe far field, the interference fringes between light from aHe–Ne laser coupled out of the waveguide and the un-coupled light diverging from the entrance face. Providedthe NA of the coupling lens is greater than that of thewaveguide, the radius at which the fringes fade gives ameasurement of the NA of the waveguide. Typical re-sults of this measurement are Dn 5 2 –3 3 1023, in goodagreement with measurements reported in theliterature.8,19
To test the waveguide performance, we coupled light atthe wavelengths of 0.633 mm and 1.5 mm. The wave-guide shown in Fig. 5, written with a circularly symmetricbeam, was, at 0.633 mm, highly multimode along the z di-rection and single mode along the y direction, while at 1.5mm it was below cut-off. The waveguides written by theastigmatic techniques (Figs. 6 and 9) supported, at 0.633mm, higher-order modes with circular symmetry, andwere found to be single-mode at 1.5 mm. The mode pro-file at 1.58 mm, measured with a Vidicon camera(Hamamatsu C2400), is shown in Fig. 10. A fit with a
Osellame et al. Vol. 20, No. 7 /July 2003 /J. Opt. Soc. Am. B 1565
Fig. 7. Optical microscope image, in the xy and yz planes, of a waveguide written by a focused astigmatic beam (w0x5 1.2 mm, w0y 5 3.6 mm, z0 5 180 mm) with pulse energies of 5 mJ.
Fig. 8. Optical microscope image, in the xy plane, of a waveguide written by a focused astigmatic beam (w0x5 1.2 mm, w0y 5 3.6 mm, z0 5 180 mm) with pulse energies of 10 mJ. Note the damaged track obtained with the high pulse energy.
Gaussian profile, also shown in Fig. 10, gave a mode waistof radius 10 mm for the 18-mm-diameter waveguide and acomparable mode waist for the 8-mm-diameter wave-guide. The mode waist did not scale with the waveguidedimension as we were expecting. The reason is therather low index change. In fact, for small waveguide di-ameter, the guided mode fast approaches the cut-off con-dition, thus being less confined in the waveguide region.Therefore to achieve a waveguide with the same diameterof a fiber and with the same mode waist, it is necessary toincrease the index change by about one order of magni-tude. The waveguide propagation losses were measuredby coupling the waveguides to standard single-mode tele-communication fibers (mode diameter of 8–10 mm) at thewavelength of 1.58 mm, outside the Er absorption band,and collecting the output light by a high-NA microscopeobjective. After subtracting the Fresnel reflections, wemeasured in both waveguides a total loss of 3 dB for apropagation length of 25 mm; this loss includes the fiber–waveguide coupling losses and the propagation losses.The coupling losses can be evaluated by calculation of theoverlap integral between the mode profiles of the wave-guide and of the coupling fiber, giving a value of 2–2.4 dB.The propagation losses can be determined, by subtraction,to be 0.6–1 dB, corresponding to 0.25–0.4 dB/cm.
The gain properties of the waveguides were character-ized in a standard optical amplifier configuration. Weused a dual-pumping configuration with two GaAlAs laserdiodes at 980 and 976 nm, providing up to 240-mW totalpump power. A tunable laser with an in-line variable at-tenuator generated a seed signal spanning the 1520–1580-nm wavelength interval; the signal power was keptconstant at 230 dBm. Pump and signal were multi-plexed by wavelength division multiplexers, and the out-put Flexcore single-mode fibers were butt coupled to thewaveguides with index-matching fluid. We tested twodifferent waveguides, with 25- and 9-mm lengths, respec-
tively. Results for the longer waveguide have alreadybeen reported in Ref. 24. A peak enhancement of 3.9 dBat the wavelength of 1534 nm has been obtained, which isinsufficient to compensate for the absorption of 5.5 dB; atwavelengths longer than 1550 nm, however, due to theredshift of the emission with respect to the absorptionspectrum, the waveguide exhibits a net internal gain ofup to 0.7 dB. This result is attributed to the very high Ybconcentration of the substrate, resulting in a strong ab-sorption of the pump light, so that only a path length ,1cm is inverted. The performance of the shorter wave-guide is reported in Fig. 11. The measured absorption ofthe unpumped waveguide is shown as circles, togetherwith an absorption spectrum (solid curve) calculated withthe nominal Er concentration and assuming the absorp-tion cross-section values reported in Ref. 25; the peak ab-sorption, scaling with the waveguide length, is now 2 dB.The gain of the pumped waveguide versus probe signal
Fig. 9. (a) Optical microscope image of the exit face of a wave-guide written by a focused astigmatic beam (w0x5 0.95 mm, w0y 5 2.85 mm, z0 5 80 mm). (b) Simulatedelectron-density profile for the same focusing conditions.
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wavelength is shown in Fig. 11 as squares, together withthe theoretical curve (dashed curve), obtained assumingthat 75% of the Er population is inverted. In this case,we were able to demonstrate internal gain over the wholeC band and with a peak gain of 1.4 dB. Achievement ofsubstantially higher gains should be possible by use of op-timized substrates, in which the Yb concentration is re-duced and the Er concentration is increased. We stressonce again that these results have been obtained by buttcoupling the waveguides with standard single-mode tele-com fibers, without use of any optimized coupling optics.
4. CONCLUSIONSIn this paper, we have demonstrated a novel technique forwaveguide fabrication by femtosecond laser pulses, basedon astigmatic shaping of the writing beam. This tech-nique removes one of the major drawbacks of the trans-verse writing geometry with low-frequency lasers, i.e., theintrinsic waveguide asymmetry. By reducing the beam-
Fig. 10. Experimental contour plot and intensity profiles in thehorizontal and vertical directions of the fundamental guidedmode at 1.58 mm for the 18-mm-diameter waveguide.
Fig. 11. Measured absorption (circles) and gain (squares) in a9-mm Er–Yb-doped waveguide. Curves are fits with the knownabsorption and emission cross sections.
waist dimension in the direction along which the beam istranslated and simultaneously offsetting the positions ofthe two waists, it is possible to obtain waveguides with asymmetric profile of variable size. This is particularlyimportant for the manufacturing of single-modewaveguides at the optical communication wavelength of1.5 mm, which can be efficiently coupled to standard opti-cal fibers. We have applied this technique to waveguidewriting in active Er–Yb-doped glass substrates and dem-onstrated a gain of 1.4 dB in a 9-mm-long waveguide.The achievement of higher gains in a longer waveguidewas prevented by the high Yb concentration, resulting inextremely short absorption lengths of a few millimeters.By use of substrates with reduced Yb doping and/or de-tuned pump diodes, it should be possible to invertwaveguides of a few centimeters length (note that thetransverse writing geometry does not pose any limitationon the waveguide length) and thus achieve substantiallyhigher gains, allowing the production of waveguide ampli-fiers and lasers. In our system, the wavelength writingspeed was limited to ;20 mm/s by the low repetition rateof the laser (1 kHz); however, the energies required forthe writing process (of the order of 1 mJ) can be easily ob-tained by cw pumped regenerative amplifiers, working ata repetition rate of up to 200 kHz.26 With these sources,the waveguide writing speed can be significantly in-creased, making the process interesting for industrial ap-plications. An additional point worth investigating is themaximum refractive-index change Dn induced by thefemtosecond laser pulse and its dependence on the glassmatrix composition. While our focusing technique allowsa full control on the waveguide size, the value of Dn de-pends on the substrate material. A more complete un-derstanding of the physical processes following the non-linear absorption and giving rise to the refractive-indexchange is indeed necessary in order to control also thisimportant parameter and to manufacture waveguideswith optimum performance in standard telecom setups.
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