Open Access
Add to BibSonomyAbstract
We consider the generation of photon pairs by spontaneous four-wave mixing in ring resonators, as described by Clemmen et al. in Opt. Express 17, 16558 (2009). We show that the theoretical limit predicted for the generation rate in their Erratum–Opt. Express 18, 14107 (2010)–is far too large due to an incorrect definition of a field enhancement factor.
© 2016 Optical Society of America
Spontaneous four-wave mixing (SFWM) in integrated structures is considered a very promising approach for the generation of nonclassical states of light, including quantum correlated photon pairs. While this topic has been investigated for more than half a decade, with particular emphasis on Silicon integrated structures, there is still debate about the efficiency limits, and thus the real potential, of this approach [1]. The work of Clemmen et al. [2] is a seminal contribution to the field, for it is one of the first experimental demonstrations of SFWM in silicon nano wires and ring resonators.
In this short communication we comment on the theoretical prediction of the photon flux reported in [2] and its Erratum [3]. Since the work of Clemmen et al. [2] is, without any doubt, an important reference for those working in SFWM in Silicon ring resonators, we believe that clarifying this prediction will be beneficial to this community.
Under the assumption of a sufficiently low pump power, when two-photon absorption and the Kerr effect are negligible, the photon spectral density flux in the limit of a continuous-wave pump can be written [2] :
with Fp, Fi, and Fs the field enhancement calculated at the frequencies of pump, idler, and signal photon respectively, γ the nonlinear parameter, P the pump power, and Lring the resonator length. It should be noticed that this result is consistent with what is reported in Eq.(63) of Helt et al. [4]. Here we stress that in both communications F indicates the field enhancement, namely the enhancement of the field amplitude due to the resonant modes [5].However the expression for the field enhancement reported in [2] is not correct, for the right-hand side is the intensity enhancement F2. That is, the value quoted as field enhancement F in [2] is in fact F2. Using the wrong expression for the field enhancement, and integrating over the spectral density flux to determine the pair generation rate, leads to a very large overestimate for that rate in the Erratum [3] and thus to a large discrepancy between calculated and measured pair generation rates. We note that the expression for a circular ring resonator, in the limit of CW pump as well as negligible two-photon absorption and Kerr effect, has been reported in [4] and experimentally verified in [1] and in [6]. We further note that it can be easily generalized to the case of a race track resonator. For a nice summary of relevant results obtained in the last few years and the current state-of-art in the generation of photon pairs by SFWM in ring resonators, we refer readers to the recent work by Savanier et al. [1].
References and links
1. M. Savanier, R. Kumar, and S. Mookherjea, “Photon pair generation from compact silicon microring resonators using microwatt-level pump powers,” Opt. Express 24, 3313–3328 (2016). [CrossRef] [PubMed]
2. S. Clemmen, K. Phan Huy, W. Bogaerts, R. G. Baets, Ph. Emplit, and S. Massar, “Continuous wave photon pair generation in silicon-on-insulator waveguides and ring resonators,” Opt. Express 17, 16558–16570 (2009). [CrossRef] [PubMed]
3. S. Clemmen, K. Phan Huy, W. Bogaerts, R. G. Baets, Ph. Emplit, and S. Massar, “Continuous wave photon pair generation in silicon-on-insulator waveguides and ring resonators: erratum,” Opt. Express 18, 14107 (2010). [CrossRef]
4. L. G. Helt, Marco Liscidini, and J. E. Sipe, “How does it scale? Comparing quantum and classical nonlinear optical processes in integrated devices,” J. Opt. Soc. Am. B 29, 2199–2212 (2012). [CrossRef]
5. P. P. Absil, J. V. Hryniewicz, B. E. Little, P. S. Cho, R. A. Wilson, L. G. Joneckis, and P.-T. Ho, “Wavelength conversion in GaAs micro-ring resonators,” Opt. Lett. 25, 554 (2000). [CrossRef]
6. S. Azzini, D. Grassani, M. Galli, L. C. Andreani, M. Sorel, M. J. Strain, L. G. Helt, J. E. Sipe, M. Liscidini, and D. Bajoni, “From Classical Four-Wave Mixing to Parametric Fluorescence in Silicon micro-ring resonators,” Opt. Lett. 37, 3807 (2012). [CrossRef] [PubMed]