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Yb co-doped fiber ring laser
Optics Communications 263 (2006) 47–51 www.elsevier.com/locate/optcom
Self-Q-switching and mode-locking in an all-fiber Er/Yb co-doped fiber ring laser Shu-min Zhang a
a,b,*
, Fu-yun Lu b, Jian Wang
b
Department of Physics, Hebei Normal University, Yuhua East Road 265, Shijiazhuang 050016, China b Institute of Physics, Nankai University, Tianjin 300071, China Received 26 January 2005; received in revised form 31 December 2005; accepted 12 January 2006
Abstract Using a section of un-pumped Er/Yb co-doped fiber (EYDF) as a saturable absorber, Self-Q-switching and self-mode-locking pulses have been obtained in an all-fiber EYDF ring laser. Such laser is with the self-Q-switched pulse threshold of 135.22 mW, the repetition rate of approximately 22.2 kHz, and the pulse duration of 2.8 ls, respectively. The self-mode-locked threshold is 591.8 mW. By incorporating the saturable absorption in an un-pumped EYDF and a Mach–Zehnder interferometer, when the pump power is increased to 1242.9 mW, the continuous-wave (CW) mode-locking with the pulse width of 26 ns has also been demonstrated experimentally for the first time. 2006 Elsevier B.V. All rights reserved. PACS: 42.60.G; 42.55.W; 42.60.F Keywords: Optical fiber laser; Q-switching; Mode-locking
1. Introduction Recently, high-energy Q-switched fiber lasers have attracted considerable interest because of their potential applications in time domain reflectometry and laser range finding. Much attention has been paid to develop passively Q-switched fiber lasers since they can provide a compact and simple design [1–3]. By using a AOM as a Q-switch or a Co2+:ZnSe crystal as a saturable absorber, in Q-switched Er3+-doped fiber lasers, the self-mode-locking effect, which causes split pulses, has been observed and reported recently [4,5], the CW mode-locking has also been reported by using an Er3+-doped fiber cooled to 4.2 K as a saturable absorber [6]. Compared with Er3+-doped fiber, Er/Yb co-doped fiber (EYDF) can be used to suppress the self-pulsing of Er3+ *
Corresponding author. Tel.: +86 31186268808; fax: +86 31186268302. E-mail address: [email protected] (S.-m. Zhang).
0030-4018/$ - see front matter 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2006.01.022
ion-pair [7], so to avoid the serious degradation of gain and pump efficiency even for high Erbium concentrations. This advantage makes it practical to apply the cladding pumping method to EYDF lasers. On the other hand, when an EYDF is pumped, the pump light is mainly absorbed by the Yb ions and then transferred to the adjacent Er ions, and thus the choice of the pumping sources is extended to a much broader range of 800–1100 nm [8]. In this paper, we report an all-fiber, cladding-pumped, self-Q-switched and mode-locked laser, which uses a section of un-pumped EYDF operating at room temperature as a saturable absorber to obtain the Q-switching and selfmode-locking pulses. In this manner, one can make the design rather convenient. It is found that the temporal pulses are related to the pump conditions. By incorporating the saturable absorption in an un-pumped EYDF and a Mach–Zehnder interferometer (MZI), when the pump power is increased to 1242.9 mW, the CW mode-locking with the pulse width of 26 ns has also been demonstrated experimentally for the first time. The output
48
S.-m. Zhang et al. / Optics Communications 263 (2006) 47–51
characteristics both in temporal and spectral domains have been described.
couplers and several pieces of fiber sections. Its transmission matrix is [9] T ¼ q1 q2 þ ð1 q1 Þð1 q2 Þ
2. Experimental setup and results
2½q1 q2 ð1 q1 Þð1 q2 Þ
The experimental setup is shown in Fig. 1. It is a traveling wave fiber-ring-laser cavity containing a 9-m-long EYDF as the gain medium. The EYDF has a core numerical aperture of 0.15, a core diameter of 5.5 lm and starshape inner cladding of 130 lm. The concentration for Er3+ and Yb3+ is 4.5 · 1025 m3 and 6 · 1026 m3, respectively. The absorption coefficients for Er3+ at 1535 nm and Yb3+ at 976 nm are 39 dB m1 and 389 dB m1, respectively. Six multimode pump LDs, which provide the total power of up to 3.6 W at 976 nm, cladding-pump EYDF through a tapered fiber bundle (TFB). An isolator is inserted in the cavity to prevent back reflection. The total cavity length is about 15 m, corresponding to a pulse repetition rate of 13 MHz. A 3-dB coupler extracts the pulse output. A power meter, a high-speed photo-detector, and an optical spectrum analyzer are used to measure the average power, temporal pulse shape and optical spectrum, respectively. The key element providing Q-switching and mode-locking of the laser is the 9-m-long EYDF. As mentioned above, the absorption coefficient for Yb3+ at 976 nm is 389 dB m1. The residual pump power is about 3.4 dB m after traveling 10 cm in the EYDF even the injected pump power is as high as 35.56 dB m. On the other hand, the absorption coefficient at 1549.3 nm is about 29 dB m1, so the total linear absorption of the un-pumped EYDF over a length of 9 m is as high as 261 dB, which is high enough and the absorption bleaching (saturated absorption) will occur, which will result in the formation of the self-Q-switched mode-locking [6]. A fiber Bragg grating (FBG), which has a central wavelength of 1549.3 nm and a peak reflectivity of 99%, is used as a wavelength selector. To generate a stable CW mode-locking pulse, a MZI is used in the cavity. The MZI is composed of two 3-dB fiber
1=2
cosðUL þ UNL Þ;
ð1Þ
where the linear and nonlinear parts of the relative phase shift are given by UL ¼ b1 L1 b2 L2 ;
UNL ¼ cP 0 ½q1 L1 ð1 q1 ÞL2 ;
ð2Þ
where q1 and q2 are the power-splitting fractions, the MZI is made up of two 3-dB couplers, so that q1 ¼ q2 ¼ 12. L1 and L2 are the lengths and b1 and b2 are the propagation constants for the two arms of the MZI, respectively, and P0 is the power of the pulse. From Eq. 1 we can see that if we choose an appropriate optical path difference between the two arms, (in our letter, we chose DL = L2 L1 is 0.3 mm), the relative linear phases will be set appropriately, and the nonlinear phase shift may lead to constructive interference near the peak of the pulse, while the wings of the pulse will experience destructive interference. As a result, such an interferometer will tend to shorten an optical pulse and act effectively as a fast-responding saturable absorber. The dependence of the average output power against the pump power is shown in Fig. 2. It shows that the lasing threshold is 103.50 mW. When the pump power is increased to 135.22 mW, the laser will transit to a selfQ-switching mode. The spectrum of laser oscillation in the self-Q-switching mode is shown in Fig. 3. The 3-dB bandwidth of the laser is less than 0.1 nm (the resolution is limited by the spectrum analyzer). The side mode suppression ratio is greater than 41 dB. Fig. 4(a) and (b) shows the typical train of Q-switching pulses and the corresponding single pulse at the pump power of 338.9 mW, respectively. The train of Q-switching pulses has the repetition rate of 22.2 kHz, and the pulse width of 2.8 ls. Fig. 4(c) and (d) shows the single pulse at different pump power. The intensity modulation will become deeper with the increase of the pump power. When
EYDF LD LDLD ISO
TFB
OSA
LD LD LD
power meter
3dB coupler
L1 3dB coupler
Photodetector
grating 3dB coupler
L2
Fig. 1. Schematic diagram of the self-Q-switched EYDF ring laser: LD, laser diode; OSA, optical spectrum analyzer; ISO, fiber isolator; EYDF, Er/Yb co-doped fiber; TFB, tapered fiber bundle.
Average output power (mW)
S.-m. Zhang et al. / Optics Communications 263 (2006) 47–51
49
350 300 250 200 150 100 50 0 0
500
1000 1500
2000 2500 3000 3500 4000
Pump power (mW) Fig. 2. Average output power versus the pump power.
Fig. 3. The measured output spectrum of the Q-switched EYDF laser.
the pump power is increased to 591.8 mW, the selfmode-locking is observed (Fig. 4(d)), with the modulation period of about 76 ns, which corresponds to the cavity transit time. It is well known that the self-mode-locking occurs when two or more longitudinal modes begin to oscillate, and their mutual interference causes a periodic amplitude fluctuation at a frequency equals to the spacing between the modes. These intensity modulations can be enhanced through the saturated absorption in the EYDF. When the pump power exceeds 683 mW, the Q-switching becomes more unstable with a timing jitter, and no clear and stable Q-switching pulses can be observed. At a further increase of the pump power, the Q-switching regime will be replaced by continuous-wave light oscillation (see Fig. 5). In order to explain this characteristic, we show the dependences of the repetition rate and the pulse width versus the pump power in Fig. 6. One can deduce from Fig. 6 that the pulses are squeezed with pump power, while the repetition rate of Q-switching linearly increases, correspondingly, the period of the pulses in Q-switching will decrease. Since the squeeze rate of the
Fig. 4. The measured (a) trains of the Q-switching pulses when the pump power was 338.9 mW, (b) wave forms of one pulse corresponding to (a, c) wave form of one pulse when pump power was 433.70 mW, and (d) wave form of self-mode-locking in a Q-switching pulse when pump power was 591.8 mW.
50
S.-m. Zhang et al. / Optics Communications 263 (2006) 47–51
Fig. 5. The CW oscillation when pump power was 701.1 mW.
50
8
40
6
30
4
20
2
10
0 100
200
300
400
500
600
700
Repetition rate (KHz)
10
Fig. 7. The measured oscillation wave forms in CW mode-locking for the pump power of 1242.9 mW when (a) the cavity length is 15 m and (b) the cavity length is 20 m.
0 800
Pump power (mW) Fig. 6. The measured pulse duration and repetition rate versus the pump power.
pulses is increased 25 ns, which is in accordance to our experiments results. 3. Conclusion
pulses is considerably slower than the change of the repetition rate, when the period between the adjacent pulses approaches the pulse duration of the Q-switching pulse, the Q-switching regime will be replaced by the continuous-wave light oscillation. If we further increase the pump power to 1242.9 mW, the CW mode-locked threshold is achieved, and because of the saturable-absorber effect and the MZI, stable CW mode-locked pulses will be observed. As shown in Fig. 7(a), the repetition rate is 13.16 MHz, and the pulse width is 26 ns. In the following experiment, by changing the cavity length from 15 m to 20 m, we can also obtain the CW mode-locking pulses as shown in Fig. 7(b), in which the pulse width is about 26 ns, and the repetition rate is approximately 9.8 MHz. According to the mode-locking theory, the interval between two adjacent pulses is Dt ¼
nL ; c
ð3Þ
where L is the cavity length and c is the velocity of light in vacuum. From Eq. (3) we can see that when the cavity length is increased 5 m, the interval between two adjacent
A self-Q-switched and mode-locked fiber ring laser operating at 1549.3 nm has been demonstrated. By using an un-pumped EYDF operation at room temperature as the saturable absorber and the FBG as the wavelength selector, a narrow line-width self-Q-switched fiber laser with the threshold of 135.22 mW, and the 3-dB bandwidth less than 0.1 nm has been obtained. The deepness of the intensity modulation of single pulse increases with the pump power. When the pump power increases to 591.8 mW, the selfmode-locking in the Q-switching pulse can be observed. It has also been found that by incorporating a Mach–Zehnder interferometer as a fast-responding saturable absorber, stable CW mode-locking with the width of 26 ns can also be obtained when the pump power is increased to 1242.9 mW. About our experimental conclusion, we offer the detailed description in principle. Acknowledgements This research was supported by Hebei Natural Science Foundation (2001241) and the Tianjin a key project Foundation of China (Grant 033183611).
S.-m. Zhang et al. / Optics Communications 263 (2006) 47–51
References [1] V.N. Filippov, A.N. Starodumov, A.V. Kiryanov, Opt. Lett. 26 (2001) 343. [2] A. Wang, H. Ming, J. Xie, X. Chen, L. Lv, W. Huang, L. Xu, Appl. Opt. 42 (2003) 3528. [3] A.V. Kiryano, V.N. Filippov, A.N. Starodumov, J. Opt. Soc. Am. B 19 (2002) 353. [4] P. Myslinski, J. Chrostowski, J.A.K. Konigstein, J.R. Simpon, Appl. Opt. 32 (1993) 286.
51
[5] V.N. Philippov, A.V. Kiryanov, S. Unger, IEEE Photonics Technnol. Lett. 16 (2004) 57. [6] M. Nakazawa, K. Suzuki, H. Kubota, Y. Kimura, Opt. Lett. 18 (1993) 613. [7] M. Ding, P.K. Cheo, Photon. Technol. Lett. 9 (1997) 324. [8] W.L. Barnes, S.B. Poole, J.E. Townsent, L. Reekie, D.J. Taylor, D.N. Payne, J. Lightwave Technol. 7 (1989) 1461. [9] G.P. Agrawal, Applications of Nonlinear Fiber Optics, Academic Press, University of Rochester, Rochester, 2001.
Self-Q-switching and mode-locking in an all-fiber Er/Yb co-doped fiber ring laser Shu-min Zhang a
a,b,*
, Fu-yun Lu b, Jian Wang
b
Department of Physics, Hebei Normal University, Yuhua East Road 265, Shijiazhuang 050016, China b Institute of Physics, Nankai University, Tianjin 300071, China Received 26 January 2005; received in revised form 31 December 2005; accepted 12 January 2006
Abstract Using a section of un-pumped Er/Yb co-doped fiber (EYDF) as a saturable absorber, Self-Q-switching and self-mode-locking pulses have been obtained in an all-fiber EYDF ring laser. Such laser is with the self-Q-switched pulse threshold of 135.22 mW, the repetition rate of approximately 22.2 kHz, and the pulse duration of 2.8 ls, respectively. The self-mode-locked threshold is 591.8 mW. By incorporating the saturable absorption in an un-pumped EYDF and a Mach–Zehnder interferometer, when the pump power is increased to 1242.9 mW, the continuous-wave (CW) mode-locking with the pulse width of 26 ns has also been demonstrated experimentally for the first time. 2006 Elsevier B.V. All rights reserved. PACS: 42.60.G; 42.55.W; 42.60.F Keywords: Optical fiber laser; Q-switching; Mode-locking
1. Introduction Recently, high-energy Q-switched fiber lasers have attracted considerable interest because of their potential applications in time domain reflectometry and laser range finding. Much attention has been paid to develop passively Q-switched fiber lasers since they can provide a compact and simple design [1–3]. By using a AOM as a Q-switch or a Co2+:ZnSe crystal as a saturable absorber, in Q-switched Er3+-doped fiber lasers, the self-mode-locking effect, which causes split pulses, has been observed and reported recently [4,5], the CW mode-locking has also been reported by using an Er3+-doped fiber cooled to 4.2 K as a saturable absorber [6]. Compared with Er3+-doped fiber, Er/Yb co-doped fiber (EYDF) can be used to suppress the self-pulsing of Er3+ *
Corresponding author. Tel.: +86 31186268808; fax: +86 31186268302. E-mail address: [email protected] (S.-m. Zhang).
0030-4018/$ - see front matter 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2006.01.022
ion-pair [7], so to avoid the serious degradation of gain and pump efficiency even for high Erbium concentrations. This advantage makes it practical to apply the cladding pumping method to EYDF lasers. On the other hand, when an EYDF is pumped, the pump light is mainly absorbed by the Yb ions and then transferred to the adjacent Er ions, and thus the choice of the pumping sources is extended to a much broader range of 800–1100 nm [8]. In this paper, we report an all-fiber, cladding-pumped, self-Q-switched and mode-locked laser, which uses a section of un-pumped EYDF operating at room temperature as a saturable absorber to obtain the Q-switching and selfmode-locking pulses. In this manner, one can make the design rather convenient. It is found that the temporal pulses are related to the pump conditions. By incorporating the saturable absorption in an un-pumped EYDF and a Mach–Zehnder interferometer (MZI), when the pump power is increased to 1242.9 mW, the CW mode-locking with the pulse width of 26 ns has also been demonstrated experimentally for the first time. The output
48
S.-m. Zhang et al. / Optics Communications 263 (2006) 47–51
characteristics both in temporal and spectral domains have been described.
couplers and several pieces of fiber sections. Its transmission matrix is [9] T ¼ q1 q2 þ ð1 q1 Þð1 q2 Þ
2. Experimental setup and results
2½q1 q2 ð1 q1 Þð1 q2 Þ
The experimental setup is shown in Fig. 1. It is a traveling wave fiber-ring-laser cavity containing a 9-m-long EYDF as the gain medium. The EYDF has a core numerical aperture of 0.15, a core diameter of 5.5 lm and starshape inner cladding of 130 lm. The concentration for Er3+ and Yb3+ is 4.5 · 1025 m3 and 6 · 1026 m3, respectively. The absorption coefficients for Er3+ at 1535 nm and Yb3+ at 976 nm are 39 dB m1 and 389 dB m1, respectively. Six multimode pump LDs, which provide the total power of up to 3.6 W at 976 nm, cladding-pump EYDF through a tapered fiber bundle (TFB). An isolator is inserted in the cavity to prevent back reflection. The total cavity length is about 15 m, corresponding to a pulse repetition rate of 13 MHz. A 3-dB coupler extracts the pulse output. A power meter, a high-speed photo-detector, and an optical spectrum analyzer are used to measure the average power, temporal pulse shape and optical spectrum, respectively. The key element providing Q-switching and mode-locking of the laser is the 9-m-long EYDF. As mentioned above, the absorption coefficient for Yb3+ at 976 nm is 389 dB m1. The residual pump power is about 3.4 dB m after traveling 10 cm in the EYDF even the injected pump power is as high as 35.56 dB m. On the other hand, the absorption coefficient at 1549.3 nm is about 29 dB m1, so the total linear absorption of the un-pumped EYDF over a length of 9 m is as high as 261 dB, which is high enough and the absorption bleaching (saturated absorption) will occur, which will result in the formation of the self-Q-switched mode-locking [6]. A fiber Bragg grating (FBG), which has a central wavelength of 1549.3 nm and a peak reflectivity of 99%, is used as a wavelength selector. To generate a stable CW mode-locking pulse, a MZI is used in the cavity. The MZI is composed of two 3-dB fiber
1=2
cosðUL þ UNL Þ;
ð1Þ
where the linear and nonlinear parts of the relative phase shift are given by UL ¼ b1 L1 b2 L2 ;
UNL ¼ cP 0 ½q1 L1 ð1 q1 ÞL2 ;
ð2Þ
where q1 and q2 are the power-splitting fractions, the MZI is made up of two 3-dB couplers, so that q1 ¼ q2 ¼ 12. L1 and L2 are the lengths and b1 and b2 are the propagation constants for the two arms of the MZI, respectively, and P0 is the power of the pulse. From Eq. 1 we can see that if we choose an appropriate optical path difference between the two arms, (in our letter, we chose DL = L2 L1 is 0.3 mm), the relative linear phases will be set appropriately, and the nonlinear phase shift may lead to constructive interference near the peak of the pulse, while the wings of the pulse will experience destructive interference. As a result, such an interferometer will tend to shorten an optical pulse and act effectively as a fast-responding saturable absorber. The dependence of the average output power against the pump power is shown in Fig. 2. It shows that the lasing threshold is 103.50 mW. When the pump power is increased to 135.22 mW, the laser will transit to a selfQ-switching mode. The spectrum of laser oscillation in the self-Q-switching mode is shown in Fig. 3. The 3-dB bandwidth of the laser is less than 0.1 nm (the resolution is limited by the spectrum analyzer). The side mode suppression ratio is greater than 41 dB. Fig. 4(a) and (b) shows the typical train of Q-switching pulses and the corresponding single pulse at the pump power of 338.9 mW, respectively. The train of Q-switching pulses has the repetition rate of 22.2 kHz, and the pulse width of 2.8 ls. Fig. 4(c) and (d) shows the single pulse at different pump power. The intensity modulation will become deeper with the increase of the pump power. When
EYDF LD LDLD ISO
TFB
OSA
LD LD LD
power meter
3dB coupler
L1 3dB coupler
Photodetector
grating 3dB coupler
L2
Fig. 1. Schematic diagram of the self-Q-switched EYDF ring laser: LD, laser diode; OSA, optical spectrum analyzer; ISO, fiber isolator; EYDF, Er/Yb co-doped fiber; TFB, tapered fiber bundle.
Average output power (mW)
S.-m. Zhang et al. / Optics Communications 263 (2006) 47–51
49
350 300 250 200 150 100 50 0 0
500
1000 1500
2000 2500 3000 3500 4000
Pump power (mW) Fig. 2. Average output power versus the pump power.
Fig. 3. The measured output spectrum of the Q-switched EYDF laser.
the pump power is increased to 591.8 mW, the selfmode-locking is observed (Fig. 4(d)), with the modulation period of about 76 ns, which corresponds to the cavity transit time. It is well known that the self-mode-locking occurs when two or more longitudinal modes begin to oscillate, and their mutual interference causes a periodic amplitude fluctuation at a frequency equals to the spacing between the modes. These intensity modulations can be enhanced through the saturated absorption in the EYDF. When the pump power exceeds 683 mW, the Q-switching becomes more unstable with a timing jitter, and no clear and stable Q-switching pulses can be observed. At a further increase of the pump power, the Q-switching regime will be replaced by continuous-wave light oscillation (see Fig. 5). In order to explain this characteristic, we show the dependences of the repetition rate and the pulse width versus the pump power in Fig. 6. One can deduce from Fig. 6 that the pulses are squeezed with pump power, while the repetition rate of Q-switching linearly increases, correspondingly, the period of the pulses in Q-switching will decrease. Since the squeeze rate of the
Fig. 4. The measured (a) trains of the Q-switching pulses when the pump power was 338.9 mW, (b) wave forms of one pulse corresponding to (a, c) wave form of one pulse when pump power was 433.70 mW, and (d) wave form of self-mode-locking in a Q-switching pulse when pump power was 591.8 mW.
50
S.-m. Zhang et al. / Optics Communications 263 (2006) 47–51
Fig. 5. The CW oscillation when pump power was 701.1 mW.
50
8
40
6
30
4
20
2
10
0 100
200
300
400
500
600
700
Repetition rate (KHz)
10
Fig. 7. The measured oscillation wave forms in CW mode-locking for the pump power of 1242.9 mW when (a) the cavity length is 15 m and (b) the cavity length is 20 m.
0 800
Pump power (mW) Fig. 6. The measured pulse duration and repetition rate versus the pump power.
pulses is increased 25 ns, which is in accordance to our experiments results. 3. Conclusion
pulses is considerably slower than the change of the repetition rate, when the period between the adjacent pulses approaches the pulse duration of the Q-switching pulse, the Q-switching regime will be replaced by the continuous-wave light oscillation. If we further increase the pump power to 1242.9 mW, the CW mode-locked threshold is achieved, and because of the saturable-absorber effect and the MZI, stable CW mode-locked pulses will be observed. As shown in Fig. 7(a), the repetition rate is 13.16 MHz, and the pulse width is 26 ns. In the following experiment, by changing the cavity length from 15 m to 20 m, we can also obtain the CW mode-locking pulses as shown in Fig. 7(b), in which the pulse width is about 26 ns, and the repetition rate is approximately 9.8 MHz. According to the mode-locking theory, the interval between two adjacent pulses is Dt ¼
nL ; c
ð3Þ
where L is the cavity length and c is the velocity of light in vacuum. From Eq. (3) we can see that when the cavity length is increased 5 m, the interval between two adjacent
A self-Q-switched and mode-locked fiber ring laser operating at 1549.3 nm has been demonstrated. By using an un-pumped EYDF operation at room temperature as the saturable absorber and the FBG as the wavelength selector, a narrow line-width self-Q-switched fiber laser with the threshold of 135.22 mW, and the 3-dB bandwidth less than 0.1 nm has been obtained. The deepness of the intensity modulation of single pulse increases with the pump power. When the pump power increases to 591.8 mW, the selfmode-locking in the Q-switching pulse can be observed. It has also been found that by incorporating a Mach–Zehnder interferometer as a fast-responding saturable absorber, stable CW mode-locking with the width of 26 ns can also be obtained when the pump power is increased to 1242.9 mW. About our experimental conclusion, we offer the detailed description in principle. Acknowledgements This research was supported by Hebei Natural Science Foundation (2001241) and the Tianjin a key project Foundation of China (Grant 033183611).
S.-m. Zhang et al. / Optics Communications 263 (2006) 47–51
References [1] V.N. Filippov, A.N. Starodumov, A.V. Kiryanov, Opt. Lett. 26 (2001) 343. [2] A. Wang, H. Ming, J. Xie, X. Chen, L. Lv, W. Huang, L. Xu, Appl. Opt. 42 (2003) 3528. [3] A.V. Kiryano, V.N. Filippov, A.N. Starodumov, J. Opt. Soc. Am. B 19 (2002) 353. [4] P. Myslinski, J. Chrostowski, J.A.K. Konigstein, J.R. Simpon, Appl. Opt. 32 (1993) 286.
51
[5] V.N. Philippov, A.V. Kiryanov, S. Unger, IEEE Photonics Technnol. Lett. 16 (2004) 57. [6] M. Nakazawa, K. Suzuki, H. Kubota, Y. Kimura, Opt. Lett. 18 (1993) 613. [7] M. Ding, P.K. Cheo, Photon. Technol. Lett. 9 (1997) 324. [8] W.L. Barnes, S.B. Poole, J.E. Townsent, L. Reekie, D.J. Taylor, D.N. Payne, J. Lightwave Technol. 7 (1989) 1461. [9] G.P. Agrawal, Applications of Nonlinear Fiber Optics, Academic Press, University of Rochester, Rochester, 2001.