Abstract

Self-mode-locking has become an emerging path to the generation of ultrashort pulses with vertical-external-cavity surface-emitting lasers. In our work, a strong Kerr nonlinearity that is so far assumed to give rise to mode-locked operation is evidenced and a strong nonlinearity enhancement by the microcavity is revealed. We present wavelength-dependent measurements of the nonlinear absorption and nonlinear refractive index change in a gain chip using the Z-scan technique. We report negative nonlinear refraction up to 5x10−12 cm2/W in magnitude in the (InGa)As/Ga(AsP) material system close to the laser design wavelength, which can lead to Kerr lensing. We show that by changing the angle of incidence of the probe beam with respect to the gain chip, the Kerr nonlinearity can be wavelength-tuned, shifting with the microcavity resonance. Such findings may ultimately lead to novel concepts with regard to tailored self-mode-locking behavior achievable by peculiar Kerr-lens chip designs for cost-effective, robust and compact fs-pulsed semiconductor lasers.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (1)

N. Vermeulen, D. Castelló-Lurbe, M. Khoder, I. Pasternak, A. Krajewska, T. Ciuk, W. Strupinski, J. Cheng, H. Thienpont, and J. Van Erps, “Graphene’s nonlinear-optical physics revealed through exponentially growing self-phase modulation,” Nat. Commun. 9(1), 2675 (2018).
[Crossref] [PubMed]

2017 (2)

R. Bek, M. Großmann, H. Kahle, M. Koch, A. Rahimi-Iman, M. Jetter, and P. Michler, “Self-mode-locked AlGaInP-VECSEL,” Appl. Phys. Lett. 111(18), 182105 (2017).
[Crossref]

C. G. E. Alfieri, D. Waldburger, S. M. Link, E. Gini, M. Golling, G. Eisenstein, and U. Keller, “Optical efficiency and gain dynamics of modelocked semiconductor disk lasers,” Opt. Express 25(6), 6402–6420 (2017).
[Crossref] [PubMed]

2016 (5)

J. Hader, M. Scheller, A. Laurain, I. Kilen, C. Baker, J. V. Moloney, and S. W. Koch, “Ultrafast non-equilibrium carrier dynamics in semiconductor laser mode-locking,” Semicond. Sci. Technol. 32(1), 013002 (2016).
[Crossref]

M. A. Gaafar, A. Rahimi-Iman, K. A. Fedorova, W. Stolz, E. U. Rafailov, and M. Koch, “Mode-locked Semiconductor Disk Lasers,” Adv. Opt. Photonics 8(3), 370–400 (2016).
[Crossref]

E. A. Shaw, A. H. Quarterman, A. P. Turnbull, T. Chen Sverre, C. R. Head, A. C. Tropper, and K. G. Wilcox, “Nonlinear Lensing in an Unpumped Antiresonant Semiconductor Disk Laser Gain Structure,” IEEE Photonics Technol. Lett. 28(13), 1395–1398 (2016).
[Crossref]

A. H. Quarterman, S. Mirkhanov, C. J. C. Smyth, and K. G. Wilcox, “Measurements of nonlinear lensing in a semiconductor disk laser gain sample under optical pumping and using a resonant femtosecond probe laser,” Appl. Phys. Lett. 109(12), 121113 (2016).
[Crossref]

E. Yüce, G. Ctistis, J. Claudon, J.-M. Gérard, and W. L. Vos, “Optimal all-optical switching of a microcavity resonance in the telecom range using the electronic Kerr effect,” Opt. Express 24(1), 239–253 (2016).
[Crossref] [PubMed]

2015 (2)

X. Zheng, Y. Zhang, R. Chen, X. Cheng, Z. Xu, and T. Jiang, “Z-scan measurement of the nonlinear refractive index of monolayer WS(2),” Opt. Express 23(12), 15616–15623 (2015).
[Crossref] [PubMed]

A. H. Quarterman, M. A. Tyrk, and K. G. Wilcox, “Z-scan measurements of the nonlinear refractive index of a pumped semiconductor disk laser gain medium,” Appl. Phys. Lett. 106(1), 011105 (2015).
[Crossref]

2014 (5)

2013 (2)

2012 (2)

L. Kornaszewski, G. Maker, G. P. A. Malcolm, M. Butkus, E. Rafailov, and C. J. Hamilton, “SESAM-free mode-locked semiconductor disk laser,” Laser Photonics Rev. 6(6), L20–L23 (2012).
[Crossref]

H. Zhang, S. Virally, Q. Bao, L. K. Ping, S. Massar, N. Godbout, and P. Kockaert, “Z-scan measurement of the nonlinear refractive index of graphene,” Opt. Lett. 37(11), 1856–1858 (2012).
[Crossref] [PubMed]

2011 (1)

2010 (1)

D. N. Christodoulides, I. C. Khoo, G. J. Salamo, G. I. Stegeman, and E. W. Van Stryland, “Nonlinear refraction and absorption: mechanisms and magnitudes,” Adv. Opt. Photonics 2(1), 60–200 (2010).
[Crossref]

2007 (1)

R. Liu, Y. Shu, G. Zhang, J. Sun, X. Xing, B. Pi, J. Yao, Z. Wang, and J. Xu, “Study of nonlinear absorption in GaAs/AlGaAs multiple quantum wells using the reflection Z-scan,” Opt. Quantum Electron. 39(14), 1207–1214 (2007).
[Crossref]

2006 (1)

A. C. Tropper and S. Hoogland, “Extended cavity surface-emitting semiconductor lasers,” Prog. Quantum Electron. 30(1), 1–43 (2006).
[Crossref]

2003 (2)

L. Brzozowski, E. H. Sargent, A. S. Thorpe, and M. Extavour, “Direct measurements of large near-band edge nonlinear index change from 1.48 to 1.55 μm in InGaAs/InAlGaAs multiquantum wells,” Appl. Phys. Lett. 82(25), 4429–4431 (2003).
[Crossref]

U. Keller, “Recent developments in compact ultrafast lasers,” Nature 424(6950), 831–838 (2003).
[Crossref] [PubMed]

2002 (1)

R. Paschotta, R. Häring, A. Garnache, S. Hoogland, A. C. 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]

1999 (1)

1996 (3)

1995 (1)

J. Mørk, A. Mecozzi, and C. Hultgren, “Spectral effects in short pulse pump-probe measurements,” Appl. Phys. Lett. 68, 449–541 (1995).
[Crossref]

1994 (2)

J. Wang, M. Sheik-Bahae, A. A. Said, D. J. Hagan, and E. W. Van Stryland, “Time-resolved Z-scan measurements of optical nonlinearities,” J. Opt. Soc. Am. B 11(6), 1009–1017 (1994).
[Crossref]

M. Sheik-Bahae and E. W. Van Stryland, “Ultrafast nonlinearities in semiconductor laser amplifiers,” Phys. Rev. B Condens. Matter 50(19), 14171–14178 (1994).
[Crossref] [PubMed]

1992 (1)

1991 (2)

M. Sheik-Bahae, D. C. D. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electron nonlinear refraction in solids,” IEEE J. Quantum Electron. 27(6), 1296–1309 (1991).
[Crossref]

D. E. Spence, P. N. Kean, and W. Sibbett, “60-fsec pulse generation from a self-mode-locked Ti:sapphire laser,” Opt. Lett. 16(1), 42–44 (1991).
[Crossref] [PubMed]

1990 (2)

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive Measurement of Optical Nonlinearities Using a Single Beam,” IEEE J. Quantum Electron. 26(4), 760–769 (1990).
[Crossref]

M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Dispersion and band-gap scaling of the electronic Kerr effect in solids associated with two-photon absorption,” Phys. Rev. Lett. 65(1), 96–99 (1990).
[Crossref] [PubMed]

1988 (2)

S. H. Park, J. F. Morhange, A. D. Jeffery, R. A. Morgan, A. Chavez-Pirson, H. M. Gibbs, S. W. Koch, N. Peyghambarian, M. Derstine, A. C. Gossard, J. H. English, and W. Weigmann, “Measurements of room-temperature band-gap-resonant optical nonlinearities of GaAs/AlGaAs multiple quantum wells and bulk GaAs,” Appl. Phys. Lett. 52(15), 1201–1203 (1988).
[Crossref]

E. W. Van Stryland, Y. Y. Wu, D. J. Hagan, M. J. Soileau, and K. Mansour, “Optical limiting with semiconductors,” J. Opt. Soc. Am. B 5(9), 1980–1988 (1988).
[Crossref]

1987 (2)

R. Adair, L. L. Chase, and S. A. Payne, “Nonlinear refractive-index measurements of glasses using three-wave frequency mixing,” J. Opt. Soc. Am. B 4(6), 875–881 (1987).
[Crossref]

A. M. Fox, A. C. Maciel, M. G. Shorthose, J. F. Ryan, M. D. Scott, J. I. Davies, and J. R. Riffat, “Nonlinear excitonic optical absorption in GaInAs/InP quantum wells,” Appl. Phys. Lett. 51(1), 30–32 (1987).
[Crossref]

1986 (1)

Y. H. Lee, A. Chavez-Pirson, S. W. Koch, H. M. Gibbs, S. H. Park, J. Morhange, A. Jeffery, N. Peyghambarian, L. Banyai, A. C. Gossard, and W. Wiegmann, “Room-temperature optical nonlinearities in GaAs,” Phys. Rev. Lett. 57(19), 2446–2449 (1986).
[Crossref] [PubMed]

1979 (1)

1975 (1)

M. J. Moran, C. Y. She, and R. L. Carman, “Interferometric Measurements of the Nonlinear Refractive-Index Coefficient Relative to CS2 in Laser-System-Related Materials,” IEEE J. Quantum Electron. 11(6), 259–263 (1975).
[Crossref]

Adair, R.

Albrecht, A. R.

Alfieri, C. G. E.

Angelow, G.

Baker, C.

J. Hader, M. Scheller, A. Laurain, I. Kilen, C. Baker, J. V. Moloney, and S. W. Koch, “Ultrafast non-equilibrium carrier dynamics in semiconductor laser mode-locking,” Semicond. Sci. Technol. 32(1), 013002 (2016).
[Crossref]

Banyai, L.

Y. H. Lee, A. Chavez-Pirson, S. W. Koch, H. M. Gibbs, S. H. Park, J. Morhange, A. Jeffery, N. Peyghambarian, L. Banyai, A. C. Gossard, and W. Wiegmann, “Room-temperature optical nonlinearities in GaAs,” Phys. Rev. Lett. 57(19), 2446–2449 (1986).
[Crossref] [PubMed]

Bao, Q.

Bek, R.

R. Bek, M. Großmann, H. Kahle, M. Koch, A. Rahimi-Iman, M. Jetter, and P. Michler, “Self-mode-locked AlGaInP-VECSEL,” Appl. Phys. Lett. 111(18), 182105 (2017).
[Crossref]

Brasch, V.

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8(2), 145–152 (2014).
[Crossref]

Brzozowski, L.

L. Brzozowski, E. H. Sargent, A. S. Thorpe, and M. Extavour, “Direct measurements of large near-band edge nonlinear index change from 1.48 to 1.55 μm in InGaAs/InAlGaAs multiquantum wells,” Appl. Phys. Lett. 82(25), 4429–4431 (2003).
[Crossref]

Butkus, M.

L. Kornaszewski, G. Maker, G. P. A. Malcolm, M. Butkus, E. Rafailov, and C. J. Hamilton, “SESAM-free mode-locked semiconductor disk laser,” Laser Photonics Rev. 6(6), L20–L23 (2012).
[Crossref]

Carman, R. L.

M. J. Moran, C. Y. She, and R. L. Carman, “Interferometric Measurements of the Nonlinear Refractive-Index Coefficient Relative to CS2 in Laser-System-Related Materials,” IEEE J. Quantum Electron. 11(6), 259–263 (1975).
[Crossref]

Castelló-Lurbe, D.

N. Vermeulen, D. Castelló-Lurbe, M. Khoder, I. Pasternak, A. Krajewska, T. Ciuk, W. Strupinski, J. Cheng, H. Thienpont, and J. Van Erps, “Graphene’s nonlinear-optical physics revealed through exponentially growing self-phase modulation,” Nat. Commun. 9(1), 2675 (2018).
[Crossref] [PubMed]

Cederberg, J. G.

Chase, L. L.

Chavez-Pirson, A.

S. H. Park, J. F. Morhange, A. D. Jeffery, R. A. Morgan, A. Chavez-Pirson, H. M. Gibbs, S. W. Koch, N. Peyghambarian, M. Derstine, A. C. Gossard, J. H. English, and W. Weigmann, “Measurements of room-temperature band-gap-resonant optical nonlinearities of GaAs/AlGaAs multiple quantum wells and bulk GaAs,” Appl. Phys. Lett. 52(15), 1201–1203 (1988).
[Crossref]

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S. H. Park, J. F. Morhange, A. D. Jeffery, R. A. Morgan, A. Chavez-Pirson, H. M. Gibbs, S. W. Koch, N. Peyghambarian, M. Derstine, A. C. Gossard, J. H. English, and W. Weigmann, “Measurements of room-temperature band-gap-resonant optical nonlinearities of GaAs/AlGaAs multiple quantum wells and bulk GaAs,” Appl. Phys. Lett. 52(15), 1201–1203 (1988).
[Crossref]

Y. H. Lee, A. Chavez-Pirson, S. W. Koch, H. M. Gibbs, S. H. Park, J. Morhange, A. Jeffery, N. Peyghambarian, L. Banyai, A. C. Gossard, and W. Wiegmann, “Room-temperature optical nonlinearities in GaAs,” Phys. Rev. Lett. 57(19), 2446–2449 (1986).
[Crossref] [PubMed]

Paschotta, R.

R. Paschotta, R. Häring, A. Garnache, S. Hoogland, A. C. 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]

Pasternak, I.

N. Vermeulen, D. Castelló-Lurbe, M. Khoder, I. Pasternak, A. Krajewska, T. Ciuk, W. Strupinski, J. Cheng, H. Thienpont, and J. Van Erps, “Graphene’s nonlinear-optical physics revealed through exponentially growing self-phase modulation,” Nat. Commun. 9(1), 2675 (2018).
[Crossref] [PubMed]

Payne, S. A.

Peceli, D.

Peyghambarian, N.

S. H. Park, J. F. Morhange, A. D. Jeffery, R. A. Morgan, A. Chavez-Pirson, H. M. Gibbs, S. W. Koch, N. Peyghambarian, M. Derstine, A. C. Gossard, J. H. English, and W. Weigmann, “Measurements of room-temperature band-gap-resonant optical nonlinearities of GaAs/AlGaAs multiple quantum wells and bulk GaAs,” Appl. Phys. Lett. 52(15), 1201–1203 (1988).
[Crossref]

Y. H. Lee, A. Chavez-Pirson, S. W. Koch, H. M. Gibbs, S. H. Park, J. Morhange, A. Jeffery, N. Peyghambarian, L. Banyai, A. C. Gossard, and W. Wiegmann, “Room-temperature optical nonlinearities in GaAs,” Phys. Rev. Lett. 57(19), 2446–2449 (1986).
[Crossref] [PubMed]

Pi, B.

R. Liu, Y. Shu, G. Zhang, J. Sun, X. Xing, B. Pi, J. Yao, Z. Wang, and J. Xu, “Study of nonlinear absorption in GaAs/AlGaAs multiple quantum wells using the reflection Z-scan,” Opt. Quantum Electron. 39(14), 1207–1214 (2007).
[Crossref]

Ping, L. K.

Quarterman, A. H.

E. A. Shaw, A. H. Quarterman, A. P. Turnbull, T. Chen Sverre, C. R. Head, A. C. Tropper, and K. G. Wilcox, “Nonlinear Lensing in an Unpumped Antiresonant Semiconductor Disk Laser Gain Structure,” IEEE Photonics Technol. Lett. 28(13), 1395–1398 (2016).
[Crossref]

A. H. Quarterman, S. Mirkhanov, C. J. C. Smyth, and K. G. Wilcox, “Measurements of nonlinear lensing in a semiconductor disk laser gain sample under optical pumping and using a resonant femtosecond probe laser,” Appl. Phys. Lett. 109(12), 121113 (2016).
[Crossref]

A. H. Quarterman, M. A. Tyrk, and K. G. Wilcox, “Z-scan measurements of the nonlinear refractive index of a pumped semiconductor disk laser gain medium,” Appl. Phys. Lett. 106(1), 011105 (2015).
[Crossref]

Rafailov, E.

L. Kornaszewski, G. Maker, G. P. A. Malcolm, M. Butkus, E. Rafailov, and C. J. Hamilton, “SESAM-free mode-locked semiconductor disk laser,” Laser Photonics Rev. 6(6), L20–L23 (2012).
[Crossref]

Rafailov, E. U.

Rahimi-Iman, A.

R. Bek, M. Großmann, H. Kahle, M. Koch, A. Rahimi-Iman, M. Jetter, and P. Michler, “Self-mode-locked AlGaInP-VECSEL,” Appl. Phys. Lett. 111(18), 182105 (2017).
[Crossref]

M. A. Gaafar, A. Rahimi-Iman, K. A. Fedorova, W. Stolz, E. U. Rafailov, and M. Koch, “Mode-locked Semiconductor Disk Lasers,” Adv. Opt. Photonics 8(3), 370–400 (2016).
[Crossref]

M. Gaafar, C. Möller, M. Wichmann, B. Heinen, B. Kunert, A. Rahimi-Iman, W. Stolz, and M. Koch, “Harmonic self-mode-locking of optically pumped semiconductor disc laser,” Electron. Lett. 50(7), 542–543 (2014).
[Crossref]

M. Gaafar, D. A. Nakdali, C. Möller, K. A. Fedorova, M. Wichmann, M. K. Shakfa, F. Zhang, A. Rahimi-Iman, E. U. Rafailov, and M. Koch, “Self-mode-locked quantum-dot vertical-external-cavity surface-emitting laser,” Opt. Lett. 39(15), 4623–4626 (2014).
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M. Gaafar, P. Richter, H. Keskin, C. Möller, M. Wichmann, W. Stolz, A. Rahimi-Iman, and M. Koch, “Self-mode-locking semiconductor disk laser,” Opt. Express 22(23), 28390–28399 (2014).
[Crossref] [PubMed]

Reed, J. M.

Reichert, M.

Richter, P.

Riffat, J. R.

A. M. Fox, A. C. Maciel, M. G. Shorthose, J. F. Ryan, M. D. Scott, J. I. Davies, and J. R. Riffat, “Nonlinear excitonic optical absorption in GaInAs/InP quantum wells,” Appl. Phys. Lett. 51(1), 30–32 (1987).
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A. M. Fox, A. C. Maciel, M. G. Shorthose, J. F. Ryan, M. D. Scott, J. I. Davies, and J. R. Riffat, “Nonlinear excitonic optical absorption in GaInAs/InP quantum wells,” Appl. Phys. Lett. 51(1), 30–32 (1987).
[Crossref]

Said, A. A.

Salamo, G. J.

D. N. Christodoulides, I. C. Khoo, G. J. Salamo, G. I. Stegeman, and E. W. Van Stryland, “Nonlinear refraction and absorption: mechanisms and magnitudes,” Adv. Opt. Photonics 2(1), 60–200 (2010).
[Crossref]

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L. Brzozowski, E. H. Sargent, A. S. Thorpe, and M. Extavour, “Direct measurements of large near-band edge nonlinear index change from 1.48 to 1.55 μm in InGaAs/InAlGaAs multiquantum wells,” Appl. Phys. Lett. 82(25), 4429–4431 (2003).
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J. Hader, M. Scheller, A. Laurain, I. Kilen, C. Baker, J. V. Moloney, and S. W. Koch, “Ultrafast non-equilibrium carrier dynamics in semiconductor laser mode-locking,” Semicond. Sci. Technol. 32(1), 013002 (2016).
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Scott, M. D.

A. M. Fox, A. C. Maciel, M. G. Shorthose, J. F. Ryan, M. D. Scott, J. I. Davies, and J. R. Riffat, “Nonlinear excitonic optical absorption in GaInAs/InP quantum wells,” Appl. Phys. Lett. 51(1), 30–32 (1987).
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Seidel, M.

Seletskiy, D. V.

Shakfa, M. K.

Shaw, E. A.

E. A. Shaw, A. H. Quarterman, A. P. Turnbull, T. Chen Sverre, C. R. Head, A. C. Tropper, and K. G. Wilcox, “Nonlinear Lensing in an Unpumped Antiresonant Semiconductor Disk Laser Gain Structure,” IEEE Photonics Technol. Lett. 28(13), 1395–1398 (2016).
[Crossref]

She, C. Y.

M. J. Moran, C. Y. She, and R. L. Carman, “Interferometric Measurements of the Nonlinear Refractive-Index Coefficient Relative to CS2 in Laser-System-Related Materials,” IEEE J. Quantum Electron. 11(6), 259–263 (1975).
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A. R. Albrecht, Y. Wang, M. Ghasemkhani, D. V. Seletskiy, J. G. Cederberg, and M. Sheik-Bahae, “Exploring ultrafast negative Kerr effect for mode-locking vertical external-cavity surface-emitting lasers,” Opt. Express 21(23), 28801–28808 (2013).
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J. Wang, M. Sheik-Bahae, A. A. Said, D. J. Hagan, and E. W. Van Stryland, “Time-resolved Z-scan measurements of optical nonlinearities,” J. Opt. Soc. Am. B 11(6), 1009–1017 (1994).
[Crossref]

M. Sheik-Bahae and E. W. Van Stryland, “Ultrafast nonlinearities in semiconductor laser amplifiers,” Phys. Rev. B Condens. Matter 50(19), 14171–14178 (1994).
[Crossref] [PubMed]

A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Van Stryland, “Determination of bound-electronic and free-carrier nonlinearities in ZnSe, GaAs, CdTe, and ZnTe,” J. Opt. Soc. Am. B 9(3), 405–414 (1992).
[Crossref]

M. Sheik-Bahae, D. C. D. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electron nonlinear refraction in solids,” IEEE J. Quantum Electron. 27(6), 1296–1309 (1991).
[Crossref]

M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Dispersion and band-gap scaling of the electronic Kerr effect in solids associated with two-photon absorption,” Phys. Rev. Lett. 65(1), 96–99 (1990).
[Crossref] [PubMed]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive Measurement of Optical Nonlinearities Using a Single Beam,” IEEE J. Quantum Electron. 26(4), 760–769 (1990).
[Crossref]

Shorthose, M. G.

A. M. Fox, A. C. Maciel, M. G. Shorthose, J. F. Ryan, M. D. Scott, J. I. Davies, and J. R. Riffat, “Nonlinear excitonic optical absorption in GaInAs/InP quantum wells,” Appl. Phys. Lett. 51(1), 30–32 (1987).
[Crossref]

Shu, Y.

R. Liu, Y. Shu, G. Zhang, J. Sun, X. Xing, B. Pi, J. Yao, Z. Wang, and J. Xu, “Study of nonlinear absorption in GaAs/AlGaAs multiple quantum wells using the reflection Z-scan,” Opt. Quantum Electron. 39(14), 1207–1214 (2007).
[Crossref]

Sibbett, W.

Smith, S. D.

Smyth, C. J. C.

A. H. Quarterman, S. Mirkhanov, C. J. C. Smyth, and K. G. Wilcox, “Measurements of nonlinear lensing in a semiconductor disk laser gain sample under optical pumping and using a resonant femtosecond probe laser,” Appl. Phys. Lett. 109(12), 121113 (2016).
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Spence, D. E.

Stegeman, G. I.

D. N. Christodoulides, I. C. Khoo, G. J. Salamo, G. I. Stegeman, and E. W. Van Stryland, “Nonlinear refraction and absorption: mechanisms and magnitudes,” Adv. Opt. Photonics 2(1), 60–200 (2010).
[Crossref]

Stolz, W.

M. A. Gaafar, A. Rahimi-Iman, K. A. Fedorova, W. Stolz, E. U. Rafailov, and M. Koch, “Mode-locked Semiconductor Disk Lasers,” Adv. Opt. Photonics 8(3), 370–400 (2016).
[Crossref]

M. Gaafar, C. Möller, M. Wichmann, B. Heinen, B. Kunert, A. Rahimi-Iman, W. Stolz, and M. Koch, “Harmonic self-mode-locking of optically pumped semiconductor disc laser,” Electron. Lett. 50(7), 542–543 (2014).
[Crossref]

M. Gaafar, P. Richter, H. Keskin, C. Möller, M. Wichmann, W. Stolz, A. Rahimi-Iman, and M. Koch, “Self-mode-locking semiconductor disk laser,” Opt. Express 22(23), 28390–28399 (2014).
[Crossref] [PubMed]

Strupinski, W.

N. Vermeulen, D. Castelló-Lurbe, M. Khoder, I. Pasternak, A. Krajewska, T. Ciuk, W. Strupinski, J. Cheng, H. Thienpont, and J. Van Erps, “Graphene’s nonlinear-optical physics revealed through exponentially growing self-phase modulation,” Nat. Commun. 9(1), 2675 (2018).
[Crossref] [PubMed]

Su, K. W.

Sun, J.

R. Liu, Y. Shu, G. Zhang, J. Sun, X. Xing, B. Pi, J. Yao, Z. Wang, and J. Xu, “Study of nonlinear absorption in GaAs/AlGaAs multiple quantum wells using the reflection Z-scan,” Opt. Quantum Electron. 39(14), 1207–1214 (2007).
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Thienpont, H.

N. Vermeulen, D. Castelló-Lurbe, M. Khoder, I. Pasternak, A. Krajewska, T. Ciuk, W. Strupinski, J. Cheng, H. Thienpont, and J. Van Erps, “Graphene’s nonlinear-optical physics revealed through exponentially growing self-phase modulation,” Nat. Commun. 9(1), 2675 (2018).
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L. Brzozowski, E. H. Sargent, A. S. Thorpe, and M. Extavour, “Direct measurements of large near-band edge nonlinear index change from 1.48 to 1.55 μm in InGaAs/InAlGaAs multiquantum wells,” Appl. Phys. Lett. 82(25), 4429–4431 (2003).
[Crossref]

Tropper, A. C.

E. A. Shaw, A. H. Quarterman, A. P. Turnbull, T. Chen Sverre, C. R. Head, A. C. Tropper, and K. G. Wilcox, “Nonlinear Lensing in an Unpumped Antiresonant Semiconductor Disk Laser Gain Structure,” IEEE Photonics Technol. Lett. 28(13), 1395–1398 (2016).
[Crossref]

K. G. Wilcox and A. C. Tropper, “Comment on SESAM-free mode-locked semiconductor disk laser,” Laser Photonics Rev. 7(3), 422–423 (2013).
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A. C. Tropper and S. Hoogland, “Extended cavity surface-emitting semiconductor lasers,” Prog. Quantum Electron. 30(1), 1–43 (2006).
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R. Paschotta, R. Häring, A. Garnache, S. Hoogland, A. C. 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).
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Tschudi, T.

Turnbull, A. P.

E. A. Shaw, A. H. Quarterman, A. P. Turnbull, T. Chen Sverre, C. R. Head, A. C. Tropper, and K. G. Wilcox, “Nonlinear Lensing in an Unpumped Antiresonant Semiconductor Disk Laser Gain Structure,” IEEE Photonics Technol. Lett. 28(13), 1395–1398 (2016).
[Crossref]

Tyrk, M. A.

A. H. Quarterman, M. A. Tyrk, and K. G. Wilcox, “Z-scan measurements of the nonlinear refractive index of a pumped semiconductor disk laser gain medium,” Appl. Phys. Lett. 106(1), 011105 (2015).
[Crossref]

Van Erps, J.

N. Vermeulen, D. Castelló-Lurbe, M. Khoder, I. Pasternak, A. Krajewska, T. Ciuk, W. Strupinski, J. Cheng, H. Thienpont, and J. Van Erps, “Graphene’s nonlinear-optical physics revealed through exponentially growing self-phase modulation,” Nat. Commun. 9(1), 2675 (2018).
[Crossref] [PubMed]

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D. N. Christodoulides, I. C. Khoo, G. J. Salamo, G. I. Stegeman, and E. W. Van Stryland, “Nonlinear refraction and absorption: mechanisms and magnitudes,” Adv. Opt. Photonics 2(1), 60–200 (2010).
[Crossref]

M. Sheik-Bahae and E. W. Van Stryland, “Ultrafast nonlinearities in semiconductor laser amplifiers,” Phys. Rev. B Condens. Matter 50(19), 14171–14178 (1994).
[Crossref] [PubMed]

J. Wang, M. Sheik-Bahae, A. A. Said, D. J. Hagan, and E. W. Van Stryland, “Time-resolved Z-scan measurements of optical nonlinearities,” J. Opt. Soc. Am. B 11(6), 1009–1017 (1994).
[Crossref]

A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Van Stryland, “Determination of bound-electronic and free-carrier nonlinearities in ZnSe, GaAs, CdTe, and ZnTe,” J. Opt. Soc. Am. B 9(3), 405–414 (1992).
[Crossref]

M. Sheik-Bahae, D. C. D. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electron nonlinear refraction in solids,” IEEE J. Quantum Electron. 27(6), 1296–1309 (1991).
[Crossref]

M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Dispersion and band-gap scaling of the electronic Kerr effect in solids associated with two-photon absorption,” Phys. Rev. Lett. 65(1), 96–99 (1990).
[Crossref] [PubMed]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive Measurement of Optical Nonlinearities Using a Single Beam,” IEEE J. Quantum Electron. 26(4), 760–769 (1990).
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E. W. Van Stryland, Y. Y. Wu, D. J. Hagan, M. J. Soileau, and K. Mansour, “Optical limiting with semiconductors,” J. Opt. Soc. Am. B 5(9), 1980–1988 (1988).
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N. Vermeulen, D. Castelló-Lurbe, M. Khoder, I. Pasternak, A. Krajewska, T. Ciuk, W. Strupinski, J. Cheng, H. Thienpont, and J. Van Erps, “Graphene’s nonlinear-optical physics revealed through exponentially growing self-phase modulation,” Nat. Commun. 9(1), 2675 (2018).
[Crossref] [PubMed]

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Vos, W. L.

Waldburger, D.

Wang, C. Y.

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8(2), 145–152 (2014).
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Wang, Z.

R. Liu, Y. Shu, G. Zhang, J. Sun, X. Xing, B. Pi, J. Yao, Z. Wang, and J. Xu, “Study of nonlinear absorption in GaAs/AlGaAs multiple quantum wells using the reflection Z-scan,” Opt. Quantum Electron. 39(14), 1207–1214 (2007).
[Crossref]

Weaire, D.

Webster, S.

Wei, T. H.

A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Van Stryland, “Determination of bound-electronic and free-carrier nonlinearities in ZnSe, GaAs, CdTe, and ZnTe,” J. Opt. Soc. Am. B 9(3), 405–414 (1992).
[Crossref]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive Measurement of Optical Nonlinearities Using a Single Beam,” IEEE J. Quantum Electron. 26(4), 760–769 (1990).
[Crossref]

Weigmann, W.

S. H. Park, J. F. Morhange, A. D. Jeffery, R. A. Morgan, A. Chavez-Pirson, H. M. Gibbs, S. W. Koch, N. Peyghambarian, M. Derstine, A. C. Gossard, J. H. English, and W. Weigmann, “Measurements of room-temperature band-gap-resonant optical nonlinearities of GaAs/AlGaAs multiple quantum wells and bulk GaAs,” Appl. Phys. Lett. 52(15), 1201–1203 (1988).
[Crossref]

Wherrett, B. S.

Wichmann, M.

Wiegmann, W.

Y. H. Lee, A. Chavez-Pirson, S. W. Koch, H. M. Gibbs, S. H. Park, J. Morhange, A. Jeffery, N. Peyghambarian, L. Banyai, A. C. Gossard, and W. Wiegmann, “Room-temperature optical nonlinearities in GaAs,” Phys. Rev. Lett. 57(19), 2446–2449 (1986).
[Crossref] [PubMed]

Wilcox, K. G.

E. A. Shaw, A. H. Quarterman, A. P. Turnbull, T. Chen Sverre, C. R. Head, A. C. Tropper, and K. G. Wilcox, “Nonlinear Lensing in an Unpumped Antiresonant Semiconductor Disk Laser Gain Structure,” IEEE Photonics Technol. Lett. 28(13), 1395–1398 (2016).
[Crossref]

A. H. Quarterman, S. Mirkhanov, C. J. C. Smyth, and K. G. Wilcox, “Measurements of nonlinear lensing in a semiconductor disk laser gain sample under optical pumping and using a resonant femtosecond probe laser,” Appl. Phys. Lett. 109(12), 121113 (2016).
[Crossref]

A. H. Quarterman, M. A. Tyrk, and K. G. Wilcox, “Z-scan measurements of the nonlinear refractive index of a pumped semiconductor disk laser gain medium,” Appl. Phys. Lett. 106(1), 011105 (2015).
[Crossref]

K. G. Wilcox and A. C. Tropper, “Comment on SESAM-free mode-locked semiconductor disk laser,” Laser Photonics Rev. 7(3), 422–423 (2013).
[Crossref]

Wu, Y. Y.

Xing, X.

R. Liu, Y. Shu, G. Zhang, J. Sun, X. Xing, B. Pi, J. Yao, Z. Wang, and J. Xu, “Study of nonlinear absorption in GaAs/AlGaAs multiple quantum wells using the reflection Z-scan,” Opt. Quantum Electron. 39(14), 1207–1214 (2007).
[Crossref]

Xu, J.

R. Liu, Y. Shu, G. Zhang, J. Sun, X. Xing, B. Pi, J. Yao, Z. Wang, and J. Xu, “Study of nonlinear absorption in GaAs/AlGaAs multiple quantum wells using the reflection Z-scan,” Opt. Quantum Electron. 39(14), 1207–1214 (2007).
[Crossref]

Xu, Z.

Yao, J.

R. Liu, Y. Shu, G. Zhang, J. Sun, X. Xing, B. Pi, J. Yao, Z. Wang, and J. Xu, “Study of nonlinear absorption in GaAs/AlGaAs multiple quantum wells using the reflection Z-scan,” Opt. Quantum Electron. 39(14), 1207–1214 (2007).
[Crossref]

Young, J.

Yüce, E.

Zhang, F.

Zhang, G.

R. Liu, Y. Shu, G. Zhang, J. Sun, X. Xing, B. Pi, J. Yao, Z. Wang, and J. Xu, “Study of nonlinear absorption in GaAs/AlGaAs multiple quantum wells using the reflection Z-scan,” Opt. Quantum Electron. 39(14), 1207–1214 (2007).
[Crossref]

Zhang, H.

Zhang, Y.

Zhao, P.

Zheng, X.

Adv. Opt. Photonics (2)

M. A. Gaafar, A. Rahimi-Iman, K. A. Fedorova, W. Stolz, E. U. Rafailov, and M. Koch, “Mode-locked Semiconductor Disk Lasers,” Adv. Opt. Photonics 8(3), 370–400 (2016).
[Crossref]

D. N. Christodoulides, I. C. Khoo, G. J. Salamo, G. I. Stegeman, and E. W. Van Stryland, “Nonlinear refraction and absorption: mechanisms and magnitudes,” Adv. Opt. Photonics 2(1), 60–200 (2010).
[Crossref]

Appl. Phys. B (1)

R. Paschotta, R. Häring, A. Garnache, S. Hoogland, A. C. 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]

Appl. Phys. Lett. (7)

J. Mørk, A. Mecozzi, and C. Hultgren, “Spectral effects in short pulse pump-probe measurements,” Appl. Phys. Lett. 68, 449–541 (1995).
[Crossref]

A. H. Quarterman, M. A. Tyrk, and K. G. Wilcox, “Z-scan measurements of the nonlinear refractive index of a pumped semiconductor disk laser gain medium,” Appl. Phys. Lett. 106(1), 011105 (2015).
[Crossref]

R. Bek, M. Großmann, H. Kahle, M. Koch, A. Rahimi-Iman, M. Jetter, and P. Michler, “Self-mode-locked AlGaInP-VECSEL,” Appl. Phys. Lett. 111(18), 182105 (2017).
[Crossref]

A. H. Quarterman, S. Mirkhanov, C. J. C. Smyth, and K. G. Wilcox, “Measurements of nonlinear lensing in a semiconductor disk laser gain sample under optical pumping and using a resonant femtosecond probe laser,” Appl. Phys. Lett. 109(12), 121113 (2016).
[Crossref]

S. H. Park, J. F. Morhange, A. D. Jeffery, R. A. Morgan, A. Chavez-Pirson, H. M. Gibbs, S. W. Koch, N. Peyghambarian, M. Derstine, A. C. Gossard, J. H. English, and W. Weigmann, “Measurements of room-temperature band-gap-resonant optical nonlinearities of GaAs/AlGaAs multiple quantum wells and bulk GaAs,” Appl. Phys. Lett. 52(15), 1201–1203 (1988).
[Crossref]

A. M. Fox, A. C. Maciel, M. G. Shorthose, J. F. Ryan, M. D. Scott, J. I. Davies, and J. R. Riffat, “Nonlinear excitonic optical absorption in GaInAs/InP quantum wells,” Appl. Phys. Lett. 51(1), 30–32 (1987).
[Crossref]

L. Brzozowski, E. H. Sargent, A. S. Thorpe, and M. Extavour, “Direct measurements of large near-band edge nonlinear index change from 1.48 to 1.55 μm in InGaAs/InAlGaAs multiquantum wells,” Appl. Phys. Lett. 82(25), 4429–4431 (2003).
[Crossref]

Electron. Lett. (1)

M. Gaafar, C. Möller, M. Wichmann, B. Heinen, B. Kunert, A. Rahimi-Iman, W. Stolz, and M. Koch, “Harmonic self-mode-locking of optically pumped semiconductor disc laser,” Electron. Lett. 50(7), 542–543 (2014).
[Crossref]

IEEE J. Quantum Electron. (3)

M. Sheik-Bahae, D. C. D. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electron nonlinear refraction in solids,” IEEE J. Quantum Electron. 27(6), 1296–1309 (1991).
[Crossref]

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Figures (9)

Fig. 1
Fig. 1 VECSEL chip characteristics: (a) Illustration of a Kerr-lens mode-locked VECSEL with the dashed lines indicating the cw beam profile while the shaded area traces the beam profile when altered by the nonlinear defocusing lens in the VECSEL chip. Such an intensity-dependent lens can lead to beam narrowing at the end mirror of the cavity and possibly favor mode-locking when a slit inserted there adds losses to the cw beam by truncating it laterally. (b) Chip structure with standing-wave electric field at the design wavelength of 960 nm. (c) Band-gap configuration of the different materials used in the gain chip compared to the stopband of the chip and the investigated wavelength range (930 – 975 nm). (d) Measured reflectivity spectrum, surface and edge photoluminescence (PL), and calculated longitudinal confinement factor (LCF) of the investigated VECSEL chip.
Fig. 2
Fig. 2 Experimental Z-scan setup and data: Different neutral-density (ND) filters are used to systematically vary the incident probe power on the VECSEL chip. The sample is translated through the focus of the 150-fs pulsed probe beam, which is chopped and analyzed by two detectors using a lock-in scheme. (b) Exemplary Z-scan measurements at 955 nm for different peak probe intensities irradiated at an angle of 20° are shown, with the corresponding open scan recorded by detector 1 (c). The solid lines are the respective fits to the measurement data according to the models from [8].
Fig. 3
Fig. 3 Coefficients for the extraction of nonlinear absorption and refraction: (a) Normalized nonlinear absorption q0 and (b) nonlinear on-axis phase shift ΔΦ0 as a function of the incident peak probe intensity for different probe center wavelengths irradiated at 20°. The errors for the respective extracted magnitudes represent the fit tolerance and were determined by varying the fit parameter (q0 or ΔΦ0) until the fit model did not match the measurements anymore (similar to [37]).
Fig. 4
Fig. 4 Wavelength and angle-dependent nonlinear absorption and nonlinear refraction: (a) Nonlinear absorption β and (b) nonlinear refraction n2 as a function of the wavelength (left axes), measured for the incidence angles of 10, 20 and 30°. The lines between the measurement points may serve as guides to the eyes. Arrows atop the diagram indicate the wavelength of the QW PL (cf. Fig. 1(d)) as well as the different angle-dependent LCF peaks. The corresponding surface PL at given angle of incidence, which is subdue to the microcavity resonance, is plotted in both graphs for comparison (shaded plots) as well as the corresponding reflectivity spectra (line plots), both normalized to 1 and with respect to the right axes. An inset represents the probe geometry with respect to the VECSEL chip. The errors were determined by performing a linear least square fit to the normalized nonlinear absorption q0 and nonlinear phase shift ΔΦ0 as a function of probe intensity (as displayed in Fig. 3) and taking the 95% confidence interval of the fit as error.
Fig. 5
Fig. 5 Ratio of real and imaginary part of the measured third order nonlinearity χ(3) and typical focal length of a Kerr-lens: The ratio of nonlinear refraction with respect to nonlinear absorption is plotted as a function of the wavelength in the left column of the diagram for the three different angles of incidence. Additionally, the focal length, which would occur in a typically self-mode-locked VECSEL configuration, is plotted here in the right column. The error bars stem from the errors in nonlinear absorption and refraction as depicted in Fig. 4.
Fig. 6
Fig. 6 Illustration of possible saturable absorber mechanisms shaping the pulse: A dominating bound-electronic contribution (BEKE) in the nonlinear response, with its dispersion given in (a) as adapted from [29], would lead to a fast saturable absorber mechanism (red solid line in the schematic time trace of action shown in (b)) similar to traditional Kerr-lens mode-locking. In contrast, a dominating free-carrier-related nonlinear response (FCN), with its dispersion around the band gap given in (c) for different carrier densities as adapted from [30], would lead to slow saturable absorber action (green dashed line in (b)) where pulse formation relies on its combination with fast gain saturation (black solid line in (b)).
Fig. 7
Fig. 7 Example of extraction of normalized nonlinear absorption in the presence of saturable absorption: (a) Open scan at 940 nm and 30° angle of incidence for different probe powers. The fit (solid line) is obtained as described in Appendix C using I s = 0.2 GW/cm2 and α 0 = 1.2x10−5 m−1 for all probe intensities. (b) Resulting nonlinear on-axis absorption as a function of the peak probe density with linear fit (solid line).
Fig. 8
Fig. 8 Angle-dependent chip characterization: (a) Measured reflectivity spectra for different angles of incidence (solid lines, left axis) as well as calculated longitudinal confinement factor (LCF) for the same angles (dashed lines, right axis). (b) Zoom on the longitudinal confinement factor (dashed lines) around the relevant wavelength range in comparison to the measured surface photoluminescence (PL) at the same angles (shaded areas).
Fig. 9
Fig. 9 Measurement data with fit model as well as manually-determined symmetrical upper and lower bounds of the fit: This is a zoom of Fig. 2(b) and 2(c). (a) Open scan and (b) Z-scan with fit (solid line) and upper and lower limit of the respective fits (dashed lines) for the estimation of the data-evaluation uncertainties.

Equations (7)

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n( I 0 )= n 0 + n 2 I 0 ,
α( I 0 )= α 0 +β I 0 ,
Re( χ (3) ) Im( χ (3) ) =| 2Δ Φ 0 q 0 |=| 2k n 2 β |,
Γ z = 1 N q q | A q + exp(i k q z q )+ A q exp(i k q z q ) | 2 | A 0 + | 2 + | A 0 | 2 ,
T(z)= m=0 [ q 0 (z) ] m (m+1/2) 3/2 ,
T sat (z)=1 α 0 1+ I(z) I s ,
T(z)=1 4Δ Φ 0 z z 0 ( ( z z 0 ) 2 +9)( ( z z 0 ) 2 +1) ,