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Influence of competition on optical sum frequency generation
Volume 59, number 4
OPTICS COMMUNICATIONS
15 September 1986
INFLUENCE OF COMPETITION ON OPTICAL SUM FREQUENCY GENERATION S.C. MEHENDALE
r, W. FORYSIAK, C. CHENG and R.G. HARRISON
Department of Physics, Heriot- Watt University, Edinburgh EH14 4AS, UK Received 13 May 1986
We present results of a theoretical analysis of sum&quency generation incorporating second harmonic generation of the incident fields. It is shown that under certain conditions, a significant reduction in conversion efficiency can occur even when phase mismatch for second harmonic gene-ration is relativeIy large. Experimental results on sum frequency generation in Cd-As2 of two CO2 laser emission tuned to the 9 pm vibrational band are presented which are in good qualitative agreement with the the&icaI predictions.
Theoretical analysis of optical frequency conversion in a nonlinear dielectric is generally restricted to a consideration of only one of several possible interactions [l] since efficient conversion requires that wavevectors of the nonlinear source polarisation and the generated field be equal and this condition is usually satisfied for only a single process under given conditions. However, when some of the frequencies involved are not widely separated and the nonlinear medium is weakly dispersive it is possible that more than one process will be nearly phase-matched. In this communication we present results of a theoretical and experimental investigation of such a case, considering specifically the process of sum frequency generation (SFC) when second harmonic generation (SHG) of the incident fields is also likely. The theoretical analysis shows that presence of competing processes alters the evolution of sum frequency wave in a qualitative as well as a quantitative manner. Thus when photon fluxes of the two incident waves are equal, it is found that in contrast to the usual case [2] of a monotonic growth of the sum-frequency field, a periodic exchange of energy between the Incident and the generated waves is expected even when the phase-mismatch for SHG is relatively large. Experimentally, we have studied SFG in CdGeAs, of two CO2 laser emissions tuned to the 9P(18) and 9P(24) rotational lines. In this case 1 On leave from the Laser Division, Bhabha Atomic Research Centre, Bombay 400 085, India.
304
the phase-matching angles for the SFG as well as the two SHG processes were nearly equal and the observed effects of competition are consistent with predictions of the theoretical analysis. Simultaneous occurrence of more than one phase-matched nonlinear processes is expected in several other nonlinear interactions such as difference frequency generation and parametric amplification when the signal and idler frequencies are nearly equal; evidence for the former case has already been observed in experiments [3]. Consider two coherent em. waves of frequencies w1 and o2 incident on a nonlinear dielectric. Let Akl, Ak2 and Akg be the wave-vector mismatches for generation of waves at frequencies w3(= 201), 04(= 20~) and ws(= w1 t 02) respectively. Also let pi and & denote the amplitudes and phases of the electric fields at frequencies wj. The directions of energy transfer for the three processes are controlled by the relative phase angles [2] 8, = Ak, z + $J~- 2&, 82=Ak2z+~4-2@2and83=Ak3z+~5+ - $2; z being the interaction length. When all the three processes are important the evolution of various waves in the nonlinear medium is described by a set of eight coupled equations - five for the amplitudes pi and three for the angles 8i - which can be readily obtained by combining the well-known equations for SHG and SFG [2]. Weuse normalised parameters viz interaction length c, field amplitude ‘fi, and wave-vector mismatch Asi which are slightly different from those in [2] and defined by 0 0304018/86/$03.50 OElsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
Volume 5 9, number 4
OPTICS COMMUNICATIONS
f = K (32~ W w; o1 q/k, Ui = (C2ki/8n
k2k,)1’z
Oi W)‘” PI )
i = 1 tO
15 September 1986
z, 5 ,
and ASi = AkiZ/t ,
i = 1 to 3 3
where ki is wave-vector at frequency Ui; IVis total power flow per unit area, given by C2/81T
Ci ki pf/ Wi 3
and K = (4n/c2) d, is the nonlinear coupling coefficient. The latter is assumed to be identical for the three processes; this is valid if w1 - o2 and if all the frequencies are welI removed from absorption regions. _From the defmitions of Ui and Wit can be seen that UT represents-the fraction of total intensity of frequency Wi. In our analysis, for simplicity, we assume all walkoff angles to be small and neglect factors such ask, w2/k2q which are of the order of unity. As an illustration of the resulting coupled equations we reproduce here the equation governing evolution of u1 with 5 viz duJd{ = -(w~/w~)zQu~ -(Ol/W5)U2U5
Fig. 1. Evolution of the sum frequency wavuintensity. Curves a,b,c correspondto ASI = 0,2 and 4 respectively while the curve d shows evolution when only SFG takes place. Initial conditions u;(O) = O.?S, u;(O) = 0.65.
sine1
sine,.
The two terms on the right hand side of this equation describe energy transfer to the second harmonic and to the sum frequency waves respectively. We have investigated evolution of thevarious waves under different conditions by a numerical integration of the coupled,equations assuming only the fields at 01 and w2 to be present initially and with 8 I, 8 2 and 133 equal to n/2 in the beginning which maximises growth of the generated fields. In the following, we use w1/05 = 0.6. Let us first consider the case when SFC is phasematched, i.e. As3 = 0. We assume that the phase mismatches for two SHG processes are equal but have opposite signs so that As2 = -As,. A representative example of the case when photon fluxes in the two incident waves (-u~(0)/ol and - ui(0)/02) are unequal is shown in fig. 1 for u&O) = 0.65 and U:(O) = 0.35. The curves labelled a, b and c show evolution of.9; with 5 for As1 = 0,2,4 while the curve d gives results when only SFG is possible. Presence of competing SHG processes results in a reduction in maximum conversion and also an increase in the interac-
tion length over which it occurs. For low conversion efficiencies the effect of competition is negligible as expected. To appreciate the significance of results shown in fig. 1, let us consider a .specific example of SFG of 10 p CO2 laser emission in CdGeAs2. In this case for a total incident intensity of 25 MW/cm2 (typical damage threshold -40 MW/cm2) a crystal length of 1 cm corresponds to 5 - 5.7 while As = 4 corresponds to Ak - 22.4 cm-l. When photon fluxes in the two beams (-&O)/ol , -u$(0)/q2) are equal, presence of SHG result in a much more dramatic change in SFG as shown in fig. 2. Here curves a, b, c and d correspond to As = 0,2, % = 4 and 10 respectively, with z&O) = 0.6 and ~~(0) 0.4. The curve e shows evolution of the wave at sum frequency when SHG is absent and follows the wellknown tanh2 dependence. The interesting feature of fig. 2 is that even for As = 10 presence of SHG results in an oscillatory dependence of sum frequency intenstiy on 5. This behaviour can be understood by examining the coupled wave equations. The direction of energy transfer in SFG reverses whenever e3 changes sign, which occurs discontinuously when ul, u2 or us becomes zero. In the absence of SHG, u1 and u2 go to 305
Volume 59, number 4
OPTICS COMMUNICATIONS
15 September 1986
(4 ,.___-_-___-__---_----_ -
OWN 0
’ 2
’
INTERACTION
Fii. 2. SFG with yual photon tuxes in the incident beams. Initial conditions ur(0) = 0.6, u?(O) = 0.4. Curves a,b,c,d correspond to Asr = 0,2,4 and 10 respectively, while the curve e corresponds to the case when SHG is absent.
zero only for 5 + 00. However, in the presence of SHG, and ~2 can become zero for finite 5 due to the additional decay mechanism, resulting in energy transfer from the sum frequency wave back to the waves at frequencies w1 and w2. As us + 0 there is once again a reversalin the sign of 8 3 leading to subsequent growth of us, and so on. Next we consider the case when one of the SHG processes is phase-matched, say As1 = 0, and investigate the influence on conversion efficiency of the presence of another wave at frequency w2 when SFG is also important. Such a situation is more suitable for an experimental verification of the effects of competition. We assume that phase-mismatch for SHG of the w2-wave is double the phase-mismatch for SFG, i.e. As2 = 2As3. The curves lavelled a, b and c in fig. 3 show the evolution of intensity at frequency 20, for As3 = 0,0.5 and 1.Orespectively with U:(O) = 0.65 and z&O) = 0.35. The curve d corresponds to the case when the wave at frequency w2 is absent, while the curves e and f show variation of intensities at frequencies w5 and w4 with { for As3 = 0. It is seen that simultaneous occurrence of SFG results in a significant reduction in the SHG efficiency. Another interesting
’
4
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LENGTH
’
6
’
(ARBITRARY
’
6
’
’
10
UNITS1
Fig. 3. Evolution of the intensity at frequency 2wt for Ass = 0,O.S and 1.0 (curves a,b,c respectively). The curve d shows SHG in the absence of any competition while curves e and f show intensities at frequencies wr + ws and 2~2 respectively for the case when all the three processes are phase-matched.
~1
306
observation from fig. 3 is that when all the three processes are phase-matched then while initially SFG dominates - nonlinear source polarisation for SFG being nearly twice that for SHG - for sufficiently long interaction lengths the incident energy is almost completely transferred into waves at the second harmonic frequencies. Again this is due to the fact that while a reversal of direction of energy transfer can occur for SFG when u1 or u2 goes to zero, a discontinuous change in the signs of 8, and 19~cannot occur because de 1/d{ and de 2/dc only contain terms varying like l/u3 and l/u4 which always remains fmite. Experimentally we have studied SFG of CO2 laser emission in CdGeAs2. The CO2 laser, employing a novel dual-cavity hybrid configuration [4], generates two synchronised single- mode emissions each of which, is independently tunable. One of the emissions was amplified in a single-pass amplifier and the two emissions, polarised parallel to each other, were combined using a Ge beam-splitter. The beam was then focussed on a 5 X 5 X 8 mm3 antireflection coated CdGeAsZ crystal cooled to liquid nitrogen temperature. The
Volume 59, number 4
OPTICS COMMUNICATIONS
I
I
I
I
CRYSTAL
I
ROTATION
15 September 1986
I
I
I
(DEGREES)
Fig. 4. Relative pulse energies of the SH of 9P(18) emission (curve a), SH of 9P(24) emission (curve b) and the sum Frequency emission (curve c) as a function of the CdCaAs2 crys,@lorientation (external angle).
undepleted CO2 laser radiation in the output after the crystal was removed using a MgO filter and the remaining emission was analysed using a spectrum analyser. Pulse energies and temporal profiles of the emissions were determined using a joulemeter and a fast room temperature HgCdTe detector respectively. In the experiments the two CO2 laser emissions were tuned to the 9P(18) and 9P(24) rotational lines. In this case the phase-matching angles for the two SHG processes, calculated using the Sellmeier parameters of [S], were quite close being -32.91’ and -32.92’ respectively with the phase-matching angle for SFG intermediate to the two values. The measured pulse energies at the three generated frequencies are shown in fig. 4 as a function of the CdGeAs, crystal orientation, The three emissions occurred simultaneously over almost the entire tuning range. To study the effects of competition, the energy of the second harmonic of the 9P(18) emission was monitored in the presence and absence of the 9P(24) emission, when the CdGeAs2 crystal was oriented so as to maximise the former. It was found that the pulse energy of second harmonic emission decreased in the presence of the second incident beam in qualitative agreement with the results of the theoretical analysis. As a typical example, the change in second harmonic energy was -20% for estimated internal input intensities of
1, m 2.9 MW/cm2 (9P(18)) and I2 cv 2.3 MW/cm2 (9P(24)). In this case the Ak values for SFG and the second SHG process were calculated to be -0.09 cm-l and -0.16 cm-l respectively. Theoretical calculations with parameter values corresponding to these ‘conditions predict a slightly larger decrease in SHG intensity, by -50%. However, the difference in the experimental and the theoretical results can be attributed to the fact that the latter are applicable strictly for plane-waves of uniform intensity only. As shown in fig. 3, the effect of competition depends upon 1 and As, both of which vary with the total intensity W, so that integration over the spatial and temporal profiles of the emissions to approximate the experimental situation closely is bound to reduce the decrease in conversion efficiency. To summarise we have presented an analysis of the process of sum frequency generation when competing second harmonic generation of the incident fields is also likely. An important result of the analysis is that under certain conditions competition can have substantial effect on the conversion efficiency even when phase-mismatch for SHG is relatively large. Experimental results were presented for SFG of two CO2 laser emissions in CdGeAs2 when all the three processes occurred simultaneously. The observed effects of competition were found to be consistent with the theoretical results. 307
Volume 59, number 4
OPTICS COMMUNICATIONS
The research work was supported by the Procurement Executive, U.K. Ministry of Defence.
References [l]
308
R.L. Byer, Non linear optics, eds. P.G. Harper and B.S. Wherrett, (New York, Academic, 1979) Ch. 2.
[2] J.A.
15 September 1986
Armstrong, N. Bloembexgen, J. Ducuing and P.S. Pershan, Phys. Rev., 127 (1962) 1918. [ 31 R.G. Harrison, P.K. Gupta, M.R. Taghizadeh and A.K. Kar, IEEE J. Quant. Electron. QE-18 (1982) 1239. [4] S.C. Mehendale and R.G. Harrison, Optics L&t. 10 (1985) 603. 151 G.C. Bhar, Appl. Optics 15 (1976) 306.
OPTICS COMMUNICATIONS
15 September 1986
INFLUENCE OF COMPETITION ON OPTICAL SUM FREQUENCY GENERATION S.C. MEHENDALE
r, W. FORYSIAK, C. CHENG and R.G. HARRISON
Department of Physics, Heriot- Watt University, Edinburgh EH14 4AS, UK Received 13 May 1986
We present results of a theoretical analysis of sum&quency generation incorporating second harmonic generation of the incident fields. It is shown that under certain conditions, a significant reduction in conversion efficiency can occur even when phase mismatch for second harmonic gene-ration is relativeIy large. Experimental results on sum frequency generation in Cd-As2 of two CO2 laser emission tuned to the 9 pm vibrational band are presented which are in good qualitative agreement with the the&icaI predictions.
Theoretical analysis of optical frequency conversion in a nonlinear dielectric is generally restricted to a consideration of only one of several possible interactions [l] since efficient conversion requires that wavevectors of the nonlinear source polarisation and the generated field be equal and this condition is usually satisfied for only a single process under given conditions. However, when some of the frequencies involved are not widely separated and the nonlinear medium is weakly dispersive it is possible that more than one process will be nearly phase-matched. In this communication we present results of a theoretical and experimental investigation of such a case, considering specifically the process of sum frequency generation (SFC) when second harmonic generation (SHG) of the incident fields is also likely. The theoretical analysis shows that presence of competing processes alters the evolution of sum frequency wave in a qualitative as well as a quantitative manner. Thus when photon fluxes of the two incident waves are equal, it is found that in contrast to the usual case [2] of a monotonic growth of the sum-frequency field, a periodic exchange of energy between the Incident and the generated waves is expected even when the phase-mismatch for SHG is relatively large. Experimentally, we have studied SFG in CdGeAs, of two CO2 laser emissions tuned to the 9P(18) and 9P(24) rotational lines. In this case 1 On leave from the Laser Division, Bhabha Atomic Research Centre, Bombay 400 085, India.
304
the phase-matching angles for the SFG as well as the two SHG processes were nearly equal and the observed effects of competition are consistent with predictions of the theoretical analysis. Simultaneous occurrence of more than one phase-matched nonlinear processes is expected in several other nonlinear interactions such as difference frequency generation and parametric amplification when the signal and idler frequencies are nearly equal; evidence for the former case has already been observed in experiments [3]. Consider two coherent em. waves of frequencies w1 and o2 incident on a nonlinear dielectric. Let Akl, Ak2 and Akg be the wave-vector mismatches for generation of waves at frequencies w3(= 201), 04(= 20~) and ws(= w1 t 02) respectively. Also let pi and & denote the amplitudes and phases of the electric fields at frequencies wj. The directions of energy transfer for the three processes are controlled by the relative phase angles [2] 8, = Ak, z + $J~- 2&, 82=Ak2z+~4-2@2and83=Ak3z+~5+ - $2; z being the interaction length. When all the three processes are important the evolution of various waves in the nonlinear medium is described by a set of eight coupled equations - five for the amplitudes pi and three for the angles 8i - which can be readily obtained by combining the well-known equations for SHG and SFG [2]. Weuse normalised parameters viz interaction length c, field amplitude ‘fi, and wave-vector mismatch Asi which are slightly different from those in [2] and defined by 0 0304018/86/$03.50 OElsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
Volume 5 9, number 4
OPTICS COMMUNICATIONS
f = K (32~ W w; o1 q/k, Ui = (C2ki/8n
k2k,)1’z
Oi W)‘” PI )
i = 1 tO
15 September 1986
z, 5 ,
and ASi = AkiZ/t ,
i = 1 to 3 3
where ki is wave-vector at frequency Ui; IVis total power flow per unit area, given by C2/81T
Ci ki pf/ Wi 3
and K = (4n/c2) d, is the nonlinear coupling coefficient. The latter is assumed to be identical for the three processes; this is valid if w1 - o2 and if all the frequencies are welI removed from absorption regions. _From the defmitions of Ui and Wit can be seen that UT represents-the fraction of total intensity of frequency Wi. In our analysis, for simplicity, we assume all walkoff angles to be small and neglect factors such ask, w2/k2q which are of the order of unity. As an illustration of the resulting coupled equations we reproduce here the equation governing evolution of u1 with 5 viz duJd{ = -(w~/w~)zQu~ -(Ol/W5)U2U5
Fig. 1. Evolution of the sum frequency wavuintensity. Curves a,b,c correspondto ASI = 0,2 and 4 respectively while the curve d shows evolution when only SFG takes place. Initial conditions u;(O) = O.?S, u;(O) = 0.65.
sine1
sine,.
The two terms on the right hand side of this equation describe energy transfer to the second harmonic and to the sum frequency waves respectively. We have investigated evolution of thevarious waves under different conditions by a numerical integration of the coupled,equations assuming only the fields at 01 and w2 to be present initially and with 8 I, 8 2 and 133 equal to n/2 in the beginning which maximises growth of the generated fields. In the following, we use w1/05 = 0.6. Let us first consider the case when SFC is phasematched, i.e. As3 = 0. We assume that the phase mismatches for two SHG processes are equal but have opposite signs so that As2 = -As,. A representative example of the case when photon fluxes in the two incident waves (-u~(0)/ol and - ui(0)/02) are unequal is shown in fig. 1 for u&O) = 0.65 and U:(O) = 0.35. The curves labelled a, b and c show evolution of.9; with 5 for As1 = 0,2,4 while the curve d gives results when only SFG is possible. Presence of competing SHG processes results in a reduction in maximum conversion and also an increase in the interac-
tion length over which it occurs. For low conversion efficiencies the effect of competition is negligible as expected. To appreciate the significance of results shown in fig. 1, let us consider a .specific example of SFG of 10 p CO2 laser emission in CdGeAs2. In this case for a total incident intensity of 25 MW/cm2 (typical damage threshold -40 MW/cm2) a crystal length of 1 cm corresponds to 5 - 5.7 while As = 4 corresponds to Ak - 22.4 cm-l. When photon fluxes in the two beams (-&O)/ol , -u$(0)/q2) are equal, presence of SHG result in a much more dramatic change in SFG as shown in fig. 2. Here curves a, b, c and d correspond to As = 0,2, % = 4 and 10 respectively, with z&O) = 0.6 and ~~(0) 0.4. The curve e shows evolution of the wave at sum frequency when SHG is absent and follows the wellknown tanh2 dependence. The interesting feature of fig. 2 is that even for As = 10 presence of SHG results in an oscillatory dependence of sum frequency intenstiy on 5. This behaviour can be understood by examining the coupled wave equations. The direction of energy transfer in SFG reverses whenever e3 changes sign, which occurs discontinuously when ul, u2 or us becomes zero. In the absence of SHG, u1 and u2 go to 305
Volume 59, number 4
OPTICS COMMUNICATIONS
15 September 1986
(4 ,.___-_-___-__---_----_ -
OWN 0
’ 2
’
INTERACTION
Fii. 2. SFG with yual photon tuxes in the incident beams. Initial conditions ur(0) = 0.6, u?(O) = 0.4. Curves a,b,c,d correspond to Asr = 0,2,4 and 10 respectively, while the curve e corresponds to the case when SHG is absent.
zero only for 5 + 00. However, in the presence of SHG, and ~2 can become zero for finite 5 due to the additional decay mechanism, resulting in energy transfer from the sum frequency wave back to the waves at frequencies w1 and w2. As us + 0 there is once again a reversalin the sign of 8 3 leading to subsequent growth of us, and so on. Next we consider the case when one of the SHG processes is phase-matched, say As1 = 0, and investigate the influence on conversion efficiency of the presence of another wave at frequency w2 when SFG is also important. Such a situation is more suitable for an experimental verification of the effects of competition. We assume that phase-mismatch for SHG of the w2-wave is double the phase-mismatch for SFG, i.e. As2 = 2As3. The curves lavelled a, b and c in fig. 3 show the evolution of intensity at frequency 20, for As3 = 0,0.5 and 1.Orespectively with U:(O) = 0.65 and z&O) = 0.35. The curve d corresponds to the case when the wave at frequency w2 is absent, while the curves e and f show variation of intensities at frequencies w5 and w4 with { for As3 = 0. It is seen that simultaneous occurrence of SFG results in a significant reduction in the SHG efficiency. Another interesting
’
4
’
LENGTH
’
6
’
(ARBITRARY
’
6
’
’
10
UNITS1
Fig. 3. Evolution of the intensity at frequency 2wt for Ass = 0,O.S and 1.0 (curves a,b,c respectively). The curve d shows SHG in the absence of any competition while curves e and f show intensities at frequencies wr + ws and 2~2 respectively for the case when all the three processes are phase-matched.
~1
306
observation from fig. 3 is that when all the three processes are phase-matched then while initially SFG dominates - nonlinear source polarisation for SFG being nearly twice that for SHG - for sufficiently long interaction lengths the incident energy is almost completely transferred into waves at the second harmonic frequencies. Again this is due to the fact that while a reversal of direction of energy transfer can occur for SFG when u1 or u2 goes to zero, a discontinuous change in the signs of 8, and 19~cannot occur because de 1/d{ and de 2/dc only contain terms varying like l/u3 and l/u4 which always remains fmite. Experimentally we have studied SFG of CO2 laser emission in CdGeAs2. The CO2 laser, employing a novel dual-cavity hybrid configuration [4], generates two synchronised single- mode emissions each of which, is independently tunable. One of the emissions was amplified in a single-pass amplifier and the two emissions, polarised parallel to each other, were combined using a Ge beam-splitter. The beam was then focussed on a 5 X 5 X 8 mm3 antireflection coated CdGeAsZ crystal cooled to liquid nitrogen temperature. The
Volume 59, number 4
OPTICS COMMUNICATIONS
I
I
I
I
CRYSTAL
I
ROTATION
15 September 1986
I
I
I
(DEGREES)
Fig. 4. Relative pulse energies of the SH of 9P(18) emission (curve a), SH of 9P(24) emission (curve b) and the sum Frequency emission (curve c) as a function of the CdCaAs2 crys,@lorientation (external angle).
undepleted CO2 laser radiation in the output after the crystal was removed using a MgO filter and the remaining emission was analysed using a spectrum analyser. Pulse energies and temporal profiles of the emissions were determined using a joulemeter and a fast room temperature HgCdTe detector respectively. In the experiments the two CO2 laser emissions were tuned to the 9P(18) and 9P(24) rotational lines. In this case the phase-matching angles for the two SHG processes, calculated using the Sellmeier parameters of [S], were quite close being -32.91’ and -32.92’ respectively with the phase-matching angle for SFG intermediate to the two values. The measured pulse energies at the three generated frequencies are shown in fig. 4 as a function of the CdGeAs, crystal orientation, The three emissions occurred simultaneously over almost the entire tuning range. To study the effects of competition, the energy of the second harmonic of the 9P(18) emission was monitored in the presence and absence of the 9P(24) emission, when the CdGeAs2 crystal was oriented so as to maximise the former. It was found that the pulse energy of second harmonic emission decreased in the presence of the second incident beam in qualitative agreement with the results of the theoretical analysis. As a typical example, the change in second harmonic energy was -20% for estimated internal input intensities of
1, m 2.9 MW/cm2 (9P(18)) and I2 cv 2.3 MW/cm2 (9P(24)). In this case the Ak values for SFG and the second SHG process were calculated to be -0.09 cm-l and -0.16 cm-l respectively. Theoretical calculations with parameter values corresponding to these ‘conditions predict a slightly larger decrease in SHG intensity, by -50%. However, the difference in the experimental and the theoretical results can be attributed to the fact that the latter are applicable strictly for plane-waves of uniform intensity only. As shown in fig. 3, the effect of competition depends upon 1 and As, both of which vary with the total intensity W, so that integration over the spatial and temporal profiles of the emissions to approximate the experimental situation closely is bound to reduce the decrease in conversion efficiency. To summarise we have presented an analysis of the process of sum frequency generation when competing second harmonic generation of the incident fields is also likely. An important result of the analysis is that under certain conditions competition can have substantial effect on the conversion efficiency even when phase-mismatch for SHG is relatively large. Experimental results were presented for SFG of two CO2 laser emissions in CdGeAs2 when all the three processes occurred simultaneously. The observed effects of competition were found to be consistent with the theoretical results. 307
Volume 59, number 4
OPTICS COMMUNICATIONS
The research work was supported by the Procurement Executive, U.K. Ministry of Defence.
References [l]
308
R.L. Byer, Non linear optics, eds. P.G. Harper and B.S. Wherrett, (New York, Academic, 1979) Ch. 2.
[2] J.A.
15 September 1986
Armstrong, N. Bloembexgen, J. Ducuing and P.S. Pershan, Phys. Rev., 127 (1962) 1918. [ 31 R.G. Harrison, P.K. Gupta, M.R. Taghizadeh and A.K. Kar, IEEE J. Quant. Electron. QE-18 (1982) 1239. [4] S.C. Mehendale and R.G. Harrison, Optics L&t. 10 (1985) 603. 151 G.C. Bhar, Appl. Optics 15 (1976) 306.