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Optical and Quantum Electronics 32: 1343±1350, 2000. Ó 2000 Kluwer Academic Publishers. Printed in the Netherlands. 1343 Power eciency of a semiconductor laser with an external cavity V. ANNOVAZZI-LODI, S. MERLO AND S. MORONI Dipartimento di Elettronica, Universita' di Pavia, Via Ferrata 1, I-27100 Pavia, Italy Received 5 July 1999; accepted 19 November 1999 Abstract. Optical feedback modi®es the power vs. current diagram of a laser diode as well as its spectrum. Though optimization of the spectral characteristics is usually the main goal in the design of an external cavity source, power eciency is also important, especially with relatively high power devices, where temperature variations due to dissipation can have an impact on the wavelength stability and on the laser lifetime. A useful parameter to describe the total power eciency of the stabilized laser, relative to that of the solitary laser, is proposed in this paper. The dependence of this parameter on the characteristics of the active device, and of the external cavity, is investigated. Key words: external cavity laser, laser diode, optical feedback, power eciency 1. Introduction As it is well known (Osmundsen and Gade 1983; Petermann 1988), optical feedback can cause strong variations of laser parameters, such as threshold current, dierential eciency, output power and line spectrum. At high injection levels, the stability of the source can be signi®cantly impaired, and under certain conditions the device can even be led to chaos or to coherence collapse (Sacher et al. 1992; Annovazzi-Lodi et al. 1998). On the other side, a smaller and controlled amount of feedback provides an ecient method of stabilization of the source emission (Petermann 1988). A semiconductor laser operated in an external cavity, which is built by a remote mirror or grating, is shown in Fig. 1. In this ®gure, L is the external cavity length, ` is the chip length, and R1 ; R2 ; R3 are the power re¯ection coecients of the mirrors at the laser wavelength. The re¯ectivity R3 of the external mirror (or grating) includes all the external cavity losses, such as those due to imperfect alignment and to a possible output tap along the cavity. With this arrangement, monomode power spectra have been reported performing a linewidth as narrow as 50 kHz (Boshier et al. 1991). Moreover, by actuating the grating with suitable mechanics, the laser wavelength can be tuned within 10 nm, and, by a speci®c design, a tunability range in excess of 200 nm can be achieved (Tabuchi and Ishikawa 1990). 1344 V. ANNOVAZZI-LODI ET AL. Fig. 1. Scheme of a laser diode of length ` stabilized by an external cavity of length L: R1 ; R2 ; R3 are the mirror re¯ectivities. Re¯ectivity R3 includes the loss of a possible output tap. Though wavelength tunability and stability are the main concern in the design of an external cavity source, variations of the static diagram (optical power P as a function of pumping current I) of the laser are also worth being considered, because of their impact on the power eciency and on the junction temperature. Indeed, in many laboratory and commercial implementations, external cavity sources employ a relatively high power laser diode (100 mW±1 W). This allows to drain an adequate output power without reducing R3 , which determines the ®nesse of the external cavity. In the following, we derive a parameter to compare the laser total eciencies with and without the external mirror. We assume that R2 R3 , as required to force the laser to oscillate on the external cavity; this condition is often met by an anti-re¯ection coating (R2 0:01±0.001) on the output mirror. Moreover, we will take L `; R1 1, as it usually holds in a practical setup. As it is well known, both the threshold current Ith and the slope g of the P vs I diagram are aected by feedback. The ratio of the threshold current Ith of the laser in the cavity, to the threshold current Itho of the solitary laser, has been obtained in (Osmundsen and Gade 1983). For r2 r3 1 it can be written as: F Ith =Itho r2 1 2f sp ln r3 r2 1 In this equation, r2 R2 1=2 ; r3 R3 1=2 are the ®eld re¯ection coecients, f is the longitudinal mode frequency spacing of the solitary laser and sp is the photon lifetime of the solitary laser. The sign in Equation (1) must be taken positive when the double cavity length 2L is equal to an integer number of wavelengths; it must be taken negative when 2L is equal to a semi-integer number of wavelengths. In the ®rst case parameter F reaches its maximum value Fmax (for given R2 ; R3 ), while in the second case it reaches its minimum value Fmin . For arbitrary L [a case which has not been considered explicitly in writing (1)], we would ®nd Fmin < F < Fmax < 1. A well-known expression for g0 dP =dI (i.e., the slope of the characteristic curve of the solitary laser above threshold), is given by (Coldren and Corzine 1995): POWER EFFICIENCY OF A SEMICONDUCTOR LASER g0 2 hm=e ÿln r2 a` ÿ ln r2 1345 2 where h is the Plank constant, m is the optical frequency, e is the electron charge, a is the loss per unit length in the laser material. The in¯uence of the external mirror on the laser can be modeled by substituting an eective re¯ectivity r2eff for r2 in (2) (Osmundsen and Gade 1983). In the general case, the re¯ectivity r2eff is a complex number, which takes into account the relative phase of the laser output ®eld and of the ®eld impinging back on the laser front mirror after re¯ection on the external mirror. Since, however, consistently with our previous assumption, we restrict ourselves to the case of 2L being an integer or semi-integer number of wavelengths, then r2eff is real, and we ®nd: r2eff r2 r3 1 ÿ r22 1 r2 r3 3 From (3), it follows that when 2L is an integer number of wavelengths (and the `+' sign applies) r2eff is larger than r2 , so that g for the laser in the cavity is reduced with respect to g0 . On the other hand, when 2L is a semi-integer number of wavelengths (and the `ÿ' sign applies), it is r2eff < r2 , and g > g0 . 2. Laser eciency in the external cavity The combined eect of threshold and slope variation is shown in Fig. 2 as measured on two 800-nm laser diodes (SDL 4510, Bonneville BW800-1-M); in the experiments, a 1200-lines/mm grating was used (total attenuation R3 0:04, inclusive of the output tap), and the lasers were temperature stabilized with a standard Peltier controller. The cavity length (L 20 cm) was accurately trimmed so as to minimize the threshold, which also corresponded to the minimum slope. For a given external mirror or grating, this condition gives the maximum deviation from the solitary laser characteristics, which are also shown in the ®gure. For one laser we have also reported a third curve obtained with the same setup, by slightly moving away (a fraction of k) from the optimum alignment. In Fig. 2, the intersection point Z IZ ; PZ of the diagrams with and without feedback has been marked for each laser. This point represents a boundary value, which separates two regions of the P vs. I plot, in which feedback has a dierent eect on the power eciency. Namely, since the voltage drop V on the laser can be considered approximately constant, for I < IZ the total power eciency P =VI of the laser in the cavity is increased with respect to the solitary laser, while for I > IZ it is reduced. 1346 V. ANNOVAZZI-LODI ET AL. Fig. 2. Power vs. current diagram for two 800 nm lasers: (a) SDL 5410 and (b) Bonneville BW 800. Curves are for (*) the solitary laser and for (+) the laser in the external cavity (R3 0:04). Point Z is the intersection of the two curves (see text). Curve (s) of laser (a) is for a non-optimized alignment. POWER EFFICIENCY OF A SEMICONDUCTOR LASER 1347 Thus, as far as dissipation is concerned, in the region on the left of IZ , safe operation is ensured, since the power lost in the semiconductor is reduced with respect to the solitary laser. Even though a power dissipation increase does not necessarily reduce the lifetime of a speci®c laser, working at higher total eciency relaxes the requirements on the source temperature stabilization and results in faster thermal transients, allowing more stable operation and a reduced line jitter on medium/long time periods. In practice, it is not always possible (or convenient) to work at I < IZ ; moreover, power dissipation is not the only cause of laser failure, and other parameters, such as power at the mirrors must be checked to ensure safe operation. Nevertheless, it is interesting to investigate the dependence of IZ on the laser and cavity parameters. Since in point Z the optical power Po of the solitary laser is equal to the power P of the laser in the cavity, i.e.: PoZ PZ g0 IoZ ÿ Itho g IZ ÿ Ith 4 the current Ith can be calculated from (1), thus obtaining: IoZ IZ Itho gF =g0 ÿ 1 : g=g0 ÿ 1 5 In the following, we will consider the dependence of IZ on the laser and the cavity characteristics, showing that all information required to compute IZ consists of standard datasheet parameters or can be easily estimated or measured. In the numerical computations, we have assumed the parameters of the laser of Fig. 2b, which is a typical device for the application we are considering in this paper. 3. Eciency dependence on laser and cavity parameters To calculate IZ from (5), we need Itho ; g0 ; g; F . The ®rst two parameters are usually available from the laser supplier, or they can be measured by drawing the static P vs. I diagram of the solitary laser. Parameter F is given by (1), while g can be calculated from (2) after substituting for r2 the eective re¯ectivity r2eff , as given by (3). To complete calculations, besides the mirror re¯ectivities r2 and r3 , we need to determine parameters a`; f ; sp . The ®rst parameter can be obtained by solving (2) for the solitary laser. Parameter f is often available from the laser supplier; otherwise, it can be measured by an optical spectrum analyzer or a Fabry±Perot interferometer, or even calculated from the laser length `, since f c= 2n`, n being the medium refractive index. Finally, parameter sp can be estimated from a measurement of the intrinsic linewidth of the solitary laser (by using self-homodyning, or another suitable method). 1348 V. ANNOVAZZI-LODI ET AL. Alternatively, one can use the expression (Osmundsen and Gade 1983): sp g0 c=nÿ1 6 where g0 , i.e., the laser gain at threshold, can be calculated on its turn from the transparency condition r1 r2 exp g0 ÿ a` 1: 7 For the laser of Fig. 2b, ` 800 lm; f 56 GHz; sp 5 10ÿ13 s, R1 0:95; R2 0:001; a` 5:5; Itho 250 mA; g0 1:2, from which we ®nd F 0:85; g 0:7; IZ 310 mA, which are in good agreement with the experimental values, as it can be seen from the same ®gure. The dependence of IZ on the cavity and the laser parameters is shown in Figs. 3 and 4. Calculations have been made for L equal to an integer number of wavelengths (i.e., assuming the `+' sign in the above formulas) since this represents the most critical situation, i.e., that corresponding to the minimum value of IZ . In Fig. 3, IZ =Itho is plotted from (5) as a function of R2 ; R3 , for dierent values of a`, i.e., for dierent laser material losses. A line at constant R2 on a surface at constant a` represents a speci®c laser (with a given output mirror) subjected to a variable amount of optical feedback (given by R3 ). On that line, g varies continuously. Parameter g0 for the solitary laser, i.e., for R3 0, is not shown in the diagram, where, for convenience, we have used logarithmic scales. Fig. 3. Dependence of IZ =Itho on the re¯ectivity of the laser output mirror R2 , and on the re¯ectivity of the external mirror R3 . Surfaces are drawn for dierent material losses a`. The curve for the laser of Fig. 2b has been marked by (s). POWER EFFICIENCY OF A SEMICONDUCTOR LASER 1349 Fig. 4. Dependence of IZ =Itho on the re¯ectivity of the laser output mirror R2 , and on the re¯ectivity of the external mirror R3 . Surfaces are drawn for dierent values of g0 . The curve for the laser of Fig. 2b has been marked by (s). Fig. 5. Two-dimension representation of the diagram of Fig. 3 for a` 5:5. The curve representing the laser of Fig. 2b is coincident with the horizontal axis. Points A; A0 are the theoretical and experimental working points for that laser in the external cavity (R3 0:04). In Fig. 4, a similar plot has been drawn, where the dierent surfaces are for dierent values of g0 (i.e., without feedback). A line at constant R2 on a curve at constant g0 represents again a speci®c laser with a variable amount of 1350 V. ANNOVAZZI-LODI ET AL. optical feedback. It is evident from the plots of Figs. 3 and 4 that in order to maximize IZ we have to work at high R3 and low R2 . It is important to observe that this requirement is not in contrast with the more compelling design speci®cations of narrow and stable linewidth, which, as already stated, are usually met by building an external cavity with a relatively high ®nesse, around a source with a low re¯ectivity output mirror. In Figs. 3 and 4, our laser is represented by the lines marked by (s). For sake of clarity, in Fig. 5 we show also a two-dimension representation of the surface a` 5:5 of Fig. 3. In this diagram, our laser is described by a straight line at R2 0:001, which is coincident with the horizontal axis. Since the equivalent re¯ectivity of our grating at 800 nm is R3 0:04, the calculated working point (A in Fig. 5) corresponds to IZ 1:24Itho , which is in good agreement with the experimental value IZ 1:20Itho (A0 in Fig. 5). The observed dierence is probably due to alignment losses which should have been included in R3 , but which are dicult to quantify. The measured source linewidth of our laser in these experimental conditions was of about 200 KHz. 4. Conclusions In conclusion, we have proposed a parameter to evaluate the power eciency of a semiconductor laser stabilized by an external cavity, and we have considered its dependence on the external cavity and the laser characteristics. We have found that, for a typical cavity stabilized source, the requirement of narrow linewidth is not in contrast with that of maximum eciency. Acknowledgements The authors wish to thank Prof. S. Donati for his assistance and guidance throughout the course of their research work. This work was performed under a MURST 40% contract. References Annovazzi-Lodi, V., A. Scire', M. Sorel and S. Donati. IEEE J. Quant. Electron. 34 2350, 1998. Boshier, M.G., D. Berkeland, E.A. Hinds and V. Sandoghar. Opt. Commun. 85 355, 1991. Coldren, L.A. and S.W. Corzine. Diode Lasers and Photonic Integrated Circuits, Wiley-Interscience, New York (USA), 455, 1995. Osmundsen, J.H. and N. Gade. IEEE J. Quant. Electron. 19 465, 1983. Petermann, K., Laser Diode Modulation and Noise, Kluwer Academic Publishers, Dordrecht (NL), Chapter 2, 1988. Sacher, J., D. Baums, P. Panknin, W. Erlasser and E.O. Gobel. Phys. Rev. A 45 1893, 1992. Tabuchi, H. and H. Ishikawa. Electron. Lett. 26 742, 1990.

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