Although lasers have found numerous applications, their design is often still based on the concept of a gain medium within a mirror cavity. Exceptions to this are distributed feedback lasers1, in which feedback develops along a periodic structure, or random lasers, which do not require any form of cavity2. Random lasers have very rich emission spectra, but are difficult to control. Distributed feedback devices, conversely, have the same limited design possibilities of regular lasers. We show, by making use of a quasi-crystalline structure in an electrically pumped device, that several advantages of a random laser can be combined with the predictability of a distributed feedback resonator. We have constructed a terahertz quantum cascade laser based on a Fibonacci distributed feedback sequence, and show that engineering of the self-similar spectrum of the grating allows features beyond those possible with traditional periodic resonators, such as directional output independent of the emission frequency and multicolour operation.
Subscribe to Journal
Get full journal access for 1 year
only $14.08 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Rent or Buy article
Get time limited or full article access on ReadCube.
All prices are NET prices.
Morthier, G. & Vankwikelberge, P. Handbook of Distributed Feedback Laser Diodes (Artech House, 1997).
Wiersma, D. The physics and applications of random lasers. Nature Phys. 4, 359–367 (2008).
Fujiwara, T. & Ogawa, T. Quasicrystals (Springer-Verlag, 1990).
Kohmoto M., Sutherland B. & Iguchi, K. Localization of optics: quasiperiodic media. Phys. Rev. Lett. 58, 2436–2438 (1987).
Gellermann, W., Kohmoto, M., Sutherland, B. & Taylor, P.C. Localization of light waves in Fibonacci dielectric multilayers. Phys. Rev. Lett. 72, 633–636 (1994).
Hattori, T., Tsurumachi, N., Kawato, S. & Nakatsuka, H. Photonic dispersion relation in a one-dimensional quasicrystal. Phys. Rev. B 50, 4220–4223 (1994).
Dal Negro, L. et al. Light transport through the band-edge states of Fibonacci quasicrystals. Phys. Rev. Lett. 90, 055501 (2003).
Man, W., Megens, M., Steinhardt, P. J. & Chaikin, P. M. Experimental measurement of the photonic properties of icosahedral quasicrystals. Nature 436, 993–996 (2005).
Ledermann, A. et al. Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths. Nature Mater. 5, 942–945 (2006).
Matsui, T., Agrawal, A., Nahata, A. & Vardeny, Z. V. Transmission resonances through aperiodic arrays of subwavelength apertures. Nature 446, 517–521 (2007).
Gumbs, G. & Ali, M. K. Dynamical maps, Cantor spectra, and localization for Fibonacci and related quasiperiodic lattices. Phys. Rev. Lett. 60, 1081–1084 (1988).
Notomi, M., Suzuki, H., Tamamura, T. & Edagawa, K. Penrose-lattice photonic quasicrystal laser. Phys. Rev. Lett. 92, 123906 (2004).
Nozaki, K. & Baba, T. Quasiperiodic photonic crystal microcavity lasers. Appl. Phys. Lett. 84, 4875–4877 (2004)
Köhler, R. et al. Terahertz semiconductor–heterostructure laser. Nature 417, 156–159 (2002).
Williams, B. S. Terahertz quantum-cascade lasers. Nature Photon. 1, 517–525 (2007).
Schubert, M. & Rana, F. Analysis of terahertz surface emitting quantum-cascade lasers. IEEE J. Quantum Electron. 42, 257–265 (2006).
Mahler, L. et al. Finite size effects in surface emitting terahertz quantum cascade lasers. Opt. Express 17, 6703–6709 (2009).
Kumar, S. et al. Surface-emitting distributed feedback terahertz quantum-cascade lasers in metal–metal waveguides. Opt. Express 15, 113–128 (2007).
Belkin, M. A. et al. Terahertz quantum-cascade-laser source based on intracavity difference-frequency generation. Nature Photon. 1, 288–292 (2007).
Tredicucci, A. et al. A multiwavelength semiconductor laser. Nature 396, 350–353 (1998).
Norton, A. & de Sterke, C. Aperiodic 1-dimensional structures for quasi-phase matching. Opt. Express 12, 841–846 (2004).
Mahler, L. et al. Vertically emitting microdisk lasers. Nature Photon. 3, 46–49 (2009).
The authors thank B. Witzigmann for useful discussions. This work was supported in part by the European Commission through the Research and Training Network ‘Physics of Intersubband Semiconductor Emitters’ and the integrated project ‘Teranova’. The authors also acknowledge support from the Italian Ministry of Research through the project ‘National Laboratory for Nanotechnology applied to Genomics and Post-Genomics’.
The authors declare no competing financial interests.
About this article
Cite this article
Mahler, L., Tredicucci, A., Beltram, F. et al. Quasi-periodic distributed feedback laser. Nature Photon 4, 165–169 (2010). https://doi.org/10.1038/nphoton.2009.285
Cavity-enhanced light–matter interaction in Vogel-spiral devices as a platform for quantum photonics
Applied Physics Letters (2021)
Scaling Law, Confined and Surface Modes in Photonic Fibonacci Stub Structures: Theory and Experiment
Applied Sciences (2020)
Nature Communications (2020)
APL Photonics (2020)