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Double phase conjugate mirror and double colour pumped oscillator using band-edge photorefractivity in InP:Fe
Optics Communications 89 (1992) 17-22 North-Holland
OPTICS COMMUNICATIONS
Double phase conjugate mirror and double colour pumped oscillator using band-edge photorefractivity in 1nP:Fe N. Wolffer, P. Gravey, G. Picoli and V. Vieux CNET Lannion B/OCM/TAC,
Route de Trkgastel, BP40, 22301 Lannion. France
Received 24 July 199 I ; revised manuscript received 24 October 199 1
We have observed the formation of a double phase-conjugate mirror (DPCM ) and a double colour pumped oscillator (DCPO ) at wavelengths near the band-edge of InP:Fe, with an external dc field of 10 kV/cm. The DCPO conversion efficiencies are respectively 63% and 26% for the couple of wavelengths 985 and 1.047 nm. These results are compared with the prediction of a calculation which takes into account the space-charge field non-linearities.
1. Introduction
The double phase conjugate mirror (DPCM) [ 1 ] and the double colour pumped oscillator (DCPO) [ 21 are particularly interesting devices for reconligurable optical interconnects [ 2-5 1. In a DPCM two mutually incoherent pump beams (at nearly identical wavelengths) incident on the opposite faces of a photorefractive (PR) crystal share a common grating which diffracts them into the phase conjugated of the opposite one. When the wavelength difference of the interacting beams is important (larger than the grating selectivity), they can still induce a common grating (DCPO). Recently DPCM has been observed in InP : Fe [ 61 and GaAs : EL2 [ 7 ] at 1.06 pm and DCPO has been achieved in InP : Fe using 1.06 and 1.32 urn wavelengths [ 8 1. This paper presents new results on both DPCM and DCPO obtained in InP:Fe at wavelengths close to its band edge. We have observed DPCM at wavelength down to 970 nm and DCPO between a fixed wavelength ( 1.047 nm) and a variable one from 1.010 to 965 nm. Using wavelengths close to the band edge has the two major implications for PR devices. There is indeed an increase of the optical absorption (Y,but the effective electro-optic coefficient is greatly enhanced through the Franz-Keldysh effect, which has already been exploited to achieve large two-wave mixing gains in GaAs [ 9 ] and InP : Fe [ lo]. The experimental set-up and experimental characteristics of particular interest for band-edge photorefractivity are briefly reported in section 2. Then, the extension to the DCPO case of a numerical procedure previously used to predict the DPCM conversion efftciency (i.e. the ratio of the diffracted beam intensity over the total transmitted one) is described in section 3. Finally, the experimental data are presented in section 4 and compared with the calculated ones.
2. Experimental set-up and sample characteristics The source used for the DPCM experiments is a Ti:sapphire laser which provides the two pump beams at the same wavelength; for DCPO studies one of these two beams has been replaced by another one issued from a diode pumped Nd: YLF laser emitting at 1.047 pm. The results reported here have been obtained with InP : Fe sample 169QC4, grown at CNET. The optical interaction length L and the distance d between the two silver pasted electrodes are both equal to 6.0 mm. The sample temperature is stabilized through a Peltier cooling 0030-4018/92/$05.00
0 1992 Elsevier Science Publishers B.V. All rights reserved.
17
Volume 89. number
1
OPTICS
I5 April 1992
COMMUNICATIONS
Franz-Keldysh/Pockelc
Absorption (cm.‘)
coeffuent
. I
. . * AA
0.5
AA . *
a 950
970
990
1010
1030
1050
950
Wavelength (nm)
Fig. 1. Band-edge
absorption
spectra of InP: Fe sample
970
990
1010
1030
IO50
Wavelength (nm)
169QC4.
r4, of 1nP:Fe sample 169QC4 at 10 kV/ Fig. 2. Ratio rFranz_Keldyrh/ cm, as a function of wavelength.
element. An external dc field is applied along the (001) axis. The sign of this field as well as the polarisation of the beams (parallel to the ( 1TO) axis) are chosen in order to maximise the 2 WM gain (and therefore the DPCM and DCPO diffraction efficiencies) by addition of the contributions of Pockels and Franz-Keldysh effects. When nearly plane waves are used, as for all the experiments reported here, the solution for the grating wave vector is degenerated, so that a continuous set of gratings is created, leading to conical diffraction [ 111. Diffracted beams are not complex conjugate of the incident ones but appear as small parts of rings. However, because all the grating wave vectors are close to the mean value, we suppose that threshold and diffraction efficiency are the same as for the true DPCM and DCPO in which conical diffraction has been eliminated by mean of spatially modulated input beams [ 21 or cylindrical lenses [ 12 1. The two pump beams enter the opposite ( 110) faces which are uncoated. Fig. 1 shows the absorption spectra. cu increases from 1.2 cm-’ at 1.047 urn to 5.4 cm-’ at 0.965 urn. For a given applied field E,, the influence of the Franz-Keldysh effect can be described [ 131 through an effective linear electrooptic coefficient r,,= Separate 2 WM experiments (gain measurements for two opposite signs of the applied field) r41 + rFranz-Keldyshhave been performed with the same sample in order to measure the wavelength dependence of the ratio r,,,,,. are shown in fig. 2 (for E,= 10 kV/cm). Finally, we have checked that the electroabKeldysh /r4,. The results sorption in presence of a field of 10 kV/cm was lower than 0.3 cm- ’ in the wavelength range used in these experiments. 3. Calculation of DPCM and DCPO conversion effkiencies 3.1. Numerical
method
Numerical simulations have been performed in order to predict the performances of this same sample in DPCM and DCPO experiments. The method used for the DCPO is an extension of the one used in the DPCM case, which has already been described in previous works on BGO [ 141 and InP: Fe [ 61; we just indicate here the main modifications. We consider two superimposed interference patterns (supposed to be in phase) at wavelengths 1, and AZ defined by 18
15 April 1992
OPTICS COMMUNICATIONS
Volume 89, number 1
Conversion efficiency
Conversion efficiency 0.8
. .
0.6
0.6
. .
0.4
A
0.2
A
. .
4
a
A . . A
x
4
x* l
l
.
.
’
.
A
.
A .
0.4
:
.
4
l
0.2
.
960
980
1000
1020
980
1000
1020
Wavelength (nm)
Wavelength (nm)
= 1.047 nm versus AZ=9651.010 nm (exp: triangles, talc: circles); applied dc field: 10 kV/ cm; mean grating period: 7 km. Fig. 3. Conversion efficiency for 1,
Z(x)=Z,(x)+Z,(x)=Zo,(l+ml
C 960
cosfi)+ZO,(l+mzcosfi).
Fig. 4. Conversion efficiency for &=965-l .OlO nm versus & (exp: triangles, talc: circles); applied dc field: 10 kV/cm; mean grating period: 7 pm.
(1)
When the standard hypothesis [ 15 ] (in particular small fringe modulation) to transform the nonlinear system governing El into a linear one are satisfied, it is possible to write El under the form: 4 =ml-%
(2)
+m2L,
where mlEscl (respectively mzEsc2) is the solution corresponding to interference pattern II (x) (respectively Z*(x) ) in presence of an additional uniform illumination Zo2(respectively Ior ). More explicitly: E I =imlZol a”‘p P To [
(
(3) with
(da) E,=K(k,Tle)
, EDp=EMp+ED,
ED,=&,+&,
(4b)
eno=eth ” 027 ” +c$‘Zol +oo2Z
(5a)
+f$ZoI +ao2Z p 029
(5b)
e
PO
=eth
P
19
I5 April 1992
OPTICS COMMUNICATIONS
Volume 89, number 1 01 O’ and ai’, 0” > CJ‘p
0:’ are the photoionization mobilities; c,,,, the capture coefficients, eLh and electrons and holes respectively). For InP: Fe, The coupling coefficients for both wavelengths
cross-sections at wavelengths 1, and AZ, respectively; P”,~, the e: are the thermal emission rates (labels n and p are used for nrO = [Fe’+ 1, pTo= [Fe’+ 1. A, and Ar are then as usual (for small angles inside the crystal)
(6)
[~3(~)~eff(~)/21-h~
C(k)=(nlk)
The calculation procedure is, like in the DPCM case, an iterative one: assuming a starting value E, =p,ESc, +p2ESE2 (in practice, we arbitrary set p, =p2=0.2),one calculates the intensities of the four beams through the standard wave-coupling equations, then calculates m, and m2 and uses E,= m,Esc, + m2Esczfor a new cycle. The procedure is repeated until E, converges. As for the DPCM, we have to take into account that for large conversion efficiencies m, and m2 are not negligible when compared to 1. To evaluate the space-charge field nonlinearities we have used an heuristic extension of the formulas of Refregier et al. [ 161 by using the following approach. Let us first come back to the DPCM case (2, =;l,=A). The intensity I(x) defined in eq. ( 1) can be rewritten as I(x)=(zo,+I,,)(l+mcosKx))
(7)
where the fringe modulation m=(m,lo,
+m2~02)l(~0i
is
+Zo2)
(8)
.
In the small m limit, E, can be alternatively
written
as
E,=mE,,
(9)
when the hypothesis m < 1 is no more valid, E, is no more proportional by an empirical expression f( m ) [ 16 1.
to m but it is possible to replace m
(10)
-6 = iXm)lml (m&,) ,
withf( m) = [ 1 - exp( -am) ] /aE,,[ 161. a is a parameter which may depend on the sample and experimental conditions. It can be determined from 2 WM gain measurements. When A, =A2, the photoionization cross-sections in the expression (3) of m,E,,,and m2Esc2are identical; therefore: Esc, 110, =Esc2lZ02
(11)
and using eq. (8) we get m= (ml&,,
+m2Esc2)/(Esc,
+&,2)
In the DCPO case, expressions
(12)
.
( 11) and ( 12) are no more valid. We use a space-charge
field modulation
MS& MS,= (m,&, and propose E, =
+m2Esc2)/(Esc,
+E,,,)
,
(13)
to modify eq. (2) as follows:
Lf~Mc)l%l(~,&
+m2Esc2) .
(14)
In the DCPO case, the modulation MS,does not any more correspond to an existing fringe modulation; this is due to the fact that the space-charge field is built from an interference pattern through the photoionization process.
20
Volume 89, number
OPTICS COMMUNICATIONS
1
15 April 1992
3.2. Parameters used for calculation
The theoretical values presented in the next section have been calculated with the set of material parameters fh and c$ used in ref. [ 131. It is worth to note that we did not change the values of the C %P, en , efph, ai b,P, photoionization cross-sections when varying the wavelength. This is due to the fact that, to our knowledge, these data have not been measured at wavelengths lower than 1 km (see for instance the fig. 2 of ref. [ 171). However, according to the trend observed in the same figure for wavelengths just above 1 km, it seems reasonable to assume that the ratio aE/aE is always much greater than 1 between 1050 and 965 nm, and thus the optical emission of holes will still dominate the one of electrons. This assumption is in agreement with the intensity resonant behaviour of the 2 WM gain in InP : Fe near the band edge [ lo]. In this case, it is possible to calculate the DPCM conversion efficiency as a function of the pump intensities multiplied by the unknown hole photoionization cross-section and to determine the maximum efficiency which can be theoretically achieved. As usual for DPCM, the maximum efficiency is obtained with equal pump intensities. On the other hand, we have estimated that for this sample [Fe”] =9x lOI cmp3, [Fe3+] ~2.3 x 1016cmm3. This estimation has been done, as already suggested [ 15 1, in two steps: we first deduce [ Fe3+ ] from the optical absorption at 1.047 pm where the photoionization cross-sections are known and then extract the ratio [Fe*+ ] / [ Fe3+ ] from the value of optimum pump intensity in separate two-wave mixing gain measurements, also at 1.047 pm. These last experiments made it possible (by varying the pump to signal intensity ratio) to determine the non linearity parameter a=0.95, with an applied field of 10 kV/cm and a grating period of 7 pm. We have kept this parameter constant versus wavelength in the calculation presented in the next section. Finally, absorption and ratio rfra,,+&ldySh /r4, are those reported in the previous section.
4. Results We first measured the DPCM conversion efficiency g for different wavelengths with an applied field Eo= 10 kV/cm and a fringe spacing K of about 6.7 pm. The sample temperature was stabilized at 28 1 K and the pump intensities were adjusted to maximise the efficiency as predicted by the model of PR effect in InP : Fe [ 15 1. The results were obtained by measurement of the pump depletion (after checking that fanning was negligible). The experimental conversion efficiencies are summarized in table 1 together with the calculated values. The agreement between the experimental data and the calculated ones is quite satisfactory. The experimental efficiency at 970 nm was not stable because at this wavelength the maximum efficiency required an higher illumination, increasing the photocurrent. An improvement of the cooling system efficiency should overcome this problem. Figs. 3 and 4 show the measured and calculated conversion efficiencies for both beams in the case of DCPO. For these experiments, the sample temperature was 279 K. In order to simplify the experimental procedure, the intensity of the 1.047 nm beam was first optimized in presence of the 1.O10 nm beam and then kept constant, while the intensity of the other was optimized for each wavelength (we adopted the same procedure for the numerical calculation). The highest conversion efficiency for the short wavelength is 63%, with 1, ~985 nm, while the highest conversion efficiency at 1.047 nm (40%) is achieved with I 1= 1.O10 nm. The agreement between measured and calculated data is still rather good, especially if one remembers the Table 1 Wavelength 970 980
1000
(nm)
1 (exp.)
1 (talc.)
zo.50 0.58 0.58
0.56 0.59 0.59
21
Volume 89, number
1
OPTICS
COMMUNICATIONS
heuristic approach used to take into account the space-charge field nonlinearities. case the efficiency was very stable, even for the lower wavelengths.
15 April 1992
In contrast
to the DPCM
5. Conclusion We have demonstrated that mutually incoherent PR interactions like DPCM and DCPO can be realized in 1nP:Fe at wavelengths near the band edge with conversion efficiencies exceeding 50%, owing to the FranzKeldysh effect. They could find, for example, applications with 0.98 urn laser diodes, which are used for pumping some fibre optical amplifiers. The agreement between calculated and experimental conversion efficiencies is rather good. In particular, using the value of the space-charge field non linearity parameter deduced from two-wave mixing experiments, allows a good estimation of both DPCM and DCPO results.
References [ 1] [2] [ 31 [4]
S. Weiss, S. Stemklar and B. Fischer, Optics Lett. 12 ( 1987) 114. S. Stemklar and B. Fischer, Optics Lett. 12 (1987) 711. H.J. Caulfield, J. Shamir and Q. He, Appl. Optics 26 ( 1987) 229 1. S. Weiss, M. Segev, S. Stemklar and B. Fischer, Appl. Optics 27 ( 1988) 3422. [ 51M. Cronin-Golomb, Appl. Phys. Lett. 54 ( 1989) 2189. [6] P. Gravey, N. Wolffer, G. Picoli and C. Ozkul, Technical digest of the topical meeting on photorefractive devices II ( Aussois-France, 1990) p. 164. [ 71 P.L. Chua, D.T.H. Liu and L.J. Cheng, Appl. Phys. Lett. 57 ( 1990) 858. [8] V. Vieux, P. Gravey, N. Wolffer and G. Picoli, Appl. Phys. L&t. 58 (1991) 2880. [9] A. Partovi, A. Kost, E.M. Garmire, G.C. Valley and M.B. Klein, Appl. Phys. Lett. 56 ( 1990) 1089. [ lo] J.E. Millerd, S.D. Koehler, E.M. Garmire, A. Partovi and A.M. Glass, Appl. Phys. Lett. 57 ( 1990) 2776. [ 111 P. Yeh, Appl. Optics 28 ( 1989) 196 1. [ 121 M.P. Petrov, S.L. Sochava and S.I. Stepanov, Optics Lett. 14 (1989) 284. [ 131 G. Picoli, P. Gravey, N. Wolffer and V. Vieux, Technical digest of the topical meeting on photorefractive devices II (Aussois-France, 1990) PD5. [ 141 N. Wolffer, P. Gravey, J.-Y. Moisan, C. Laulan and J.-C. Launay, Optics Comm. 73 ( 1989) 351. [ 151 G. Picoli, P. Gravey, C. Ozkul and V. Vieux, J. Appl. Phys. 66 ( 1989) 3798. [ 161 Ph. Refregier, L. Solymar, H. Rajbenbach and J.P. Huignard, J. Appl. Phys. 58 ( 1985) 45. [ 171 G. Bremond, G. Guillot and A. Nouilhat, Rev. Phys. Appl. 22 ( 1987) 873.
22
material,
effects, and
material,
effects, and
OPTICS COMMUNICATIONS
Double phase conjugate mirror and double colour pumped oscillator using band-edge photorefractivity in 1nP:Fe N. Wolffer, P. Gravey, G. Picoli and V. Vieux CNET Lannion B/OCM/TAC,
Route de Trkgastel, BP40, 22301 Lannion. France
Received 24 July 199 I ; revised manuscript received 24 October 199 1
We have observed the formation of a double phase-conjugate mirror (DPCM ) and a double colour pumped oscillator (DCPO ) at wavelengths near the band-edge of InP:Fe, with an external dc field of 10 kV/cm. The DCPO conversion efficiencies are respectively 63% and 26% for the couple of wavelengths 985 and 1.047 nm. These results are compared with the prediction of a calculation which takes into account the space-charge field non-linearities.
1. Introduction
The double phase conjugate mirror (DPCM) [ 1 ] and the double colour pumped oscillator (DCPO) [ 21 are particularly interesting devices for reconligurable optical interconnects [ 2-5 1. In a DPCM two mutually incoherent pump beams (at nearly identical wavelengths) incident on the opposite faces of a photorefractive (PR) crystal share a common grating which diffracts them into the phase conjugated of the opposite one. When the wavelength difference of the interacting beams is important (larger than the grating selectivity), they can still induce a common grating (DCPO). Recently DPCM has been observed in InP : Fe [ 61 and GaAs : EL2 [ 7 ] at 1.06 pm and DCPO has been achieved in InP : Fe using 1.06 and 1.32 urn wavelengths [ 8 1. This paper presents new results on both DPCM and DCPO obtained in InP:Fe at wavelengths close to its band edge. We have observed DPCM at wavelength down to 970 nm and DCPO between a fixed wavelength ( 1.047 nm) and a variable one from 1.010 to 965 nm. Using wavelengths close to the band edge has the two major implications for PR devices. There is indeed an increase of the optical absorption (Y,but the effective electro-optic coefficient is greatly enhanced through the Franz-Keldysh effect, which has already been exploited to achieve large two-wave mixing gains in GaAs [ 9 ] and InP : Fe [ lo]. The experimental set-up and experimental characteristics of particular interest for band-edge photorefractivity are briefly reported in section 2. Then, the extension to the DCPO case of a numerical procedure previously used to predict the DPCM conversion efftciency (i.e. the ratio of the diffracted beam intensity over the total transmitted one) is described in section 3. Finally, the experimental data are presented in section 4 and compared with the calculated ones.
2. Experimental set-up and sample characteristics The source used for the DPCM experiments is a Ti:sapphire laser which provides the two pump beams at the same wavelength; for DCPO studies one of these two beams has been replaced by another one issued from a diode pumped Nd: YLF laser emitting at 1.047 pm. The results reported here have been obtained with InP : Fe sample 169QC4, grown at CNET. The optical interaction length L and the distance d between the two silver pasted electrodes are both equal to 6.0 mm. The sample temperature is stabilized through a Peltier cooling 0030-4018/92/$05.00
0 1992 Elsevier Science Publishers B.V. All rights reserved.
17
Volume 89. number
1
OPTICS
I5 April 1992
COMMUNICATIONS
Franz-Keldysh/Pockelc
Absorption (cm.‘)
coeffuent
. I
. . * AA
0.5
AA . *
a 950
970
990
1010
1030
1050
950
Wavelength (nm)
Fig. 1. Band-edge
absorption
spectra of InP: Fe sample
970
990
1010
1030
IO50
Wavelength (nm)
169QC4.
r4, of 1nP:Fe sample 169QC4 at 10 kV/ Fig. 2. Ratio rFranz_Keldyrh/ cm, as a function of wavelength.
element. An external dc field is applied along the (001) axis. The sign of this field as well as the polarisation of the beams (parallel to the ( 1TO) axis) are chosen in order to maximise the 2 WM gain (and therefore the DPCM and DCPO diffraction efficiencies) by addition of the contributions of Pockels and Franz-Keldysh effects. When nearly plane waves are used, as for all the experiments reported here, the solution for the grating wave vector is degenerated, so that a continuous set of gratings is created, leading to conical diffraction [ 111. Diffracted beams are not complex conjugate of the incident ones but appear as small parts of rings. However, because all the grating wave vectors are close to the mean value, we suppose that threshold and diffraction efficiency are the same as for the true DPCM and DCPO in which conical diffraction has been eliminated by mean of spatially modulated input beams [ 21 or cylindrical lenses [ 12 1. The two pump beams enter the opposite ( 110) faces which are uncoated. Fig. 1 shows the absorption spectra. cu increases from 1.2 cm-’ at 1.047 urn to 5.4 cm-’ at 0.965 urn. For a given applied field E,, the influence of the Franz-Keldysh effect can be described [ 131 through an effective linear electrooptic coefficient r,,= Separate 2 WM experiments (gain measurements for two opposite signs of the applied field) r41 + rFranz-Keldyshhave been performed with the same sample in order to measure the wavelength dependence of the ratio r,,,,,. are shown in fig. 2 (for E,= 10 kV/cm). Finally, we have checked that the electroabKeldysh /r4,. The results sorption in presence of a field of 10 kV/cm was lower than 0.3 cm- ’ in the wavelength range used in these experiments. 3. Calculation of DPCM and DCPO conversion effkiencies 3.1. Numerical
method
Numerical simulations have been performed in order to predict the performances of this same sample in DPCM and DCPO experiments. The method used for the DCPO is an extension of the one used in the DPCM case, which has already been described in previous works on BGO [ 141 and InP: Fe [ 61; we just indicate here the main modifications. We consider two superimposed interference patterns (supposed to be in phase) at wavelengths 1, and AZ defined by 18
15 April 1992
OPTICS COMMUNICATIONS
Volume 89, number 1
Conversion efficiency
Conversion efficiency 0.8
. .
0.6
0.6
. .
0.4
A
0.2
A
. .
4
a
A . . A
x
4
x* l
l
.
.
’
.
A
.
A .
0.4
:
.
4
l
0.2
.
960
980
1000
1020
980
1000
1020
Wavelength (nm)
Wavelength (nm)
= 1.047 nm versus AZ=9651.010 nm (exp: triangles, talc: circles); applied dc field: 10 kV/ cm; mean grating period: 7 km. Fig. 3. Conversion efficiency for 1,
Z(x)=Z,(x)+Z,(x)=Zo,(l+ml
C 960
cosfi)+ZO,(l+mzcosfi).
Fig. 4. Conversion efficiency for &=965-l .OlO nm versus & (exp: triangles, talc: circles); applied dc field: 10 kV/cm; mean grating period: 7 pm.
(1)
When the standard hypothesis [ 15 ] (in particular small fringe modulation) to transform the nonlinear system governing El into a linear one are satisfied, it is possible to write El under the form: 4 =ml-%
(2)
+m2L,
where mlEscl (respectively mzEsc2) is the solution corresponding to interference pattern II (x) (respectively Z*(x) ) in presence of an additional uniform illumination Zo2(respectively Ior ). More explicitly: E I =imlZol a”‘p P To [
(
(3) with
(da) E,=K(k,Tle)
, EDp=EMp+ED,
ED,=&,+&,
(4b)
eno=eth ” 027 ” +c$‘Zol +oo2Z
(5a)
+f$ZoI +ao2Z p 029
(5b)
e
PO
=eth
P
19
I5 April 1992
OPTICS COMMUNICATIONS
Volume 89, number 1 01 O’ and ai’, 0” > CJ‘p
0:’ are the photoionization mobilities; c,,,, the capture coefficients, eLh and electrons and holes respectively). For InP: Fe, The coupling coefficients for both wavelengths
cross-sections at wavelengths 1, and AZ, respectively; P”,~, the e: are the thermal emission rates (labels n and p are used for nrO = [Fe’+ 1, pTo= [Fe’+ 1. A, and Ar are then as usual (for small angles inside the crystal)
(6)
[~3(~)~eff(~)/21-h~
C(k)=(nlk)
The calculation procedure is, like in the DPCM case, an iterative one: assuming a starting value E, =p,ESc, +p2ESE2 (in practice, we arbitrary set p, =p2=0.2),one calculates the intensities of the four beams through the standard wave-coupling equations, then calculates m, and m2 and uses E,= m,Esc, + m2Esczfor a new cycle. The procedure is repeated until E, converges. As for the DPCM, we have to take into account that for large conversion efficiencies m, and m2 are not negligible when compared to 1. To evaluate the space-charge field nonlinearities we have used an heuristic extension of the formulas of Refregier et al. [ 161 by using the following approach. Let us first come back to the DPCM case (2, =;l,=A). The intensity I(x) defined in eq. ( 1) can be rewritten as I(x)=(zo,+I,,)(l+mcosKx))
(7)
where the fringe modulation m=(m,lo,
+m2~02)l(~0i
is
+Zo2)
(8)
.
In the small m limit, E, can be alternatively
written
as
E,=mE,,
(9)
when the hypothesis m < 1 is no more valid, E, is no more proportional by an empirical expression f( m ) [ 16 1.
to m but it is possible to replace m
(10)
-6 = iXm)lml (m&,) ,
withf( m) = [ 1 - exp( -am) ] /aE,,[ 161. a is a parameter which may depend on the sample and experimental conditions. It can be determined from 2 WM gain measurements. When A, =A2, the photoionization cross-sections in the expression (3) of m,E,,,and m2Esc2are identical; therefore: Esc, 110, =Esc2lZ02
(11)
and using eq. (8) we get m= (ml&,,
+m2Esc2)/(Esc,
+&,2)
In the DCPO case, expressions
(12)
.
( 11) and ( 12) are no more valid. We use a space-charge
field modulation
MS& MS,= (m,&, and propose E, =
+m2Esc2)/(Esc,
+E,,,)
,
(13)
to modify eq. (2) as follows:
Lf~Mc)l%l(~,&
+m2Esc2) .
(14)
In the DCPO case, the modulation MS,does not any more correspond to an existing fringe modulation; this is due to the fact that the space-charge field is built from an interference pattern through the photoionization process.
20
Volume 89, number
OPTICS COMMUNICATIONS
1
15 April 1992
3.2. Parameters used for calculation
The theoretical values presented in the next section have been calculated with the set of material parameters fh and c$ used in ref. [ 131. It is worth to note that we did not change the values of the C %P, en , efph, ai b,P, photoionization cross-sections when varying the wavelength. This is due to the fact that, to our knowledge, these data have not been measured at wavelengths lower than 1 km (see for instance the fig. 2 of ref. [ 171). However, according to the trend observed in the same figure for wavelengths just above 1 km, it seems reasonable to assume that the ratio aE/aE is always much greater than 1 between 1050 and 965 nm, and thus the optical emission of holes will still dominate the one of electrons. This assumption is in agreement with the intensity resonant behaviour of the 2 WM gain in InP : Fe near the band edge [ lo]. In this case, it is possible to calculate the DPCM conversion efficiency as a function of the pump intensities multiplied by the unknown hole photoionization cross-section and to determine the maximum efficiency which can be theoretically achieved. As usual for DPCM, the maximum efficiency is obtained with equal pump intensities. On the other hand, we have estimated that for this sample [Fe”] =9x lOI cmp3, [Fe3+] ~2.3 x 1016cmm3. This estimation has been done, as already suggested [ 15 1, in two steps: we first deduce [ Fe3+ ] from the optical absorption at 1.047 pm where the photoionization cross-sections are known and then extract the ratio [Fe*+ ] / [ Fe3+ ] from the value of optimum pump intensity in separate two-wave mixing gain measurements, also at 1.047 pm. These last experiments made it possible (by varying the pump to signal intensity ratio) to determine the non linearity parameter a=0.95, with an applied field of 10 kV/cm and a grating period of 7 pm. We have kept this parameter constant versus wavelength in the calculation presented in the next section. Finally, absorption and ratio rfra,,+&ldySh /r4, are those reported in the previous section.
4. Results We first measured the DPCM conversion efficiency g for different wavelengths with an applied field Eo= 10 kV/cm and a fringe spacing K of about 6.7 pm. The sample temperature was stabilized at 28 1 K and the pump intensities were adjusted to maximise the efficiency as predicted by the model of PR effect in InP : Fe [ 15 1. The results were obtained by measurement of the pump depletion (after checking that fanning was negligible). The experimental conversion efficiencies are summarized in table 1 together with the calculated values. The agreement between the experimental data and the calculated ones is quite satisfactory. The experimental efficiency at 970 nm was not stable because at this wavelength the maximum efficiency required an higher illumination, increasing the photocurrent. An improvement of the cooling system efficiency should overcome this problem. Figs. 3 and 4 show the measured and calculated conversion efficiencies for both beams in the case of DCPO. For these experiments, the sample temperature was 279 K. In order to simplify the experimental procedure, the intensity of the 1.047 nm beam was first optimized in presence of the 1.O10 nm beam and then kept constant, while the intensity of the other was optimized for each wavelength (we adopted the same procedure for the numerical calculation). The highest conversion efficiency for the short wavelength is 63%, with 1, ~985 nm, while the highest conversion efficiency at 1.047 nm (40%) is achieved with I 1= 1.O10 nm. The agreement between measured and calculated data is still rather good, especially if one remembers the Table 1 Wavelength 970 980
1000
(nm)
1 (exp.)
1 (talc.)
zo.50 0.58 0.58
0.56 0.59 0.59
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heuristic approach used to take into account the space-charge field nonlinearities. case the efficiency was very stable, even for the lower wavelengths.
15 April 1992
In contrast
to the DPCM
5. Conclusion We have demonstrated that mutually incoherent PR interactions like DPCM and DCPO can be realized in 1nP:Fe at wavelengths near the band edge with conversion efficiencies exceeding 50%, owing to the FranzKeldysh effect. They could find, for example, applications with 0.98 urn laser diodes, which are used for pumping some fibre optical amplifiers. The agreement between calculated and experimental conversion efficiencies is rather good. In particular, using the value of the space-charge field non linearity parameter deduced from two-wave mixing experiments, allows a good estimation of both DPCM and DCPO results.
References [ 1] [2] [ 31 [4]
S. Weiss, S. Stemklar and B. Fischer, Optics Lett. 12 ( 1987) 114. S. Stemklar and B. Fischer, Optics Lett. 12 (1987) 711. H.J. Caulfield, J. Shamir and Q. He, Appl. Optics 26 ( 1987) 229 1. S. Weiss, M. Segev, S. Stemklar and B. Fischer, Appl. Optics 27 ( 1988) 3422. [ 51M. Cronin-Golomb, Appl. Phys. Lett. 54 ( 1989) 2189. [6] P. Gravey, N. Wolffer, G. Picoli and C. Ozkul, Technical digest of the topical meeting on photorefractive devices II ( Aussois-France, 1990) p. 164. [ 71 P.L. Chua, D.T.H. Liu and L.J. Cheng, Appl. Phys. Lett. 57 ( 1990) 858. [8] V. Vieux, P. Gravey, N. Wolffer and G. Picoli, Appl. Phys. L&t. 58 (1991) 2880. [9] A. Partovi, A. Kost, E.M. Garmire, G.C. Valley and M.B. Klein, Appl. Phys. Lett. 56 ( 1990) 1089. [ lo] J.E. Millerd, S.D. Koehler, E.M. Garmire, A. Partovi and A.M. Glass, Appl. Phys. Lett. 57 ( 1990) 2776. [ 111 P. Yeh, Appl. Optics 28 ( 1989) 196 1. [ 121 M.P. Petrov, S.L. Sochava and S.I. Stepanov, Optics Lett. 14 (1989) 284. [ 131 G. Picoli, P. Gravey, N. Wolffer and V. Vieux, Technical digest of the topical meeting on photorefractive devices II (Aussois-France, 1990) PD5. [ 141 N. Wolffer, P. Gravey, J.-Y. Moisan, C. Laulan and J.-C. Launay, Optics Comm. 73 ( 1989) 351. [ 151 G. Picoli, P. Gravey, C. Ozkul and V. Vieux, J. Appl. Phys. 66 ( 1989) 3798. [ 161 Ph. Refregier, L. Solymar, H. Rajbenbach and J.P. Huignard, J. Appl. Phys. 58 ( 1985) 45. [ 171 G. Bremond, G. Guillot and A. Nouilhat, Rev. Phys. Appl. 22 ( 1987) 873.
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