Light intensity-voltage correlations and leakage-current excess noise in a single-mode semiconductor laser I. Maurin, 1 I. Protsenko, 2,3,4 J.-P. Hermier, 1,5 A. Bramati, 1 P. Grangier, 2 and E. Giacobino 1 1 Laboratoire Kastler Brossel, Université Pierre et Marie Curie, Ecole Normale Supérieure et CNRS, UPMC Case 74, 4 Place Jussieu, 75252 Paris Cedex 05, France 2 Laboratoire Charles Fabry de l’Institut d’Optique (UMR 8501), Bâtiment 503, 91403 Orsay Cedex, France 3 Lebedev Physical Institute, Leninsky Prospekt, 53, Moscow, Russia 4 Scientific Center for Applied Research, JINR, Dubna, Russia 5 Laboratoire Matériaux et Phénomènes Quantiques, Université Denis Diderot, 2 Place Jussieu, 75251 Paris Cedex 05, France Received 10 March 2005; published 27 September 2005 Semiconductor lasers are particularly well suited for the implementation of pump-noise suppression, yield- ing a reduction of the intensity noise in the laser. In this simple picture, the maximal amount of squeezing is equal to the quantum efficiency. However, experimental results on intensity noise reduction by pump-noise suppression are usually above this limit. This discrepancy suggests that additional noise sources must be involved. Here we successfuly interpret the full noise behavior of a single-mode laser diode far above threshold by considering two excess noise sources: the leakage current fluctuations across the laser and the Petermann excess noise. We have estimated the contribution of each noise source using the results of the correlations between the laser output intensity noise and the voltage fluctuations across the laser diode light-voltage correlations and obtained good agreement between our theory and experimental results. DOI: 10.1103/PhysRevA.72.033823 PACS numbers: 42.55.Px, 42.50.Ct I. INTRODUCTION Semiconductor lasers have been studied in detail recently because of several interesting characteristics that make them attractive for applications, such as optical information pro- cessing, communications, and precision measurements 1. They are compact, tunable, and have a high quantum effi- ciency and a low threshold. Besides, semiconductor lasers are very good candidates for the generation of intensity- squeezed light—i.e., with the intensity noise below the shot noise level, by driving them with a “quiet” pump, which is a constant current source 2–8. With this pump noise suppres- sion principle, squeezing of the intensity noise in a semicon- ductor laser with a quiet pump was first demonstrated by Michida, Yamamoto, and Itaya 2. However, subsequent ex- periments on different types of semiconductor lasers re- vealed that relatively few quietly pumped lasers exhibit squeezing, and if they do, they often stay above the theoreti- cally expected squeezed-noise level that is the laser quantum efficiency 9,10. For a long time, the mode partition noise— that is, the influence of multimode effects and mode interac- tion on the intensity noise 11–13—was investigated as a mechanism responsible for this discrepancy. However, the mode partition noise can be eliminated by line-narrowing techniques using feedback from an external grating or injec- tion locking 11,14. Using these techniques, the intensity noise can be made negligible small on all subthreshold modes with the respect to the lasing mode. But even in that case, the measured intensity noise in the lasing mode is still higher than expected from the laser quantum efficiency 9,10,15,16. This discrepancy points out that additional noise sources are involved. In this article, we investigate the Petermann excess noise and the leakage current fluctuations across the laser as an explanation for the bottleneck of the observed squeezing. The Petermann factor was first introduced in 1979 by Pe- termann 17. In the laser brought to a single-mode operation by the line-narrowing technique the subthreshold modes with negligible intensity still contain some amplified spontaneous emission noise. Because of the nonorthogonality of the eigenmodes, this noise from other modes is homodyned into the lasing mode, leading to an excess noise in the laser light, which is the Petermann excess noise 17–20. Indeed, even if the field fluctuations of the side modes are small, the field fluctuations of the side modes can be multiplied by the large lasing mode intensity, leading to a large noise and reducing squeezing. Previous works on the same type of semiconduc- tor lasers studied in this paper quantum well, index guided devices indicate clearly that the Petermann excess noise is mainly due to the presence of nonorthogonal spatial eigen- modes 21. The leakage current and its fluctuations are well known in a heterojunction 22 and in quantum well lasers 23–25.A sizable amount of additional noise can even be found in an ideally single-mode laser 9, which points to a noise in the current through the junction, even if the current in the exter- nal circuit does not fluctuate. A microscopic mechanism for such current noise is related to the pump blocking, studied in 26 with the pump model suggested in 27. The pump blocking is the decrease of the pumping rate when the lasing transition saturates and the number of vacancies electrons in the conductive valence band is reduced. The pump- blocking rate term is proportional to the pumping rate; it depends on carriers numbers and, therefore, it fluctuates, which leads to an excess noise in the current even at high pumping. The question is then how the current can fluctuate inside the laser, while it does not fluctuate in the external circuit, and which macroscopic parameters characterize the pump blocking. The answer is that the leakage current flows PHYSICAL REVIEW A 72, 033823 2005 1050-2947/2005/723/03382311/$23.00 ©2005 The American Physical Society 033823-1