Multi-photon absorption and third-order nonlinearity in silicon at mid-infrared wavelengths.

Silicon based nonlinear photonics has been extensively researched at telecom wavelengths in recent years. However, studies of Kerr nonlinearity in silicon at mid-infrared wavelengths still remain limited. Here, we report the wavelength dependency of third-order nonlinearity in the spectral range from 1.6 μm to 6 μm, as well as multi-photon absorption coefficients in the same range. The third-order nonlinear coefficient n2 was measured with a peak value of 1.65 × 10(−13) cm2/W at a wavelength of 2.1 μm followed by the decay of nonlinear refractive index n2 up to 2.6 μm. Our latest measurements extend the wavelength towards 6 μm, which show a sharp decrement of n2 beyond 2.1 μm and steadily retains above 3 μm. In addition, the analysis of three-photon absorption and four-photon absorption processes are simultaneously performed over the wavelength range from 2.3 μm to 4.4 μm. Furthermore, the effect of multi-photon absorption on nonlinear figure of merit in silicon is discussed in detail.

[1]  Philippe M. Fauchet,et al.  Dispersion of silicon nonlinearities in the near infrared region , 2007 .

[2]  Hagan,et al.  Dispersion and band-gap scaling of the electronic Kerr effect in solids associated with two-photon absorption. , 1990, Physical review letters.

[3]  Q. Zheng,et al.  Frequency-upconverted stimulated emission by simultaneous five-photon absorption , 2013, Nature Photonics.

[4]  D. Schroder,et al.  Free carrier absorption in silicon , 1978, IEEE Transactions on Electron Devices.

[5]  Brian S. Wherrett,et al.  Scaling rules for multiphoton interband absorption in semiconductors , 1984 .

[6]  Richard A. Soref,et al.  The third-order nonlinear optical coefficients of Si, Ge, and Si1−xGex in the midwave and longwave infrared , 2011 .

[7]  G. Steinmeyer,et al.  Kramers-Kronig Relations and high order nonlinear susceptibilities , 2012 .

[8]  Mansoor Sheik-Bahae,et al.  Time-resolved Z-scan measurements of optical nonlinearities , 1994 .

[9]  T. Kato,et al.  Measurement of the nonlinear refractive index in optical fiber by the cross-phase-modulation method with depolarized pump light. , 1995, Optics letters.

[10]  D. Rao,et al.  Size dependent multiphoton absorption and refraction of CdSe nanoparticles. , 2007, Optics express.

[11]  Mihaela Dinu,et al.  Third-order nonlinearities in silicon at telecom wavelengths , 2003 .

[12]  Ian W. Boyd,et al.  Simultaneous measurement of the two-photon coefficient and free-carrier cross section above the bandgap of crystalline silicon , 1986 .

[13]  S. V. Chernikov,et al.  Direct continuous-wave measurement of n2 in various types of telecommunication fiber at 1.55 μm , 1996 .

[14]  G I Stegeman,et al.  Two-photon absorption as a limitation to all-optical switching. , 1989, Optics letters.

[15]  D. K. Schroder,et al.  Free carrier absorption in silicon , 1978 .

[16]  H. Driel,et al.  Two-photon absorption and Kerr coefficients of silicon for 850–2200nm , 2007 .

[17]  Shaul Pearl,et al.  Three photon absorption in silicon for 2300–3300nm , 2008 .

[18]  Martin M. Fejer,et al.  Multiphoton absorption and nonlinear refraction of GaAs in the mid-infrared , 2007 .

[19]  E. W. Stryland,et al.  Sensitive Measurement of Optical Nonlinearities Using a Single Beam Special 30th Anniversary Feature , 1990 .

[20]  Sanja Zlatanovic,et al.  Third-order nonlinearity in silicon beyond 2350 nm , 2011 .