- Email: [email protected]
Diode-pumped femtosecond Nd:glass fiber laser started with a moving mirror
__ __ fi!B
I5 April 1997
2s
OPTICS COMMUNICATIONS
ELSEVIER
Optics Communications
I37 ( 1997) 64-68
Diode-pumped femtosecond Nd:glass fiber laser started with a moving mirror J.M. Lee ‘, M.K. Chun, C.H. Nam Depurtment
ofPhy.xics and Center forElectra-Optics, Korea Aduanced Institute 373-I Kusong-dong, Received 30 August
of’science and Technology,
Yusong-gu. Taejon 305-701. South Korea
1996; revised 3 December
1996; accepted
3 December
1996
Abstract The start-up of passive mode-locking with a moving mirror was demonstrated in a Nd:glass fiber laser pumped by a single-stripe laser diode and pulses with a duration of 250 fs were generated. A relatively long fiber was used to lower the mode-locking threshold by increasing the Kerr effect in the fiber and the variation of the threshold for the start-up of mode-locking was investigated by changing the length of the fiber from 0.74 to 2 m. It was found that the restriction of the lasing spectrum using an intracavity slit was crucial for a low start-up threshold of mode-locking in a Nd:glass fiber laser. PACS: 42.55.-f; 42.55.Wd; 42.65.Re Keyworrls: Fiber laser; Ultrashort pulse; Moving mirror, Diode pumping
Nd:glass is an attractive gain medium with its broad emission bandwidth for the generation of femtosecond pulses [I] and with its absorption band near 800 nm for pumping by a laser diode (LD) [2]. A Nd:glass fiber laser [3-61, in particular, has the advantage of a low pumping threshold for lasing and mode-locking over a bulk Nd:glass laser, and does not suffer from thermal problems like a bulk laser does [7]. An LD-pumped femtosecond Nd:glass fiber laser may be utilized as an all-solid-state femtosecond front-end oscillator of a chirped-pulse amplification (CPA) Nd:glass laser, as an alternative to a femtosecond Ti:sapphire laser operating at 1.05 p,m [8]. Femtosecond Nd:glass fiber lasers could not be selfstarted, and needed a starter to initiate passive mode-locking. When a Kr+ laser was used as a pumping source, an acousto-optic (AO) modulator [3,4] or a moving mirror [5] was used as the starter. For practical application, a diodepumped system is more favorable as an all-solid-state
’ E-mail: [email protected]. 0030~4018/97/!§17.00
laser [9]. In an LD-pumped Nd:glass fiber laser, femtosecond pulses were generated using an A0 modulator as the starter [6], but the output power of a commercial single-stripe LD of 150 mW, though suitable for pumping the Nd:glass fiber laser, was not enough to utilize a moving mirror as a starter [5]. We demonstrated, for the first time, the generation of femtosecond pulses from an LD-pumped Nd:glass fiber laser started with a moving mirror. A relatively long fiber was used to increase the Kerr effect in the fiber for passive mode-locking, and the polarization state through the fiber was adjusted using a polarization controller consisting of two fiber loops. The variation of the start-up threshold of mode-locking with different lengths of fiber was investigated, and the selection of a cw lasing wavelength and bandwidth was found to be an important factor for the start-up. femtosecond
1. Introduction
Copyright
PI/ SOO30-4018(96)00766-3
2. Start-up of mode-locking Passive mode-locking in the fiber laser is based on nonlinear birefringence due to self-phase modulation @PM)
0 1997 Elsevier Science B.V. All rights reserved.
J.M. Lee et ul. / Oprics Communicutinns
and cross-phase modulation (XPM) [3,4]. The total linear and nonlinear birefringence in the fiber should be set such that the high intensity part experiences a minimal loss, while the weak part experiences a strong loss in the polarizing components, such as the Brewster prisms. In the present experiment, most of the fiber was coiled on two quarter-wave loops to constitute birefringent axes due to mechanical stress in the fiber. The two loops were crossed at right angles to minimize the birefringence tuning effect and the group-velocity walkoff [4] by canceling out the linear birefringence in the two loops, leaving only the nonlinear birefringence. The final polarization in the fiber was controlled by adjusting linear birefringence with another two quarter-wave loops. The experimental setup is shown in Fig. 1. A singlestripe laser diode (LD) of 150 mW was used as a pumping source, and the lasing wavelength was set at 804 nm near the absorption peak of the Nd:glass fiber. A 2 m length of Nd:glass fiber doped with 500 ppm of Nd3+ and with a core diameter of 6 pm was used as a gain and nonlinear medium. The front end of the fiber, where the LD pumping beam and intracavity lasing beam are coupled, was polished at an angle of 10”. The other end was butt-coupled to a high reflectance mirror and an index matching oil was inserted to eliminate stray reflections which are known to increase the mode-locking threshold [9]. It was designed to prevent damage to the index oil by the pumping beam and to the LD itself by the feedback from the fiber tip. About 35% of the pumping beam was coupled to the fiber and as the absorption coefficient was measured to be O.O19/cm, about 97% of the coupled beam was absorbed through the 2 m fiber. The intracavity chirp induced through the fiber is compensated for by using two sets of three Brewster-cut SF10 prisms, separated by 1.65 m, and the total round-trip GVD is about - 50000 fs*. An output coupler of 84% reflectivity was mounted on a shaker composed of a rail and a small speaker, and it was moved at 60 Hz to start mode-locking. A slit of variable width was located between the second prism set and the output coupler. Once the mode-locking is initiated with the shaker, by adjusting the polarization controller and the slit, it can be
rpil SFlOprism
Ndxiber
Fig.
I. Experimental
setup of LD-pumped
L
DM
L
Nd:glass fiber laser.
DM: dichroic mirror, M: mirror, L: lens, OC: output coupler with 84% reflectance, PC: polarization controller, S: slit.
65
137 I1997) 64-68
a
Ideal
autocorrelation
6
3
3. 0
Ideal autocorrelation
a-
(b)
envelopeof
% g
6 4
J
I
I
-2
0
2
Time delay (ps) Fig. 2. Interferometric autocorrelation trace of mode-locked pulses with pulse duration of (a) 290 fs and (b) 250 fs.
maintained without dropout for several hours after turning off the shaker. The minimum absorbed pumping power for the start-up of the mode-locking was as low as 43 mW. The mode-locking, once started, could be sustained even at the absorbed pumping power of I5 mW, which is a little above the cw threshold of 7 mW. An autocorrelation trace of mode-locked pulses is shown in Fig. 2(a). Assuming sech* pulse shape, the pulse width is about 290 fs, compared with a theoretical autocorrelation function, and the time-bandwidth product is about 0.49. Using the same setup, pulses of 250 fs were also generated, but in this case, there were small wings at the outer edge of the autocorrelation signal as shown in Fig. 2(b). With an absorbed pumping power of 55 mW, the maximum cw and mode-locked output powers were 7.5 and 4.5 mW, respectively. The difference comes from the fact that the polarization controller is adjusted so as to remove the low power portion in the mode-locked case, causing a larger cavity loss. The pulse repetition rate is about 25 MHz; thus, a pulse energy of 180 pJ is extractable from the system. As shown in Fig. 3, the cw lasing spectrum of 4.5 nm width with several spikes changed into a smooth Gaussian-like shape of 6.3 nm width, peaked at 1.056 pm, as the mode-locking started. The fluorescence spectrum of the fiber spreads asymmetrically from 1.045 to 1.09 pm. The output power increased as the slit was located near the spectral peak, and the mode-locking could be started most
66
J.M. Lee et d/Optics
Communications
137 (1997) 64-68
For the self-start-up of mode-locking, a longitudinalmode-beating fluctuation should last until it becomes large enough for mode-locking. Equivalently, the lifetime of the fluctuation set by the mutual coherence time, rc defined as [91
should be larger than the critical build-up time for modelocking, T, [9]:
b)
T, =
TR KPgh(m)
(3)
where A v3da is the 3 dB full width of the first beat note of a free-running laser, T, is the cavity round-trip time, P, is the internal power, m is the number of longitudinal modes contained in a free-running laser, and K is given by [4]
x 1.045
’
YLf K =
J 1.055
1.065
Lasing wavelength ( pm ) Fig. 3. Lasing spectrum of the fiber laser in the cases of (a) CW lasing, (b) mode-locking, and (c) an increased slit width from (b).
easily in this case. It was possible to tune the lasing spectrum to 1.053 km, the gain peak of a Nd:phosphate glass amplifier, by controlling the position of the slit. Thus the pulse can be used as a seed pulse for Nd:phosphate glass amplifiers. When the slit was opened wider while the mode-locking was sustained, two spectral peaks were observed at 1.054 km and 1.059 km, breaking the symmetry of the spectrum, as shown in Fig. 3(c). The mode-locking state became unstable as the slit opened even wider, demonstrating that proper adjustment of the slit is important for the maintenance of the mode-locking.
3. Mode-locking threshold of a fiber laser The self-starting, passive mode-locking is attractive since ultrashort optical pulses can be produced without any extra element of external control. The passive mode-locking in a Nd:glass fiber laser, however, could not be self-started, though the nonlinear amplitude modulation was comparable to that of a self-starting, additive-pulse mode-locked (APM) Nd:phosphate glass laser [9].
6 sin4cu sin2 Lysin2 S ’
(4)
where y is the nonlinearity constant of the fiber [lo], L, is the fiber length, a is the angle between the linear polarization of the incident beam to the fiber and the birefringence axis of the fiber, and 6 is the overall phase difference between the eigenmodes set by the linear birefringence. A ‘3dB was measured to be about 150 kHz in the current setup, which corresponds to a mutual coherence time of about 2 t~s. It is much shorter than the expected value of T,, about 50 ps, and the mutual coherence time of bulk Nd:YLF, and lasers, - 100 l.~s, such as Ti:sapphire, Nd:glass lasers 191. Compared to bulk lasers, a fiber laser has a long length of gain medium and inevitable internal reflections at the tip of the fiber and components to couple the beam to the fiber in the resonator, which may cause the short mutual coherence time. The short mutual coherence time makes the self-starting difficult in a Nd:glass fiber laser, and requires the use of a starter for the initiation of mode-locking, such as an acousto-optic (AO) modulator [3,4] or a moving mirror [5]. The start-up method with a moving mirror is more attractive for its simplicity than that with an A0 modulator, while the mechanism for the start-up with a moving mirror was not clearly understood yet. One possible mechanism is the saturable-absorber-like behavior due to the combined effect of the linear phase shift imposed by the moving mirror and the nonlinear phase shift in the Kerr medium [l I]. In other words, a cw part with a sharp spectrum in the resonator leaves the gain region due to the repeated Doppler shifts caused by the moving mirror, while a pulsed part with a broad spectrum survives the Doppler shift due to a frequency pulling effect. By the Doppler shift in the current setup, the frequency of each mode can be shifted by about 200 kHz per round-trip when
Communications 137 f 1997) 64-68
J.M. Lee et al./Optics
the velocity of the moving mirror is 100 mm/s. The process should repeat enough within the mutual coherence time because the saturable-absorber-like behavior should start again if a new fluctuation appears after the previous fluctuation dies out. The overall shift within the mutual coherence time of 2 us, or 5 100 round-trip time, is about 20 MHz, which is far less than the lasing bandwidth of over 100 GHz. Consequently, the saturable-absorber-like behavior is too slow to influence the start-up of the Nd:glass fiber laser. For a practical application of fiber lasers, the achievement of a low start-up threshold of mode-locking is as important as the generation of the shortest pulses possible. Most of Nd:glass fiber laser investigations utilized a short fiber to obtain the shortest solitary pulses by minimizing the discreteness in the laser [3-61. In order to lower the mode-locking threshold, however, it is necessary to use a long fiber to increase the nonlinearity in the cavity. In a chirped-pulse amplification (CPA) Nd:glass laser system, for instance, the time duration of pulses that can possibly be amplified is limited to about 400 fs by the gain bandwidth of a N&glass amplifier. In this case, it is beneficial to use a long fiber to lower the mode-locking threshold as far as the pulse duration is short enough for a Nd:glass amplifier. The optimization of the fiber length will allow the generation of pulses with a low mode-locking threshold, while satisfying a required short pulse duration. The dependence of the mode-locking threshold on the fiber length can be estimated by modifying the self-starting condition, Eq. (2). If the cavity is composed only of fiber, without any bulk parts, the critical buildup time will not depend on the fiber length because K and Ta in Eq. (3) are proportional to it. For cavities containing bulk parts, such as GVD compensation prisms in a typical mode-locked Nd:glass fiber laser, however, the buildup time depends on the fiber length. Consequently, the optimization of the fiber length for mode-locking is necessary for such lasers with bulk parts.
J
0’ 50
100
150
200
250
Length of N&glass fiber (cm)
Fig. 4. Variation of the minimum absorbed pump power for the start-up of mode-locking with respect to the length of Nd:glass fiber.
6-I
In the present experiment, the mode-locking was observed to bulid up in about 2 ps, significantly shorter than the expected build-up time, T,. It means that the build-up time of mode-locking T, can be reduced with the use of a moving mirror. Consequently, F&J. (2) can be modified as
rc 2 5 T, ,
(5)
where 5 is introduced to take into account the reduction of the build-up time. Then, the variation of the absorbed pump power, Pa at the threshold of the start-up of the mode-locking with different lengths of fiber, while other parts of the laser are fixed, is expected to be 1-R a,
TR
P,=
=
5
Kln(m)T,
+ P,,,w
5 sin2o sin4o sin28 12(& x yLrln(2
+ &J/c
AA(n,&+
,&)/h2)r,
1-R us
+R’x~
’
(7) where R is the reflectance of the output coupler, us is the slope efficiency of the fiber laser, n, is the refractive index of the fiber, L, is the effective optical path length of the bulk part, Al\ is the lasing bandwidth, and P,,,w is the absorbed pump power at the threshold of the cw lasing. To confirm the validity of Eq. (71, we measured the minimum absorbed pump power for the start-up by changing the fiber length from 2 m to 0.74 m, while the other setup was kept fixed. For a fiber length of 0.74 m, a Ti:sapphire laser operating at 802 nm was used because the mode-locking could not be initiated by LD pumping with a fiber shorter than 1.3 m. The minimal absorbed pump power needed for the start-up of mode-locking is shown in Fig. 4. With the measured values of Q = 30”, 6 = 0.22P, P,,@ = 7 mW, a,= 0.16, La== 2.9 m, and with y = 0.007 W - ‘m- I from the parameters of the Nd:glass fiber used, the estimated absorbed pump power from Eq. (7) is well in accord with the experimental data, as shown in Fig. 4, with 5 of about 0.07. Here, us and P B,cw were the values for the maximum cw power, not the ones obtained after adjusting the polarization controller for mode-locking. The cw output power near the mode-lccking threshold was not suitable as a reference because the output power varied with the adjustment of the polarization controller. The ratio of the average mode-locked output power to the maximum cw power was about 60% So, the ratio of the internal power for the self-starting condition to that of the start-up with a moving mirror will be about c/1.7, that is, the build-up time is reduced to about 4% and only about that fraction of pump power was necessary for the start-up with a moving mirror compared to self-starting. From this result, it is clear that the threshold of the mode-locking can be decreased using a long fiber in the fiber lasers including the bulk parts.
68
J.M. Lee et d/Optics
Communications
The start-up was also sensitively dependent on the cw lasing spectrum adjusted by the intracavity slit. The modelocking could not be started with the cw lasing bandwidth over 4.5 nm, and the mode-locking could be started most easily when the cw lasing bandwidth decreased to about 0.5 nm, while the average power was decreased by only about 5%. The improvement of the femtosecond pulse generation using a slit is comparable to the Kerr-shift mode-locking [ 12,131 in which the gain profile was reshaped to a broad bandwidth using a knife edge, while it was reshaped to a narrow lasing bandwidth in the present work. The shaping of the gain profile plays a critical role for the start-up of mode-locking. The bandwidth can be extended, after the initiation of mode-locking, to about 6 nm and the time duration of the pulse is shortened from - ps to about 250 fs as the slit opens wider while maintaining the mode-locking, and the center wavelength was tunable from 1.053 pm to 1.070 pm as the position of the slit was adjusted.
4. Conclusion We demonstrated the start-up of the passive mode-locking with a moving mirror in a Nd:glass fiber laser pumped by a single-stripe laser diode and the variation of the threshold for the start-up was investigated by changing the fiber length. It was found that the equation for the selfstarting condition could be applied to the laser started with a moving mirror by introducing a proportional constant, about 0.04, to take into account the reduction of the build-up time of mode-locking due to the moving mirror, and that an intracavity slit adjusting the lasing spectrum helped the start-up and maintenance of the mode-locking. As the lasing wavelength of the N&glass fiber laser matched well with the gain peak of the Nd:phosphate glass, the Nd:glass fiber laser pumped by an LD is well suited as a cost effective, femtosecond front-end oscillator for a CPA Nd:glass laser.
137 (19971 M-68
Acknowledgements
We are grateful to advice. This research Defence Development, tro-Optics at the Korea Technology.
BY. Kim and B.T. Kim for their was supported by the Agency for Korea, through the Center for ElecAdvanced Institute of Science and
References
[ll Ch. Spielmann, F. Krausz, T. Brabec, E. Winmer and A.J. Schmidt, Appl. Phys. Lett. 58 (1991) 247’0. [2] D.W. Hughes and J.R.M. Barr, J. Phys. D 25 (1992) 563. [3] M. Hofer, M.E. Fermann, F. Haberl, M.H. Ober and A.J. Schmidt, Optics Lett. 16 (1991) 502. [4] M. Hofer, M.H. Ober, F. Haberl and M.E. Fermann, IEEE J. Quantum Electron. 28 ( 1992) 720. [5] M.H. Ober, M. Hofer and M.E. Fermann, Optics Lctt. 18 ( 1993) 367. 161 M.H. Ober, F. Haberl and M.F. Fermann, Appl. Phys. Lett. 60 (1992) 2177. [7] F. Krausz, E. Wintner, A.J. Schmidt and A. Dienes, IEEE J. Quantum Electron. 26 (1990) 158. [8] C. Rouyer, E. Mazataud, I. Allais, A. Pierre, S. Seznec, C. Sauteret, G. Mourou and A. Migus, Optics Lett. 18 (1993) 214. 191 F. Krausz, M.E. Fermann, T. Brabec, P.F. Curley, M. Hofer, M.H. Ober, Ch. Spielmann, E. Wmtner and A.J. Schmidt, IEEE J. Quantum Electron. 28 (1992) 2097. [ 101 G.P. Agrawal, Nonlinear Fiber Optics (Academic, New York, 1989) Sec. 2.3. [I 11 Q. Wu, J.Y. Zhou, X.G. Huang, Z.X. Li and Q.X. Li, J. Opt. See. Am. B 10 (1993) 2080. [12] II. Keller, T.H. Chiu and J.F. Ferguson, Optics Lett. 18 (1993) 1077. [13] D. Kopf, F.X. Khmer, K.J. Weingarten and U. Keller, Optics Lett. 19 (1994) 2146.
I5 April 1997
2s
OPTICS COMMUNICATIONS
ELSEVIER
Optics Communications
I37 ( 1997) 64-68
Diode-pumped femtosecond Nd:glass fiber laser started with a moving mirror J.M. Lee ‘, M.K. Chun, C.H. Nam Depurtment
ofPhy.xics and Center forElectra-Optics, Korea Aduanced Institute 373-I Kusong-dong, Received 30 August
of’science and Technology,
Yusong-gu. Taejon 305-701. South Korea
1996; revised 3 December
1996; accepted
3 December
1996
Abstract The start-up of passive mode-locking with a moving mirror was demonstrated in a Nd:glass fiber laser pumped by a single-stripe laser diode and pulses with a duration of 250 fs were generated. A relatively long fiber was used to lower the mode-locking threshold by increasing the Kerr effect in the fiber and the variation of the threshold for the start-up of mode-locking was investigated by changing the length of the fiber from 0.74 to 2 m. It was found that the restriction of the lasing spectrum using an intracavity slit was crucial for a low start-up threshold of mode-locking in a Nd:glass fiber laser. PACS: 42.55.-f; 42.55.Wd; 42.65.Re Keyworrls: Fiber laser; Ultrashort pulse; Moving mirror, Diode pumping
Nd:glass is an attractive gain medium with its broad emission bandwidth for the generation of femtosecond pulses [I] and with its absorption band near 800 nm for pumping by a laser diode (LD) [2]. A Nd:glass fiber laser [3-61, in particular, has the advantage of a low pumping threshold for lasing and mode-locking over a bulk Nd:glass laser, and does not suffer from thermal problems like a bulk laser does [7]. An LD-pumped femtosecond Nd:glass fiber laser may be utilized as an all-solid-state femtosecond front-end oscillator of a chirped-pulse amplification (CPA) Nd:glass laser, as an alternative to a femtosecond Ti:sapphire laser operating at 1.05 p,m [8]. Femtosecond Nd:glass fiber lasers could not be selfstarted, and needed a starter to initiate passive mode-locking. When a Kr+ laser was used as a pumping source, an acousto-optic (AO) modulator [3,4] or a moving mirror [5] was used as the starter. For practical application, a diodepumped system is more favorable as an all-solid-state
’ E-mail: [email protected]. 0030~4018/97/!§17.00
laser [9]. In an LD-pumped Nd:glass fiber laser, femtosecond pulses were generated using an A0 modulator as the starter [6], but the output power of a commercial single-stripe LD of 150 mW, though suitable for pumping the Nd:glass fiber laser, was not enough to utilize a moving mirror as a starter [5]. We demonstrated, for the first time, the generation of femtosecond pulses from an LD-pumped Nd:glass fiber laser started with a moving mirror. A relatively long fiber was used to increase the Kerr effect in the fiber for passive mode-locking, and the polarization state through the fiber was adjusted using a polarization controller consisting of two fiber loops. The variation of the start-up threshold of mode-locking with different lengths of fiber was investigated, and the selection of a cw lasing wavelength and bandwidth was found to be an important factor for the start-up. femtosecond
1. Introduction
Copyright
PI/ SOO30-4018(96)00766-3
2. Start-up of mode-locking Passive mode-locking in the fiber laser is based on nonlinear birefringence due to self-phase modulation @PM)
0 1997 Elsevier Science B.V. All rights reserved.
J.M. Lee et ul. / Oprics Communicutinns
and cross-phase modulation (XPM) [3,4]. The total linear and nonlinear birefringence in the fiber should be set such that the high intensity part experiences a minimal loss, while the weak part experiences a strong loss in the polarizing components, such as the Brewster prisms. In the present experiment, most of the fiber was coiled on two quarter-wave loops to constitute birefringent axes due to mechanical stress in the fiber. The two loops were crossed at right angles to minimize the birefringence tuning effect and the group-velocity walkoff [4] by canceling out the linear birefringence in the two loops, leaving only the nonlinear birefringence. The final polarization in the fiber was controlled by adjusting linear birefringence with another two quarter-wave loops. The experimental setup is shown in Fig. 1. A singlestripe laser diode (LD) of 150 mW was used as a pumping source, and the lasing wavelength was set at 804 nm near the absorption peak of the Nd:glass fiber. A 2 m length of Nd:glass fiber doped with 500 ppm of Nd3+ and with a core diameter of 6 pm was used as a gain and nonlinear medium. The front end of the fiber, where the LD pumping beam and intracavity lasing beam are coupled, was polished at an angle of 10”. The other end was butt-coupled to a high reflectance mirror and an index matching oil was inserted to eliminate stray reflections which are known to increase the mode-locking threshold [9]. It was designed to prevent damage to the index oil by the pumping beam and to the LD itself by the feedback from the fiber tip. About 35% of the pumping beam was coupled to the fiber and as the absorption coefficient was measured to be O.O19/cm, about 97% of the coupled beam was absorbed through the 2 m fiber. The intracavity chirp induced through the fiber is compensated for by using two sets of three Brewster-cut SF10 prisms, separated by 1.65 m, and the total round-trip GVD is about - 50000 fs*. An output coupler of 84% reflectivity was mounted on a shaker composed of a rail and a small speaker, and it was moved at 60 Hz to start mode-locking. A slit of variable width was located between the second prism set and the output coupler. Once the mode-locking is initiated with the shaker, by adjusting the polarization controller and the slit, it can be
rpil SFlOprism
Ndxiber
Fig.
I. Experimental
setup of LD-pumped
L
DM
L
Nd:glass fiber laser.
DM: dichroic mirror, M: mirror, L: lens, OC: output coupler with 84% reflectance, PC: polarization controller, S: slit.
65
137 I1997) 64-68
a
Ideal
autocorrelation
6
3
3. 0
Ideal autocorrelation
a-
(b)
envelopeof
% g
6 4
J
I
I
-2
0
2
Time delay (ps) Fig. 2. Interferometric autocorrelation trace of mode-locked pulses with pulse duration of (a) 290 fs and (b) 250 fs.
maintained without dropout for several hours after turning off the shaker. The minimum absorbed pumping power for the start-up of the mode-locking was as low as 43 mW. The mode-locking, once started, could be sustained even at the absorbed pumping power of I5 mW, which is a little above the cw threshold of 7 mW. An autocorrelation trace of mode-locked pulses is shown in Fig. 2(a). Assuming sech* pulse shape, the pulse width is about 290 fs, compared with a theoretical autocorrelation function, and the time-bandwidth product is about 0.49. Using the same setup, pulses of 250 fs were also generated, but in this case, there were small wings at the outer edge of the autocorrelation signal as shown in Fig. 2(b). With an absorbed pumping power of 55 mW, the maximum cw and mode-locked output powers were 7.5 and 4.5 mW, respectively. The difference comes from the fact that the polarization controller is adjusted so as to remove the low power portion in the mode-locked case, causing a larger cavity loss. The pulse repetition rate is about 25 MHz; thus, a pulse energy of 180 pJ is extractable from the system. As shown in Fig. 3, the cw lasing spectrum of 4.5 nm width with several spikes changed into a smooth Gaussian-like shape of 6.3 nm width, peaked at 1.056 pm, as the mode-locking started. The fluorescence spectrum of the fiber spreads asymmetrically from 1.045 to 1.09 pm. The output power increased as the slit was located near the spectral peak, and the mode-locking could be started most
66
J.M. Lee et d/Optics
Communications
137 (1997) 64-68
For the self-start-up of mode-locking, a longitudinalmode-beating fluctuation should last until it becomes large enough for mode-locking. Equivalently, the lifetime of the fluctuation set by the mutual coherence time, rc defined as [91
should be larger than the critical build-up time for modelocking, T, [9]:
b)
T, =
TR KPgh(m)
(3)
where A v3da is the 3 dB full width of the first beat note of a free-running laser, T, is the cavity round-trip time, P, is the internal power, m is the number of longitudinal modes contained in a free-running laser, and K is given by [4]
x 1.045
’
YLf K =
J 1.055
1.065
Lasing wavelength ( pm ) Fig. 3. Lasing spectrum of the fiber laser in the cases of (a) CW lasing, (b) mode-locking, and (c) an increased slit width from (b).
easily in this case. It was possible to tune the lasing spectrum to 1.053 km, the gain peak of a Nd:phosphate glass amplifier, by controlling the position of the slit. Thus the pulse can be used as a seed pulse for Nd:phosphate glass amplifiers. When the slit was opened wider while the mode-locking was sustained, two spectral peaks were observed at 1.054 km and 1.059 km, breaking the symmetry of the spectrum, as shown in Fig. 3(c). The mode-locking state became unstable as the slit opened even wider, demonstrating that proper adjustment of the slit is important for the maintenance of the mode-locking.
3. Mode-locking threshold of a fiber laser The self-starting, passive mode-locking is attractive since ultrashort optical pulses can be produced without any extra element of external control. The passive mode-locking in a Nd:glass fiber laser, however, could not be self-started, though the nonlinear amplitude modulation was comparable to that of a self-starting, additive-pulse mode-locked (APM) Nd:phosphate glass laser [9].
6 sin4cu sin2 Lysin2 S ’
(4)
where y is the nonlinearity constant of the fiber [lo], L, is the fiber length, a is the angle between the linear polarization of the incident beam to the fiber and the birefringence axis of the fiber, and 6 is the overall phase difference between the eigenmodes set by the linear birefringence. A ‘3dB was measured to be about 150 kHz in the current setup, which corresponds to a mutual coherence time of about 2 t~s. It is much shorter than the expected value of T,, about 50 ps, and the mutual coherence time of bulk Nd:YLF, and lasers, - 100 l.~s, such as Ti:sapphire, Nd:glass lasers 191. Compared to bulk lasers, a fiber laser has a long length of gain medium and inevitable internal reflections at the tip of the fiber and components to couple the beam to the fiber in the resonator, which may cause the short mutual coherence time. The short mutual coherence time makes the self-starting difficult in a Nd:glass fiber laser, and requires the use of a starter for the initiation of mode-locking, such as an acousto-optic (AO) modulator [3,4] or a moving mirror [5]. The start-up method with a moving mirror is more attractive for its simplicity than that with an A0 modulator, while the mechanism for the start-up with a moving mirror was not clearly understood yet. One possible mechanism is the saturable-absorber-like behavior due to the combined effect of the linear phase shift imposed by the moving mirror and the nonlinear phase shift in the Kerr medium [l I]. In other words, a cw part with a sharp spectrum in the resonator leaves the gain region due to the repeated Doppler shifts caused by the moving mirror, while a pulsed part with a broad spectrum survives the Doppler shift due to a frequency pulling effect. By the Doppler shift in the current setup, the frequency of each mode can be shifted by about 200 kHz per round-trip when
Communications 137 f 1997) 64-68
J.M. Lee et al./Optics
the velocity of the moving mirror is 100 mm/s. The process should repeat enough within the mutual coherence time because the saturable-absorber-like behavior should start again if a new fluctuation appears after the previous fluctuation dies out. The overall shift within the mutual coherence time of 2 us, or 5 100 round-trip time, is about 20 MHz, which is far less than the lasing bandwidth of over 100 GHz. Consequently, the saturable-absorber-like behavior is too slow to influence the start-up of the Nd:glass fiber laser. For a practical application of fiber lasers, the achievement of a low start-up threshold of mode-locking is as important as the generation of the shortest pulses possible. Most of Nd:glass fiber laser investigations utilized a short fiber to obtain the shortest solitary pulses by minimizing the discreteness in the laser [3-61. In order to lower the mode-locking threshold, however, it is necessary to use a long fiber to increase the nonlinearity in the cavity. In a chirped-pulse amplification (CPA) Nd:glass laser system, for instance, the time duration of pulses that can possibly be amplified is limited to about 400 fs by the gain bandwidth of a N&glass amplifier. In this case, it is beneficial to use a long fiber to lower the mode-locking threshold as far as the pulse duration is short enough for a Nd:glass amplifier. The optimization of the fiber length will allow the generation of pulses with a low mode-locking threshold, while satisfying a required short pulse duration. The dependence of the mode-locking threshold on the fiber length can be estimated by modifying the self-starting condition, Eq. (2). If the cavity is composed only of fiber, without any bulk parts, the critical buildup time will not depend on the fiber length because K and Ta in Eq. (3) are proportional to it. For cavities containing bulk parts, such as GVD compensation prisms in a typical mode-locked Nd:glass fiber laser, however, the buildup time depends on the fiber length. Consequently, the optimization of the fiber length for mode-locking is necessary for such lasers with bulk parts.
J
0’ 50
100
150
200
250
Length of N&glass fiber (cm)
Fig. 4. Variation of the minimum absorbed pump power for the start-up of mode-locking with respect to the length of Nd:glass fiber.
6-I
In the present experiment, the mode-locking was observed to bulid up in about 2 ps, significantly shorter than the expected build-up time, T,. It means that the build-up time of mode-locking T, can be reduced with the use of a moving mirror. Consequently, F&J. (2) can be modified as
rc 2 5 T, ,
(5)
where 5 is introduced to take into account the reduction of the build-up time. Then, the variation of the absorbed pump power, Pa at the threshold of the start-up of the mode-locking with different lengths of fiber, while other parts of the laser are fixed, is expected to be 1-R a,
TR
P,=
=
5
Kln(m)T,
+ P,,,w
5 sin2o sin4o sin28 12(& x yLrln(2
+ &J/c
AA(n,&+
,&)/h2)r,
1-R us
+R’x~
’
(7) where R is the reflectance of the output coupler, us is the slope efficiency of the fiber laser, n, is the refractive index of the fiber, L, is the effective optical path length of the bulk part, Al\ is the lasing bandwidth, and P,,,w is the absorbed pump power at the threshold of the cw lasing. To confirm the validity of Eq. (71, we measured the minimum absorbed pump power for the start-up by changing the fiber length from 2 m to 0.74 m, while the other setup was kept fixed. For a fiber length of 0.74 m, a Ti:sapphire laser operating at 802 nm was used because the mode-locking could not be initiated by LD pumping with a fiber shorter than 1.3 m. The minimal absorbed pump power needed for the start-up of mode-locking is shown in Fig. 4. With the measured values of Q = 30”, 6 = 0.22P, P,,@ = 7 mW, a,= 0.16, La== 2.9 m, and with y = 0.007 W - ‘m- I from the parameters of the Nd:glass fiber used, the estimated absorbed pump power from Eq. (7) is well in accord with the experimental data, as shown in Fig. 4, with 5 of about 0.07. Here, us and P B,cw were the values for the maximum cw power, not the ones obtained after adjusting the polarization controller for mode-locking. The cw output power near the mode-lccking threshold was not suitable as a reference because the output power varied with the adjustment of the polarization controller. The ratio of the average mode-locked output power to the maximum cw power was about 60% So, the ratio of the internal power for the self-starting condition to that of the start-up with a moving mirror will be about c/1.7, that is, the build-up time is reduced to about 4% and only about that fraction of pump power was necessary for the start-up with a moving mirror compared to self-starting. From this result, it is clear that the threshold of the mode-locking can be decreased using a long fiber in the fiber lasers including the bulk parts.
68
J.M. Lee et d/Optics
Communications
The start-up was also sensitively dependent on the cw lasing spectrum adjusted by the intracavity slit. The modelocking could not be started with the cw lasing bandwidth over 4.5 nm, and the mode-locking could be started most easily when the cw lasing bandwidth decreased to about 0.5 nm, while the average power was decreased by only about 5%. The improvement of the femtosecond pulse generation using a slit is comparable to the Kerr-shift mode-locking [ 12,131 in which the gain profile was reshaped to a broad bandwidth using a knife edge, while it was reshaped to a narrow lasing bandwidth in the present work. The shaping of the gain profile plays a critical role for the start-up of mode-locking. The bandwidth can be extended, after the initiation of mode-locking, to about 6 nm and the time duration of the pulse is shortened from - ps to about 250 fs as the slit opens wider while maintaining the mode-locking, and the center wavelength was tunable from 1.053 pm to 1.070 pm as the position of the slit was adjusted.
4. Conclusion We demonstrated the start-up of the passive mode-locking with a moving mirror in a Nd:glass fiber laser pumped by a single-stripe laser diode and the variation of the threshold for the start-up was investigated by changing the fiber length. It was found that the equation for the selfstarting condition could be applied to the laser started with a moving mirror by introducing a proportional constant, about 0.04, to take into account the reduction of the build-up time of mode-locking due to the moving mirror, and that an intracavity slit adjusting the lasing spectrum helped the start-up and maintenance of the mode-locking. As the lasing wavelength of the N&glass fiber laser matched well with the gain peak of the Nd:phosphate glass, the Nd:glass fiber laser pumped by an LD is well suited as a cost effective, femtosecond front-end oscillator for a CPA Nd:glass laser.
137 (19971 M-68
Acknowledgements
We are grateful to advice. This research Defence Development, tro-Optics at the Korea Technology.
BY. Kim and B.T. Kim for their was supported by the Agency for Korea, through the Center for ElecAdvanced Institute of Science and
References
[ll Ch. Spielmann, F. Krausz, T. Brabec, E. Winmer and A.J. Schmidt, Appl. Phys. Lett. 58 (1991) 247’0. [2] D.W. Hughes and J.R.M. Barr, J. Phys. D 25 (1992) 563. [3] M. Hofer, M.E. Fermann, F. Haberl, M.H. Ober and A.J. Schmidt, Optics Lett. 16 (1991) 502. [4] M. Hofer, M.H. Ober, F. Haberl and M.E. Fermann, IEEE J. Quantum Electron. 28 ( 1992) 720. [5] M.H. Ober, M. Hofer and M.E. Fermann, Optics Lctt. 18 ( 1993) 367. 161 M.H. Ober, F. Haberl and M.F. Fermann, Appl. Phys. Lett. 60 (1992) 2177. [7] F. Krausz, E. Wintner, A.J. Schmidt and A. Dienes, IEEE J. Quantum Electron. 26 (1990) 158. [8] C. Rouyer, E. Mazataud, I. Allais, A. Pierre, S. Seznec, C. Sauteret, G. Mourou and A. Migus, Optics Lett. 18 (1993) 214. 191 F. Krausz, M.E. Fermann, T. Brabec, P.F. Curley, M. Hofer, M.H. Ober, Ch. Spielmann, E. Wmtner and A.J. Schmidt, IEEE J. Quantum Electron. 28 (1992) 2097. [ 101 G.P. Agrawal, Nonlinear Fiber Optics (Academic, New York, 1989) Sec. 2.3. [I 11 Q. Wu, J.Y. Zhou, X.G. Huang, Z.X. Li and Q.X. Li, J. Opt. See. Am. B 10 (1993) 2080. [12] II. Keller, T.H. Chiu and J.F. Ferguson, Optics Lett. 18 (1993) 1077. [13] D. Kopf, F.X. Khmer, K.J. Weingarten and U. Keller, Optics Lett. 19 (1994) 2146.