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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 15 — Jul. 16, 2012
  • pp: 16174–16179
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Theory of passive mode-locking of semiconductor disk lasers in the blue spectral range by metal nanocomposites

Kwang-Hyon Kim, Uwe Griebner, and Joachim Herrmann  »View Author Affiliations


Optics Express, Vol. 20, Issue 15, pp. 16174-16179 (2012)
http://dx.doi.org/10.1364/OE.20.016174


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Abstract

We theoretically study femtosecond pulse generation by passive mode-locking of semiconductor disk lasers operating in the blue spectral range using metal nanocomposites as slow saturable absorbers. By using the relation for the nonlinear dielectric response of a layer of silica glass doped with spherical silver nanoparticles and the master equation for mode-locking, we investigate the dynamics of pulse formation and the achievable pulse parameters and predict the generation of pulses as short as 50 fs at 420 nm in such lasers.

© 2012 OSA

1. Introduction

Metal nanocomposites exhibit saturable absorption most prominently in the visible spectral range (see e.g. [1

1. R. A. Ganeev, A. I. Ryasnyansky, A. L. Stepanov, and T. Usmanov, “Saturated absorption and nonlinear refraction of silicate glasses doped with silver nanoparticles at 532 nm,” Opt. Quantum Electron. 36(10), 949–960 (2004). [CrossRef]

,2

2. K.-H. Kim, A. Husakou, and J. Herrmann, “Saturable absorption in composites doped with metal nanoparticles,” Opt. Express 18(21), 21918–21925 (2010). [CrossRef] [PubMed]

]). The recovery time of such materials is in the range of a few picoseconds [3

3. V. Halté, J. Guille, J.-C. Merle, I. Perakis, and J.-Y. Bigot, “Electron dynamics in silver nanoparticles: comparison between thin films and glass embedded nanoparticles,” Phys. Rev. B 60(16), 11738–11746 (1999). [CrossRef]

,4

4. J. S. Melinger, V. D. Kleiman, D. McMorrow, F. Gröhn, B. J. Bauer, and E. Amis, “Ultrafast dynamics of gold-based nanocomposite materials,” J. Phys. Chem. B 107(18), 3424–3431 (2003). [CrossRef]

]. A prospective application of this type of absorbers is passive mode-locking. In comparison with other well-established mode-locking elements such as semiconductor saturable absorber mirrors (SESAMs) [5

5. U. Keller, K. J. Weingarten, F. X. Kartner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Honninger, N. Matuschek, and J. Aus der Au, “Semiconductor saturable absorber mirrors (SESAMs) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Top. Quantum Electron. 2(3), 435–453 (1996). [CrossRef]

], quantum dots [6

6. K. Wundke, S. Pötting, J. Auxier, A. Schülzgen, N. Peyghambarian, and N. F. Borrelli, “PbS quantum-dot doped glasses for ultrashort-pulse generation,” Appl. Phys. Lett. 76(1), 10–12 (2000). [CrossRef]

] and carbon nanotubes [7

7. A. Schmidt, S. Rivier, G. Steinmeyer, J. H. Yim, W. B. Cho, S. Lee, F. Rotermund, M. C. Pujol, X. Mateos, M. Aguiló, F. Díaz, V. Petrov, and U. Griebner, “Passive mode locking of Yb:KLuW using a single-walled carbon nanotube saturable absorber,” Opt. Lett. 33(7), 729–731 (2008). [CrossRef] [PubMed]

,8

8. S. Y. Set, H. Yaguchi, Y. Tanaka, and M. Jablonski, “Laser mode locking using a saturable absorber incorporating carbon nanotubes,” J. Lightwave Technol. 22(1), 51–56 (2004). [CrossRef]

], its operation range can be extended to much shorter wavelengths, down to the blue spectral range and exhibit several additional advantages. In the early works of mode-locking, saturable absorbers in the visible spectral range consisted of dyes dissolved in different solvents [9

9. J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena, 2nd ed. (Elsevier, Amsterdam, 2006).

]. The disadvantages of such saturable dyes, such as maintaining a constant stream in the dye jet, temperature sensitivity and long-term instability restricted their versatility.

In this paper, we analyze passive mode-locking of SDLs in the blue spectral range with metal nanocomposites as slow saturable absorbers from a theoretical point of view. To utilize the strong saturable absorption of NPs one has to ensure that the surface plasmon resonance (SPR) is located at the central lasing wavelength of the gain medium. In general, this is accomplished by tailoring the size and shape of metal NPs and choosing an appropriated embedding medium. Here we study passive mode-locking of a GaN-based SDL operating at a central wavelength of 420 nm. As will be shown, such laser can be mode-locked by a thin layer of silica glass doped with spherical silver NPs. The plasmon resonance of the latter is located at 414 nm.

2. Theoretical fundamentals

For a moderate pump fluence the change of the dielectric function of the metal is proportional to the change of the temperature of the electrons in the metal NPs. Based on these facts, an equation for the transient dielectric function of the metal NPs can be derived, which is given by [19

19. K.-H. Kim, U. Griebner, and J. Herrmann, “Theory of passive mode locking of solid-state lasers using metal nanocomposites as slow saturable absorbers,” Opt. Lett. 37(9), 1490–1492 (2012). [CrossRef] [PubMed]

]
εmt=εmεm(0)τep+χm(3)τeeτept|x(t')E(t')|2exp(tt'τee)dt',
(1)
where εm(0) is the linear and εm(t) the nonlinear dielectric function,χm(3) the degenerate third-order susceptibility of the metal at the pump wavelength, τee and τep are the electron-electron scattering time and the electron-phonon coupling time, respectively, x(t)=3εh/[εm(t)+2εh] is the time-dependent field enhancement factor,εh is the permittivity of host medium, and E(t) is the electric field of the incident light.

The effective dielectric function of metal nanocomposites can be directly calculated by using the Maxwell-Garnett model for nanospheres smaller than 10 nm, given by
εeff=εh1+2f(1x)1f(1x),
(2)
where f is the volume filling factor of the metal NPs. For larger or non-spherical NPs, the effective medium approximation in combination with the discrete dipole approximation can be used (for details, see [19

19. K.-H. Kim, U. Griebner, and J. Herrmann, “Theory of passive mode locking of solid-state lasers using metal nanocomposites as slow saturable absorbers,” Opt. Lett. 37(9), 1490–1492 (2012). [CrossRef] [PubMed]

]).

To study the lasing dynamics of SDLs containing a metal nanocomposite as a slow saturable absorber in the laser cavity, we apply the following standard master equation
TRA(T,t)T=iD2At2+[(1iα)gl+Dg,f2At2q(T,t)]A(T,t),
(3)
where TR is the round trip time, A is the envelope of the intracavity field, α is the linewidth enhancement factor, D is the group delay dispersion (GDD), Dg,f=g/Ωg2+1/Ωf2 is the gain and intracavity filter dispersion, Ωg and Ωf are the gain and filter bandwidth (HWHM), g(t) and l are the gain and the loss of passive cavity, and q(t) describes the saturable absorber loss and the nonlinear refractive index of the NP-nanocomposite, respectively (see e. g [14

14. E. J. Saarinen, R. Herda, and O. G. Okhotnikov, “Dynamics of pulse formation in mode-locked semiconductor disk lasers,” J. Opt. Soc. Am. B 24(11), 2784–2790 (2007). [CrossRef]

,15

15. R. Paschotta, R. Häring, A. Garnache, S. Hoogland, A. Tropper, and U. Keller, “Soliton-like pulse-shaping mechanism in passively mode-locked surface-emitting semiconductor lasers,” Appl. Phys. B 75(4-5), 445–451 (2002). [CrossRef]

,17

17. T.-C. Lu, B.-S. Cheng, and M.-C. Liu, “Temperature dependent gain characteristics in GaN-based vertical-cavity surface-emitting lasers,” Opt. Express 17(22), 20149–20154 (2009). [CrossRef] [PubMed]

].). In the above equation, the gain coefficient g(t) is given by
gt=gg0τgg|A(t)|2Eg,
(4)
where τg is the gain recovery time, Eg is the gain saturation energy dependent on the saturation fluence and the beam diameter on the gain medium. The absorber loss is given by
q(T,t)=i4πλLεeffd,
(5)
where λL is the central wavelength of the laser, εeff is the effective dielectric function of the composite, and d is its thickness. Since the effective dielectric function εeff is complex, q(T,t) becomes also a complex quantity leading to the modulation of both the loss and the refractive index during one round trip.

3. Numerical results

Figure 1(a)
Fig. 1 (a) Transient transmittance of silica glass doped with spherical Ag NPs smaller than 10 nm at 430 nm for different pump pulse fluences; Ag NP filling factor: 10−4, thickness of composite layer: 1 μm, pump pulse duration: 50 fs. (b)-(d) Pulse evolution in the GaN-based semiconductor disk laser (operating at 420 nm) passively mode-locked by silica glass doped with Ag nanospheres for GDD parameterD=100 fs2 and filling factor f=3.5×103. (b) Behavior of gain and loss during the pulse formation, (c) evolution of pulse energy on a µs-time scale, (d) pulse intensity and frequency shift during the pulse.
shows the transient transmittance of a 1-µm thin silica glass layer doped with Ag nanospheres smaller than 10 nm for different pump pulse fluences at 430 nm. The pump pulse duration is 50 fs and τee and τep were chosen to be 100 fs and 1 ps, respectively. The dielectric functions of silver and silica have been taken from [20

20. W. D. Lynch and W. R. Hunter, “Comments on the optical constants of metals and an introduction to the data for several metals,” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, Orlando, Fla., 1985).

] and χm(3) from [21

21. E. L. Falcão-Filho, C. B. de Araujo, A. Galembeck, M. M. Oliveira, and A. J. G. Zarbin, “Nonlinear susceptibility of colloids consisting of silver nanoparticles in carbon disulfide,” J. Opt. Soc. Am. B 22(11), 2444–2449 (2005). [CrossRef]

]. The calculated recovery time of the NP-nanocomposite yields 3 ps and compiles with the needed requirements of an absorber recovery time of few ps for femtosecond SDLs [13

13. P. Klopp, U. Griebner, M. Zorn, and M. Weyers, “Pulse repetition rate up to 92 GHz or pulse duration shorter than 110 fs from a mode-locked semiconductor disk laser,” Appl. Phys. Lett. 98(7), 071103 (2011). [CrossRef]

].

In Figs. 1(b)-1(d), we present calculated results and properties of the passively mode-locked laser operation of this laser with a group delay dispersion (GDD) of D=100 fs2 and a beam area on the metal nanocomposite of 0.002 mm2. Figure 1(b) demonstrates the mechanism of mode-locking. Pulse shortening and stability is explained by the combined action of the dynamics of saturable gain and saturable loss. This can be seen in Fig. 1(b) because the net gain is negative both at the leading and the trailing fronts of the generated pulse. The leading edge of the pulse is suppressed by the action of the absorber, until the pulse energy has reached a value at which the absorption is greatly diminished due to saturation. On the other hand, the trailing edge is suppressed as well because above a certain pulse energy the amplification is decreased due to the depletion of the population inversion in the gain medium. This mechanism is similar as in passively mode-locked dye lasers. In Fig. 1(c) the evolution of the pulse energy is presented. The formation of a pulse containing the highest pulse energy occurs at the very beginning of the process (~20 ns) while the pulse stabilization with the formation of a cw regime takes place on a much longer timescale (200 ns) because of the energy-depending dynamic of the pulse build-up with increasing round-trip numbers. After reaching the cw-regime, the resultant pulse duration is 83 fs. Figure 1(d) shows the intensity profile and the chirp of the pulse. The pulse is positively chirped which can be explained by the nonlinear index of gain and absorber.

Figure 2
Fig. 2 Pulse duration (a) and pulse energy (b) as a function of the group delay dispersion D for the GaN-based semiconductor disk laser at 420 nm passively mode-locked by Ag nanospheres doped silica glass: filling factor is f=3.5×103.
shows the dependencies of pulse duration and energy on the GDD. The other parameters are the same as in Fig. 1. Pulse shaping is unstable only for a small dispersion range between −150 fs2 and 40 fs2. This is attributed to the imbalance between the dispersion-induced pulse broadening and compression by the dynamic gain and loss due to the slow response of the gain and the metal NP-nanocomposite. The pulse duration in the positive and negative GDD ranges attain similar values. However, for the same pulse duration the absolute value of negative GDD is larger than those for positive GDD value which can be interpreted by the fact that the pulse broadening effect is stronger for positive GDD because of the positive chirp of the pulses. As Fig. 2(a) indicates the shortest pulse duration of about 54 fs is achieved for a negative dispersion parameter of D=160 fs2, while the shortest duration in the positive GDD range is very similar, about 55 fs for D = 50 fs2. In Fig. 2(b), the dependence of the pulse energy on the GDD parameter is presented. A remarkable point is the larger pulse energy in the positive GDD range than in the negative GDD range, which can be explained by the advancement of the pulse due to the negative GDD and the positive chirp leading to strong suppression in the leading part of the pulse by the absorber loss. Since the shortest pulse durations are very similar, the positive GDD range is more favorable due to the higher pulse energy.

Passive mode-locking by NP-composites is possible only in a small interval of filling factors. For filling factors smaller than f=3×103 the mode-locked operation becomes unstable due to the excessive dynamic range of saturable loss. For filling factors larger than f=4×103, lasing itself becomes impossible due to the negative small signal net gain. For f=3×103and f=3.5×103, the resultant pulse durations and pulse energies are τ0=87 and τ0=83 fs, and E=1.75 and E=0.55 nJ, respectively. These values are calculated for D=300 fs2. Other parameters were taken to be the same as in Fig. 2.

In Fig. 3
Fig. 3 Dependencies of pulse duration and energy on the beam area on the saturable absorber for D=300 fs2 (a) and D=300 fs2 (b).
we show the dependencies of pulse duration and energy on the beam area on the metal nanocomposite absorbers for the same absolute values of the pump power for GDD parameters D=300 fs2 and D=300 fs2. The other parameters are the same as in Fig. 1. The figure shows that the pulse duration has a shortest value for an optimum beam area (or correspondingly for an optimum pump fluence) but is not altered significantly when changing the beam area. This is in contrast to the case of dielectric solid-state lasers mode-locked by metal NP-nanocomposites, where the pulse duration depends much stronger on the beam area [18

18. D. A. Parthenopoulos and P. M. Rentzepis, “Three-dimensional optical storage memory,” Science 245(4920), 843–845 (1989). [CrossRef] [PubMed]

]. With the above given parameters, the fluence on the silver NP saturable absorber is in the range from ~15 to ~45 µJ/cm2.

4. Conclusion

To conclude, we have theoretically studied passive mode-locking of semiconductor disk lasers with metal nanocomposites as saturable absorbers in blue spectral range. For a GaN-based semiconductor disk laser operating at 420 nm and 1µm thick layer of silica glass doped with silver NPs, we studied the dependence of pulse parameters on the absorber and laser parameters and predicted a shortest pulse duration of about 50 fs. Compared with other saturable absorbers, the application of composites containing metal NPs offers several advantages. It allows the development of very compact and cheap mode-locking devices with tunable operation regions, extending from IR down to the blue spectral range.

References and links

1.

R. A. Ganeev, A. I. Ryasnyansky, A. L. Stepanov, and T. Usmanov, “Saturated absorption and nonlinear refraction of silicate glasses doped with silver nanoparticles at 532 nm,” Opt. Quantum Electron. 36(10), 949–960 (2004). [CrossRef]

2.

K.-H. Kim, A. Husakou, and J. Herrmann, “Saturable absorption in composites doped with metal nanoparticles,” Opt. Express 18(21), 21918–21925 (2010). [CrossRef] [PubMed]

3.

V. Halté, J. Guille, J.-C. Merle, I. Perakis, and J.-Y. Bigot, “Electron dynamics in silver nanoparticles: comparison between thin films and glass embedded nanoparticles,” Phys. Rev. B 60(16), 11738–11746 (1999). [CrossRef]

4.

J. S. Melinger, V. D. Kleiman, D. McMorrow, F. Gröhn, B. J. Bauer, and E. Amis, “Ultrafast dynamics of gold-based nanocomposite materials,” J. Phys. Chem. B 107(18), 3424–3431 (2003). [CrossRef]

5.

U. Keller, K. J. Weingarten, F. X. Kartner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Honninger, N. Matuschek, and J. Aus der Au, “Semiconductor saturable absorber mirrors (SESAMs) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Top. Quantum Electron. 2(3), 435–453 (1996). [CrossRef]

6.

K. Wundke, S. Pötting, J. Auxier, A. Schülzgen, N. Peyghambarian, and N. F. Borrelli, “PbS quantum-dot doped glasses for ultrashort-pulse generation,” Appl. Phys. Lett. 76(1), 10–12 (2000). [CrossRef]

7.

A. Schmidt, S. Rivier, G. Steinmeyer, J. H. Yim, W. B. Cho, S. Lee, F. Rotermund, M. C. Pujol, X. Mateos, M. Aguiló, F. Díaz, V. Petrov, and U. Griebner, “Passive mode locking of Yb:KLuW using a single-walled carbon nanotube saturable absorber,” Opt. Lett. 33(7), 729–731 (2008). [CrossRef] [PubMed]

8.

S. Y. Set, H. Yaguchi, Y. Tanaka, and M. Jablonski, “Laser mode locking using a saturable absorber incorporating carbon nanotubes,” J. Lightwave Technol. 22(1), 51–56 (2004). [CrossRef]

9.

J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena, 2nd ed. (Elsevier, Amsterdam, 2006).

10.

O. G. Okhotnikov, Semiconductor Disk Laser (Wiley-VHC, Weinheim, 2010).

11.

U. Keller and A. C. Tropper, “Passively mode-locked surface-emitting semiconductor lasers,” Phys. Rep. 429(2), 67–120 (2006). [CrossRef]

12.

F. Quinlan, G. Ycas, S. Osterman, and S. A. Diddams, “A 12.5 GHz-spaced optical frequency comb spanning >400 nm for near-infrared astronomical spectrograph calibration,” Rev. Sci. Instrum. 81(6), 063105 (2010). [CrossRef] [PubMed]

13.

P. Klopp, U. Griebner, M. Zorn, and M. Weyers, “Pulse repetition rate up to 92 GHz or pulse duration shorter than 110 fs from a mode-locked semiconductor disk laser,” Appl. Phys. Lett. 98(7), 071103 (2011). [CrossRef]

14.

E. J. Saarinen, R. Herda, and O. G. Okhotnikov, “Dynamics of pulse formation in mode-locked semiconductor disk lasers,” J. Opt. Soc. Am. B 24(11), 2784–2790 (2007). [CrossRef]

15.

R. Paschotta, R. Häring, A. Garnache, S. Hoogland, A. Tropper, and U. Keller, “Soliton-like pulse-shaping mechanism in passively mode-locked surface-emitting semiconductor lasers,” Appl. Phys. B 75(4-5), 445–451 (2002). [CrossRef]

16.

T.-C. Lu, J.-T. Chu, S.-W. Chen, B.-S. Cheng, H.-C. Kuo, and S.-C. Wang, “Lasing behavior, gain property, and strong coupling effects in GaN-based vertical-cavity surface-emitting lasers,” Jpn. J. Appl. Phys. 47(8), 6655–6659 (2008). [CrossRef]

17.

T.-C. Lu, B.-S. Cheng, and M.-C. Liu, “Temperature dependent gain characteristics in GaN-based vertical-cavity surface-emitting lasers,” Opt. Express 17(22), 20149–20154 (2009). [CrossRef] [PubMed]

18.

D. A. Parthenopoulos and P. M. Rentzepis, “Three-dimensional optical storage memory,” Science 245(4920), 843–845 (1989). [CrossRef] [PubMed]

19.

K.-H. Kim, U. Griebner, and J. Herrmann, “Theory of passive mode locking of solid-state lasers using metal nanocomposites as slow saturable absorbers,” Opt. Lett. 37(9), 1490–1492 (2012). [CrossRef] [PubMed]

20.

W. D. Lynch and W. R. Hunter, “Comments on the optical constants of metals and an introduction to the data for several metals,” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, Orlando, Fla., 1985).

21.

E. L. Falcão-Filho, C. B. de Araujo, A. Galembeck, M. M. Oliveira, and A. J. G. Zarbin, “Nonlinear susceptibility of colloids consisting of silver nanoparticles in carbon disulfide,” J. Opt. Soc. Am. B 22(11), 2444–2449 (2005). [CrossRef]

22.

Y.-K. Song, H. Zhou, M. Diagne, A. V. Nurmikko, R. P. Schneider, C. P. Kuo, M. R. Krames, R. S. Kern, C. Carter-Coman, and F. A. Kish, “A quasicontinuous wave, optically pumped violet vertical cavity surface emitting laser,” Appl. Phys. Lett. 76(13), 1662–1664 (2000). [CrossRef]

23.

I. V. Smetanin, P. P. Vasil’ev, and D. L. Boiko, “Theory of the ultrafast mode-locked GaN lasers in a large-signal regime,” Opt. Express 19(18), 17114–17120 (2011). [CrossRef] [PubMed]

24.

P. K. Jain, K. S. Lee, I. H. El-Sayed, and M. A. El-Sayed, “Calculated absorption and scattering properties of gold nanoparticles of different size, shape, and composition: applications in biological imaging and biomedicine,” J. Phys. Chem. B 110(14), 7238–7248 (2006). [CrossRef] [PubMed]

OCIS Codes
(320.7090) Ultrafast optics : Ultrafast lasers
(250.5403) Optoelectronics : Plasmonics

ToC Category:
Ultrafast Optics

History
Original Manuscript: March 23, 2012
Revised Manuscript: April 18, 2012
Manuscript Accepted: May 4, 2012
Published: July 2, 2012

Citation
Kwang-Hyon Kim, Uwe Griebner, and Joachim Herrmann, "Theory of passive mode-locking of semiconductor disk lasers in the blue spectral range by metal nanocomposites," Opt. Express 20, 16174-16179 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-15-16174


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References

  1. R. A. Ganeev, A. I. Ryasnyansky, A. L. Stepanov, and T. Usmanov, “Saturated absorption and nonlinear refraction of silicate glasses doped with silver nanoparticles at 532 nm,” Opt. Quantum Electron.36(10), 949–960 (2004). [CrossRef]
  2. K.-H. Kim, A. Husakou, and J. Herrmann, “Saturable absorption in composites doped with metal nanoparticles,” Opt. Express18(21), 21918–21925 (2010). [CrossRef] [PubMed]
  3. V. Halté, J. Guille, J.-C. Merle, I. Perakis, and J.-Y. Bigot, “Electron dynamics in silver nanoparticles: comparison between thin films and glass embedded nanoparticles,” Phys. Rev. B60(16), 11738–11746 (1999). [CrossRef]
  4. J. S. Melinger, V. D. Kleiman, D. McMorrow, F. Gröhn, B. J. Bauer, and E. Amis, “Ultrafast dynamics of gold-based nanocomposite materials,” J. Phys. Chem. B107(18), 3424–3431 (2003). [CrossRef]
  5. U. Keller, K. J. Weingarten, F. X. Kartner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Honninger, N. Matuschek, and J. Aus der Au, “Semiconductor saturable absorber mirrors (SESAMs) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Top. Quantum Electron.2(3), 435–453 (1996). [CrossRef]
  6. K. Wundke, S. Pötting, J. Auxier, A. Schülzgen, N. Peyghambarian, and N. F. Borrelli, “PbS quantum-dot doped glasses for ultrashort-pulse generation,” Appl. Phys. Lett.76(1), 10–12 (2000). [CrossRef]
  7. A. Schmidt, S. Rivier, G. Steinmeyer, J. H. Yim, W. B. Cho, S. Lee, F. Rotermund, M. C. Pujol, X. Mateos, M. Aguiló, F. Díaz, V. Petrov, and U. Griebner, “Passive mode locking of Yb:KLuW using a single-walled carbon nanotube saturable absorber,” Opt. Lett.33(7), 729–731 (2008). [CrossRef] [PubMed]
  8. S. Y. Set, H. Yaguchi, Y. Tanaka, and M. Jablonski, “Laser mode locking using a saturable absorber incorporating carbon nanotubes,” J. Lightwave Technol.22(1), 51–56 (2004). [CrossRef]
  9. J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena, 2nd ed. (Elsevier, Amsterdam, 2006).
  10. O. G. Okhotnikov, Semiconductor Disk Laser (Wiley-VHC, Weinheim, 2010).
  11. U. Keller and A. C. Tropper, “Passively mode-locked surface-emitting semiconductor lasers,” Phys. Rep.429(2), 67–120 (2006). [CrossRef]
  12. F. Quinlan, G. Ycas, S. Osterman, and S. A. Diddams, “A 12.5 GHz-spaced optical frequency comb spanning >400 nm for near-infrared astronomical spectrograph calibration,” Rev. Sci. Instrum.81(6), 063105 (2010). [CrossRef] [PubMed]
  13. P. Klopp, U. Griebner, M. Zorn, and M. Weyers, “Pulse repetition rate up to 92 GHz or pulse duration shorter than 110 fs from a mode-locked semiconductor disk laser,” Appl. Phys. Lett.98(7), 071103 (2011). [CrossRef]
  14. E. J. Saarinen, R. Herda, and O. G. Okhotnikov, “Dynamics of pulse formation in mode-locked semiconductor disk lasers,” J. Opt. Soc. Am. B24(11), 2784–2790 (2007). [CrossRef]
  15. R. Paschotta, R. Häring, A. Garnache, S. Hoogland, A. Tropper, and U. Keller, “Soliton-like pulse-shaping mechanism in passively mode-locked surface-emitting semiconductor lasers,” Appl. Phys. B75(4-5), 445–451 (2002). [CrossRef]
  16. T.-C. Lu, J.-T. Chu, S.-W. Chen, B.-S. Cheng, H.-C. Kuo, and S.-C. Wang, “Lasing behavior, gain property, and strong coupling effects in GaN-based vertical-cavity surface-emitting lasers,” Jpn. J. Appl. Phys.47(8), 6655–6659 (2008). [CrossRef]
  17. T.-C. Lu, B.-S. Cheng, and M.-C. Liu, “Temperature dependent gain characteristics in GaN-based vertical-cavity surface-emitting lasers,” Opt. Express17(22), 20149–20154 (2009). [CrossRef] [PubMed]
  18. D. A. Parthenopoulos and P. M. Rentzepis, “Three-dimensional optical storage memory,” Science245(4920), 843–845 (1989). [CrossRef] [PubMed]
  19. K.-H. Kim, U. Griebner, and J. Herrmann, “Theory of passive mode locking of solid-state lasers using metal nanocomposites as slow saturable absorbers,” Opt. Lett.37(9), 1490–1492 (2012). [CrossRef] [PubMed]
  20. W. D. Lynch and W. R. Hunter, “Comments on the optical constants of metals and an introduction to the data for several metals,” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, Orlando, Fla., 1985).
  21. E. L. Falcão-Filho, C. B. de Araujo, A. Galembeck, M. M. Oliveira, and A. J. G. Zarbin, “Nonlinear susceptibility of colloids consisting of silver nanoparticles in carbon disulfide,” J. Opt. Soc. Am. B22(11), 2444–2449 (2005). [CrossRef]
  22. Y.-K. Song, H. Zhou, M. Diagne, A. V. Nurmikko, R. P. Schneider, C. P. Kuo, M. R. Krames, R. S. Kern, C. Carter-Coman, and F. A. Kish, “A quasicontinuous wave, optically pumped violet vertical cavity surface emitting laser,” Appl. Phys. Lett.76(13), 1662–1664 (2000). [CrossRef]
  23. I. V. Smetanin, P. P. Vasil’ev, and D. L. Boiko, “Theory of the ultrafast mode-locked GaN lasers in a large-signal regime,” Opt. Express19(18), 17114–17120 (2011). [CrossRef] [PubMed]
  24. P. K. Jain, K. S. Lee, I. H. El-Sayed, and M. A. El-Sayed, “Calculated absorption and scattering properties of gold nanoparticles of different size, shape, and composition: applications in biological imaging and biomedicine,” J. Phys. Chem. B110(14), 7238–7248 (2006). [CrossRef] [PubMed]

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