- Email: [email protected]
Mechanisms of wave mixing and polarisation sensitivity of the wavelength conversion in semiconductor optical amplifiers using two parallel polarised pumps
1 May 1999
Optics Communications 163 Ž1999. 49–54
Mechanisms of wave mixing and polarisation sensitivity of the wavelength conversion in semiconductor optical amplifiers using two parallel polarised pumps I. Tomkos a , I. Zacharopoulos a , E. Roditi b, D. Syvridis
a,)
, A. Uskov
c
a
Informatics Department, DiÕision of Communications and Signal Processing, UniÕersity of Athens, TYPA Buildings, Panepistimiopolis Ilisia, Athens, GR15784, Greece b Department of Physics, DiÕision of Applied Physics, UniÕersity of Athens, TYPA buildings, Panepistimiopolis Ilisia, Athens, GR15784, Greece c P.N. LebedeÕ Physical Institute, Leninsky pr. 53, 117924 Moscow, Russian Federation Received 14 January 1999; received in revised form 3 March 1999; accepted 4 March 1999
Abstract We report on an experimental and theoretical study of wavelength conversion based on four wave mixing ŽFWM. in a bulk semiconductor optical amplifier ŽSOA., using two parallel polarised pumps. The mechanisms responsible for the generation of the frequency converted products of the input signal are discussed. It is shown that the polarisation sensitivity of this scheme depends strongly on the position of the signal wavelength relative to the pump wavelengths. q 1999 Elsevier Science B.V. All rights reserved. Keywords: Optical communications; Wavelength conversion; Wave mixing; Polarisation insensitivity; Semiconductor optical amplifiers
1. Introduction Four wave mixing ŽFWM. in semiconductor optical amplifiers ŽSOAs. has been acknowledged as the unique wavelength conversion method that offers transparency in terms of both bit rate and modulation format, while permitting arbitrary wavelength mapping w1x. It is also a useful tool for the investigation of the nonlinear processes that take place in semiconductor gain media w2x. The sensitivity of the conventional single pump FWM to polarisation of signal wave is a substantial drawback for applications in optical communications. A number of solutions have been proposed in order to overcome this problem w3–9x. The use of two optical pumps is a simple and effective method to achieve polarisation insensitivity w5–7x. ) Corresponding author. Tel.: q30-1-722-8991; E-mail: [email protected]
When the two pumps are orthogonal polarised and closely spaced in wavelength, one polarisation-insensitive, phase conjugated product is generated. In the case of parallel polarised and arbitrarily wavelength spaced pumps, two wavelength shifted but not phase conjugated replicas are generated w8x. Under certain conditions, the wavelength conversion efficiency in the latter case, can also be insensitive to the polarisation of the signal wave. To our knowledge, no detailed experimental or theoretical investigation of the wave mixing mechanisms and the resulting polarization sensitivity of this approach has been reported in the literature. In this paper, we analyse the highly non-degenerate wave mixing processes in SOAs when two parallel polarised pumps are used, and study both experimentally and theoretically the polarisation sensitivity characteristics of the resulting wavelength conversion. We show that the generation of the two converted signals results from the
0030-4018r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 0 - 4 0 1 8 Ž 9 9 . 0 0 1 3 4 - 0
50
I. Tomkos et al.r Optics Communications 163 (1999) 49–54
interference between two physical mechanisms. One of these is insensitive and the other sensitive to the polarisation state of the input signal. The overall polarisation sensitivity of the scheme depends strongly on the wavelength spacing between the signal and the pumps, being minimal for large wavelength spacing between the signal to be converted and the two pumps. The experimental results are in good agreement with the theoretical considerations.
2. Description of the mixing processes At the considered FWM scheme, two parallel TE polarised pumps ŽP1, P2. are injected together with the input signal ŽS. into a SOA. The input waves are amplified as they co-propagate along the SOA and generate new products. The optical spectrum at the output of the SOA is schematically presented in Fig. 1. The products, R1 and R2, are replicas of the original signal. Their conversion efficiencies are defined as the ratio of their powers at the output of the SOA to the power of the signal injected at the input of the SOA. In general, the generation of R1 and R2 results from the following mechanisms, M1 and M2. The first mechanism ŽM1. is related to the beating between the pumps P1 and P2, which leads to the generation of dynamic gain and index gratings at the frequency V 12 s v P1 y v P2 where v P1, v P2 are the optical frequencies of P1, P2. The diffraction of the signal S to these dynamic gratings leads to the generation of two sidebands of the signal S at frequencies v R1 s v S q V 12 and v R2 s
v S y V 12 where v S is the optical frequency of S. Since the gratings are created only by the two parallel polarised pumps P1 and P2, the contribution from M1 to the generation of R1 and R2 is insensitive to the polarisation of the input signal S. The second mechanism ŽM2. is related to the beatings of the signal S with P1 and P2. Assuming that the polarisation state of the signal S at the input of the SOA is arbitrary, there is a component of the signal, parallel polarised relative to the pumps. This component will beat with the pump waves leading to the formation of additional gratings inside the medium, at frequencies V 2S s v P2 y v S , V 1S s v P1 y v S . The diffraction of the pump P1 ŽP2. to the gratings formed by the beating of the signal S with the pump P2 ŽP1. contributes into the generation of the sideband R1 ŽR2. at frequency v R1 s v P1 y V 2SŽs v S q V 12 .Ž v R2 s v P2 y V 1SŽs v S y V 12 ... The contribution from mechanism M2 is maximised when the polarisation of the input signal S is parallel polarised relative to the pumps, while it becomes negligible when S is orthogonal polarised to them. Therefore, the contribution from mechanism M2 is polarisation-sensitive. The contributions from these two mechanisms ŽM1 and M2. add to each other, and the result of this addition depends on their relative magnitudes and phases, affecting the overall conversion efficiencies of the products R1 and R2. The overall conversion efficiencies depend on the signal polarisation only due to the contribution from M2, assuming that the SOA is polarisation-insensitive. The above wave mixing processes in the SOA can be modelled extending the approach described in Refs. w10,11x. Assuming that the polarisation of the signal is parallel to the polarisation of the pumps, the following equations
Fig. 1. Schematic of the spectrum at the SOA output showing the signal S, the two pumps P1 and P2 and the two generated replicas R1 and R2.
I. Tomkos et al.r Optics Communications 163 (1999) 49–54
which describe the generation of the two replicas R1 and R2, can be derived: d A R1
G s
dz
2
gA R1 q
1 SN
= Ž1 y i a X . d AR 2
G s
dz
2
gA R 2 q
a g G A 2 AU1 A S Ý Ž Ž yb X . X
FXR1
1 SN
Ž1.
.
dz
X
= Ž 1 y i a X . FXR 2 .
Ž2.
The sums in Eqs. Ž1. and Ž2. include four terms, corresponding to carrier density pulsation ŽCDP., spectral hole burning ŽSHB., carrier heating ŽCH. and ultra-fast nonlinearities ŽUF. w10x. A R1, A R2 , A1, A 2 and A S , are the slowly varying amplitudes of the waves R1, R2, P1, P2 and S, respectively, G is the confinement factor and g is the material gain under saturation conditions. The factor a is a normalisation constant for the photon density, and S N is the inverse saturation photon density w11x. The relative strength of the nonlinearity X is denoted by b X and the corresponding a-parameter by a X w11x. The factor FX , is given by: FXR1 s
1
Ž 1 y i V 12t X .Ž 1 y i V 12t 1 . 1 q
Ž 1 q i V 2St X .Ž 1 q i V 2 St 1 . FXR 2 s
Ž3.
1
Ž 1 q i V 12t X .Ž 1 q i V 12t 1 . 1 q
Ž 1 q i V 1St X .Ž 1 q i V 1St 1 .
The above terms are complex and add constructively or destructively depending on their relative phases, affecting the overall conversion efficiency of the replicas. Assuming that the waves R1 and R2 do not affect the propagation of the waves P1, P2 and S in SOA, the equations for the their amplitudes A j Ž j s P1, P2, S. can be written as: d Aj
a g G A1 AU2 A S Ý Ž Ž yb X .
Ž4.
where t 1 the intraband carrier–carrier scattering time, and t X are the characteristic times for each nonlinearity X. The first term in Eqs. Ž3. and Ž4. describes the mechanism M1, while the second corresponds to the mechanism M2.
51
G s 2
gA j
Ž5.
Eqs. Ž1., Ž2. and Ž5. are solved numerically, and the conversion efficiencies for R1 and R2 are calculated. In the case of the signal S being orthogonal polarised relative to the pumps, Eqs. Ž1. – Ž5. can been used again for the efficiency calculation, but the second term in Eqs. Ž3. and Ž4. must be omitted since the mechanism M2 is completely inefficient. In the calculations, the experimentally determined saturated gain vs. wavelength curves have been taken into account.
3. Experimental set-up The experimental set-up is shown in Fig. 2. The amplifier used in the experiments was a 1-mm long ridge waveguide, bulk active layer structure with angled antireflection coated facets. The peak gain wavelength of the SOA resulting from its saturation by the strong ASE noise, was at about 1560 nm, and the small signal gain was 35 dB. The pump P1 was a tuneable external cavity source emitting at lP1 s 1554 nm while the pump P2 was a distributed feedback laser emitting at lP2 s 1556 nm. The signal S was also an external cavity laser tuneable within the range 1515–1575 nm. The polarisation state of the optical inputs was adjusted with polarisation controllers. The maximum conversion efficiency was achieved for equal pump powers Žy13 dBm.. The signal power was y20 dBm. The optical spectrum at the output of the SOA and for lS s 1542 nm is shown in Fig. 3, for the signal
Fig. 2. Experimental set-up.
52
I. Tomkos et al.r Optics Communications 163 (1999) 49–54
Fig. 3. Optical spectra measured at the output of the SOA for signal being either orthogonal Žsolid line. or parallel Ždotted line. to P1 and P2 Žthe spectra are shifted horizontally relative to each other by 0.5 nm..
being either parallel or orthogonal polarised relative to the pumps.
4. Results and discussion The polarisation sensitivity of the SOA has been characterised by measuring the TE and TM saturated gain of the signal in the presence of the pumps P1 and P2 ŽFig. 4.. For wavelengths between 1515 nm and 1540 nm the amplifier is almost polarisation-insensitive. As the wavelength increases at values higher that 1545 nm, the amplifier becomes more sensitive to polarisation, reaching its maximum sensitivity of approximately 4 dB at 1575 nm. In Fig. 5, the measurements of the conversion efficiency for R1 and R2 as a function of the signal wavelength for the two cases of signal being parallel or orthogonal polarised relative to the pumps P1 and P2 are presented. For the calculated curves which are depicted with lines in Fig. 5, the experimentally determined saturated gain vs. wavelength has been taken into account. The
Fig. 4. Saturated gain of the signal being parallel Žsolid symbols. and orthogonal Žopen symbols. to the pumps.
Fig. 5. Efficiency of the converted replica R1 Ža., and R2 Žb. vs. the signal wavelength. Parallel and orthogonal polarisation of S relative to P1 and P2 are represented by solid and open symbols, respectively. Solid and dashed lines correspond to the calculated results.
values for the parameters used in the calculations have been taken mainly by previous reported results wRef. w11x and references thereinx. The calculated results are in good agreement with the experiment. A strong asymmetry has been observed in these results, in the case of S being parallel polarised to P1 and P2, when the signal is tuned from wavelengths shorter towards wavelengths longer than
Fig. 6. Polarisation sensitivity of the replica R1 Žsquares. and R2 Žcircles., in the case of the polarisation-sensitive SOA used in the experiments.
I. Tomkos et al.r Optics Communications 163 (1999) 49–54
Fig. 7. Calculated polarisation sensitivity of the replicas in the case of polarisation-insensitive SOA. Solid and dashed lines correspond to the results for the replica R1 and R2, respectively.
the pump wavelengths. This behaviour stems from the interference effects between the mechanisms M1 and M2. When the signal is at shorter wavelength relative to pump wavelengths, the two mechanisms interfere constructively for the replica R1 and destructively for R2. If the signal is at a longer wavelength relative to pump wavelengths, the two mechanisms interfere destructively for the replica R1 and constructively for R2. The polarisation sensitivity of each replica, defined as the conversion efficiency difference between the cases of signal being parallel or orthogonal polarised relative to the pumps P1 and P2, is presented in Fig. 6. One can see that polarisation sensitivity depends strongly on the position of the signal wavelength relative to the pump wavelengths. Indeed, for a polarisation sensitivity of less than 1 dB, the wavelength spacing between the signal and the pump P1 should be at least 16 nm for the specific experimental conditions Ž lS s 1538 nm.. The observed sensitivity results from both, the inherent polarisation sensitivity of the mixing processes under certain conditions and the polarisation sensitivity of the SOA ŽFig. 4.. The inherent polarisation sensitivity of the mixing processes is presented in Fig. 7 for the up- and down-converted replicas, where an ideal, totally polarisation-insensitive amplifier, has been assumed. The polarisation state of the two pumps was assumed to be parallel to the TE axis of the amplifier. It is obvious that polarisation sensitivity is expected as the signal wavelength approaches the pump wavelengths, while it is strongly reduced for large wavelength spacing between the signal and the two pumps. The disadvantage of such configuration is the strong reduction of the conversion efficiency when Ža. the pump spacing, which determines the desired wavelength shift of the two replicas from the signal, increases and Žb. the signal is shifted away from the pumps in order to achieve polarisation-insensitive operation. For example, in the case of 2-nm wavelength shift, polarisation sensitivity of just 1 dB for the replica R1 Žachieved for 16 nm wavelength
53
spacing between the signal and pump P2., results in approximately 11 dB efficiency reduction relative to its maximum measured value obtained when the signal wavelength is close to the pump P2 Žsee Fig. 5.. However, the corresponding reduction of the signal to background noise ratio ŽSBR. was measured to be only about 2 dB, due to the reduction of the amplified spontaneous emission noise level. Moreover, as a result of the large wavelength spacing between the converted replicas and the pumps, it is easier to filter the replicas R1 and R2 at the output of the SOA from the powerful pumps, which is an additional advantage of this configuration in system applications. Thus, for practical applications where the SBR values for the converted signal, and the pump suppression determine mainly the performance of the converter w5x, the observed efficiency reduction is not expected to cause any severe problem.
5. Conclusions An experimental and theoretical investigation of the wavelength conversion scheme based on FWM in SOAs using two parallel polarised pumps has been performed. The generation of the converted waves results from two interfering mechanisms, one insensitive and another sensitive to the signal polarisation. It was experimentally demonstrated that the efficiency of these mechanisms depends on the wavelength spacing between the pumps and the signal, leading to a strong polarisation sensitivity when the signal wavelength is close to that of the pumps. The theory describing the interfering mechanisms have been derived and can predict, in a satisfactory way, the experimental behaviour.
Acknowledgements The authors would like to thank Prof. C. Caroubalos, Prof. T. Sphicopoulos and Prof. Guekos for their help and support. This work was supported in part by the European ACTS project ‘MIDAS-AC 053’.
References w1x G. Hunziker, R. Paiella, A. D’Ottavi, P. Spano, R. Dall’ara, G. Guekos, K.J. Vahala, Proc. OFC ’98, WB7, 1998, p. 108. w2x J. Zhou, N. Park, J.W. Dawson, K.J. Vahala, M.A. Newkirk, B.I. Miller, Appl. Phys. Lett. 63 Ž1993. 1179. w3x J.P.R. Lacey, S.J. Madden, M.A. Summerfield, IEEE Photonics Technol. Lett. 9 Ž1997. 1355. w4x G. Hunziker, R. Paiella, D.F. Geraghty, K.J. Vahala, U. Koren, IEEE Photonics Technol. Lett. 8 Ž1996. 1633. w5x R.M. Jopson, R.E. Tench, Electron. Lett. 29 Ž1993. 2216. w6x I. Zacharopoulos, I. Tomkos, D. Syvridis, T. Sphicopoulos,
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I. Tomkos et al.r Optics Communications 163 (1999) 49–54
C. Caroubalos, E. Roditi, IEEE Photonics Technol. Lett. 10 Ž1998. 352. w7x L.Y. Lin, J.M. Wiesenfeld, J.S. Perino, A.H. Gnauck, IEEE Photonics Technol. Lett. 10 Ž1998. 955. w8x R. Schnabel, U. Hilbk, T. Hermes, P. Meibner, C. Helmolt, K. Magani, F. Raub, W. Pieper, F.J. Westphal, R. Ludwig, L. Kuller, H.G. Weber, IEEE Photonics Technol. Lett. 6 Ž1994. 56.
w9x J.P.R. Lacey, M.A. Summerfield, S.J. Madden, IEEE Photonics Technol. Lett. 16 Ž1998. 2419. w10x A. Uskov, J. Mork, J. Mark, M.C. Tatham, G. Sherlock, Appl. Phys. Lett. 65 Ž1994. 944. w11x S. Scotti, L. Graziani, A. D’Ottavi, F. Martelli, A. Mecozzi, P. Spano, R. Dall’ara, F. Girardin, G. Guekos, IEEE J. Sel. Top. Quantum Electron. 3 Ž1997. 1156.
Optics Communications 163 Ž1999. 49–54
Mechanisms of wave mixing and polarisation sensitivity of the wavelength conversion in semiconductor optical amplifiers using two parallel polarised pumps I. Tomkos a , I. Zacharopoulos a , E. Roditi b, D. Syvridis
a,)
, A. Uskov
c
a
Informatics Department, DiÕision of Communications and Signal Processing, UniÕersity of Athens, TYPA Buildings, Panepistimiopolis Ilisia, Athens, GR15784, Greece b Department of Physics, DiÕision of Applied Physics, UniÕersity of Athens, TYPA buildings, Panepistimiopolis Ilisia, Athens, GR15784, Greece c P.N. LebedeÕ Physical Institute, Leninsky pr. 53, 117924 Moscow, Russian Federation Received 14 January 1999; received in revised form 3 March 1999; accepted 4 March 1999
Abstract We report on an experimental and theoretical study of wavelength conversion based on four wave mixing ŽFWM. in a bulk semiconductor optical amplifier ŽSOA., using two parallel polarised pumps. The mechanisms responsible for the generation of the frequency converted products of the input signal are discussed. It is shown that the polarisation sensitivity of this scheme depends strongly on the position of the signal wavelength relative to the pump wavelengths. q 1999 Elsevier Science B.V. All rights reserved. Keywords: Optical communications; Wavelength conversion; Wave mixing; Polarisation insensitivity; Semiconductor optical amplifiers
1. Introduction Four wave mixing ŽFWM. in semiconductor optical amplifiers ŽSOAs. has been acknowledged as the unique wavelength conversion method that offers transparency in terms of both bit rate and modulation format, while permitting arbitrary wavelength mapping w1x. It is also a useful tool for the investigation of the nonlinear processes that take place in semiconductor gain media w2x. The sensitivity of the conventional single pump FWM to polarisation of signal wave is a substantial drawback for applications in optical communications. A number of solutions have been proposed in order to overcome this problem w3–9x. The use of two optical pumps is a simple and effective method to achieve polarisation insensitivity w5–7x. ) Corresponding author. Tel.: q30-1-722-8991; E-mail: [email protected]
When the two pumps are orthogonal polarised and closely spaced in wavelength, one polarisation-insensitive, phase conjugated product is generated. In the case of parallel polarised and arbitrarily wavelength spaced pumps, two wavelength shifted but not phase conjugated replicas are generated w8x. Under certain conditions, the wavelength conversion efficiency in the latter case, can also be insensitive to the polarisation of the signal wave. To our knowledge, no detailed experimental or theoretical investigation of the wave mixing mechanisms and the resulting polarization sensitivity of this approach has been reported in the literature. In this paper, we analyse the highly non-degenerate wave mixing processes in SOAs when two parallel polarised pumps are used, and study both experimentally and theoretically the polarisation sensitivity characteristics of the resulting wavelength conversion. We show that the generation of the two converted signals results from the
0030-4018r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 0 - 4 0 1 8 Ž 9 9 . 0 0 1 3 4 - 0
50
I. Tomkos et al.r Optics Communications 163 (1999) 49–54
interference between two physical mechanisms. One of these is insensitive and the other sensitive to the polarisation state of the input signal. The overall polarisation sensitivity of the scheme depends strongly on the wavelength spacing between the signal and the pumps, being minimal for large wavelength spacing between the signal to be converted and the two pumps. The experimental results are in good agreement with the theoretical considerations.
2. Description of the mixing processes At the considered FWM scheme, two parallel TE polarised pumps ŽP1, P2. are injected together with the input signal ŽS. into a SOA. The input waves are amplified as they co-propagate along the SOA and generate new products. The optical spectrum at the output of the SOA is schematically presented in Fig. 1. The products, R1 and R2, are replicas of the original signal. Their conversion efficiencies are defined as the ratio of their powers at the output of the SOA to the power of the signal injected at the input of the SOA. In general, the generation of R1 and R2 results from the following mechanisms, M1 and M2. The first mechanism ŽM1. is related to the beating between the pumps P1 and P2, which leads to the generation of dynamic gain and index gratings at the frequency V 12 s v P1 y v P2 where v P1, v P2 are the optical frequencies of P1, P2. The diffraction of the signal S to these dynamic gratings leads to the generation of two sidebands of the signal S at frequencies v R1 s v S q V 12 and v R2 s
v S y V 12 where v S is the optical frequency of S. Since the gratings are created only by the two parallel polarised pumps P1 and P2, the contribution from M1 to the generation of R1 and R2 is insensitive to the polarisation of the input signal S. The second mechanism ŽM2. is related to the beatings of the signal S with P1 and P2. Assuming that the polarisation state of the signal S at the input of the SOA is arbitrary, there is a component of the signal, parallel polarised relative to the pumps. This component will beat with the pump waves leading to the formation of additional gratings inside the medium, at frequencies V 2S s v P2 y v S , V 1S s v P1 y v S . The diffraction of the pump P1 ŽP2. to the gratings formed by the beating of the signal S with the pump P2 ŽP1. contributes into the generation of the sideband R1 ŽR2. at frequency v R1 s v P1 y V 2SŽs v S q V 12 .Ž v R2 s v P2 y V 1SŽs v S y V 12 ... The contribution from mechanism M2 is maximised when the polarisation of the input signal S is parallel polarised relative to the pumps, while it becomes negligible when S is orthogonal polarised to them. Therefore, the contribution from mechanism M2 is polarisation-sensitive. The contributions from these two mechanisms ŽM1 and M2. add to each other, and the result of this addition depends on their relative magnitudes and phases, affecting the overall conversion efficiencies of the products R1 and R2. The overall conversion efficiencies depend on the signal polarisation only due to the contribution from M2, assuming that the SOA is polarisation-insensitive. The above wave mixing processes in the SOA can be modelled extending the approach described in Refs. w10,11x. Assuming that the polarisation of the signal is parallel to the polarisation of the pumps, the following equations
Fig. 1. Schematic of the spectrum at the SOA output showing the signal S, the two pumps P1 and P2 and the two generated replicas R1 and R2.
I. Tomkos et al.r Optics Communications 163 (1999) 49–54
which describe the generation of the two replicas R1 and R2, can be derived: d A R1
G s
dz
2
gA R1 q
1 SN
= Ž1 y i a X . d AR 2
G s
dz
2
gA R 2 q
a g G A 2 AU1 A S Ý Ž Ž yb X . X
FXR1
1 SN
Ž1.
.
dz
X
= Ž 1 y i a X . FXR 2 .
Ž2.
The sums in Eqs. Ž1. and Ž2. include four terms, corresponding to carrier density pulsation ŽCDP., spectral hole burning ŽSHB., carrier heating ŽCH. and ultra-fast nonlinearities ŽUF. w10x. A R1, A R2 , A1, A 2 and A S , are the slowly varying amplitudes of the waves R1, R2, P1, P2 and S, respectively, G is the confinement factor and g is the material gain under saturation conditions. The factor a is a normalisation constant for the photon density, and S N is the inverse saturation photon density w11x. The relative strength of the nonlinearity X is denoted by b X and the corresponding a-parameter by a X w11x. The factor FX , is given by: FXR1 s
1
Ž 1 y i V 12t X .Ž 1 y i V 12t 1 . 1 q
Ž 1 q i V 2St X .Ž 1 q i V 2 St 1 . FXR 2 s
Ž3.
1
Ž 1 q i V 12t X .Ž 1 q i V 12t 1 . 1 q
Ž 1 q i V 1St X .Ž 1 q i V 1St 1 .
The above terms are complex and add constructively or destructively depending on their relative phases, affecting the overall conversion efficiency of the replicas. Assuming that the waves R1 and R2 do not affect the propagation of the waves P1, P2 and S in SOA, the equations for the their amplitudes A j Ž j s P1, P2, S. can be written as: d Aj
a g G A1 AU2 A S Ý Ž Ž yb X .
Ž4.
where t 1 the intraband carrier–carrier scattering time, and t X are the characteristic times for each nonlinearity X. The first term in Eqs. Ž3. and Ž4. describes the mechanism M1, while the second corresponds to the mechanism M2.
51
G s 2
gA j
Ž5.
Eqs. Ž1., Ž2. and Ž5. are solved numerically, and the conversion efficiencies for R1 and R2 are calculated. In the case of the signal S being orthogonal polarised relative to the pumps, Eqs. Ž1. – Ž5. can been used again for the efficiency calculation, but the second term in Eqs. Ž3. and Ž4. must be omitted since the mechanism M2 is completely inefficient. In the calculations, the experimentally determined saturated gain vs. wavelength curves have been taken into account.
3. Experimental set-up The experimental set-up is shown in Fig. 2. The amplifier used in the experiments was a 1-mm long ridge waveguide, bulk active layer structure with angled antireflection coated facets. The peak gain wavelength of the SOA resulting from its saturation by the strong ASE noise, was at about 1560 nm, and the small signal gain was 35 dB. The pump P1 was a tuneable external cavity source emitting at lP1 s 1554 nm while the pump P2 was a distributed feedback laser emitting at lP2 s 1556 nm. The signal S was also an external cavity laser tuneable within the range 1515–1575 nm. The polarisation state of the optical inputs was adjusted with polarisation controllers. The maximum conversion efficiency was achieved for equal pump powers Žy13 dBm.. The signal power was y20 dBm. The optical spectrum at the output of the SOA and for lS s 1542 nm is shown in Fig. 3, for the signal
Fig. 2. Experimental set-up.
52
I. Tomkos et al.r Optics Communications 163 (1999) 49–54
Fig. 3. Optical spectra measured at the output of the SOA for signal being either orthogonal Žsolid line. or parallel Ždotted line. to P1 and P2 Žthe spectra are shifted horizontally relative to each other by 0.5 nm..
being either parallel or orthogonal polarised relative to the pumps.
4. Results and discussion The polarisation sensitivity of the SOA has been characterised by measuring the TE and TM saturated gain of the signal in the presence of the pumps P1 and P2 ŽFig. 4.. For wavelengths between 1515 nm and 1540 nm the amplifier is almost polarisation-insensitive. As the wavelength increases at values higher that 1545 nm, the amplifier becomes more sensitive to polarisation, reaching its maximum sensitivity of approximately 4 dB at 1575 nm. In Fig. 5, the measurements of the conversion efficiency for R1 and R2 as a function of the signal wavelength for the two cases of signal being parallel or orthogonal polarised relative to the pumps P1 and P2 are presented. For the calculated curves which are depicted with lines in Fig. 5, the experimentally determined saturated gain vs. wavelength has been taken into account. The
Fig. 4. Saturated gain of the signal being parallel Žsolid symbols. and orthogonal Žopen symbols. to the pumps.
Fig. 5. Efficiency of the converted replica R1 Ža., and R2 Žb. vs. the signal wavelength. Parallel and orthogonal polarisation of S relative to P1 and P2 are represented by solid and open symbols, respectively. Solid and dashed lines correspond to the calculated results.
values for the parameters used in the calculations have been taken mainly by previous reported results wRef. w11x and references thereinx. The calculated results are in good agreement with the experiment. A strong asymmetry has been observed in these results, in the case of S being parallel polarised to P1 and P2, when the signal is tuned from wavelengths shorter towards wavelengths longer than
Fig. 6. Polarisation sensitivity of the replica R1 Žsquares. and R2 Žcircles., in the case of the polarisation-sensitive SOA used in the experiments.
I. Tomkos et al.r Optics Communications 163 (1999) 49–54
Fig. 7. Calculated polarisation sensitivity of the replicas in the case of polarisation-insensitive SOA. Solid and dashed lines correspond to the results for the replica R1 and R2, respectively.
the pump wavelengths. This behaviour stems from the interference effects between the mechanisms M1 and M2. When the signal is at shorter wavelength relative to pump wavelengths, the two mechanisms interfere constructively for the replica R1 and destructively for R2. If the signal is at a longer wavelength relative to pump wavelengths, the two mechanisms interfere destructively for the replica R1 and constructively for R2. The polarisation sensitivity of each replica, defined as the conversion efficiency difference between the cases of signal being parallel or orthogonal polarised relative to the pumps P1 and P2, is presented in Fig. 6. One can see that polarisation sensitivity depends strongly on the position of the signal wavelength relative to the pump wavelengths. Indeed, for a polarisation sensitivity of less than 1 dB, the wavelength spacing between the signal and the pump P1 should be at least 16 nm for the specific experimental conditions Ž lS s 1538 nm.. The observed sensitivity results from both, the inherent polarisation sensitivity of the mixing processes under certain conditions and the polarisation sensitivity of the SOA ŽFig. 4.. The inherent polarisation sensitivity of the mixing processes is presented in Fig. 7 for the up- and down-converted replicas, where an ideal, totally polarisation-insensitive amplifier, has been assumed. The polarisation state of the two pumps was assumed to be parallel to the TE axis of the amplifier. It is obvious that polarisation sensitivity is expected as the signal wavelength approaches the pump wavelengths, while it is strongly reduced for large wavelength spacing between the signal and the two pumps. The disadvantage of such configuration is the strong reduction of the conversion efficiency when Ža. the pump spacing, which determines the desired wavelength shift of the two replicas from the signal, increases and Žb. the signal is shifted away from the pumps in order to achieve polarisation-insensitive operation. For example, in the case of 2-nm wavelength shift, polarisation sensitivity of just 1 dB for the replica R1 Žachieved for 16 nm wavelength
53
spacing between the signal and pump P2., results in approximately 11 dB efficiency reduction relative to its maximum measured value obtained when the signal wavelength is close to the pump P2 Žsee Fig. 5.. However, the corresponding reduction of the signal to background noise ratio ŽSBR. was measured to be only about 2 dB, due to the reduction of the amplified spontaneous emission noise level. Moreover, as a result of the large wavelength spacing between the converted replicas and the pumps, it is easier to filter the replicas R1 and R2 at the output of the SOA from the powerful pumps, which is an additional advantage of this configuration in system applications. Thus, for practical applications where the SBR values for the converted signal, and the pump suppression determine mainly the performance of the converter w5x, the observed efficiency reduction is not expected to cause any severe problem.
5. Conclusions An experimental and theoretical investigation of the wavelength conversion scheme based on FWM in SOAs using two parallel polarised pumps has been performed. The generation of the converted waves results from two interfering mechanisms, one insensitive and another sensitive to the signal polarisation. It was experimentally demonstrated that the efficiency of these mechanisms depends on the wavelength spacing between the pumps and the signal, leading to a strong polarisation sensitivity when the signal wavelength is close to that of the pumps. The theory describing the interfering mechanisms have been derived and can predict, in a satisfactory way, the experimental behaviour.
Acknowledgements The authors would like to thank Prof. C. Caroubalos, Prof. T. Sphicopoulos and Prof. Guekos for their help and support. This work was supported in part by the European ACTS project ‘MIDAS-AC 053’.
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