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Conventional-band and long-wavelength-band efficient wavelength conversion by difference-frequency generation in sinusoidally chirped optical superlattice waveguides
Optics Communications 239 (2004) 333–338 www.elsevier.com/locate/optcom
Conventional-band and long-wavelength-band efficient wavelength conversion by difference-frequency generation in sinusoidally chirped optical superlattice waveguides Shiming Gao *, Changxi Yang, Guofan Jin State Key Laboratory of Precision Measurement Technology and Instruments, Department of Precision Instruments, Tsinghua University, Beijing 100084, China Received 26 February 2004; received in revised form 10 May 2004; accepted 1 June 2004
Abstract We report difference-frequency generation (DFG)-based wavelength conversion with sinusoidally chirped optical superlattices (SCOSs) in lithium niobate waveguides. The SCOS shows much broader bandwidth, larger pump-wavelength tolerance and flatter response with some conversion efficiency penalty than the periodic grating with the same length. Especially, the conversion bandwidth of the SCOS is over the whole conventional band and long-wavelength band, which is very helpful to broadband optical communications. The main advantages of the DFG-based wavelength conversion with SCOS structures over the cascaded second-order effect-based wavelength conversion are higher conversion efficiency, broader bandwidth, better pump-wavelength tolerance and response flatness when the device is shorter. In order to ensure the conversion quality, analysis shows that the manufacture tolerance of the SCOS period should not more than 0.02 lm. 2004 Elsevier B.V. All rights reserved. PACS: 42.65.K; 42.79.N; 42.65.H,K; 42.65 Keywords: Wavelength conversion; Difference-frequency generation; Sinusoidally chirped optical superlattice
1. Introduction
*
Corresponding author. Tel.: +86-10-6279-5433; fax: +8610-6278-4691. E-mail address: [email protected] (S. Gao).
Wavelength conversion is an essential operation in modern wavelength division multiplexing (WDM) transmission systems [1]. Wave-mixing schemes due to second-order susceptibilities in lithium niobate crystals are promising for all-opti-
0030-4018/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2004.06.001
334
S. Gao et al. / Optics Communications 239 (2004) 333–338
cal wavelength conversion. They have ultrafast response and strict transparency. Since waveguides were fabricated to reduce interaction area, and quasi-phase matching (QPM) technology was implemented, the conversion efficiency has been dramatically increased. Difference-frequency generation (DFG) [2] and cascaded second-order interaction (v(2)) [3,4] are well studied theoretically and experimentally. The devices based on cascaded v(2) effect suffer from low conversion efficiency, because the effect consists of a second-harmonic generation (SHG) and a DFG processes. The conversion efficiency is high in principle by direct DFG. However, it was difficult to couple pump and signals into the fundamental guided-wave mode simultaneously without exciting higher-order modes that are not involved in the wavelength conversion process. This problem was solved by use of a subsequent adiabatically tapered periodic segmentation of channel waveguides [5]. As two important wavelength conversion schemes, the performances of DFG and cascaded v(2) effect in periodically poled lithium niobate waveguides have been compared in detail [6]. In order to efficiently utilize the telecommunication band, flattened broadband wavelength converters are very attractive. In a periodic structure, the conversion bandwidth is narrow. Many schemes have been demonstrated to broaden the bandwidth by chirping grating periods [7–12]. An aperiodic grating with sustainedly sinusoidal chirps has been used for SHG [13], where the sine function is continuously oscillated. However, it is not suitable for wavelength conversion based on DFG. As a wavelength converter, the conversion efficiency should be concerned besides the conversion bandwidth. To keep a higher efficiency, the QPM condition should be well satisfied in a distance from the beginning of the structure, that is, where the chirp coefficient should be small. On the other hand, the chirp coefficient has to be increased gradually along the structure to enhance the conversion bandwidth. To satisfy this requirement, we design a sinusoidally chirped optical superlattice (SCOS), whose period is chirped as a composite diverging sine function. In this paper, we investigate the DFG wavelength conversion scheme in the SCOS, and evaluate it in terms
of conversion efficiency, 3-dB conversion bandwidth, pump-wavelength tolerance and response flatness.
2. Theoretical analysis The SCOS structure is implemented in a Z-cut and X-propagating titanium-diffused lithium niobate channel waveguide. Accounting for the propagation loss with ai (i = P, S, or C, which stands for pump, signal, or converted difference-frequency signal, respectively) and the field amplitude with Ai, the coupled equations of DFG for arbitrary structures are expressed as: dAP 1 aP ¼ j jAS AC exp½jDUðxÞ AP ; kP dx 2
ð1Þ
dAS 1 aS ¼ j jAC AP exp½jDUðxÞ AS ; kS dx 2
ð2Þ
dAC 1 aC ¼ j jAS AP exp½jDUðxÞ AC ; kC dx 2
ð3Þ
where the nonlinear coupling constant is sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2cl0 j ¼ 2pd eff S eff N P N S N C
ð4Þ
and the phase mismatch is DUðxÞ ¼ 2pxðN P =kP N S =kS N C =kC Þ Z x 2p=KðxÞ dx:
ð5Þ
0
In Eqs. (4) and (5), Ni (i = P, S, or C) is the modal index, deff is the effective nonlinear coefficient, Seff is the effective interaction area, and K(x) is the period of the modulated structure. For the SCOS we designed, the period is expressed as [14] 2N px 2N px 2N px þ cos KðxÞ ¼ K0 1 þ r 1 þ sin ; L L L ð6Þ where r is the chirp coefficient, L is the device length, N is the period number of sine function, and K0 is the exact QPM period for the degenerate case of kS = 2kP. The SCOS is schematically described in Fig. 1.
S. Gao et al. / Optics Communications 239 (2004) 333–338
335
Fig. 1. Schematic description of the SCOS structure.
3. Results and discussion The QPM period should be K0 = 15.170 lm when the pump wavelength kP = 0.775 lm for a waveguide whose width and depth are 10 and 3 lm, respectively. The effective interaction area is calculated as Seff = 47 lm2, and the effective nonlinear coefficient is deff = (2/p)d33 where d33 = 27 pm/V. We define response flatness as the difference between the maximum and mean conversion efficiencies within the 3-dB bandwidth. Smaller flatness represents flatter response. Considering the response flatness as the aim function, the period number of sine function is optimized as N = 1.822, and the optimal chirp coefficient r is shown in Table 1 for various device lengths. The coefficient is approximately an exponential function of the device length and depends on the waveguide transverse index profile. Without considering the waveguide loss, the conversion responses versus the signal wavelength are simulated in Fig. 2 for the SCOS and the periodic grating (K0). Here the device length is 3 cm, the signal power is 1 mW, and the pump is 300 mW at 0.775 lm. The vertical axis is the conversion efficiency in decibels, which is defined as the ratio of the converted power with respect to the signal power. It is shown that the 3-dB bandwidth of the SCOS is much broader than that of
Fig. 2. Conversion responses versus the signal wavelength for the SCOS and the periodic grating.
the periodic grating, but the conversion efficiency is lower. As shown in Fig. 3, the 3-dB conversion bandwidths and the mean efficiencies are plotted versus the device length for the SCOS and the periodic grating. The bandwidth is reduced and the efficiency is increased exponentially when the device length increases. The bandwidth of the SCOS is enhanced 72% averagely than that of the periodic grating when the device length changes in the region of 1–5 cm. The bandwidth is over
Table 1 The optimal chirp coefficients for different device lengths Device length L (cm)
Chirp coefficient r (·104)
1 1.5 2 2.5 3 3.5 4 4.5 5
7.02 4.69 3.52 2.81 2.33 1.99 1.74 1.54 1.38
Fig. 3. Dependence of the 3-dB conversion bandwidths and the mean efficiencies on the device length for the SCOS and the periodic grating.
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the whole conventional band (C-band) and longwavelength band (L-band) for a SCOS device shorter than 4 cm. On the other hand, the mean efficiency of the SCOS is 6.6–10.5 dB lower than that of the periodic grating. Fortunately, it is easy to be amplified by using erbium-doped fiber amplifiers because their bandwidths just tally with each other. Moreover, if necessary the SCOS efficiency can be compensated by moderately increasing the device length with some bandwidth penalty. The 4-cm-long SCOS and the 2-cm-long periodic grating have the same mean efficiency of 0.5 dB, and their bandwidths are 90 and 72 nm, respectively. The SCOS bandwidth is still 25% broader than that of the periodic grating. Fig. 4 shows the pump-wavelength tolerances, which are defined as 3-dB pump-tuning bandwidth in wavelength [6], as functions of the device length for the SCOS and the periodic grating when the signal wavelength is fixed at 1.57 lm. The pumpwavelength tolerance decreases exponentially by increasing the device length. The SCOS pumpwavelength tolerance is much broader than the periodic grating one. For example, when the device length is 3 cm, the tolerance of the SCOS is 74% larger than that of the periodic grating, that is, the SCOS device is much simpler to control. For a wavelength converter, the response flatness is also a crucial performance, which is defined as the conversion efficiency difference between the maximum and the mean within the 3-dB bandwidth. The SCOS device shows more flattened
response compared with the periodic device, as shown in Fig. 5. Here the response flatness is simulated as a function of the device length. The SCOS response is about 0.1 dB flatter than that of the periodic grating. DFG- and cascaded v(2)-based wavelength conversions are both important schemes for WDM application. Both of them in SCOS devices show excellent performances, as shown in Table 2 [14]. The pump wavelengths used in the simulation are 0.775 and 1.55 lm for the DFG and the cascaded v(2) effect, respectively. Their pump powers are 300 mW, and their signal powers are 1 mW. The 3-dB bandwidth and the pump-wavelength tolerance of the DFG are 73% and 62% of those of the cascaded v(2) interaction, respectively. However, the DFG efficiency is much higher than the cascaded v(2) interaction one, which makes it possible to enhance the 3-dB bandwidth and the pump-wavelength tolerance by reducing the device length moderately. For example, the efficiency of the 1cm-long DFG-based device is 13 dB, just like that of the 2.4-cm-long cascaded v(2)-based one, but the 3-dB bandwidth and the pump-wavelength tolerance of the DFG-based device are 21 and 0.34 nm broader, which are 13% and 51% of those of the cascaded v(2)-based one, respectively. Both of their response flatnesses are almost equal. The comparison shows that the DFG-based wavelength conversion has better combined performances than the cascaded v(2)-based one when the SCOS device length is not more than 3 cm. Es-
Fig. 4. Pump-wavelength tolerances as functions of the device length for the SCOS and the periodic grating.
Fig. 5. Response flatnesses against the device length for the SCOS and the periodic grating.
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337
Table 2 Performance comparison of DFG- and cascaded v(2)-based wavelength conversions in SCOS devices Device length (cm)
1 1.5 2 2.5 3 3.5 4 4.5 5
3-dB Bandwidth (nm)
Pump-wavelength tolerance (nm)
Mean efficiency (dB)
Response flatness (dB)
DFG
v(2):v(2)
DFG
v(2):v(2)
DFG
v(2):v(2)
DFG
v(2):v(2)
178 145 126 114 103 96 90 85 81
242 199 173 155 142 132 123 117 112
1.01 0.68 0.50 0.40 0.33 0.28 0.26 0.22 0.21
1.50 1.04 0.81 0.65 0.55 0.48 0.42 0.37 0.34
13.05 9.43 6.78 4.63 2.71 1.02 0.53 2.04 3.50
27.68 20.91 16.23 12.67 9.86 7.52 5.48 3.75 2.21
0.50 0.46 0.45 0.46 0.42 0.43 0.42 0.42 0.43
0.59 0.54 0.50 0.46 0.45 0.44 0.45 0.45 0.48
pecially, to achieve the same property the required length of the DFG-based device is much less than that of the cascaded v(2)-based one. It is easier to fabricate the device and improve the machining accuracy. The above analysis is based on a continuous variation of the period along the device length. In fact, the period is a discrete sequence of domains of alternating polarity. It is essential to analyze the translation from a continuous to a discretized structure. Here we take an example of the 3-cm-long structure. According to the beginning position of a SCOS period and the period length calculated from Eq. (6), we can make the ideal SCOS period discretized and array them in sequence to retrieve a discretized SCOS structure. In order to analyze the permitted manufacture tolerance, the SCOS period is accurate to different levels, such as 0.001, 0.01, 0.02, and 0.025 lm. As shown in Fig. 6, the conversion responses of these cases are simulated, where the conversion efficiency is considered as a function of the signal wavelength. The pump power is 300 mW, and the signal power is 1 mW. The conversion response of the SCOS structure, whose accuracy is 0.001 lm, accords well with that of the ideal structure. It can be noticed that with the decrease of the period accuracy the conversion response becomes worse, and the conversion efficiency decreases by comparing the cases of 0.001, 0.01, and 0.02 lm. When the manufacture error is enhanced more than 0.02 lm, the response flatness becomes worse
Fig. 6. Conversion responses versus the signal wavelength for the SCOS structures with different manufacture accuracy levels.
rapidly. For a 3-cm-long device, the maximum permitted manufacture tolerance should be no more than 0.02 lm.
4. Conclusion A DFG-based wavelength conversion scheme with the SCOS waveguide has been investigated. The SCOS device, whose conversion bandwidth covers the whole C-band and L-band, shows excellent performances for WDM application. When the device is short, the DFG-based wavelength conversion in SCOS devices has better combined properties than the cascaded v(2)-based one. The DFG-based SCOS wavelength converter is more
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S. Gao et al. / Optics Communications 239 (2004) 333–338
suitable to practical applications because it is shorter and easier to fabricate and control. The manufacture tolerance of the SCOS period should not be more than 0.02 lm to preserve the conversion quality.
Acknowledgement The work is supported in part by the TransCentury Training Programme Foundation for the Talents by the Ministry of Education of China.
References [1] S.J.B. Yoo, J. Lightwave Technol. 14 (1996) 955. [2] C.Q. Xu, H. Okayama, K. Shinozaki, K. Watanabe, M. Kawahara, Appl. Phys. Lett. 63 (1993) 1170.
[3] K. Gallo, G. Assanto, G.I. Stegeman, Appl. Phys. Lett. 71 (1997) 1020. [4] M.H. Chou, I. Brener, M.M. Fejer, E.E. Chaban, S.B. Christman, IEEE Photon. Technol. Lett. 11 (1999) 653. [5] M.H. Chou, M.A. Arbore, M.M. Fejer, Opt. Lett. 21 (1996) 794. [6] B. Zhou, C.Q. Xu, B. Chen, J. Opt. Soc. Am. B 20 (2003) 846. [7] X. Liu, H. Zhang, Y. Guo, Y. Li, IEEE J. Quantum Electron. 38 (2002) 1225. [8] K. Mizuuchi, K. Yamamoto, Opt. Lett. 23 (1998) 1880. [9] S. Gao, C. Yang, G. Jin, Chin. Phys. Lett. 20 (2003) 1272. [10] M.H. Chou, K.R. Parameswaran, M.M. Fejer, I. Brener, Opt. Lett. 24 (1999) 1157. [11] M. Asobe, O. Tadanaga, H. Miyazawa, Y. Nishida, H. Suzuki, Opt. Lett. 28 (2003) 558. [12] Y.W. Lee, F.C. Fan, Y.C. Huang, B.Y. Gu, B.Z. Dong, M.H. Chou, Opt. Lett. 27 (2002) 2191. [13] O. Bang, C.B. Clausen, P.L. Christiansen, L. Torner, Opt. Lett. 24 (1999) 1413. [14] S. Gao, C. Yang, G. Jin, IEEE Photon. Technol. Lett. 16 (2004) 557.
Conventional-band and long-wavelength-band efficient wavelength conversion by difference-frequency generation in sinusoidally chirped optical superlattice waveguides Shiming Gao *, Changxi Yang, Guofan Jin State Key Laboratory of Precision Measurement Technology and Instruments, Department of Precision Instruments, Tsinghua University, Beijing 100084, China Received 26 February 2004; received in revised form 10 May 2004; accepted 1 June 2004
Abstract We report difference-frequency generation (DFG)-based wavelength conversion with sinusoidally chirped optical superlattices (SCOSs) in lithium niobate waveguides. The SCOS shows much broader bandwidth, larger pump-wavelength tolerance and flatter response with some conversion efficiency penalty than the periodic grating with the same length. Especially, the conversion bandwidth of the SCOS is over the whole conventional band and long-wavelength band, which is very helpful to broadband optical communications. The main advantages of the DFG-based wavelength conversion with SCOS structures over the cascaded second-order effect-based wavelength conversion are higher conversion efficiency, broader bandwidth, better pump-wavelength tolerance and response flatness when the device is shorter. In order to ensure the conversion quality, analysis shows that the manufacture tolerance of the SCOS period should not more than 0.02 lm. 2004 Elsevier B.V. All rights reserved. PACS: 42.65.K; 42.79.N; 42.65.H,K; 42.65 Keywords: Wavelength conversion; Difference-frequency generation; Sinusoidally chirped optical superlattice
1. Introduction
*
Corresponding author. Tel.: +86-10-6279-5433; fax: +8610-6278-4691. E-mail address: [email protected] (S. Gao).
Wavelength conversion is an essential operation in modern wavelength division multiplexing (WDM) transmission systems [1]. Wave-mixing schemes due to second-order susceptibilities in lithium niobate crystals are promising for all-opti-
0030-4018/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2004.06.001
334
S. Gao et al. / Optics Communications 239 (2004) 333–338
cal wavelength conversion. They have ultrafast response and strict transparency. Since waveguides were fabricated to reduce interaction area, and quasi-phase matching (QPM) technology was implemented, the conversion efficiency has been dramatically increased. Difference-frequency generation (DFG) [2] and cascaded second-order interaction (v(2)) [3,4] are well studied theoretically and experimentally. The devices based on cascaded v(2) effect suffer from low conversion efficiency, because the effect consists of a second-harmonic generation (SHG) and a DFG processes. The conversion efficiency is high in principle by direct DFG. However, it was difficult to couple pump and signals into the fundamental guided-wave mode simultaneously without exciting higher-order modes that are not involved in the wavelength conversion process. This problem was solved by use of a subsequent adiabatically tapered periodic segmentation of channel waveguides [5]. As two important wavelength conversion schemes, the performances of DFG and cascaded v(2) effect in periodically poled lithium niobate waveguides have been compared in detail [6]. In order to efficiently utilize the telecommunication band, flattened broadband wavelength converters are very attractive. In a periodic structure, the conversion bandwidth is narrow. Many schemes have been demonstrated to broaden the bandwidth by chirping grating periods [7–12]. An aperiodic grating with sustainedly sinusoidal chirps has been used for SHG [13], where the sine function is continuously oscillated. However, it is not suitable for wavelength conversion based on DFG. As a wavelength converter, the conversion efficiency should be concerned besides the conversion bandwidth. To keep a higher efficiency, the QPM condition should be well satisfied in a distance from the beginning of the structure, that is, where the chirp coefficient should be small. On the other hand, the chirp coefficient has to be increased gradually along the structure to enhance the conversion bandwidth. To satisfy this requirement, we design a sinusoidally chirped optical superlattice (SCOS), whose period is chirped as a composite diverging sine function. In this paper, we investigate the DFG wavelength conversion scheme in the SCOS, and evaluate it in terms
of conversion efficiency, 3-dB conversion bandwidth, pump-wavelength tolerance and response flatness.
2. Theoretical analysis The SCOS structure is implemented in a Z-cut and X-propagating titanium-diffused lithium niobate channel waveguide. Accounting for the propagation loss with ai (i = P, S, or C, which stands for pump, signal, or converted difference-frequency signal, respectively) and the field amplitude with Ai, the coupled equations of DFG for arbitrary structures are expressed as: dAP 1 aP ¼ j jAS AC exp½jDUðxÞ AP ; kP dx 2
ð1Þ
dAS 1 aS ¼ j jAC AP exp½jDUðxÞ AS ; kS dx 2
ð2Þ
dAC 1 aC ¼ j jAS AP exp½jDUðxÞ AC ; kC dx 2
ð3Þ
where the nonlinear coupling constant is sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2cl0 j ¼ 2pd eff S eff N P N S N C
ð4Þ
and the phase mismatch is DUðxÞ ¼ 2pxðN P =kP N S =kS N C =kC Þ Z x 2p=KðxÞ dx:
ð5Þ
0
In Eqs. (4) and (5), Ni (i = P, S, or C) is the modal index, deff is the effective nonlinear coefficient, Seff is the effective interaction area, and K(x) is the period of the modulated structure. For the SCOS we designed, the period is expressed as [14] 2N px 2N px 2N px þ cos KðxÞ ¼ K0 1 þ r 1 þ sin ; L L L ð6Þ where r is the chirp coefficient, L is the device length, N is the period number of sine function, and K0 is the exact QPM period for the degenerate case of kS = 2kP. The SCOS is schematically described in Fig. 1.
S. Gao et al. / Optics Communications 239 (2004) 333–338
335
Fig. 1. Schematic description of the SCOS structure.
3. Results and discussion The QPM period should be K0 = 15.170 lm when the pump wavelength kP = 0.775 lm for a waveguide whose width and depth are 10 and 3 lm, respectively. The effective interaction area is calculated as Seff = 47 lm2, and the effective nonlinear coefficient is deff = (2/p)d33 where d33 = 27 pm/V. We define response flatness as the difference between the maximum and mean conversion efficiencies within the 3-dB bandwidth. Smaller flatness represents flatter response. Considering the response flatness as the aim function, the period number of sine function is optimized as N = 1.822, and the optimal chirp coefficient r is shown in Table 1 for various device lengths. The coefficient is approximately an exponential function of the device length and depends on the waveguide transverse index profile. Without considering the waveguide loss, the conversion responses versus the signal wavelength are simulated in Fig. 2 for the SCOS and the periodic grating (K0). Here the device length is 3 cm, the signal power is 1 mW, and the pump is 300 mW at 0.775 lm. The vertical axis is the conversion efficiency in decibels, which is defined as the ratio of the converted power with respect to the signal power. It is shown that the 3-dB bandwidth of the SCOS is much broader than that of
Fig. 2. Conversion responses versus the signal wavelength for the SCOS and the periodic grating.
the periodic grating, but the conversion efficiency is lower. As shown in Fig. 3, the 3-dB conversion bandwidths and the mean efficiencies are plotted versus the device length for the SCOS and the periodic grating. The bandwidth is reduced and the efficiency is increased exponentially when the device length increases. The bandwidth of the SCOS is enhanced 72% averagely than that of the periodic grating when the device length changes in the region of 1–5 cm. The bandwidth is over
Table 1 The optimal chirp coefficients for different device lengths Device length L (cm)
Chirp coefficient r (·104)
1 1.5 2 2.5 3 3.5 4 4.5 5
7.02 4.69 3.52 2.81 2.33 1.99 1.74 1.54 1.38
Fig. 3. Dependence of the 3-dB conversion bandwidths and the mean efficiencies on the device length for the SCOS and the periodic grating.
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S. Gao et al. / Optics Communications 239 (2004) 333–338
the whole conventional band (C-band) and longwavelength band (L-band) for a SCOS device shorter than 4 cm. On the other hand, the mean efficiency of the SCOS is 6.6–10.5 dB lower than that of the periodic grating. Fortunately, it is easy to be amplified by using erbium-doped fiber amplifiers because their bandwidths just tally with each other. Moreover, if necessary the SCOS efficiency can be compensated by moderately increasing the device length with some bandwidth penalty. The 4-cm-long SCOS and the 2-cm-long periodic grating have the same mean efficiency of 0.5 dB, and their bandwidths are 90 and 72 nm, respectively. The SCOS bandwidth is still 25% broader than that of the periodic grating. Fig. 4 shows the pump-wavelength tolerances, which are defined as 3-dB pump-tuning bandwidth in wavelength [6], as functions of the device length for the SCOS and the periodic grating when the signal wavelength is fixed at 1.57 lm. The pumpwavelength tolerance decreases exponentially by increasing the device length. The SCOS pumpwavelength tolerance is much broader than the periodic grating one. For example, when the device length is 3 cm, the tolerance of the SCOS is 74% larger than that of the periodic grating, that is, the SCOS device is much simpler to control. For a wavelength converter, the response flatness is also a crucial performance, which is defined as the conversion efficiency difference between the maximum and the mean within the 3-dB bandwidth. The SCOS device shows more flattened
response compared with the periodic device, as shown in Fig. 5. Here the response flatness is simulated as a function of the device length. The SCOS response is about 0.1 dB flatter than that of the periodic grating. DFG- and cascaded v(2)-based wavelength conversions are both important schemes for WDM application. Both of them in SCOS devices show excellent performances, as shown in Table 2 [14]. The pump wavelengths used in the simulation are 0.775 and 1.55 lm for the DFG and the cascaded v(2) effect, respectively. Their pump powers are 300 mW, and their signal powers are 1 mW. The 3-dB bandwidth and the pump-wavelength tolerance of the DFG are 73% and 62% of those of the cascaded v(2) interaction, respectively. However, the DFG efficiency is much higher than the cascaded v(2) interaction one, which makes it possible to enhance the 3-dB bandwidth and the pump-wavelength tolerance by reducing the device length moderately. For example, the efficiency of the 1cm-long DFG-based device is 13 dB, just like that of the 2.4-cm-long cascaded v(2)-based one, but the 3-dB bandwidth and the pump-wavelength tolerance of the DFG-based device are 21 and 0.34 nm broader, which are 13% and 51% of those of the cascaded v(2)-based one, respectively. Both of their response flatnesses are almost equal. The comparison shows that the DFG-based wavelength conversion has better combined performances than the cascaded v(2)-based one when the SCOS device length is not more than 3 cm. Es-
Fig. 4. Pump-wavelength tolerances as functions of the device length for the SCOS and the periodic grating.
Fig. 5. Response flatnesses against the device length for the SCOS and the periodic grating.
S. Gao et al. / Optics Communications 239 (2004) 333–338
337
Table 2 Performance comparison of DFG- and cascaded v(2)-based wavelength conversions in SCOS devices Device length (cm)
1 1.5 2 2.5 3 3.5 4 4.5 5
3-dB Bandwidth (nm)
Pump-wavelength tolerance (nm)
Mean efficiency (dB)
Response flatness (dB)
DFG
v(2):v(2)
DFG
v(2):v(2)
DFG
v(2):v(2)
DFG
v(2):v(2)
178 145 126 114 103 96 90 85 81
242 199 173 155 142 132 123 117 112
1.01 0.68 0.50 0.40 0.33 0.28 0.26 0.22 0.21
1.50 1.04 0.81 0.65 0.55 0.48 0.42 0.37 0.34
13.05 9.43 6.78 4.63 2.71 1.02 0.53 2.04 3.50
27.68 20.91 16.23 12.67 9.86 7.52 5.48 3.75 2.21
0.50 0.46 0.45 0.46 0.42 0.43 0.42 0.42 0.43
0.59 0.54 0.50 0.46 0.45 0.44 0.45 0.45 0.48
pecially, to achieve the same property the required length of the DFG-based device is much less than that of the cascaded v(2)-based one. It is easier to fabricate the device and improve the machining accuracy. The above analysis is based on a continuous variation of the period along the device length. In fact, the period is a discrete sequence of domains of alternating polarity. It is essential to analyze the translation from a continuous to a discretized structure. Here we take an example of the 3-cm-long structure. According to the beginning position of a SCOS period and the period length calculated from Eq. (6), we can make the ideal SCOS period discretized and array them in sequence to retrieve a discretized SCOS structure. In order to analyze the permitted manufacture tolerance, the SCOS period is accurate to different levels, such as 0.001, 0.01, 0.02, and 0.025 lm. As shown in Fig. 6, the conversion responses of these cases are simulated, where the conversion efficiency is considered as a function of the signal wavelength. The pump power is 300 mW, and the signal power is 1 mW. The conversion response of the SCOS structure, whose accuracy is 0.001 lm, accords well with that of the ideal structure. It can be noticed that with the decrease of the period accuracy the conversion response becomes worse, and the conversion efficiency decreases by comparing the cases of 0.001, 0.01, and 0.02 lm. When the manufacture error is enhanced more than 0.02 lm, the response flatness becomes worse
Fig. 6. Conversion responses versus the signal wavelength for the SCOS structures with different manufacture accuracy levels.
rapidly. For a 3-cm-long device, the maximum permitted manufacture tolerance should be no more than 0.02 lm.
4. Conclusion A DFG-based wavelength conversion scheme with the SCOS waveguide has been investigated. The SCOS device, whose conversion bandwidth covers the whole C-band and L-band, shows excellent performances for WDM application. When the device is short, the DFG-based wavelength conversion in SCOS devices has better combined properties than the cascaded v(2)-based one. The DFG-based SCOS wavelength converter is more
338
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suitable to practical applications because it is shorter and easier to fabricate and control. The manufacture tolerance of the SCOS period should not be more than 0.02 lm to preserve the conversion quality.
Acknowledgement The work is supported in part by the TransCentury Training Programme Foundation for the Talents by the Ministry of Education of China.
References [1] S.J.B. Yoo, J. Lightwave Technol. 14 (1996) 955. [2] C.Q. Xu, H. Okayama, K. Shinozaki, K. Watanabe, M. Kawahara, Appl. Phys. Lett. 63 (1993) 1170.
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