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Designer femtosecond pulse shaping using grating-engineered quasi-phase-matching in lithium niobate Łukasz Kornaszewski,1,* Markus Kohler,1 Usman K. Sapaev,2 and Derryck T. Reid1 1
Ultrafast Optics Group, School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK 2 NPO Akadempribor, Academy of Sciences of Uzbekistan, Tashkent 700125, Uzbekistan *Corresponding author:
[email protected]
Received November 21, 2007; revised January 10, 2008; accepted January 10, 2008; posted January 18, 2008 (Doc. ID 90032); published February 14, 2008 The generation of tailored femtosecond pulses with fully engineered intensity and phase profiles is demonstrated using second-harmonic generation of an Er:fiber laser in an aperiodically poled lithium niobate crystal in the undepleted pump regime. Second-harmonic pulse shapes, including Gaussian, stepped, square, and multiple pulses have been characterized using cross-correlation frequency-resolved optical gating and have been shown to agree well with theory. © 2008 Optical Society of America OCIS codes: 190.2620, 190.4400, 320.5540.
A prerequisite for designer pulse shaping is the ability to independently manipulate the spectral intensity and phase of an optical waveform. One class of shaping technique uses optoelectronic modulation, such as adaptive optics [1,2] or an acousto-optic dispersive filter [3], to actively shape pulses in a programmable fashion. Alternatively, passive devices, such as superstructured fiber-Bragg gratings [4] or dispersion-managed optical fiber lines [5], can be used to modify the amplitude and phase of an ultrashort pulse according to a design determined by the physical structure of the device. Pulse shaping using aperiodically poled quasi-phase-matched (QPM) crystals falls into this second category, and such crystals have already produced compressed [6] and shaped multipicosecond-duration pulses [7] by second-harmonic generation (SHG) and have been applied to increase the bandwidth and reduce the threshold in a femtosecond optical parametric oscillator [8]. This concept can be extended to shape individual femtosecond pulses by exercising suitable control over the local duty cycle and the period within a QPM grating. In this way, one can control the amplitude and phase of the second-harmonic (SH) pulses, and in a previous work we introduced an algorithm for designing suitable QPM gratings [9,10]. We now present the first experimental validation of this approach, in which we have created tailored femtosecond pulses by frequency doubling a 1530 nm Er:fiber laser. This work differs from previous studies of aperiodically poled lithium niobate (APPLN) pulse shaping, which freely modulated the grating period but used only binary modulation of the grating duty cycle [7]. This approach is successful for creating shaped pulses that are significantly longer than the fundamental pulses, but it is not optimal for creating SH pulses with durations comparable with those of the input pulses. In the present study the created pulses are similar in duration to the fundamental pulses; therefore the domain duty cycle is a key shaping parameter that must be fully controlled. The previous 0146-9592/08/040378-3/$15.00
work of Imeshev et al. [7] operated in the limit of a crystal length that significantly exceeded the groupvelocity walkaway length between the fundamental and SH pulses. In such a regime the crystal bandwidth is enhanced by the aperiodic poling so that it significantly exceeds the intrinsic crystal bandwidth, or 2共n1 − n2兲⌬⌳G Ⰷ
12
冉
1
1
2cL vg2
−
vg1
冊
−1
共1兲
,
where vg, , and n designate, respectively, the group velocity, the wavelength, and the refractive index of wave 1 (fundamental) and wave 2 (SH). The crystal length is L, and the grating period variation is ⌬⌳G. Because the variation in the period is distributed along the crystal length, in this regime there is a slowly varying spatial localization of the conversion that dominates the pulse shaping, because it allows conversion across a broader bandwidth than in an unchirped crystal of the same length. Our earlier work [9,10] described a theoretical model containing a crystal transfer function that took account of each domain size and its position in the crystal, evaluated using the analytical formula [9,10] ECRYS共兲 = −
dijk ⌬k共兲
再
1 − 共− 1兲n exp关i⌬k共兲Qn兴
n−1
+
兺 2共− 1兲m exp关i⌬k共兲Qm兴
m=1
冎
,
共2兲
where is −SHG / cnSHG, dijk is the absolute value of the nonlinear coefficient, ⌬k共兲 is the magnitude of the frequency-dependent wave-vector mismatch in the process, and Qm is the end position of domain m in the grating that contains a total of n domains, as described in [9]. Using the crystal transfer function it is straightforward to calculate the SH pulse, EOUT共t兲, generated from an input pulse, EIN共t兲, by a grating whose transfer function is given by ECRYS共兲 [11] © 2008 Optical Society of America
February 15, 2008 / Vol. 33, No. 4 / OPTICS LETTERS 2 EOUT共t兲 = F−1兵F关EIN 共t兲兴ECRYS共兲其,
379
共3兲
where F and F−1 are the direct and inverse Fouriertransform operators, respectively. Following the procedure outlined in [10] we used a simulated annealing algorithm to find the appropriate grating designs for nine different target SH pulses. The design assumed an unchirped 150 fs Gaussian fundamental pulse that was spectrally centered at 1530 nm and that was similar but not identical to the actual pulses used in the experiment. The design process proceeded by defining a target SH pulse in terms of its polarization-gated frequencyresolved optical gating (FROG) trace, which is a real, two-dimensional function that uniquely represents the pulse in the time-frequency domain. We used Eqs. (2) and (3) to find the SH pulse produced by an initial guess for a grating Q and, by calculating the rms difference between its FROG trace and that of the target pulse, we derived an error value. This error was minimized by making random changes to Q and repeating the process until the FROG traces of the target and calculated pulses were identical. A single, 4 mm long, APPLN crystal containing parallel domain patterns corresponding to the nine target designs was obtained commercially. The fabricated designs used the gratings calculated in [10] and a lithographic process with a tolerance of 50 nm to create the poling mask. For details of the domain patterns we refer the reader to [10]. The laser used for the experiments was an Er:fiber oscillator, delivering 40 mW of average power (measured at the crystal) and with a non-Gaussian spectral profile. The crystal transfer functions corresponding to the nine target designs are shown in Fig. 1, together with their correspondence with the laser spectrum. The experimental arrangement is shown in Fig. 2, and the inset shows the target designs based on the original assumption of 150 fs Gaussian input pulses. The positions and lengths of the fabricated gratings
Fig. 1. Input pulse spectrum (dotted gray curve and lowerwavelength axis) and the crystal transfer functions, ECRYS共兲 (solid black curve and upper-wavelength axis) for the nine gratings used in the experiment. The results for gratings 1–9 are presented in (a)–(i), respectively.
Fig. 2. Experimental configuration. Pulses from the Er:fiber oscillator are compressed and then focused into the APPLN crystal, where the second-harmonic light is generated. After collimation, the second-harmonic (SH) and the fundamental wave (FW) light enter an XFROG apparatus. A dichroic mirror (DM) that is highly reflecting at 765 nm and highly transmitting at 1530 nm forms the interferometer, and the nonlinear mixing occurs in a 100 m-thick BBO crystal. FW⫹SH denotes the sum-frequency beam resulting from nonlinear mixing in the BBO crystal. L1 and L2 are lenses with focal lengths of 100 mm and 15 mm, respectively. Inset; schematic of the APPLN crystal, and the target SH profiles designed assuming 150 fs Gaussian input pulses.
are illustrated in Fig. 2 and correspond to SHG designs of short and long Gaussian pulses (1, 2), stepped and square pulses (3, 4), triangular pulses (5), identical but oppositely chirped pulses (6, 7), and double (8) and triple (9) pulses, as detailed in [10]. Before the crystal, the pulses from the Er:fiber laser were compressed to their minimum duration using a double pass of a silicon-prism dispersive delay line. Instead of optimal tight focusing we used a 10 cm focal-length lens to provide uniform illumination intensity along the crystal length so that every domain in the crystal experienced the same local intensity, and this was verified by ensuring that the crosscorrelation trace between the fundamental and SH pulses was invariant under axial translation of the crystal. The use of loose focusing also allowed us to avoid possible noncollinear phase-matching, which would change the transfer characteristics of the crystal. Using a Michelson interferometer we mixed the fundamental and SH pulses in a thin BBO crystal and recorded the delay-resolved sum-frequencymixing light on a spectrometer to record a crosscorrelation FROG (XFROG) trace. Retrieved results are shown as solid curves (intensity) and open circles (phase) in Fig. 3. The XFROG traces indicated qualitative agreement between experiment and theory, but to allow a quantitative comparison we used Eq. (2), along with the complex field amplitude of the Er:fiber pulses determined from the XFROG measurements, to evaluate the expected SH pulse shapes. The dotted curve in Fig. 3 represents the pulse intensity calculated using this procedure, and the filled circles represent the corresponding phase. The agreement between the experimental and calculated SHG pulses is generally good, in terms of both their amplitude and their phase. For shorter grating designs, particularly gratings 1 and 2, there is a significant error between the observed pulses and
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Fig. 3. XFROG measurements of the second-harmonic pulses (solid thick curve, intensity; open circles, phase) and a comparison with the shapes calculated using the fundamental pulses (dotted thin curve, intensity; filled circles, phase), also determined by XFROG. The results for gratings 1–9 are presented in (a)–(i), respectively.
those expected from theory, despite the bandwidth of the fundamental pulses being sufficient. This might be expected, because any local duty-cycle errors due to domain-boundary diffusion have a greater influence for a shorter grating, because fewer domains contribute to the overall crystal response. In particular, experience from poling uniform gratings shows that a 50:50 duty cycle is normally obtained only for one particular grating period because of the way the domain walls propagate during the poling process. It is therefore challenging to fabricate designs, such as those studied in this paper, whose local period and duty cycle are both modulated. Longer crystals are not affected as seriously by domain-boundary diffusion, because the shaping is influenced by a greater number of domains, so there is greater resilience to random duty-cycle errors in any single grating period. Cumulative phase errors arising from an error in the mean period of the grating would have a more serious impact on longer crystals; however, these do not occur, because the lithographic mask defines the center position of each domain precisely [12]. A different source of error arises because the spectrum of the fundamental pulses used in the experiment was strongly modulated, and therefore the shape of the generated pulses depended sensitively on the precise
spectral alignment between the fundamental spectrum and the crystal transfer function ECRYS共兲. In this work we had no way of directly measuring the crystal transfer function; therefore the center of the function was assumed to be correct on the basis of the available Sellmeier equations for lithium niobate. Small changes in the crystal temperature or angle could detune the transfer function sufficiently to modify the shapes of the SH pulses. In conclusion, the use of fully grating-engineered crystals for femtosecond pulse shaping is a simple and robust alternative to a more-complex adaptiveoptics system, and these results show the potential of the technique to fully manipulate the shapes of individual femtosecond pulses within the limits of the available optical bandwidth. Extension of the technique to the high-depletion regime will widen its applicability. The authors wish to acknowledge the UK Engineering and Physical Sciences Research Council for its support of this work in the form of research studentship funding. U. K. Sapaev acknowledges support from the Royal Society and NATO. References 1. A. M. Weiner, D. E. Leaird, J. S. Patel, and J. R. Wullert, IEEE J. Quantum Electron. QE-28, 908 (1992). 2. E. Zeek, K. Maginnis, S. Backus, U. Russek, M. Murnane, G. Mourou, H. Kapteyn, and G. Vdovin, Opt. Lett. 24, 493 (1999). 3. F. Verluise, V. Laude, Z. Cheng, C. Spielmann, and P. Tournois, Opt. Lett. 25, 575 (2000). 4. P. Petropoulos, M. Ibsen, A. D. Ellis, and D. J. Richardson, J. Lightwave Technol. 19, 746 (2001). 5. S. K. Turitsyn, V. K. Mezentsev, and E. G. Shapiro, Opt. Fiber Technol. 4, 384 (1998). 6. M. A. Arbore, A. Galvanauskas, D. Harter, M. H. Chou, and M. M. Fejer, Opt. Lett. 22, 1341 (1997). 7. G. Imeshev, A. Galvanauskas, D. Harter, M. A. Arbore, M. Proctor, and M. M. Fejer, Opt. Lett. 23, 864 (1998). 8. K. A. Tillman, D. T. Reid, D. Artigas, J. Hellström, V. Pasiskevicius, and F. Laurell, Opt. Lett. 28, 543 (2003). 9. D. T. Reid, J. Opt. A: Pure Appl. Opt. 5, S97 (2003). 10. U. K. Sapaev and D. T. Reid, Opt. Express 13, 3264 (2005). 11. M. A. Arbore, O. Marco, and M. M. Fejer, Opt. Lett. 22, 865 (1997). 12. L. E. Myers, in Advances in Lasers and Applications, D. M. Finlayson and B. D. Sinclair, eds. (Institute of Physics Publishing, 1999), pp. 141–180.
