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Optical and Quantum Electronics 32: 1343±1350, 2000.
Ó 2000 Kluwer Academic Publishers. Printed in the Netherlands.
Power eciency of a semiconductor laser with an
external cavity
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 eciency 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 eciency 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 eciency
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, di€erential eciency, 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 ecient 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
coecients 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
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 eciency 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 eciencies 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 ˆ 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 a€ected 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 ˆ Ith =Itho
ˆ 1 ‡ 2f sp ln
r3 r2
In this equation, r2 ˆ …R2 †1=2 ; r3 ˆ …R3 †1=2 are the ®eld re¯ection coecients,
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 ˆ dP =dI (i.e., the slope of the characteristic curve of the solitary laser
above threshold), is given by (Coldren and Corzine 1995):
g0 ˆ 2…hm=e†
ÿln r2
a` ÿ …ln r2 †
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 e€ective
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 ˆ r2 r3 …1 ÿ r22 †
1 r2 r3
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 eciency in the external cavity
The combined e€ect 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 ˆ 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 ˆ …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 di€erent e€ect on the power eciency. Namely, since the
voltage drop V on the laser can be considered approximately constant, for
I < IZ the total power eciency P =VI of the laser in the cavity is increased
with respect to the solitary laser, while for I > IZ it is reduced.
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 ˆ 0:04). Point Z is the
intersection of the two curves (see text). Curve (s) of laser (a) is for a non-optimized alignment.
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 eciency 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 ˆ PZ ˆ g0 …IoZ ÿ Itho † ˆ g…IZ ÿ Ith †
the current Ith can be calculated from (1), thus obtaining:
IoZ ˆ IZ ˆ Itho
gF =g0 ÿ 1
g=g0 ÿ 1
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. Eciency 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 e€ective
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 ˆ 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).
Alternatively, one can use the expression (Osmundsen and Gade 1983):
sp ˆ …g0 c=n†ÿ1
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†` ˆ 1:
For the laser of Fig. 2b, ` ˆ 800 lm; f ˆ 56 GHz; sp ˆ 5 10ÿ13 s, R1 ˆ 0:95;
R2 ˆ 0:001; a` ˆ 5:5; Itho ˆ 250 mA; g0 ˆ 1:2, from which we ®nd F ˆ 0:85;
g ˆ 0:7; IZ ˆ 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 di€erent
values of a`, i.e., for di€erent 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 ˆ 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 di€erent material losses a`. The curve for the laser of Fig. 2b
has been marked by (s).
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 di€erent 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` ˆ 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 ˆ 0:04).
In Fig. 4, a similar plot has been drawn, where the di€erent surfaces are for
di€erent 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
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` ˆ 5:5 of Fig. 3. In this diagram, our laser is described by a straight line at
R2 ˆ 0:001, which is coincident with the horizontal axis. Since the equivalent
re¯ectivity of our grating at 800 nm is R3 ˆ 0:04, the calculated working point
(A in Fig. 5) corresponds to IZ ˆ 1:24Itho , which is in good agreement with the
experimental value IZ ˆ 1:20Itho (A0 in Fig. 5). The observed di€erence is
probably due to alignment losses which should have been included in R3 , but
which are dicult 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 eciency
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 eciency.
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.
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