- Email: [email protected]
Kerr-lens mode-locking of Nd:glass laser
15 December 2001
Optics Communications 200 (2001) 159±163 www.elsevier.com/locate/optcom
Kerr-lens mode-locking of Nd:glass laser Wei Lu a, Li Yan a,*, Curtis R. Menyuk a,b a
Department of Computer Science and Electrical Engineering, University of Maryland, Baltimore County, Baltimore, MD 21250, USA b PhotonEx Corporation, 200 MetroWest Technology Park, Maynard, MA 01754, USA Received 10 September 2001; accepted 24 October 2001
Abstract We report what is to our best knowledge the ®rst Kerr-lens mode-locking of a Nd:silicate glass laser. Pulses as short as 64 fs were generated. For a broadband inhomogeneously broadened laser, the formation of the soliton-like pulses requires a minimum amount of negative group velocity dispersion (GVD), and more negative GVD is needed to have stable, self-sustained mode locking. Ó 2001 Elsevier Science B.V. All rights reserved. Keywords: Mode-locked lasers; Kerr-lens mode locking; Nd:glass laser; Inhomogeneously broadened laser
Neodymium (Nd) doped glasses have broad ¯uorescence emission linewidth of 20±30 nm that potentially support sub-100 fs pulses at a wavelength of 1:06 lm. In the past few years, considerable progresses have been reported in generation of ultrashort pulses from Nd:glass lasers. While active mode locking of Nd:glass usually generates only picosecond pulses [1,2], passive mode locking shows superiority in generation of femtosecond pulses. By using either the technique of additive pulse mode-locking (APM) [3] or semiconductor saturable absorber mirror (SESAM) [4], sub-100 fs pulses have been produced from Nd:glass lasers. Nevertheless, APM is a complex and sensitive technique since it requires
*
Corresponding author. Tel.: +1-410-455-3558; fax: +1-410455-3969. E-mail address: [email protected] (L. Yan).
an additional auxiliary cavity that needs precise alignment and interferometric stabilization for reliable operation. Although the intracavity SESAM scheme is simple, the fabrication of SESAM requires careful design and it is not easily available for many laser users. Kerr-lens mode locking (KLM) is another technique that can be realized in a simple cavity without the need of an auxiliary cavity [5]. Since KLM relies on the nonresonant Kerr nonlinearity, it is independent of the lasing wavelength and bandwidth and gives ultrafast response. KLM has been successful in many solidstate lasers such as Ti:sapphire [5], Cr:fosterite [6], Cr:LiSAF [7] and Nd:YLF [8]. Indeed, the shortest optical pulses (sub-two optical cycles) ever generated directly from a laser oscillator were from a KLM Ti:sapphire laser [9]. However, to date KLM has not been demonstrated in a Nd:glass laser. In this paper, we report to our best knowledge the ®rst demonstration of Kerr-lens mode-locking of a
0030-4018/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 0 - 4 0 1 8 ( 0 1 ) 0 1 6 4 1 - 8
160
W. Lu et al. / Optics Communications 200 (2001) 159±163
Nd:silicate glass laser. The shortest pulses were 64 fs. We found that to obtain coherent soliton-like pulses, the laser needs to operate in a deeply negative group velocity dispersion (GVD) regime, and more negative GVD is required to have stable selfsustained mode locking operation. The schematic diagram of the mode-locked Nd:glass laser is shown in Fig. 1. The cavity was formed by two concave mirrors with radii of curvature equal to 10 cm, a high-re¯ection mirror, and an output coupler with transmittance of 1.5%. A Nd:silicate glass (LG-680) plate with thickness of 4.5 mm was placed at the Brewster's angle and used as the gain medium. The two concave mirrors were tilted at an incident angle of 8:5°. An acousto-optic modulator (AOM) was placed at the end of one arm. A knife-edge was placed in this arm to enhance the mode locking performance. A pair of intracavity SF10 prisms was placed in the output arm. The prisms were separated with an apex-to-apex distance of approximately 51 cm. A cw Ti:sapphire laser was tuned at 810 nm to pump the Nd:glass. The AOM was driven at about 46 MHz, half of the round-trip frequency of the cavity. When the AOM was o, the free-running Nd:silicate glass laser lased with a bandwidth 5 nm centered near 1064 nm. The threshold pump power was about 75 mW. The maximum output power was about 50 mW with a pump power of 1 W. We estimated the round-trip GVD contributed from the gain medium and the AOM to be d2 /=dx2 2600 fs2 at 1064 nm. Taking into account the additional material dis-
Fig. 1. Schematic diagram of the mode-locked Nd:glass laser.
persion by the prisms, the net round-trip negative GVD was about 1200 fs2 . With the AOM on, the laser could generate pulses of 340 fs down to sub-100 fs depending on the alignment of intracavity components which we will discuss later. These pulses had a much shorter duration than what active mode locking can produce, which resulted from the soliton formation mechanism. After we turned the AOM o, stable and selfsustaining femtosecond pulses were obtained. We found that when the distance between the two folding mirrors was varied within most of the stability range the self-sustaining operation was achievable. After optimization of the cavity we were able to obtain the self-sustaining pulse with duration of about 77 fs. The pulse bandwidth was 21:1 nm centered at 1073 nm. The femtosecond pulses were robust and could sustain themselves for hours. Mechanical shaking of an intracavity component would stop mode locking. However, slightly tapping the end mirror or simply turning the AOM on and then o could regenerate the femtosecond pulses. We observed that with the AOM on, there were large ¯uctuations on the background level of the autocorrelation trace, which indicated that the pulses were not stable. One possible reason is that the resonant dispersion from the gain medium might cause a group delay for the intracavity circulating pulse. When the group delay accumulates after many round trips, the circulating pulse experiences a restoring force from the AOM, which might lead to the disturbance and timing jitter of the soliton-like pulse [10]. This o-synchronization may be removed with either a regenerative active mode-locking scheme or by the self-sustaining operation. Indeed, in the experiment the autocorrelation trace was smooth and stable when the soliton-like pulses were self-sustaining. In order to stabilize the soliton-like pulses, some amplitude modulation is needed. In the selfsustaining operation, no active amplitude modulation was present. Therefore, there had to be some self-amplitude modulation which we believe to be the KLM eect to provide the stabilization mechanism. We used the knife-edge to act as a hard aperture in the tangential plane to cut the intracavity laser beam in the AOM arm as shown
W. Lu et al. / Optics Communications 200 (2001) 159±163
in Fig. 1. With a certain amount of knife-edge cutting, the AOM could be turned o and pulses could sustain themselves. Alternatively, without the knife-edge, by carefully moving the AOM edge to near the laser beam, a similar self-sustaining operation was achieved. We examined the laser beam out from the AOM arm using a CCD diode array. The beam spatial pro®les in the cw and selfsustaining operations are shown in Fig. 2. In the cw state, the laser beam was wide with a multispike structure. In contrast, the laser beam was small and smooth in the self-sustaining operation. It con®rms that the Kerr-lens eect favors the high power pulsed mode that experiences a smaller diraction loss at the hard aperture. Further, we observed that only above a certain intracavity energy level (12 nJ in our experiment) self-sustaining pulses could be obtained. Below this en-
(a)
(b) Fig. 2. Spatial pro®les of the laser beam in (a) cw operation and (b) self-sustaining operation.
161
ergy level, active modulation was needed to sustain the soliton-like pulses. At higher pulse energy levels shorter pulses were obtained as predicted from the soliton theory. We noticed that some narrow spikes were superposed on the self-sustaining pulse spectrum. They were supported by a residual gain peak at 1064 nm and corresponded to the low intensity continuum, which should be suppressed by KLM in a clean mode-locking process. As we moved the knife-edge gradually into the laser beam, these spikes became smaller. However, they could not be removed completely even when we cut the intracavity laser beam so much that the soliton-like pulse collapsed. To further enhance the KLM, we added another piece of Nd:silicate glass in the resonator and adjusted the folding mirrors' incident angle to 10°. In this con®guration the narrow spikes in the spectrum can be removed. The shortest self-sustaining pulses were 64 fs, and the pulse bandwidth was 28 nm. The output power was about 30 mW. Fig. 3 shows the autocorrelation of the pulses and the spectrum. The time±bandwidth product was about 0.46. We notice that the pulse spectrum deviates somewhat from that of an ideal sech2 pulse. We found experimentally that to obtain sub-100 fs pulses, two things are important. One is that the pulse spectrum had to be shifted to a longer wavelength by about 10 nm from its cw lasing position (1064 nm). The spectral shifting was achieved by slightly cutting the intracavity laser beam using the prism near the output mirror. Because the Nd:silicate glass has a gain pro®le which peaks at about 1064 nm and is ¯atter in the longer wavelength region, the short-wavelength-cutting by the prism ¯attens the gain pro®le and allows the pulse bandwidth to broaden in the longer wavelength region [10]. The other is that KLM was needed. Without the knife-edge cutting or AOMedge cutting, we could not obtain sub-100 fs soliton-like pulses even when the AOM was on. This result shows that the nearly instantaneous KLM is more eective than active amplitude modulation to shorten the soliton-like pulses into sub-100 fs scale. As predicted from the soliton theory, a broader pulse bandwidth could be achieved by decreasing the negative GVD. This was observed in our ex-
162
W. Lu et al. / Optics Communications 200 (2001) 159±163
Fig. 4. Pulse spectra with dierent negative GVDs in the selfsustained mode locking operation when two pieces of Nd:silicate glass were used.
Fig. 3. (a) Interferometric autocorrelation trace. A sech2 pulse shape is assumed. (b) The corresponding pulse spectrum.
periment. Fig. 4 shows the pulse spectra with different negative GVDs in the self-sustaining state using two pieces of Nd:silicate glass. The pulse bandwidth increased from about 21.1±36.3 nm when we decreased the negative GVD from about 860 to 710 fs2 . We found, however, that the mode locking operation tends to be less stable when the negative GVD is decreased too much. With GVD of 860 or 810 fs2 , we obtained smooth pulse spectra as shown in Fig. 4(a) and (b), and the soliton-like pulses could sustain themselves for hours. When the negative GVD was reduced to 760 fs2 , a narrow spike appeared in the pulse spectrum, and it became larger when GVD was reduced to 710 fs2 . Correspondingly, the pulse self-sustaining period became shorter. When
GVD was reduced to 660 fs2 , the spike grew so large that the mode locking became unstable and the soliton-like pulses could sustain only for seconds. Fig. 4(e) shows one moment of the spectrum. We want to point out that, when using only one piece of Nd:silicate glass, the KLM eect was weak, and consequently the requirement on GVD was stronger. The self-sustaining operation could not succeed when the negative GVD was less than 900 fs2 , and the narrow spike on the pulse spectrum could not be removed completely even when we increased the negative GVD to 1600 fs2 . We had attempted to attain self-starting of KLM, but the active modulation or external perturbation was always needed for starting. KLM needs high enough intracavity peak power. Apparently, our laser in the free running state could not produce sucient peak power to initiate KLM. Thus, a seed pulse built up from the free running state is needed at the initial stage of KLM. Active modulation combined with soliton pulse
W. Lu et al. / Optics Communications 200 (2001) 159±163
163
mogeneously broadened laser wherein a minimum amount of negative GVD is required to disperse the continuum [10,11]. However, there are still some dierences in details of the dynamics and characteristics of formation of soliton-like pulses in a homogeneously broadened laser and an inhomogeneously broadened laser. In summary, we demonstrated the ®rst KLM of a Nd:glass laser, and the shortest pulses were 64 fs. Our experiment shows that formation of the soliton-like pulses requires a minimum amount of negative GVD, and more negative GVD is needed to have stable self-sustained mode locking. Fig. 5. Pulse width and time±bandwidth product in dierent GVD regions in the active mode locking operation.
shaping can generate pulses of a few hundred femtoseconds, which can provide sucient peak intensity for KLM to take place. We found that GVD plays an important role in the formation of femtosecond soliton-like pulses. Fig. 5 shows the mode locking performance (with the AOM on) using a single gain medium with dierent net GVDs. To focus on the dispersion eect, we did not reshape the gain pro®le so that the pulse bandwidth remained between 3 and 5 nm, and no hard aperture was used in the AOM arm. Between zero GVD and about 400 fs2 , we failed to obtain soliton-like pulses, and the actively mode-locked pulses were incoherent with duration of tens of picosecond. Increasing the negative GVD to above 460 fs2 , pulses shortened drastically to about 1±4 ps. As the net GVD was adjusted over 750 fs2 , pulses shortened further to a few hundred femtoseconds and were transform-limited. From Fig. 5, it is clear that some minimum amount of negative GVD was required to generate soliton-like pulses in an inhomogeneously broadened laser. The basic physics of this behavior is similar to that of soliton pulse formation in an actively mode-locked, ho-
Acknowledgements This work was supported by the National Science Foundation under grant ECS-9703988. References [1] L. Yan, P.T. Ho, C.H. Lee, G.L. Burdge, IEEE J. Quantum Electron. 25 (1989) 2431. [2] L. Yan, B. Guo, Appl. Phys. Lett. 70 (1997) 3501. [3] C. Spielmann, F. Krausz, T. Brabec, E. Wintner, A.J. Schmidt, Appl. Phys. Lett. 58 (1991) 2470. [4] J. Aus der Au, D. Kopf, F. Morier-Genoud, M. Moser, U. Keller, Opt. Lett. 22 (1997) 307. [5] D.E. Spence, P.N. Kean, W. Sibbett, Opt. Lett. 16 (1991) 42. [6] A. Seas, V. Petricevic, R.R. Alfano, Opt. Lett. 17 (1992) 937. [7] J.M. Evans, D.E. Spence, W. Sibbett, B.H.T. Chai, A. Miller, Opt. Lett. 17 (1992) 1447. [8] G.P.A. Malcolm, A.I. Ferguson, Opt. Lett. 16 (1991) 1967. [9] U. Morgner, F.X. Kartner, S.H. Cho, Y. Chen, H.A. Haus, J.G. Fujimoto, E.P. Ippen, V. Scheuer, G. Angelow, T. Tschudi, Opt. Lett. 24 (1999) 411. [10] F.X. Kartner, D. Kopf, U. Keller, J. Opt. Soc. Am. B 12 (1995) 486. [11] H.A. Haus, Y. Silberberg, IEEE J. Quantum Electron. 22 (1986) 325.
Optics Communications 200 (2001) 159±163 www.elsevier.com/locate/optcom
Kerr-lens mode-locking of Nd:glass laser Wei Lu a, Li Yan a,*, Curtis R. Menyuk a,b a
Department of Computer Science and Electrical Engineering, University of Maryland, Baltimore County, Baltimore, MD 21250, USA b PhotonEx Corporation, 200 MetroWest Technology Park, Maynard, MA 01754, USA Received 10 September 2001; accepted 24 October 2001
Abstract We report what is to our best knowledge the ®rst Kerr-lens mode-locking of a Nd:silicate glass laser. Pulses as short as 64 fs were generated. For a broadband inhomogeneously broadened laser, the formation of the soliton-like pulses requires a minimum amount of negative group velocity dispersion (GVD), and more negative GVD is needed to have stable, self-sustained mode locking. Ó 2001 Elsevier Science B.V. All rights reserved. Keywords: Mode-locked lasers; Kerr-lens mode locking; Nd:glass laser; Inhomogeneously broadened laser
Neodymium (Nd) doped glasses have broad ¯uorescence emission linewidth of 20±30 nm that potentially support sub-100 fs pulses at a wavelength of 1:06 lm. In the past few years, considerable progresses have been reported in generation of ultrashort pulses from Nd:glass lasers. While active mode locking of Nd:glass usually generates only picosecond pulses [1,2], passive mode locking shows superiority in generation of femtosecond pulses. By using either the technique of additive pulse mode-locking (APM) [3] or semiconductor saturable absorber mirror (SESAM) [4], sub-100 fs pulses have been produced from Nd:glass lasers. Nevertheless, APM is a complex and sensitive technique since it requires
*
Corresponding author. Tel.: +1-410-455-3558; fax: +1-410455-3969. E-mail address: [email protected] (L. Yan).
an additional auxiliary cavity that needs precise alignment and interferometric stabilization for reliable operation. Although the intracavity SESAM scheme is simple, the fabrication of SESAM requires careful design and it is not easily available for many laser users. Kerr-lens mode locking (KLM) is another technique that can be realized in a simple cavity without the need of an auxiliary cavity [5]. Since KLM relies on the nonresonant Kerr nonlinearity, it is independent of the lasing wavelength and bandwidth and gives ultrafast response. KLM has been successful in many solidstate lasers such as Ti:sapphire [5], Cr:fosterite [6], Cr:LiSAF [7] and Nd:YLF [8]. Indeed, the shortest optical pulses (sub-two optical cycles) ever generated directly from a laser oscillator were from a KLM Ti:sapphire laser [9]. However, to date KLM has not been demonstrated in a Nd:glass laser. In this paper, we report to our best knowledge the ®rst demonstration of Kerr-lens mode-locking of a
0030-4018/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 0 - 4 0 1 8 ( 0 1 ) 0 1 6 4 1 - 8
160
W. Lu et al. / Optics Communications 200 (2001) 159±163
Nd:silicate glass laser. The shortest pulses were 64 fs. We found that to obtain coherent soliton-like pulses, the laser needs to operate in a deeply negative group velocity dispersion (GVD) regime, and more negative GVD is required to have stable selfsustained mode locking operation. The schematic diagram of the mode-locked Nd:glass laser is shown in Fig. 1. The cavity was formed by two concave mirrors with radii of curvature equal to 10 cm, a high-re¯ection mirror, and an output coupler with transmittance of 1.5%. A Nd:silicate glass (LG-680) plate with thickness of 4.5 mm was placed at the Brewster's angle and used as the gain medium. The two concave mirrors were tilted at an incident angle of 8:5°. An acousto-optic modulator (AOM) was placed at the end of one arm. A knife-edge was placed in this arm to enhance the mode locking performance. A pair of intracavity SF10 prisms was placed in the output arm. The prisms were separated with an apex-to-apex distance of approximately 51 cm. A cw Ti:sapphire laser was tuned at 810 nm to pump the Nd:glass. The AOM was driven at about 46 MHz, half of the round-trip frequency of the cavity. When the AOM was o, the free-running Nd:silicate glass laser lased with a bandwidth 5 nm centered near 1064 nm. The threshold pump power was about 75 mW. The maximum output power was about 50 mW with a pump power of 1 W. We estimated the round-trip GVD contributed from the gain medium and the AOM to be d2 /=dx2 2600 fs2 at 1064 nm. Taking into account the additional material dis-
Fig. 1. Schematic diagram of the mode-locked Nd:glass laser.
persion by the prisms, the net round-trip negative GVD was about 1200 fs2 . With the AOM on, the laser could generate pulses of 340 fs down to sub-100 fs depending on the alignment of intracavity components which we will discuss later. These pulses had a much shorter duration than what active mode locking can produce, which resulted from the soliton formation mechanism. After we turned the AOM o, stable and selfsustaining femtosecond pulses were obtained. We found that when the distance between the two folding mirrors was varied within most of the stability range the self-sustaining operation was achievable. After optimization of the cavity we were able to obtain the self-sustaining pulse with duration of about 77 fs. The pulse bandwidth was 21:1 nm centered at 1073 nm. The femtosecond pulses were robust and could sustain themselves for hours. Mechanical shaking of an intracavity component would stop mode locking. However, slightly tapping the end mirror or simply turning the AOM on and then o could regenerate the femtosecond pulses. We observed that with the AOM on, there were large ¯uctuations on the background level of the autocorrelation trace, which indicated that the pulses were not stable. One possible reason is that the resonant dispersion from the gain medium might cause a group delay for the intracavity circulating pulse. When the group delay accumulates after many round trips, the circulating pulse experiences a restoring force from the AOM, which might lead to the disturbance and timing jitter of the soliton-like pulse [10]. This o-synchronization may be removed with either a regenerative active mode-locking scheme or by the self-sustaining operation. Indeed, in the experiment the autocorrelation trace was smooth and stable when the soliton-like pulses were self-sustaining. In order to stabilize the soliton-like pulses, some amplitude modulation is needed. In the selfsustaining operation, no active amplitude modulation was present. Therefore, there had to be some self-amplitude modulation which we believe to be the KLM eect to provide the stabilization mechanism. We used the knife-edge to act as a hard aperture in the tangential plane to cut the intracavity laser beam in the AOM arm as shown
W. Lu et al. / Optics Communications 200 (2001) 159±163
in Fig. 1. With a certain amount of knife-edge cutting, the AOM could be turned o and pulses could sustain themselves. Alternatively, without the knife-edge, by carefully moving the AOM edge to near the laser beam, a similar self-sustaining operation was achieved. We examined the laser beam out from the AOM arm using a CCD diode array. The beam spatial pro®les in the cw and selfsustaining operations are shown in Fig. 2. In the cw state, the laser beam was wide with a multispike structure. In contrast, the laser beam was small and smooth in the self-sustaining operation. It con®rms that the Kerr-lens eect favors the high power pulsed mode that experiences a smaller diraction loss at the hard aperture. Further, we observed that only above a certain intracavity energy level (12 nJ in our experiment) self-sustaining pulses could be obtained. Below this en-
(a)
(b) Fig. 2. Spatial pro®les of the laser beam in (a) cw operation and (b) self-sustaining operation.
161
ergy level, active modulation was needed to sustain the soliton-like pulses. At higher pulse energy levels shorter pulses were obtained as predicted from the soliton theory. We noticed that some narrow spikes were superposed on the self-sustaining pulse spectrum. They were supported by a residual gain peak at 1064 nm and corresponded to the low intensity continuum, which should be suppressed by KLM in a clean mode-locking process. As we moved the knife-edge gradually into the laser beam, these spikes became smaller. However, they could not be removed completely even when we cut the intracavity laser beam so much that the soliton-like pulse collapsed. To further enhance the KLM, we added another piece of Nd:silicate glass in the resonator and adjusted the folding mirrors' incident angle to 10°. In this con®guration the narrow spikes in the spectrum can be removed. The shortest self-sustaining pulses were 64 fs, and the pulse bandwidth was 28 nm. The output power was about 30 mW. Fig. 3 shows the autocorrelation of the pulses and the spectrum. The time±bandwidth product was about 0.46. We notice that the pulse spectrum deviates somewhat from that of an ideal sech2 pulse. We found experimentally that to obtain sub-100 fs pulses, two things are important. One is that the pulse spectrum had to be shifted to a longer wavelength by about 10 nm from its cw lasing position (1064 nm). The spectral shifting was achieved by slightly cutting the intracavity laser beam using the prism near the output mirror. Because the Nd:silicate glass has a gain pro®le which peaks at about 1064 nm and is ¯atter in the longer wavelength region, the short-wavelength-cutting by the prism ¯attens the gain pro®le and allows the pulse bandwidth to broaden in the longer wavelength region [10]. The other is that KLM was needed. Without the knife-edge cutting or AOMedge cutting, we could not obtain sub-100 fs soliton-like pulses even when the AOM was on. This result shows that the nearly instantaneous KLM is more eective than active amplitude modulation to shorten the soliton-like pulses into sub-100 fs scale. As predicted from the soliton theory, a broader pulse bandwidth could be achieved by decreasing the negative GVD. This was observed in our ex-
162
W. Lu et al. / Optics Communications 200 (2001) 159±163
Fig. 4. Pulse spectra with dierent negative GVDs in the selfsustained mode locking operation when two pieces of Nd:silicate glass were used.
Fig. 3. (a) Interferometric autocorrelation trace. A sech2 pulse shape is assumed. (b) The corresponding pulse spectrum.
periment. Fig. 4 shows the pulse spectra with different negative GVDs in the self-sustaining state using two pieces of Nd:silicate glass. The pulse bandwidth increased from about 21.1±36.3 nm when we decreased the negative GVD from about 860 to 710 fs2 . We found, however, that the mode locking operation tends to be less stable when the negative GVD is decreased too much. With GVD of 860 or 810 fs2 , we obtained smooth pulse spectra as shown in Fig. 4(a) and (b), and the soliton-like pulses could sustain themselves for hours. When the negative GVD was reduced to 760 fs2 , a narrow spike appeared in the pulse spectrum, and it became larger when GVD was reduced to 710 fs2 . Correspondingly, the pulse self-sustaining period became shorter. When
GVD was reduced to 660 fs2 , the spike grew so large that the mode locking became unstable and the soliton-like pulses could sustain only for seconds. Fig. 4(e) shows one moment of the spectrum. We want to point out that, when using only one piece of Nd:silicate glass, the KLM eect was weak, and consequently the requirement on GVD was stronger. The self-sustaining operation could not succeed when the negative GVD was less than 900 fs2 , and the narrow spike on the pulse spectrum could not be removed completely even when we increased the negative GVD to 1600 fs2 . We had attempted to attain self-starting of KLM, but the active modulation or external perturbation was always needed for starting. KLM needs high enough intracavity peak power. Apparently, our laser in the free running state could not produce sucient peak power to initiate KLM. Thus, a seed pulse built up from the free running state is needed at the initial stage of KLM. Active modulation combined with soliton pulse
W. Lu et al. / Optics Communications 200 (2001) 159±163
163
mogeneously broadened laser wherein a minimum amount of negative GVD is required to disperse the continuum [10,11]. However, there are still some dierences in details of the dynamics and characteristics of formation of soliton-like pulses in a homogeneously broadened laser and an inhomogeneously broadened laser. In summary, we demonstrated the ®rst KLM of a Nd:glass laser, and the shortest pulses were 64 fs. Our experiment shows that formation of the soliton-like pulses requires a minimum amount of negative GVD, and more negative GVD is needed to have stable self-sustained mode locking. Fig. 5. Pulse width and time±bandwidth product in dierent GVD regions in the active mode locking operation.
shaping can generate pulses of a few hundred femtoseconds, which can provide sucient peak intensity for KLM to take place. We found that GVD plays an important role in the formation of femtosecond soliton-like pulses. Fig. 5 shows the mode locking performance (with the AOM on) using a single gain medium with dierent net GVDs. To focus on the dispersion eect, we did not reshape the gain pro®le so that the pulse bandwidth remained between 3 and 5 nm, and no hard aperture was used in the AOM arm. Between zero GVD and about 400 fs2 , we failed to obtain soliton-like pulses, and the actively mode-locked pulses were incoherent with duration of tens of picosecond. Increasing the negative GVD to above 460 fs2 , pulses shortened drastically to about 1±4 ps. As the net GVD was adjusted over 750 fs2 , pulses shortened further to a few hundred femtoseconds and were transform-limited. From Fig. 5, it is clear that some minimum amount of negative GVD was required to generate soliton-like pulses in an inhomogeneously broadened laser. The basic physics of this behavior is similar to that of soliton pulse formation in an actively mode-locked, ho-
Acknowledgements This work was supported by the National Science Foundation under grant ECS-9703988. References [1] L. Yan, P.T. Ho, C.H. Lee, G.L. Burdge, IEEE J. Quantum Electron. 25 (1989) 2431. [2] L. Yan, B. Guo, Appl. Phys. Lett. 70 (1997) 3501. [3] C. Spielmann, F. Krausz, T. Brabec, E. Wintner, A.J. Schmidt, Appl. Phys. Lett. 58 (1991) 2470. [4] J. Aus der Au, D. Kopf, F. Morier-Genoud, M. Moser, U. Keller, Opt. Lett. 22 (1997) 307. [5] D.E. Spence, P.N. Kean, W. Sibbett, Opt. Lett. 16 (1991) 42. [6] A. Seas, V. Petricevic, R.R. Alfano, Opt. Lett. 17 (1992) 937. [7] J.M. Evans, D.E. Spence, W. Sibbett, B.H.T. Chai, A. Miller, Opt. Lett. 17 (1992) 1447. [8] G.P.A. Malcolm, A.I. Ferguson, Opt. Lett. 16 (1991) 1967. [9] U. Morgner, F.X. Kartner, S.H. Cho, Y. Chen, H.A. Haus, J.G. Fujimoto, E.P. Ippen, V. Scheuer, G. Angelow, T. Tschudi, Opt. Lett. 24 (1999) 411. [10] F.X. Kartner, D. Kopf, U. Keller, J. Opt. Soc. Am. B 12 (1995) 486. [11] H.A. Haus, Y. Silberberg, IEEE J. Quantum Electron. 22 (1986) 325.