Frequency-tunable supercontinuum generation in photonic-crystal ...

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J. Opt. Soc. Am. B / Vol. 19, No. 9 / September 2002

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Frequency-tunable supercontinuum generation in photonic-crystal fibers by femtosecond pulses of an optical parametric amplifier Andrei B. Fedotov, Aleksandr N. Naumov, and Aleksei M. Zheltikov Physics Department, International Laser Center, M. V. Lomonosov Moscow State University, 119899 Moscow, Russia

Ignac Bugar, Dusan Chorvat, Jr., and Dusan Chorvat International Laser Center, Ilkovicˇova 3, 81219 Bratislava, Slovak Republic

Alexander P. Tarasevitch and Dietrich von der Linde Institut fu¨r Laser- und Plasmaphysik, Universita¨t Essen, D-45117 Essen, Germany Received November 30, 2001; revised manuscript received March 29, 2002; accepted March 29, 2002 Supercontinuum emission is generated by the propagation of frequency-tunable femtosecond pulses of 1.1– 1.5-␮m radiation of an optical parametric amplifier through a photonic-crystal fiber. Nearly an octave’s spectral broadening was observed when laser pulses with a duration of 80–100 fs and an energy of several nanojoules per pulse were coupled into a photonic-crystal fiber with a core radius of 1.5–3 ␮m. The spectral broadening of femtosecond pulses at 1.1–1.5 ␮m is shown to be much more efficient than the spectral broadening of femtosecond pulses of 800-nm Ti:sapphire laser radiation. The role of dispersion in spectral broadening and supercontinuum generation is discussed. In experiments on supercontinuum generation with an optical parametric amplifier, the influence of dispersion effects was reduced by decreasing the size of the fiber core, which allowed the efficiency of supercontinuum generation to be improved without increasing the laser intensity. © 2002 Optical Society of America OCIS codes: 190.2640, 190.4370.

1. INTRODUCTION Supercontinuum generation has long been used as a convenient experimental technique for producing broadband radiation for various spectroscopic applications, as well as pump–probe measurements.1 It was demonstrated recently2,3 that the light intensities needed to generate a supercontinuum can be substantially lowered by use of photonic-crystal fibers4–15 (PCFs) (also called more generally microstructure or holey fibers) and tapered fibers.3 Physically, the capability of PCFs and tapered fibers to enhance nonlinear optical processes is due to the high degree of light localization in the cores of such fibers, permitting high intensities of laser radiation to be achieved with relatively low-energy laser pulses. Few-nanojoule and even subnanojoule femtosecond pulses lead to supercontinuum generation2,3,16 under these conditions, giving rise to emission spectra sometimes spanning more than two octaves. This result already resulted in a major breakthrough in optical metrology,17–22 allowing the creation of compact frequency chains that phase coherently link rf reference sources to the optical region through frequency combs generated by femtosecond mode-locked lasers. The function of PCFs in these metrological systems is to broaden femtosecond frequency combs spectrally, making them span more than an octave and allowing the 0740-3224/2002/092156-09$15.00

offset frequency related to intracavity dispersion to be measured and controlled. Supercontinuum generation in holey and tapered fibers also offers a way to create new broadband sources for spectroscopic applications and suggests a new approach to pulse compression.6 In general, the possibility of tuning and tailoring the dispersion of waveguide modes that is offered by PCFs2,6,14,23 makes these fibers extremely useful for ultrafast optics, including the transmission of short pulses, frequency conversion (e.g., through efficient harmonic generation9,24,25), compression, and spectral control of ultrashort laser pulses and even opening the way for subfemtosecond fiber optics. Application of such fibers in telecommunication technologies6,9 is another very important topic that is being actively explored at the moment. Until recently, most of the nonlinear optical experiments with holey and tapered fibers, including supercontinuum generation and high-precision measurements with femtosecond frequency combs, were performed with Ti:sapphire laser pulses. At the same time the extension of new concepts in ultrafast optics and optical metrology based on the use of PCFs to longer wavelengths seems to be quite promising for biomedical applications and highprecision measurements. The first experiments with a © 2002 Optical Society of America

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femtosecond Cr:forsterite laser recently demonstrated two-octave spectral broadening of subnanojoule femtosecond pulses of 1.25-␮m radiation in tapered fibers,16 as well as the generation of cross-phase-modulated third harmonics in a PCF.25 In this paper, we use a frequency-tunable laser source—an optical parametric amplifier (OPA)— generating radiation within the range of wavelengths from 1.1 to 1.5 ␮m to observe spectral broadening and supercontinuum generation with low-energy femtosecond pulses. Comparison of the results of these experiments with the properties of spectral broadening of femtosecond Ti:sapphire laser pulses reveals important aspects that are related to the role of dispersion effects. The influence of dispersion in supercontinuum generation, as shown by the results of our measurements with OPA femtosecond pulses, can be reduced by one’s decreasing the core radius of the PCF. The plan of this paper is as follows: In Section 2, we provide a qualitative analysis of light localization and dispersion in a PCF by using an approximate approach based on the scalar wave equation for the field distribution in a circular unit cell with symmetric boundary conditions. Our experimental system and microstructurefiber samples are described in Section 3. The results of experiments on supercontinuum generation with the use of frequency-tunable OPA femtosecond pulses are discussed in Section 4. The main conclusions are briefly summarized in Section 5.

2. PHYSICS BEHIND SUPERCONTINUUM GENERATION IN PHOTONIC-CRYSTAL FIBERS A. Light Confinement Supercontinuum generation generally involves a rather complicated combination of nonlinear optical processes, such as four-wave mixing, self- and cross-phase modulation, stimulated Raman scattering, and others. The efficiency of supercontinuum generation can therefore be improved by the enhancement of all the nonlinear optical interactions contributing to this process. The general idea of using PCFs for this purpose is based on the possibility of increasing the degree of light localization in the fiber core by one’s changing the geometry of the fiber cladding.26,27 This change would allow nonlinear optical interactions to be enhanced without increasing the energy of light pulses. The effective size of a waveguide mode in an optical fiber depends on the difference between the refractive indices of the fiber and the cladding and can roughly be described by use of the formula26,28 a ⫽ w ⫹ ␭/ 关 2 ␲ 冑n c 2 cos ␾ ⫺ neff2)], where w is the fibercore radius, ␭ is the radiation wavelength, n c is the refractive index of the fiber core, ␾ is the incidence angle characterizing the mode in the core of the fiber, and n eff is the effective refractive index of the cladding. Rigorously speaking, this formula is applicable for standard, stepindex fibers. However, it also provides, as is shown in Refs. 26 and 27, a qualitative understanding of the increase in the light-localization degree in microstructure

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Fig. 1. Effective area of the fundamental mode of a PCF with an air-filling fraction of 16% and core radii of curve 1: 1.5 ␮m; curve 2: 2 ␮m; and curve 3: 3 ␮m plotted as functions of the radiation wavelength. The pitch of the cladding is equal to the core radius.

fibers when the effective refractive index is introduced as n eff ⫽ ␤cl /k, where ␤ cl is the propagation constant of the fundamental space-filling mode, i.e., the fundamental mode of an infinite structure obtained by the periodic translation of a unit cell of the PCF cladding. Following the method of analysis proposed by Birks et al.,5 we found an estimate for ␤ cl by solving the scalar wave equation for the field distribution ␺ (Ref. 28) in a circular unit cell with symmetric boundary conditions ⳵ ␺ / ⳵ s ⫽ 0, where s is the coordinate along the axis oriented in the direction perpendicular to the boundary of the unit cell. This field distribution can be expressed in terms of zeroth-order Bessel functions. The abovespecified boundary condition supplemented with the continuity conditions for ␺ and ⳵ ␺ / ⳵ s on the glass–air interface gives the characteristic equation for ␤ cl . Figure 1 displays the effective area of the fundamental mode in a PCF with an air-filling fraction of 16% plotted as a function of radiation wavelength for different values of the fiber-core radius. Dependencies presented in Fig. 1 provide a qualitative understanding of how nonlinear optical processes can be enhanced by one’s increasing the degree of light localization in a PCF and show the ways of optimizing the parameters of microstructure fibers for nonlinear optical experiments. The possibility of improving the efficiency of the spectral broadening of femtosecond pulses in PCFs by an increase in the air-filling fraction of the cladding was experimentally demonstrated in Ref. 26.

B. Dispersion of Photonic-Crystal Fibers Supercontinuum generation, as mentioned above, is often a result of the joint action of many nonlinear optical processes involving the generation of new spectral components and spectral broadening of these components. The efficiencies of these processes are highly sensitive to the dispersion of the nonlinear medium, which gives rise to the phase mismatch of different spectral components and leads to group-delay and pulse-spreading effects. The possibility of tailoring the dispersion of PCFs by means of changing their structure is, therefore, another important

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and very useful property of these fibers that offers much promise for the enhancement of nonlinear optical interactions. To assess the dispersion properties of the PCFs used in our experiments, we employed, similar to the approach described in Subsection 2.A, standard expressions for the dispersion of a step-index fiber, replacing the propagation constant for the fiber cladding in these expressions by the propagation constant ␤ cl found by the solution of the scalar wave equation for the field distribution ␺ in a circular unit cell with symmetric boundary conditions (see Subsection 2.A). Figure 2 shows the group index calculated by use of this procedure plotted as a function of the wavelength for PCFs with fiber-core radii equal to 1.5, 2, and 3 ␮m (fibers with these core radii were employed in our experiments; see Section 3 below). The decrease in the fiber-core radius, as can be seen from Figs. 2 and 3, increases the influence of waveguide dispersion. In particular, zero group-velocity dispersion can be achieved in the area of 1.3–1.5 ␮m, depending on the fiber-core diameter. It can also be seen from Fig. 2 that the groupvelocity dispersion for Ti:sapphire laser pulses is much higher in our case than for radiation within the wavelength range of 1.1–1.5 ␮m, which is typical of a femtosecond OPA (see Section 3 below). The dispersion length l d estimated for 100-fs pulses of 1.25-␮m radiation propagating in a PCF with a core radius of 1.5 ␮m (l d ⬇ 50 cm) is approximately 5 times larger than the dispersion length for 100-fs pulses of 0.8-␮m radiation, with zero group-velocity dispersion achieved at a wavelength of approximately 1.5 ␮m for such a fiber. This observation may be crucial for understanding why femtosecond pulses of 1.1–1.5-␮m radiation, produced in our experiments by an OPA, resulted in much more efficient spectral broadening than did Ti:sapphire laser pulses (see Section 4 below). Because the superbroadening of femtosecond pulses involves the generation of new frequency components and nonlinear optical interactions between these components, group-delay effects for these spectral components may become an important factor, influencing the efficiency of supercontinuum generation. Figure 3 shows the spectral

Fig. 2. Group index plotted as a function of the radiation wavelength for the fundamental mode of a PCF with an air-filling fraction of 16% and the core radii of curve 1: 1.5 ␮m; curve 2: 2 ␮m; and curve 3: 3 ␮m. The pitch of the cladding is equal to the core radius.

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Fig. 3. Spectral dependence of the walk-off length L w of 100-fs light pulses with the wavelength ␭ with respect to 100-fs light pulses with a wavelength of 1.2 ␮m in a PCF with an air-filling fraction of 16% and the core radii of curve 1: 1.5 ␮m; curve 2: 2 ␮m; and curve 3: 3 ␮m. The pitch of the cladding is equal to the core radius.

dependence of the walk-off length (i.e., the length at which the temporal separation of light pulses becomes approximately equal to the pulse duration) for 100-fs light pulses with a wavelength ␭ with respect to 100-fs light pulses with a wavelength of 1.2 ␮m. The walk-off length can be increased quite substantially, as can be seen from this figure, by a reduction of the fiber-core radius from 3 to 1.5 ␮m. We should expect an improvement in the efficiency of supercontinuum generation under these conditions. This expectation is verified by our experiments (see Section 4 below), which demonstrate that the efficiency of spectral superbroadening of femtosecond pulses in PCFs increases as the core radius of the fiber decreases from 3.0 to 1.5 ␮m.

3. EXPERIMENTS Spectral broadening and supercontinuum generation in PCFs were studied in our experiments by use of two laser systems—a Ti:sapphire laser and an OPA. The Ti:sapphire laser system was employed to investigate the influence of the structure of a PCF on the efficiency of selfphase modulation in the fiber core. The OPA system included its own, independent Ti:sapphire pump laser and allowed us to generate frequency-tunable supercontinuum radiation by the propagation of femtosecond OPA pulses through a PCF. Although many properties of spectral broadening of femtosecond Ti:sapphire laser pulses were explored in detail in earlier investigations,26,27 the use of an OPA allowed us to add frequency-tunability aspects to the numerous advantages of supercontinuum generation in PCFs. The Ti:sapphire laser consisted of an oscillator and a multipass amplifier (MPA) pumped by a pulsed Nd:YAG laser. Light pulses produced by this laser at a repetition rate of 1 kHz had a duration of 70 fs. The energy of these pulses may be as high as 1 mJ, but we never used more than 1 ␮J of this energy in our experiments. The frequency-tunable femtosecond laser system (Fig. 4) included a Ti:sapphire master oscillator, a MPA, and an

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OPA. The Ti:sapphire master oscillator was pumped with a Coherent Model Verdi diode-pumped Nd:YAG laser. The master oscillator generated 50-fs pulses of 800-nm radiation with an average power of 250 mW that were amplified in a Nd:YAG-pumped MPA. Laser pulses of 800-nm radiation coming out of this MPA had a duration of approximately 80 fs, energy of as high as 0.2 mJ/ pulse, and a repetition rate of 1 kHz. These pulses were used to pump an OPA based on a BBO crystal. Part of the pump Ti:sapphire laser radiation generates white light in a sapphire plate, while the remaining part of the pump radiation is used to seed the parametricamplification process. An adjustable optical delay line is used to match the optical paths of white-light-generating and seeding pulses. The wavelength of the signal generated as a result of this parametric process is tuned by rotation of the BBO crystal. A double-pass scheme of optical parametric amplification is used to improve the efficiency of parametric frequency conversion, with an additional delay line employed to compensate for groupdelay effects. The signal radiation is selected by use of a dichroic mirror at the output of the OPA system. We were able to tune the wavelength of radiation produced by the OPA within the range of 1.1–1.5 ␮m. The best performance of the OPA system was achieved at a wavelength of 1.25 ␮m from which light pulses with a duration of approximately 80 fs and energy as high as 20 ␮J were produced. To measure the pulse width of near-infrared pulses from the OPA system within the spectral region of 1.10– 1.30 ␮m, we used a single-shot autocorrelator (CDP, Model ASF20). The autocorrelation signal in this autocorrelator originates from the second harmonic generated by two replicas of the laser pulse in a 1-mm-thick BBO crystal. The spatially distributed autocorrelation signal is imaged onto a CCD camera with an active area of 164 ⫻ 192 pixels. A secant approximation of the pulse shape was used to evaluate the pulse width from the results of autocorrelation measurements. The FWHM pulse width was then estimated by the averaging of the

Fig. 4. Frequency-tunable femtosecond system based on an OPA: pump laser; MO1, MO2, micro-objectives.


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results of 10 autocorrelation measurements, yielding pulse widths of 109.8 ⫾ 2.5 fs, 127.1 ⫾ 7.9 fs, 77.4 ⫾ 3.8 fs, and 74.9 ⫾ 2.8 fs at wavelengths of 1140, 1200, 1250, and 1300 nm, respectively. The energy of light pulses coupled into PCFs was varied by use of calibrated neutral-density filters. The laser beam was expanded with a telescope and then focused on the entrance face of a fiber sample, placed on a threedimensional translation stage, with a Zeiss planachromat 20⫻ micro-objective with a numerical aperture of 0.4 (MO1). Because of the filters and the optics that we used, the pulse width of the OPA could be broadened to as many as 100 fs. The efficiency of waveguide mode excitation in a PCF was monitored by the imaging of the light field distribution at the output end of the fiber onto a CCD camera. The details of the technology employed to fabricate the HFs used in our experiments, which was similar to the process developed by Knight et al.,4 were described elsewhere.14 Briefly, the fabrication process involved drawing identical glass capillaries stacked into a periodic preform at an elevated temperature, cutting the resulting structure into segments, and repeating the technological cycle again. This procedure allowed the fabrication of HFs with a cladding pitch ranging from 400 nm to 32 ␮m, as reported in Ref. 14. To analyze the influence of the structure of a PCF on the properties of the spectral broadening of femtosecond laser pulses, we employed several PCF samples with different pitches and air-filling fractions of the cladding and different core diameters (Fig. 5). Although the PCFs shown in Fig. 5(a) have small air holes in the claddings and are characterized by an air-filling fraction f that is equal to approximately 16%, the holes in the PCF cladding shown in Fig. 5(b) are much larger, corresponding to an air-filling fraction f of approximately 65%. The pitch of the cladding and the core diameter of our PCFs were related to each other as a result of the technological process employed to fabricate the fibers (see the details elsewhere, e.g., Ref. 14). PCFs with different pitches and

Ti:S, Ti:sapphire femtosecond master oscillator; Nd:YAG, Nd:YAG

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Fig. 5.


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Cross-sectional images of holey fibers with a cladding pitch equal to 3 ␮m.

core diameters allowed us to explore the influence of dispersion on the spectral broadening of femtosecond pulses. Dispersion effects, as one might expect based on Figs. 2 and 3, a played more and more important role in spectral broadening and supercontinuum generation in our experiments as the core radius of the fiber was increased from 1.5 to 3 ␮m. Radiation coming out of the fiber was collimated with a Zeiss planachromat 10⫻ micro-objective with a numerical aperture of 0.2 (MO2) and focused on the entrance slit of a spectrograph (Fig. 4). The spectra of this radiation were studied with a Model SpectraPro-300i (Acton Research Corp.) spectrograph and a cooled NTE/CCD camera (Roper Scientific). All the spectra were corrected to exclude the transmission of filters that were used to attenuate the radiation coming to the detection system, the spectral dependence of the sensitivity of the CCD camera, and the spectral characteristics of the grating of the spectrometer. In addition, the spectra of Ti:sapphire laser pulses measured at the output of PCFs were normalized to their maximum values.

4. RESULTS AND DISCUSSION A. Spectral Broadening of Ti:Sapphire Laser Pulses To explore the ways of enhancing nonlinear optical processes in a PCF that are due to light confinement in the fiber core, we employed short pieces of PCF samples, typically with a length of l ⫽ 3 cm, to reduce pulse spreading resulting from group-velocity dispersion (the typical dispersion length for 100-fs pulses in a PCF with a core radius of 1.5 ␮m was estimated as l d ⫽ 10 cm). Because the nonlinear lengths L nl characterizing the efficiency of self-phase modulation were less than 0.3 cm for all the experiments presented in this paper, the inequalities L nl Ⰶ l ⬍ l d were satisfied with such a choice of the fibersample length.

The air-filling fraction is (a) 16% and (b) 65%.

The spectra of 70-fs Ti:sapphire laser pulses at the input and the output of a PCF with a length of 3 cm, the pitch of the cladding (equal to 3 ␮m), and the air-filling fraction of f ⫽ 16% are shown in Fig. 6. The bold curve in this figure shows the spectrum of the pulse coming into the fiber. In Fig. 6 the output-pulse spectra are labeled 1–7 and correspond to input-pulse energies of 0.5, 5, 10, 20, 30, 40, and 50 nJ, respectively. The dependence of the spectral broadening ⌬␻ of the pulse coming out of the fiber on the pulse energy coupled into the fiber can be approximated satisfactorily under these conditions by a linear function, as can be seen from Fig. 7. This regime is especially convenient for studying the enhancement of nonlinear optical processes that are due to light confinement in the core of the fiber. This type of enhancement was investigated by comparison of the spectral broadening of femtosecond laser pulses propagated through PCFs with different air-filling fractions of the cladding. Figure 7 presents the spectral broadening of 70-fs pulses of 800-nm Ti:sapphire laser radiation at the output of a 2-␮m-pitch PCF sample with a length of 3 cm and airfilling fractions equal to 65% (dependence 1) and 16% (dependence 2) plotted as a function of the radiation energy coupled into the fiber. The enhancement in the spectralbroadening efficiency can be deduced from the ratio of the slopes of dependences 1 and 2 shown in Fig. 7. Such an estimate yields an enhancement factor of approximately 1.46 in the case of 2-␮m-pitch PCFs. The spectral broadening of femtosecond pulses observed in the above-described experiments performed with Ti:sapphire laser radiation even with long fibers was much less efficient than the spectral broadening achieved in experiments2,21 in which subnanojoule femtosecond pulses were shown to allow supercontinuum generation under certain experimental conditions. One of the essential factors that lowered the efficiency of spectral broadening in our experiments was related to dispersion effects, leading to the temporal walk-off of the pump pulse and the spectral components that were produced through

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pitch size and the core radius of the fiber. The spectra of light pulses coming out of PCFs with an air-filling fraction of 16%, a length of 4 cm, and core radii equal to 1.5, 2, and 3 ␮m, with 1.25-␮m radiation used as a pump, are shown in Figs. 8(a)–8(c). The spectra of output radiation, as can be seen from these figures, become as broad as approximately one octave starting with pulse energies of approximately 3, 8, and 20 nJ for fibers with core radii of 1.5, 2, and 3 ␮m, respectively. Because zero group-velocity dispersion was achieved within the wavelength range of 1.3–1.5 ␮m for our PCFs with core radii of 1.5–3 ␮m, the use of OPA radiation alFig. 6. Spectra of 70-fs Ti:sapphire laser pulses (bold curve) at the input and the output of a holey fiber with a length of 3 cm, a cladding pitch equal to 3 ␮m, and an air-filling fraction of f ⫽ 16% for pulse energies of curve 1: 0.5 nJ; curve 2: 5 nJ; curve 3: 10 nJ; curve 4: 20 nJ; curve 5: 30 nJ; curve 6: 40 nJ; and curve 7: 50 nJ.

Fig. 7. Spectral width ⌬␻ of 70-fs pulses of 800-nm Ti:sapphire laser radiation transmitted through 2-␮m-pitch PCF samples with a length of 3 cm and an air-filling fraction equal to curve 1: 65% and curve 2: 16% plotted as a function of the radiation energy coupled into the fiber.

various nonlinear optical processes. In contrast to experiments performed by Ranka et al.,2 for example, where zero group-velocity dispersion was achieved at approximately 770 nm, our experiments with Ti:sapphire laser radiation were performed in the regime of normal groupvelocity dispersion. A considerable dispersion characteristic of our fiber samples in the spectral range about 800 nm (see Figs. 2 and 3) prevented us from using longer fiber samples and achieving more efficient spectral broadening. Radically higher efficiencies of spectral broadening and supercontinuum generation were achieved with our PCFs for radiation wavelengths lying within the range 1.1–1.5 ␮m covered by our OPA. The results of these experiments are discussed in Subsection 4.B. B. Supercontinuum Generation with Femtosecond Optical Parametric Amplifier Pulses We studied supercontinuum generation in PCFs by using 80–100-fs pulses of 1.1–1.5-␮m radiation produced by a Ti:sapphire laser-pumped optical parametric oscillator. Propagation through PCFs resulted in an octave’s spectral broadening of OPA pulses starting with pulse energies from several to tens of nanojoules, depending on the

Fig. 8. Spectra of laser pulses coming out of PCFs with an airfilling fraction of 16%, a length of 4 cm, and core radii equal to (a) 3, (b) 2, and (c) 1.5 ␮m. OPA pulses with a duration of approximately 80 fs and a wavelength of 1.25 ␮m are coupled into the fiber. The energies of pulses coupled into the fiber are specified near the curves.

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Fig. 9. Spectra of laser pulses coming out of PCFs with an airfilling fraction of 16%, a length of 4 cm, and core radii equal to (a) 1.5 and (b) 2 ␮m. OPA radiation pulses with (a) wavelengths of 1.10 and 1.25 ␮m and energies of 5 nJ and (b) wavelengths of 1.10 and 1.30 ␮m and energies of 8 nJ are coupled into the fiber. The initial duration of light pulses is 80–100 fs.

lowed us to generate supercontinuum in the regimes of both normal and anomalous group-velocity dispersions. This wavelength range is, therefore, very interesting for understanding the possibilities of controlling the properties of a supercontinuum by the tuning of the wavelength of the input pulse with respect to the wavelength corresponding to zero group-velocity dispersion. The results of our studies of supercontinuum parameters as functions of the wavelength of incident radiation are presented below in this subsection. In both normal and anomalous group-velocity dispersion regimes it was possible to precompensate for the dispersion spreading of the pump pulse in the fiber with an appropriate choice of the initial chirp of the pulse. However, variation of the initial chirp also resulted in changes in the initial pulse duration in our experiments, which prevented us from measuring supercontinuum parameters as functions of the initial pulse chirp in a systematic way. Even at the edges of the spectral range covered by our OPA source the dispersion length l d for 80–100-fs pulses propagating through PCFs (approximately 50 cm for a PCF with a core radius of 1.5 ␮m) remained much

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longer than the fiber-sample length l, which, in its turn, was much longer than the nonlinear length L nl characteristic of self-phase modulation (less than 0.3 cm), leading to the following hierarchy of spatial scales: L nl Ⰶ l Ⰶ l d . The characteristic length of shock-wave formation (estimated as L s ⬇ 50 L nl for 0.8-␮m laser pulses and L s ⬇ 30 L nl for 1.25-␮m laser pulses), on the other hand, was comparable with the fiber length, leading to a noticeable contribution of shock waves to the asymmetry of spectral broadening. Spectra of supercontinuum emission produced with 80– 100-fs pulses of OPA radiation with different wavelengths are compared in Figs. 9(a) and 9(b). Figure 9(a) displays the spectra of 1.10- and 1.25-␮m OPA pulses at the output of a 4-cm PCF sample with a core radius of 1.5 ␮m. The durations of input pulses were approximately 100 and 80 fs for 1.10- and 1.25-␮m radiation, respectively. The pulse energy at the input of the fiber was approximately 5 nJ in both cases. The results of similar spectral measurements carried out with 1.10- and 1.30-␮m OPA pulses with initial durations of approximately 100 and 75 fs, respectively, and transmitted through a PCF with the core radius of 2 ␮m are presented in Fig. 9(b). These experiments demonstrate how the spectral range covered by supercontinuum emission can be tuned by variation of the wavelength of OPA radiation. Although the processes that contribute to supercontinuum generation (self- and cross-phase modulation, four-wave mixing, self-steepening, stimulated Raman scattering, and modulation instabilities) are well known1 and have been extensively studied both experimentally and theoretically,29 it is very difficult to quantify the contributions of each of these processes to supercontinuum generation not only in experiments but also in numerical simulations performed for physically realistic situations.30 In our experiments, we were able to identify quite reliably self-phase modulation as a process responsible for the spectral broadening of femtosecond pulses at low energies of input pulses (see also the discussion in Subsection 4 A). At higher input pulse energies several ␹ ( 3 ) processes came into play virtually simultaneously, resulting in the generation of supercontinuum emission with broad and asymmetric spectra. It would be important to emphasize, however, an important difference between supercontinuum generation under our conditions and supercontinuum generation with highintensity laser pulses in gases. Although supercontinuum generation in gases is often observed near the critical power of self-focusing, which makes the contribution of spatial self-action processes quite noticeable31,32 high degrees of light localization and long propagation lengths that are attainable with PCFs even without selfchanneling and multiple-refocusing phenomena, typical of high-field supercontinuum-generation experiments,33 allow supercontinuum emission to be generated in such fibers with laser pulse powers much lower than those leading to noticeable spatial self-action effects. In particular, as can be seen from the results of the experiments presented in this paper, supercontinuum emission with spectra spanning nearly an octave can be produced with 100-fs pulses whose peak power is less than 10 kW. With a typical estimate for the critical power of self-focusing of

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1 MW, we can conclude that self-action effects (which may, of course, become quite important for higher inputpulse powers) are negligible in this regime. The results of our measurements demonstrate that the efficiency of supercontinuum generation is quite sensitive to the parameters of the fiber. In particular, the intensity of light pulses required to achieve an octave’s spectral broadening in the case of fibers with a core radius of 1.5 ␮m is substantially lower than the intensity required to achieve a similar broadening in fibers with a core radius of 3.0 ␮m (to estimate the laser intensities coupled into the fiber, we measured the radiation energy at the output of the fiber and divided this result by the effective mode area calculated in Subsection 2.A). The correlation with dispersion properties of the fibers is easily observed here. Dispersion of PCFs with a core radius of 1.5 ␮m near the wavelength of 1.25 ␮m is noticeably weaker than the dispersion of fibers with core radii of 2 and 3 ␮m (see Figs. 2 and 3). Group-delay and pulse-spreading effects are, therefore, less pronounced in PCFs with smaller core diameters. This situation allows much higher efficiencies of spectral superbroadening to be achieved with PCFs with smaller core diameters. The results of measurements performed with OPA pulses of different wavelengths, as can be seen from Figs. 9(a) and 9(b), generally confirm the above conclusions. The efficiency of supercontinuum generation with 1.25and 1.30-␮m light was noticeably higher than the efficiency of supercontinuum generation with 1.10-␮m OPA pulses of the same initial power. This finding may also be explained in terms of the dispersion properties of PCFs, as the group-velocity dispersion of the fibers used in these experiments near 1.10 ␮m is higher than the group-velocity dispersion of these fibers within the range of 1.25–1.30 ␮m (Fig. 2). An even more striking demonstration of the influence of dispersion effects on spectral broadening and supercontinuum generation in PCFs is provided by the comparison of the results of experiments performed with 800-nm and 1.25-␮m light pulses of approximately the same pulse duration (cf. Figs. 6–9). In particular, coupling a 70-fs Ti:sapphire laser with an energy of 8 nJ into a PCF with a cladding pitch that is equal to 2 ␮m, we ended up with a spectral broadening of approximately 20 nm at the output of the fiber (Fig. 7). Much higher efficiencies of spectral broadening were achieved with 100-fs 8-nJ OPA pulses, which allowed an octave’s spectral broadening to be achieved with a 2-␮m-pitch fiber. Comparison of the dispersion characteristics of PCFs for 800-nm and 1.25-␮m radiation suggests a natural explanation for these findings. The dispersion spreading of the pump pulse and the group delay of spectral components arising during the process of spectral broadening are much weaker close to the wavelength of 1.25 ␮m, which is characteristic of OPA radiation. This result leads to much more efficient spectral broadening of femtosecond pulses and allows the supercontinuum to be generated starting with much lower pulse energies. These results demonstrate that the efficiency of supercontinuum generation in a PCF can be improved quite substantially by optimization of the fiber dispersion and suggest several practical recipes for such dispersion optimization.


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5. CONCLUSION We have demonstrated supercontinuum generation by propagating frequency-tunable femtosecond pulses of 1.1–1.5-␮m radiation of an OPA through a PCF. Comparison of the results of experiments carried out by use of Ti:sapphire and OPA femtosecond pulses indicates a considerable role of fiber dispersion in the process of shortpulse spectral broadening. Although dispersion effects prevented us from achieving a high efficiency of spectral broadening in the case of Ti:sapphire laser pulses, spectra spanning nearly an octave were obtained when OPA laser pulses with a duration of 80–100 fs and the energy of several nanojoules per pulse were coupled into a PCF with a core radius of 1.5–3 ␮m. In experiments on supercontinuum generation with an OPA the influence of dispersion effects was reduced by our decreasing the size of the fiber core, which allowed the efficiency of supercontinuum generation to be improved without increasing the laser intensity. PCFs with different pitches and core diameters allowed us to explore the influence of dispersion on the spectral broadening of femtosecond pulses. Dispersion effects played a more and more important role in spectral broadening and supercontinuum generation in our experiments as the core radius of the fiber was increased from 1.5 to 3 ␮m. Although many aspects of the spectral broadening of femtosecond Ti:sapphire laser pulses have been studied comprehensively in extensive earlier microstructure-fiber experiments, the use of an OPA allowed us to add frequency-tunability aspects to the numerous advantages of supercontinuum generation in PCFs. Demonstration of supercontinuum generation with a 1.1–1.5-␮m femtosecond radiation source also permits the extension of new concepts of ultrafast optics and optical metrology, related to the use of PCFs, to the range of longer wavelengths, which seems to be very promising for biomedical applications and high-precision measurements.

ACKNOWLEDGMENTS We are grateful to V. I. Beloglazov and N. B. Skibina for fabricating microstructure fiber samples. This study was supported in part by the Volkswagen Foundation (project I/76 869). The work of A. B. Fedotov, A. N. Naumov and A. M. Zheltikov was also supported in part by the President of Russian Federation grant 00-15-99304, the Russian Foundation for Basic Research project 00-02-17567, and awards RP2-2266 and RP2-2275 of the U.S. Civilian Research and Development Foundation for the Independent States of the former Soviet Union (CRDF).

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