Absorber saturation in lasers with nonuniform excitation

Volume 29A,

PHYSICS

number 8

ABSORBER

SATURATION

IN

LASERS

LETTERS

WITH

30 June 1969

NONUNIFORM

EXCITATION

A. V. USPENSKII Scientific Institute of Physical-Technical and Radio-Technical Measurements, Moscow, USSR

All-Union

Received

19 May 1969

Absorber saturation in lasers with nonuniform excitation reveals a possibility of realization ln such lasers of several stable lasing states. States belong to adjacent laser modes and differ in frequencies and amplitudes

of emitted

radiation.

Many articles have appeared in the literature concerning various physical effects in semiconductor lasers with nonuniform excitation [l-3]. Some of these effects are due to absorber saturation (nonlinear absorption of light) in such lasers. A laser with nonuniform excitation consists of a Fabry-Perot injection laser whose plated pcontact is divided into two electrically isolated portions. So, there are two laser blocks [1,2] with different levels of excitation (different injection currents). First of all let us discuss some physical aspects of absorber saturation in lasers with nonuniform excitation. Let G be an average bulk gain in the laser G = gl + yg2, where y = V2/VI; Vi ,2 are the volumes of active layers in blocks 1, 2 and gI ,2 are bulk gains in blocks 1,2. Let us takeg1,2 m the form [l]: 81,2 =K(n1,2-fb),

b ’ 79,2;

g1,2

= Kb(l -f

b < 9,2

),

(I)

where n1,2 are the densities of the electrons ln the active layers of blocks 1,2, b is a function of the frequency, f determines the position of the quasi-Fermi level for holes andK is a constant. Let us assume that the frequency of generation coincides with frequency at which G has a maximum, i.e., b = nl =Jl/[l + sb(l -f )]. Then G = Go + AG =

J1(I+r)(I-f) l+%(A-f)

1 -

zc

Fig. 1. The shape of the curve G(Sb) (thick line) curve Gb#b.) shows an average bulk gain in the laser for severa “1 bi = const: I - straight line (constant losses): 1, 2.3.. . - stable lasing states.

uniformity of excitation and may be interpreted as some additional losses. These losses fall when the number of photons in a laser grows. Because of absorber saturation in a semiconductor laser with nonuniform excitation there may exist several lasing states. All states are stable for the same injection currents. In fact, lasing can take place at one of several discrete frequencies bm (Fabry-Perot modes). At a fixed frequency (bm = const) (3) \-I

-&

(51 -J2)

(2)

where Jl 2 are bulk densities of excitation, and Sb is proportional to the number of photons in the laser. In (2) Go is an average bulk gain in a laser with uniform excitation (JI =J2 = JI). The second term AG = - y(~1~2)/(1+Sb) is due to non-

I K

Gbm(Sbm)

=

r(J, -fb,)

L

1 +sbm

+bm(l-f)

&++YJ2-(~+y)fbm] m

If J2 < fbm

(i.e. g2 < 0) then Gf,,(Sb,)

I

q’bm q’bm

as a func485

Volume 29A, number 8

PHYSICS

LETTERS

The program performed with g1,2 in a form (1) was also performed with gain

tion of St,,,., has a maximum (see fig. 1) and the straight line 1 (constant losses) intersects Gb,(Sb,) twice. The intersection on the falling part of the curve G&_(Sb,) give the stable lasing state. The losses may intersect several functions Gb,(Sb,) with a different value of m. As a result, there are several stable lasing states (1,2,3... onfig. 1). The maximum number m ’ of such states (m’ is much more then in ref. 1 is m’ M 2/&, where constant E. determines a density of z = AL&E,; states in the conduction band; Aw - is the fre-

g1,2 =A expg

1

l+exp{(hw!F~~,2),~~}

- + f

Here A is a constant value, Fnl -quasi-Fermi level for electrons. This form o? gain is usually used to interpret the action of the GaAs injection laser. Qualitative results are the same.

quency interval between adjacent modes. For example, if z = 0, 1 then m’ = 6. We may strongly change m ’ if we change the size of the injection laser (change Aw ), or take a laser material with various E,. ****

THE

30 June 1969

HYPERFINE SPLITTING OF AND THE QUADRUPOLE

References

1. G. J. Lasher Solid State Electronics 7 (1964) ‘70’7. 2. N. G. Basov, V. V. Nikitin, A. A. Sheronov and Tu. P. Zakharov, Fiz. Tver. Tela 7 (1965) 3128. 3. V. V. Nikitin, A. P. Oraevskii, V. D.Samoilov and A. V. Uspenskii, FTP 2 (1968) 1662.

:*

THE 3d64s4p LEVELS MOMENT OF 55Mn

OF

Mn I

E. HANDRICH, A. STEUDEL and H. WALTHER Institut ftir Experimentalphysik

A der Technischen

Universittit,

Hannover,

Germany

Received 19 May 1969

The hyperfine structure of the 3d54sp ZIP+,+ ,f levels of Mn I investigated by the level crossing method, and also former experimental hyperfine results for other levels of 3d54s4p are discussed. The quadrupole moment Q(55Mn) = O-40(2) b is derived.

The investigation of the hyperfine splitting of the 3d54s4p ZIPS,+ ,+ levels of Mn I by the level crossing method has been shortly described [l]. The results for the hyperfine coupling constants obtained from the experimental data are given in table 1. The first order evaluation of the crossing data gives a finite C-factor besides the magnetic dipole (A-factor) and the electric quadrupole (B-factor) constants. Since the fine structure splitting of the 26~ multiplet is rather small (about 19 cm-l) also second order corrections for the hyperfine splitting have to be considered. These corrections were calculated using the effective tensor operator formalism deduced by Woodgate [2]. The corrected hyperfine constants are also given in table 1. (For the z6Pi no second order corrections have been calc*ulated because of the large experimental 466

errors. ) The errors in table 1 are given by the rms errors of the measurements and by the residuals of the least-squares fit procedure used to calculate the hyperfine constants in first order from the crossing data. A better fit is obtained if the second order hyperfine interaction is taken into account. Thus the errors become smaller in this case. The errors of the C-factors are still so large that there is no evidence of a real octupole interaction. The discussion of the A- and B-factors is performed by means of the eigenfunctions for intermediate coupling deduced by Mehlhorn [3]. For 8 levels of 3d54s4p the A- and B-factors are known. All are included in the theoretical discussion. The A-factors are given by