Kerr lens (original) (raw)
Definition: a lensing effect arising from the Kerr nonlinearity
Categories: 
nonlinear optics, 
physical foundations
- optical nonlinearities
Related: dioptric powerfocal lengthKerr effectlensesself-focusinglaser-induced damageKerr lens mode lockingself-phase modulation
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DOI: 10.61835/v1l Cite the article: BibTex BibLaTex plain textHTML Link to this page! LinkedIn
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What is a Kerr Lens?
When intense light propagates through a nonlinear medium, the Kerr effect leads to an optical phase delay which is largest on the beam axis (where the optical intensity is highest) and smaller outside the axis. This is similar to the action of a lens: The wavefronts are deformed, so that the pulse is focused (assuming a positive nonlinear index ($n_2$)). This effect is called self-focusing and has important implications for passive mode locking of lasers (→ Kerr lens mode locking) and for optical damage of media (catastrophic self-focusing). For negative ($n_2$), the nonlinearity is self-defocusing.
When a Gaussian beam with optical power ($P$) and beam radius ($w$) propagates through a thin piece (thickness ($d$)) of a nonlinear medium with nonlinear index ($n_2$), the dioptric power (inverse focal length) of the Kerr lens is {f^{ - 1}} = \frac{{8{n_2}d}}{{\pi {w^4}}}P$$
when considering only the phase changes near the beam axis in a parabolic approximation. This equation can be derived by calculating the radially dependent nonlinear phase change and comparing it with that of a lens.
The equation shows that for a given optical power Kerr lensing becomes more important for stronger beam focusing: this increases the optical intensities and even more so the intensity gradients.
Frequently Asked Questions
What is a Kerr lens?
A Kerr lens is an effective lens experienced by a light beam in a nonlinear medium. Due to the Kerr effect, the medium's refractive index is intensity-dependent, causing a phase shift that deforms the wavefronts and focuses the beam, similar to a conventional lens.
What is self-focusing?
Self-focusing is the phenomenon where a beam focuses itself while propagating through a medium with a positive nonlinear index ($n_2$). This is a direct consequence of the Kerr lens effect.
How does the strength of a Kerr lens depend on beam properties?
The dioptric power (inverse focal length) of a Kerr lens is proportional to the optical power and inversely proportional to the fourth power of the beam radius ($w^4$). Therefore, the effect becomes much stronger for tightly focused beams.
What are important applications and consequences of the Kerr lens effect?
The Kerr lens effect is crucial for Kerr lens mode locking, a technique for generating ultrashort pulses in lasers. It can also lead to catastrophic self-focusing, which may cause optical damage to materials.
What happens if the nonlinear index is negative?
For a medium with a negative nonlinear index ($n_2$), the effect is reversed. The nonlinearity becomes self-defocusing, causing the beam to diverge instead of converge.
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Bibliography
| [1] | P. A. Belanger and C. Pare, “Self-focusing of Gaussian beams: an alternate derivation”, Appl. Opt. 22 (9), 1293 (1983); doi:10.1364/AO.22.001293 |
|---|---|
| [2] | F. Salin et al., “Modelocking of Ti:sapphire lasers and self-focusing: a Gaussian approximation”, Opt. Lett. 16 (21), 1674 (1991); doi:10.1364/OL.16.001674 |
| [3] | V. Magni et al., “Astigmatism in Gaussian-beam self-focusing and in resonators for Kerr-lens mode locking”, J. Opt. Soc. Am. B 12 (3), 476 (1995); doi:10.1364/JOSAB.12.000476 |
| [4] | J. H. Marburger, “Self-focusing: theory”, in Progress in Quantum Electronics, J. H. Sanders and S. Stenholm, eds. (Pergamon, Oxford, 1977), Vol. 4, pp. 35–110 (1977) |
| [5] | Y. R. Shen, “Self-focusing: experimental”, in Progress in Quantum Electronics, J. H. Sanders and S. Stenholm, eds. (Pergamon, Oxford, 1977), Vol. 4, pp. 1–34 (1977) |
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