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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 13 — Jun. 23, 2008
  • pp: 9726–9738
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Cascaded wavelength conversion as favorable application of nonlinear optical polymers

Min-su Kim, Jung Jin Ju, Seung Koo Park, Jung Yun Do, and Myung-Hyun Lee  »View Author Affiliations


Optics Express, Vol. 16, Issue 13, pp. 9726-9738 (2008)
http://dx.doi.org/10.1364/OE.16.009726


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Abstract

Nonlinear optical (NLO) polymers have been considered promising materials for wavelength conversion at a low pump power. However, they have not been readily adopted to practical applications due to their high absorption coefficients, especially at a shorter interacting wavelength. Our theoretical analysis proves that the influence of absorption coefficients can be mitigated significantly in cascaded wavelength conversion (CWC) processes. According to our example study, maximum conversion efficiencies for CWC can compare even with those for second-harmonic generation in many NLO polymers. Thus CWC can become a pertinent application of NLO polymers. However, to obtain such efficient CWC, several realistic problems should be resolved in practical devices.

© 2008 Optical Society of America

1. Introduction

Optical polymers present great advantages for the development of various optical communication devices by grace of the wide spectrum of their material properties [1

1. M.-H. Lee, J. J. Ju, S. Park, J. Y. Do, and S. K. Park, “Polymer-based devices for optical communications,” ETRI J. 24, 259–269 (2002). [CrossRef]

, 2

2. L. Eldada and L. W. Shacklette, “Advances in polymer integrated optics,” IEEE J. Sel. Top. Quantum Electron. 6, 54–68 (2000). [CrossRef]

]. They also can acquire very high second-order optical nonlinearities by attaching prominent nonlinear optical (NLO) chromophores and then aligning molecular dipoles using an electric poling process. Such NLO polymers typically exhibit ultrafast optical response times. Thus, they have been regarded as excellent materials for efficient and ultrafast electro-optic (EO) or NLO waveguide devices. For instance, EO devices with very low half-wave voltages were successfully demonstrated with NLO polymers [3

3. Y. Shi, C. Zhang, H. Zhang, J. H. Bechtel, L. R. Dalton, B. H. Robinson, and W. H. Steier, “Low (sub-1-volt) halfwave voltage polymeric electro-optic modulators achieved by controlling chromophore shape,” Science 288, 119–122 (2000). [CrossRef]

, 4

4. M.-C. Oh, H. Zhang, C. Zhang, H. Erlig, Y. Chang, B. Tsap, D. Chang, A. Szep, W. H. Steier, H. R. Fetterman, and L. R. Dalton, “Recent advances in electrooptic polymer modulators incorporating highly nonlinear chromophore,” IEEE J. Sel. Top. Quantum Electron. 7, 826–835 (2001). [CrossRef]

].

However, those polymers have hardly been accepted into practical NLO wavelength conversion (WC) devices. This is mainly due to their high optical absorption coefficients at a shorter interacting wavelength region, e.g., at a second-harmonic (SH) wavelength [5

5. A. Otomo, M. Jäger, G. I. Stegeman, M. C. Flipse, and M. Diemeer, “Key trade-offs for second harmonic generation in poled polymers,” Appl. Phys. Lett. 69, 1991–1993 (1996). [CrossRef]

,6

6. M.-s. Kim, J. J. Ju, S. K. Park, J. Y. Do, and M.-H. Lee, “Evaluation of nonlinear optical polymers for secondharmonic generation: toward the balance of absorption and nonlinearity against intrinsic trade-off,” Chem. Phys. Lett. 417, 277–281 (2006). [CrossRef]

], and also the material deterioration effects induced by the high absorption [7

7. M. Cha, W. E. Torruellas, G. I. Stegeman, W. H. G. Horsthuis, G. R. Möhlmann, and J. Meth, “Two photon absorption of di-alkyl-amino-nitro-stilbene side chain polymer,” Appl. Phys. Lett. 65, 2648–2650 (1994). [CrossRef]

,8

8. Q. Zhang, M. Canva, and G. Stegeman, “Wavelength dependence of 4-dimethylamino-4’-nitrostilbene polymer thin film photodegradation,” Appl. Phys. Lett. 73, 912–914 (1998). [CrossRef]

]. The high absorption coefficient at the shorter wavelength region originates from the trails of the absorption peaks of NLO chromophores [5

5. A. Otomo, M. Jäger, G. I. Stegeman, M. C. Flipse, and M. Diemeer, “Key trade-offs for second harmonic generation in poled polymers,” Appl. Phys. Lett. 69, 1991–1993 (1996). [CrossRef]

]. Thus, it has not been achieved ordinarily to lower the absorption without sacrificing the high nonlinearity owing to the intrinsic trade-off relationship between them. Instead, peculiar phase-matching (PM) schemes were proposed to alleviate the absorption effect [5

5. A. Otomo, M. Jäger, G. I. Stegeman, M. C. Flipse, and M. Diemeer, “Key trade-offs for second harmonic generation in poled polymers,” Appl. Phys. Lett. 69, 1991–1993 (1996). [CrossRef]

,9

9. H. Sato, H. Matsuno, and I. Seo, “Enhancement of Čerenkovian second-harmonic generation power with ultraviolet irradiation-formed nonlinear optical χ(2) corrugation and channel waveguide,” J. Opt. Soc. Am. B 15, 773–780 (1998). [CrossRef]

]. However, there still remain various obstacles to realize practical efficientWC devices with these schemes.

For several years, our group has developed a number of NLO polymers applicable to practical EO or NLO devices. They possess favorable nonlinear optical properties along with superior thin-film quality and thermal stability [10–15

10. J. Y. Do, S. K. Park, J. J. Ju, S. Park, and M.-H. Lee, “Improved electro-optic effect by hyperbranched chromophore structures in side-chain polyimide,” Macromol. Chem. Phys. 204, 410–416 (2003). [CrossRef]

]. Moreover, some of them exhibit relatively low absorption coefficients at both fundamental and SH regions (~1.55 µm and ~0.78 µm, respectively) of an optical communication wavelength [11

11. S. K. Park, J. Y. Do, J.-J. Ju, S. Park, M.-s. Kim, and M.-H. Lee, “Transparent nonlinear optical polymers for all-optical wavelength converters in optical fiber communications,” Macromol. Rapid Commun. 24, 772–777 (2003). [CrossRef]

, 15

15. J. J. Ju, J. Kim, J. Y. Do, M.-s. Kim, S. K. Park, S. Park, and M.-H. Lee, “Second-harmonic generation in periodically poled nonlinear polymer waveguides,” Opt. Lett. 29, 89–91 (2004). [CrossRef] [PubMed]

]. Based on these NLO polymers, we have demonstrated remarkable conversion efficiencies in quasi-phase-matched (QPM) SH generation (SHG) experiments [15

15. J. J. Ju, J. Kim, J. Y. Do, M.-s. Kim, S. K. Park, S. Park, and M.-H. Lee, “Second-harmonic generation in periodically poled nonlinear polymer waveguides,” Opt. Lett. 29, 89–91 (2004). [CrossRef] [PubMed]

, 16

16. J. J. Ju, S. K. Park, S. Park, J. Kim, M.-s. Kim, M.-H. Lee, and J. Y. Do, “Wavelength conversion in nonlinear optical polymer waveguides,” Appl. Phys. Lett. 88, 241106-1–241106-3 (2006). [CrossRef]

]. In the meantime, we have reported our comprehensive analyses on the influence of absorption and nonlinearity in NLO wavelength conversion, and have disseminated our approach to the development of practical NLO polymers with a superb combination of nonlinear and absorption coefficients [6

6. M.-s. Kim, J. J. Ju, S. K. Park, J. Y. Do, and M.-H. Lee, “Evaluation of nonlinear optical polymers for secondharmonic generation: toward the balance of absorption and nonlinearity against intrinsic trade-off,” Chem. Phys. Lett. 417, 277–281 (2006). [CrossRef]

, 17

17. M.-s. Kim, J. J. Ju, S. K. Park, J. Y. Do, and M.-H. Lee, “Balancing the trade-off between absorption and nonlinearity in NLO polymers for practical applications,” in Linear and Nonlinear Optics of Organic Materials V, M. Eich, ed., Proc. SPIE5935, 593509-1–593509-8 (2005). [CrossRef]

].

In this paper, we analyze theoretically the effects of the absorption coefficients and optical nonlinearity on the CWC process under the undepleted-pump regime. We utilize the analytical results directly to evaluate several NLO polymers by estimating and comparing their maximum achievable CWC efficiencies, and demonstrate that the CWC process can be applied as a potential application of NLO polymers. We also discuss several realistic problems encountered in our development of practical NLO WC devices.

2. Theoretical Analysis

2.1. Loss Effect on Conversion Efficiency

dAldz=αl2Al+iωlnlc(m,n)deffAmAn.
(1)

Here the subscripts l, m, and n indicate the subscripts p, sh, s, or c. AlA(ωl) represents the complex amplitude of the electric field at the angular frequency component ωl, and satisfies the relation of A(-ωl)=A*(ωl).αl is the absorption coefficient at ωl and d eff is the effective second-order NLO coefficient. The summation is to be performed over all the ordered pairs of (m, n) that satisfy ωl=ωm+ωn. We here disregard the effect of third-order optical nonlinearity for simplicity.

If we adopt the undepleted-pump assumption given by

ApAs,AshAc,
(2)

the intensities of the pump and signal waves can be simply represented in the form of Il(z)=Il(0)exp(-αlz), where l=p or s. We also obtain the intensities of the SH and converted waves expressed as

Ish(z)=8π2deff2cε0np2nshλp2Ip2(0)z2𝓛SHG(Z)
(3)

and

Ic(z)=16π4deff4c2ε02np2nsh2nsncλp2λc2Ip2(0)Is(0)z4CWC(Z)
(4)

under the situation of type-I SHG PM and nondegenerate DFG. SHG(z) and CWC(z) are the loss factors for phase-matched SHG and CWC processes, respectively, that are given by

SHG(z)=exp[(αsh+2αp)z2]{sinh[(αsh2αp)z4](αsh2αp)z4}2
(5)

and

CWC(z)=exp(αcz)[(αsh2αp)z4]2[g((αsh+αsαc)z)g((2αp+αsαc)z)]2
exp(αpz)[(αsh2αp)z4]2[g(αshz)g(2αpz)]2,
(6)

where g(x) is defined by

g(x)exp(x4)sinh(x4)x4.
(7)

In the second line of Eq. (6), we suppose αpαsαc because our interest converges on the CWC process in the 1.55-µm optical communication band. We note here that the result in Eq. (6) is slightly different with that in Ref. [17

17. M.-s. Kim, J. J. Ju, S. K. Park, J. Y. Do, and M.-H. Lee, “Balancing the trade-off between absorption and nonlinearity in NLO polymers for practical applications,” in Linear and Nonlinear Optics of Organic Materials V, M. Eich, ed., Proc. SPIE5935, 593509-1–593509-8 (2005). [CrossRef]

], which was miswritten by our mistake. Although the above results are based directly on type-I SHG PM, they can be easily adopted to the CWC process involving type-II SHG PM as in Ref. [6

6. M.-s. Kim, J. J. Ju, S. K. Park, J. Y. Do, and M.-H. Lee, “Evaluation of nonlinear optical polymers for secondharmonic generation: toward the balance of absorption and nonlinearity against intrinsic trade-off,” Chem. Phys. Lett. 417, 277–281 (2006). [CrossRef]

].

Fig. 1. Loss factors for phase-matched (a) SHG and (b) CWC processes as functions of the absorption coefficients at the pump and SH waves.

It must be noted that Fig. 1(a) is identical to the result for 𝒟(z) in Ref. [6

6. M.-s. Kim, J. J. Ju, S. K. Park, J. Y. Do, and M.-H. Lee, “Evaluation of nonlinear optical polymers for secondharmonic generation: toward the balance of absorption and nonlinearity against intrinsic trade-off,” Chem. Phys. Lett. 417, 277–281 (2006). [CrossRef]

], which was obtained under the phase-matched SHG condition and was termed the diminution factor. This identical result is a direct consequence of the assumption |Ash|≫|Ac| given in Eq. (2). Therefore, we will not include in this paper all the relevant results for the SHG process that are the same as those in Ref. [6

6. M.-s. Kim, J. J. Ju, S. K. Park, J. Y. Do, and M.-H. Lee, “Evaluation of nonlinear optical polymers for secondharmonic generation: toward the balance of absorption and nonlinearity against intrinsic trade-off,” Chem. Phys. Lett. 417, 277–281 (2006). [CrossRef]

]. From Fig. 1(b), we can find that CWC(z) shows somewhat insensitive dependence on αsh z, as we expected. On top of that, the loss effect in the CWC process is rather insignificant than in the SHG process when αsh>2αp.

Further qualitative comparison must be made with the conversion efficiencies for the SHG and CWC processes that are defined as η SHG(z)≡Ish(z)/Ip (0) and η CWC(z)≡Ic(z)/Is(0), respectively. A simple substitution leads us to obtain the relationship between η SHG(z) and η CWC(z) as

Fig. 2. The benefit factor of the CWC process, relative to the SHG process, as a function of absorption coefficients.
ηCWC(z)14ηSHG2(z)CWC(z)SHG2(z).
(8)

If all the absorption coefficients can be ignorable, both SHG and CWC are given by 1. Then, we can estimate the value of η CWC from a known value of η SHG using the simple relationship of η CWCη 2 SHG/4. However, when the absorption coefficients have unignorable values, we must consider the additional factor given by CWC(z)/ 2 SHG(z). The dependence of this factor on the absorption coefficients is plotted in Fig. 2. The factor has the value of 1 in the lossless situation and yields values higher than 1 in all other practical situations. For this reason, CWC(z)/ 2 SHG(z) can be identified as the benefit factor of the CWC process, in comparison to the SHG process, in the presence of absorption losses. In particular, we can obtain a high benefit factor at a large value of αsh z, while the values are near 1 when αsh z<1. This result evidently reflects the advantageous aspect of the CWC process in an NLO medium with a large αsh value.

2.2. Maximum CWC Efficiency

Provided the loss effect is not ignorable, the intensities of the SH and converted waves do not increase monotonously as the NLO interaction length increases. Therefore, we take interest in the maximum available value of the conversion efficiency for the development of a practical CWC device. As expressed in Eqs. (3) and (4), we must consider the explicit effect of the NLO interaction length as well as the loss factor to obtain the maximum CWC efficiency.

Although the NLO and absorption coefficients cause conflicting effects on the CWC efficiency, the optimum interaction length for the maximum CWC efficiency is determined solely by the absorption coefficients as in the SHG process [6

6. M.-s. Kim, J. J. Ju, S. K. Park, J. Y. Do, and M.-H. Lee, “Evaluation of nonlinear optical polymers for secondharmonic generation: toward the balance of absorption and nonlinearity against intrinsic trade-off,” Chem. Phys. Lett. 417, 277–281 (2006). [CrossRef]

]. Based on Eq. (4), we can obtain the optimum CWC interaction length z max CWC from the condition of d[z 4 CWC(z)]/dz=0. However, z max CWC can not be simply expressed by a definite form. Instead, it is possible to obtain its values by solving numerically the relation of

(1+αpαsh)exp(αshzCWCmax2)αpαsh=32exp(αpzCWCmax)12.
(9)
Fig. 3. The optimum CWC interaction length calculated numerically as a function of the absorption coefficients.
Fig. 4. The ratio between the optimum CWC and SHG interaction lengths as a function of the absorption coefficients.

Though, it must be considered that Eq. (9) can not yield a definite solution when αsh=2αp, and Eq. (9) is also satisfied by the trivial solution of z max CWC=0, where the CWC efficiency actually has the minimum value. Figure 3 shows the calculated values of z max CWC. We can notice from this result that a little decrease of αp gives rise to a considerable increase in z max CWC in the region of αp≤2 dB/cm, while αsh yields much insensitive influence on z max CWC.

In Fig. 4, we exhibit the result of comparison between the optimum CWC and SHG interaction lengths. The numerical comparison leads us to find that z max CWC is greater than the optimum SHG interaction length z max SHG if αsh>αp/5.65. Considering that the NLO interaction length is involved in the CWC efficiency with quartic dependence, rather than quadratic dependence as in the SHG conversion efficiency, the increased optimum interaction lengths in that region result in significantly enhanced CWC efficiencies compared with available SHG conversion efficiencies.

Fig. 5. The coefficient h max CWC calculated for a typical NLO polymer at λp=1.55 µm and λs=1.56 µm when the values of d eff and Ip(0) are given in the units of pm/V and kW/cm2, respectively: (a) a three-dimensional contour map and (b) a two-dimensional plot for several specific αp values.

With the calculated values of z max CWC, maximum CWC efficiencies can be obtained from the definition of η max CWCIc(z max CWC)/Is(0). Then we can express the result as

ηCWCmax=hCWCmax(αp,αsh)deff4Ip2(0),
(10)

or equivalently as

ηCWCmax(indB)=hCWCmax(indB)+40logdeff+20logIp(0)
(10’)
Fig. 6. The maximum CWC efficiency calculated under the condition of d eff=10 pm/V and Ip(0)=100 kW/cm2.

in the unit of dB, where we represent separately the dependence on the NLO coefficient and the pump intensity. The coefficient h max CWC includes the effects of all the linear optical parameters of a given material. However, it can be simply regarded as just a function of absorption coefficients because other parameters vary only within limited ranges in various NLO polymers for the CWC process of a wavelength in the 1.55-µm band.

Figure 5 shows the values of h max CWC calculated with the refractive index data of a PEI-DASS polymer [a polyetherimide-based side-chain polymer with a kind of 4-(dialkylamino)-4’-(styrylsulfonyl)-stilbene chromophore], which was developed in our laboratory. The calculation is carried out with λp=1.55 µm and λs=1.56 µm, provided that the values of d eff and Ip(0) are given in the units of pm/V and kW/cm2, respectively. The calculated result reconfirms that αp makes a decisive effect on the CWC efficiency, while the effect of αsh is rather insignificant. Upon closer examination with Fig. 5(b), it is found that the dependence on αp is expressed by h max CWC (in dB) ∝-40logαp at αsh=0 dB, and shows the tendency to approach the relation of h max CWC (in dB) ∝-20logαp as the ratio αsh/αpincreases. In the meantime, the effect of αsh is represented quite well by rational equations, and also can be described by linear equations in wide range of αsh when αp≫1 dB/cm.

Figure 6 presents the values of η max CWC calculated under the condition of d eff=10 pm/V and Ip(0)=100 kW/cm2, as a typical example. We note here that, contrary to the case of the SHG process, it is possible for the CWC process to obtain a conversion efficiency higher than 0 dB, which corresponds to the conversion efficiency of 100%, in the region of αp<0.5 dB/cm. Moreover, the region of such high conversion efficiencies can be rather extended if the values of d eff and Ip(0) are increased. This is not a strange fact in the CWC process because the pump wave is different from the signal wave and, thus, Is(z) can also have a much higher value than Is(0) as Ic(z) increases.

As mentioned above, the CWC efficiency can be estimated from the relation of η CWCη 2 SHG/4 when the absorption coefficients can be ignorable. Thus the ratio of 4ηCWCmaxηSHGmax2 can be adopted as an important figure-of-merit (FOM) of NLO polymers for the CWC application, with respect to SHG, on the condition of unignorable absorption coefficients. From Fig. 7, we can comprehend that the values of the FOM is higher than 0 dB, except only for the condition of αsh/αp≈0, and exhibits a tendency to be enhanced more rapidly as αsh/αp increases.

Fig. 7. Relational comparison between the maximum conversion efficiencies of the CWC and SHG processes, which can be used as a figure-of-merit of NLO polymers for the application to CWC.

3. Discussions

3.1. Validity Criteria

Since all the above results are derived under the assumption given by Eq. (2), we should take care not to utilize them beyond their validity limit. Thus, we have to examine their validity condition, in the first place. Based on the above analytical approach and the results of numerical simulations with a system of equations more comprehensive than Eq. (1), we find the validity criteria expressed as

ηSHG(z)cε0np2nshαp2λp232π2deff2Ip(0)
(11)

and

zzSHGmax.
(12)

Although we obtained an additional criterion given by

ηSHG(z)·ηCWC(z)cε0nsncnshαs2λs232π2deff2Ip(0)·exp(αsz)
(13)

from Eq. (1), it looks a much looser condition compared to Eq. (11) in our situation, and hence, is not accepted.

One may notice that Eq. (11) looks very dubious because Eq. (11) connotes that the above results in section II are valid when the SH intensity, given by I sh(z)=η SHG(z)Ip(0), is far below a constant value determined by material parameters and the pump wavelength, but unconcerned with a ratio to the pump intensity. However, it can be proved that Eq. (11) implies the condition of Ish(z)Ip(0) properly since it can be rewritten after a little algebra as

ηSHG(z)12αpzSHG12(z)
(11’)

and the relation of αp2zSHGmax2SHGmax1 is always satisfied according to the analytical results of Ref. [6

6. M.-s. Kim, J. J. Ju, S. K. Park, J. Y. Do, and M.-H. Lee, “Evaluation of nonlinear optical polymers for secondharmonic generation: toward the balance of absorption and nonlinearity against intrinsic trade-off,” Chem. Phys. Lett. 417, 277–281 (2006). [CrossRef]

]. It should be also noted that the validity conditions of Eqs. (11) and (12) are identical to those for SHG [6

6. M.-s. Kim, J. J. Ju, S. K. Park, J. Y. Do, and M.-H. Lee, “Evaluation of nonlinear optical polymers for secondharmonic generation: toward the balance of absorption and nonlinearity against intrinsic trade-off,” Chem. Phys. Lett. 417, 277–281 (2006). [CrossRef]

] and correspond to very tight conditions if we are interested only in the results for the CWC efficiency. Thus, the conditions can be much alleviated in such cases. However, it seems impossible to derive such alleviated criteria in a finite form because of the complicate contribution of the SH intensity to the CWC process.

Till now, we have considered only the second-order NLO interactions. In most cases where one deals with the cascaded second-order processes, one needs to consider the effects due to direct third-order processes as well. Actually several authors have reported that both effects often have comparable magnitudes and thus the third-order NLO effects cannot be simply neglected [21–23

21. L. Zhang, A. Shirakawa, S. Morita, and T. Kobayahsi, “Nonlinear phase shift and detuning by second- and thirdorder nonlinearities,” Jpn. J. Appl. Phys. 36, Part 2, L1294–L1296 (1997). [CrossRef]

]. By looking over those reports, we can reach the conclusion that the effects of direct third- and cascaded second-order processes are comparable when a third-order process is phase-matched. In this situation, the two successive second-order processes, which contribute to the third-order effect, have their respective phase mismatches that countervail each other. Then, the effective third-order susceptibility due to the cascaded second-order processes is expressed by [χ(2)]2/nΔn, where n is a refractive index and Δn is the index mismatch derived from the phase mismatch [22

22. B. Boulanger, J. P. Fève, P. Delarue, I. Rousseau, and G. Marnier, “Cubic optical nonlinearity in KTiOPO4,” J. Phys. B: At. Mol. Opt. Phys. 32, 475–488 (1999). [CrossRef]

, 24

24. H. Tan, G. P. Banfi, and A. Tomaselli, “Optical frequency mixing through cascaded second-order processes in β-barium borate,” Appl. Phys. Lett. 63, 2472–2474 (1993). [CrossRef]

, 25

25. M.-s. Kim and C. S. Yoon, “Theoretical analysis of third-harmonic generation via direct third-order and cascaded second-order processes in CsLiB6O10 crystals,” Phys. Rev. A 65, 033831-1–033831-9 (2002). [CrossRef]

]. Considering the facts that χ(2) and χ(3) are roughly on the order of 1 pm/V and 100 pm2/V2, respectively, and that Δn is typically of order 10-2, we can certify the comparable magnitudes of direct third- and cascaded second-order effects.

However, in the situation of the CWC process, all of the relevant third- and second-order processes satisfy almost their PM conditions simultaneously. As the result, the effect of the cascaded second-order processes becomes predominant over that of the direct third-order process, for Δn approaches to zero. This fact is reflected in Eq. (4) by the dependence of z 4, while a typical second- or third-order phase-matched process is represented by the dependence of z 2. Therefore the neglect of a direct third-order NLO interaction in Eq. (1) can be justified well enough.

3.2. Estimation of the Maximum CWC Efficiency

3.2.1. Case I

Till now, our group has developed a number of NLO polymers. Some of them exhibit very high NLO coefficients of d 33≃60 pm/V. These values correspond to the reported EO coefficients of r 33≃32 pm/V [10

10. J. Y. Do, S. K. Park, J. J. Ju, S. Park, and M.-H. Lee, “Improved electro-optic effect by hyperbranched chromophore structures in side-chain polyimide,” Macromol. Chem. Phys. 204, 410–416 (2003). [CrossRef]

], which were attained by metal-contact electric poling at an applied electric field of 100 V/µm. The absorption coefficients of these polymers were measured as αp≃3.0 dB/cm and αsh≳30 dB/cm at the 1.55-µm and 0.78-µm wavelength regions, respectively. Since they were developed for EO applications [26–28

26. S. Park, J. J. Ju, J. Y. Do, S. K. Park, and M.-H. Lee, “Thermal bias operation in electro-optic polymer modulators,” Appl. Phys. Lett. 83, 827–829 (2003). [CrossRef]

], their absorption coefficients at the SH wavelength region were not carefully controlled.

3.2.2. Case II

We developed another kind of NLO polymers as well, which exhibit much reduced absorption coefficients of αp≃1.8 dB/cm and αsh≃3.8 dB/cm at 1.55 µm and 0.78 µm, respectively. They also possess somewhat lowered NLO coefficients given by d 33≃35 pm/V [11

11. S. K. Park, J. Y. Do, J.-J. Ju, S. Park, M.-s. Kim, and M.-H. Lee, “Transparent nonlinear optical polymers for all-optical wavelength converters in optical fiber communications,” Macromol. Rapid Commun. 24, 772–777 (2003). [CrossRef]

] owing to the trade-off between the nonlinearity and absorption coefficients [5

5. A. Otomo, M. Jäger, G. I. Stegeman, M. C. Flipse, and M. Diemeer, “Key trade-offs for second harmonic generation in poled polymers,” Appl. Phys. Lett. 69, 1991–1993 (1996). [CrossRef]

, 6

6. M.-s. Kim, J. J. Ju, S. K. Park, J. Y. Do, and M.-H. Lee, “Evaluation of nonlinear optical polymers for secondharmonic generation: toward the balance of absorption and nonlinearity against intrinsic trade-off,” Chem. Phys. Lett. 417, 277–281 (2006). [CrossRef]

].

For these polymers, h max CWC is obtained as -108.5 dB at z max CWC=4.5 cm and the FOM for CWC is given by 10.4 dB. With an ideal QPM structure having d eff≃22 pm/V, we can then achieve η max CWC=13.9% (-8.6 dB) at Ip(0)=200 kW/cm2 when Is(0)≪Ip(0). This is also a much comparable value to η max SHG=22.4% (-6.5 dB) obtained at z max SHG=2.35 cm for the same polymer [6

6. M.-s. Kim, J. J. Ju, S. K. Park, J. Y. Do, and M.-H. Lee, “Evaluation of nonlinear optical polymers for secondharmonic generation: toward the balance of absorption and nonlinearity against intrinsic trade-off,” Chem. Phys. Lett. 417, 277–281 (2006). [CrossRef]

]. In the meantime, direct numerical simulation gives the result of η max CWC=9.2% at z max CWC=4.2 cm when Ip(0)=200 kW/cm2 and Is(0)=1 kW/cm2. The difference in η max CWC arises also from the saturation effect of the SHG and CWC efficiencies.

3.2.3. Case III

From these parameters, we obtain h max CWC=-108.8 dB at z max CWC=12.2 cm. Meanwhile, the FOM for CWC exhibits a very high value of 30.5 dB mainly due to the very low value of αp. Then, an ideal QPM structure with d eff≃16 pm/V is expected to yield η max CWC=3.4% (-14.7 dB) at Ip(0)=200 kW/cm2 and Is(0)≪Ip(0), while the maximum SHG conversion efficiency is estimated as η max SHG=1.1% (-19.8 dB) at z max SHG=1.08 cm [6

6. M.-s. Kim, J. J. Ju, S. K. Park, J. Y. Do, and M.-H. Lee, “Evaluation of nonlinear optical polymers for secondharmonic generation: toward the balance of absorption and nonlinearity against intrinsic trade-off,” Chem. Phys. Lett. 417, 277–281 (2006). [CrossRef]

]. It is quite remarkable that the value of η max CWC is even higher than that of η max SHG for this polymer. This is due to the fact that η max CWC can be significantly increased relatively to η max SHG in the region of αsh/αp≫1, as shown in Fig. 7. Though, the increased value is still much lower than the value of η max CWC estimated for the case II even with a longer z max CWC.

From the results of our numerical simulation, η max CWC=2.1% is obtained at z max CWC=10.3 cm when Ip(0)=200 kW/cm2 and Is(0)=1 kW/cm2. Since z max CWC is greatly higher than z max SHG for this polymer, the saturation effect is considerable for the SHG conversion efficiency. Hence, a relatively high difference is generated between the estimated and simulated values of η max CWC.

3.3. Further Considerations

It is appreciated from Fig. 6 that a further improvement of η max CWC can be achieved by a decrease in αp even though such material tuning may accompany a noticeable increase in αsh. Thus NLO polymers adequate for CWC applications may have a somewhat higher absorption coefficient at the SH wavelength region. This relieves considerably the knotty restriction in the development and application of NLO polymers, which is originated from the trade-off between low absorption at the SH wavelength and high nonlinearity [5

5. A. Otomo, M. Jäger, G. I. Stegeman, M. C. Flipse, and M. Diemeer, “Key trade-offs for second harmonic generation in poled polymers,” Appl. Phys. Lett. 69, 1991–1993 (1996). [CrossRef]

, 6

6. M.-s. Kim, J. J. Ju, S. K. Park, J. Y. Do, and M.-H. Lee, “Evaluation of nonlinear optical polymers for secondharmonic generation: toward the balance of absorption and nonlinearity against intrinsic trade-off,” Chem. Phys. Lett. 417, 277–281 (2006). [CrossRef]

]. However, such promising NLO polymers must exhibit a sharp declination in the absorption spectrum to ensure a low absorption coefficient at the pump wavelength, as discussed in Refs. [6

6. M.-s. Kim, J. J. Ju, S. K. Park, J. Y. Do, and M.-H. Lee, “Evaluation of nonlinear optical polymers for secondharmonic generation: toward the balance of absorption and nonlinearity against intrinsic trade-off,” Chem. Phys. Lett. 417, 277–281 (2006). [CrossRef]

] and [11

11. S. K. Park, J. Y. Do, J.-J. Ju, S. Park, M.-s. Kim, and M.-H. Lee, “Transparent nonlinear optical polymers for all-optical wavelength converters in optical fiber communications,” Macromol. Rapid Commun. 24, 772–777 (2003). [CrossRef]

].

Till now, we have considered only ideal QPM conditions that are described by the effective NLO coefficients given by d eff=2d 33/π. However, it was already reported that such high values of d eff cannot be obtained with usual periodic poling methods in non-ferroelectric media [15

15. J. J. Ju, J. Kim, J. Y. Do, M.-s. Kim, S. K. Park, S. Park, and M.-H. Lee, “Second-harmonic generation in periodically poled nonlinear polymer waveguides,” Opt. Lett. 29, 89–91 (2004). [CrossRef] [PubMed]

,29

29. J. Kim, J. J. Ju, and an M.-s. Kim, “Distributions of electric field and induced nonlinearity in periodic poling,” Jpn. J. Appl. Phys. 42, Part 1, 7304–7312 (2003). [CrossRef]

]. According to the results in Ref. [29

29. J. Kim, J. J. Ju, and an M.-s. Kim, “Distributions of electric field and induced nonlinearity in periodic poling,” Jpn. J. Appl. Phys. 42, Part 1, 7304–7312 (2003). [CrossRef]

], the maximum achievable value of d eff is limited to ~0.34·2d 33/π. Besides, the induced d 33 values of practical QPM WC devices cannot reach to the maximum available values of the applied NLO polymers themselves. This is due to the fact that the poling electric field applied for practical polymeric QPM devices should be generally restricted to a value much lower than that applied for material characterization in order to obtain devices with good stability and low propagation losses [15

15. J. J. Ju, J. Kim, J. Y. Do, M.-s. Kim, S. K. Park, S. Park, and M.-H. Lee, “Second-harmonic generation in periodically poled nonlinear polymer waveguides,” Opt. Lett. 29, 89–91 (2004). [CrossRef] [PubMed]

, 16

16. J. J. Ju, S. K. Park, S. Park, J. Kim, M.-s. Kim, M.-H. Lee, and J. Y. Do, “Wavelength conversion in nonlinear optical polymer waveguides,” Appl. Phys. Lett. 88, 241106-1–241106-3 (2006). [CrossRef]

]. Hence it is requisite to develop a sophisticated device scheme or poling method to utilize the advantage of the high NLO coefficients of NLO polymer materials.

4. Conclusion

We have investigated theoretically the effect of the absorption and optical nonlinearity of NLO polymers on the CWC process, and also applied the analytical results to estimate the CWC efficiencies for several kinds of NLO polymers. According to the results, we could comprehend that the high absorption coefficient at the SH wavelength of a typical NLO polymer does not affect significantly the CWC efficiency, and thus, it is possible to obtain a CWC efficiency that is comparable to or even higher than the expected SHG conversion efficiency. These facts demonstrate that the CWC process can be utilized effectively as a promising WC technique for wavelength-division multiplexed optical communication networks. We also discussed several important restrictions of practical polymericQPM WC devices and proposed probable solutions applicable to the development of NLO polymers and QPM WC devices for CWC applications.

Acknowledgments

This work was supported by the IT R&D program [2006-S-073-02] of the MKE/IITA, Korea.

References and links

1.

M.-H. Lee, J. J. Ju, S. Park, J. Y. Do, and S. K. Park, “Polymer-based devices for optical communications,” ETRI J. 24, 259–269 (2002). [CrossRef]

2.

L. Eldada and L. W. Shacklette, “Advances in polymer integrated optics,” IEEE J. Sel. Top. Quantum Electron. 6, 54–68 (2000). [CrossRef]

3.

Y. Shi, C. Zhang, H. Zhang, J. H. Bechtel, L. R. Dalton, B. H. Robinson, and W. H. Steier, “Low (sub-1-volt) halfwave voltage polymeric electro-optic modulators achieved by controlling chromophore shape,” Science 288, 119–122 (2000). [CrossRef]

4.

M.-C. Oh, H. Zhang, C. Zhang, H. Erlig, Y. Chang, B. Tsap, D. Chang, A. Szep, W. H. Steier, H. R. Fetterman, and L. R. Dalton, “Recent advances in electrooptic polymer modulators incorporating highly nonlinear chromophore,” IEEE J. Sel. Top. Quantum Electron. 7, 826–835 (2001). [CrossRef]

5.

A. Otomo, M. Jäger, G. I. Stegeman, M. C. Flipse, and M. Diemeer, “Key trade-offs for second harmonic generation in poled polymers,” Appl. Phys. Lett. 69, 1991–1993 (1996). [CrossRef]

6.

M.-s. Kim, J. J. Ju, S. K. Park, J. Y. Do, and M.-H. Lee, “Evaluation of nonlinear optical polymers for secondharmonic generation: toward the balance of absorption and nonlinearity against intrinsic trade-off,” Chem. Phys. Lett. 417, 277–281 (2006). [CrossRef]

7.

M. Cha, W. E. Torruellas, G. I. Stegeman, W. H. G. Horsthuis, G. R. Möhlmann, and J. Meth, “Two photon absorption of di-alkyl-amino-nitro-stilbene side chain polymer,” Appl. Phys. Lett. 65, 2648–2650 (1994). [CrossRef]

8.

Q. Zhang, M. Canva, and G. Stegeman, “Wavelength dependence of 4-dimethylamino-4’-nitrostilbene polymer thin film photodegradation,” Appl. Phys. Lett. 73, 912–914 (1998). [CrossRef]

9.

H. Sato, H. Matsuno, and I. Seo, “Enhancement of Čerenkovian second-harmonic generation power with ultraviolet irradiation-formed nonlinear optical χ(2) corrugation and channel waveguide,” J. Opt. Soc. Am. B 15, 773–780 (1998). [CrossRef]

10.

J. Y. Do, S. K. Park, J. J. Ju, S. Park, and M.-H. Lee, “Improved electro-optic effect by hyperbranched chromophore structures in side-chain polyimide,” Macromol. Chem. Phys. 204, 410–416 (2003). [CrossRef]

11.

S. K. Park, J. Y. Do, J.-J. Ju, S. Park, M.-s. Kim, and M.-H. Lee, “Transparent nonlinear optical polymers for all-optical wavelength converters in optical fiber communications,” Macromol. Rapid Commun. 24, 772–777 (2003). [CrossRef]

12.

J. Y. Do and J. J. Ju, “Polyester dendrimers carrying NLO chromophores: synthesis and optical characterization,” Macromol. Chem. Phys. 206, 1326–1331 (2005). [CrossRef]

13.

S. K. Park, J. Y. Do, J. J. Ju, S. Park, M.-s. Kim, and M.-H. Lee, “Nonlinear optical polymer applicable for all-optical wavelength converters in communications bands near 1.5 µm,” Mater. Lett. 59, 2872–2875 (2005). [CrossRef]

14.

S. K. Park, J. Y. Do, J. J. Ju, S. Park, M.-s. Kim, and M.-H. Lee, “Polyamic alkyl ester system promising for side-chain electro-optic polymer,” React. Funct. Polym. 66, 974–983 (2006). [CrossRef]

15.

J. J. Ju, J. Kim, J. Y. Do, M.-s. Kim, S. K. Park, S. Park, and M.-H. Lee, “Second-harmonic generation in periodically poled nonlinear polymer waveguides,” Opt. Lett. 29, 89–91 (2004). [CrossRef] [PubMed]

16.

J. J. Ju, S. K. Park, S. Park, J. Kim, M.-s. Kim, M.-H. Lee, and J. Y. Do, “Wavelength conversion in nonlinear optical polymer waveguides,” Appl. Phys. Lett. 88, 241106-1–241106-3 (2006). [CrossRef]

17.

M.-s. Kim, J. J. Ju, S. K. Park, J. Y. Do, and M.-H. Lee, “Balancing the trade-off between absorption and nonlinearity in NLO polymers for practical applications,” in Linear and Nonlinear Optics of Organic Materials V, M. Eich, ed., Proc. SPIE5935, 593509-1–593509-8 (2005). [CrossRef]

18.

M. H. Chou, I. Brener, M. M. Fejer, E. E. Chaban, and S. B. Christman, “1.5-µm-band wavelength conversion based on cascaded second-order nonlinearity in LiNbO3 waveguides,” IEEE Photon. Technol. Lett. 11, 653–655 (1999). [CrossRef]

19.

M.-s. Kim, J. J. Ju, S. K. Park, J. Y. Do, and M.-H. Lee, “Absorption effects on second-harmonic generation and cascaded wavelength conversion in nonlinear optical polymers,” J. Nonlinear Opt. Phys. Mater. 13, 367–371 (2004). [CrossRef]

20.

M.-s. Kim, J. T. Ahn, J. Kim, J. J. Ju, and M.-H. Lee, “Chromatic dispersion compensation via mid-span spectal inversion with periodically poled LiNbO3 wavelength converter at low pump power,” ETRI J. 27, 312–318 (2005). [CrossRef]

21.

L. Zhang, A. Shirakawa, S. Morita, and T. Kobayahsi, “Nonlinear phase shift and detuning by second- and thirdorder nonlinearities,” Jpn. J. Appl. Phys. 36, Part 2, L1294–L1296 (1997). [CrossRef]

22.

B. Boulanger, J. P. Fève, P. Delarue, I. Rousseau, and G. Marnier, “Cubic optical nonlinearity in KTiOPO4,” J. Phys. B: At. Mol. Opt. Phys. 32, 475–488 (1999). [CrossRef]

23.

M.-s. Kim and C. S. Yoon, “Full characterization of third harmonic generation in CsLiB6O10 (CLBO) crystals,” in Technical Digest of the 4th Pacific Rim Conference on Lasers and Electro-Optics (Institute of Electrical and Electronics Engineers, Piscataway, 2001), Vol. II, pp. 398–399.

24.

H. Tan, G. P. Banfi, and A. Tomaselli, “Optical frequency mixing through cascaded second-order processes in β-barium borate,” Appl. Phys. Lett. 63, 2472–2474 (1993). [CrossRef]

25.

M.-s. Kim and C. S. Yoon, “Theoretical analysis of third-harmonic generation via direct third-order and cascaded second-order processes in CsLiB6O10 crystals,” Phys. Rev. A 65, 033831-1–033831-9 (2002). [CrossRef]

26.

S. Park, J. J. Ju, J. Y. Do, S. K. Park, and M.-H. Lee, “Thermal bias operation in electro-optic polymer modulators,” Appl. Phys. Lett. 83, 827–829 (2003). [CrossRef]

27.

S. Park, J. J. Ju, J. Y. Do, S. K. Park, and M.-H. Lee, “Thermal stability enhancement of electrooptic polymer modulator,” IEEE Photon. Technol. Lett. 16, 93–95 (2004). [CrossRef]

28.

S. Park, J. J. Ju, J. Y. Do, S. K. Park, J. T. Ahn, S.-I. Kim, and M.-H. Lee, “16-arrayed electrooptic polymer modulator,” IEEE Photon. Technol. Lett. 16, 1834–1836 (2004). [CrossRef]

29.

J. Kim, J. J. Ju, and an M.-s. Kim, “Distributions of electric field and induced nonlinearity in periodic poling,” Jpn. J. Appl. Phys. 42, Part 1, 7304–7312 (2003). [CrossRef]

OCIS Codes
(160.4330) Materials : Nonlinear optical materials
(160.5470) Materials : Polymers
(190.4390) Nonlinear optics : Nonlinear optics, integrated optics
(300.1030) Spectroscopy : Absorption
(130.7405) Integrated optics : Wavelength conversion devices

ToC Category:
Materials

History
Original Manuscript: April 29, 2008
Revised Manuscript: June 12, 2008
Manuscript Accepted: June 13, 2008
Published: June 17, 2008

Citation
Min-su Kim, Jung Jin Ju, Seung Koo Park, Jung Yun Do, and Myung-Hyun Lee, "Cascaded wavelength conversion as favorable application of nonlinear optical polymers," Opt. Express 16, 9726-9738 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-13-9726


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References

  1. M.-H. Lee, J. J. Ju, S. Park, J. Y. Do, and S. K. Park, "Polymer-based devices for optical communications," ETRI J. 24, 259-269 (2002). [CrossRef]
  2. L. Eldada and L. W. Shacklette, "Advances in polymer integrated optics," IEEE J. Sel. Top. Quantum Electron. 6, 54-68 (2000). [CrossRef]
  3. Y. Shi, C. Zhang, H. Zhang, J. H. Bechtel, L. R. Dalton, B. H. Robinson, and W. H. Steier, "Low (sub-1-volt) halfwave voltage polymeric electro-optic modulators achieved by controlling chromophore shape," Science 288, 119-122 (2000). [CrossRef]
  4. M.-C. Oh, H. Zhang, C. Zhang, H. Erlig, Y. Chang, B. Tsap, D. Chang, A. Szep, W. H. Steier, H. R. Fetterman, and L. R. Dalton, "Recent advances in electrooptic polymer modulators incorporating highly nonlinear chromophore," IEEE J. Sel. Top. Quantum Electron. 7, 826-835 (2001). [CrossRef]
  5. A. Otomo, M. Jager, G. I. Stegeman, M. C. Flipse, and M. Diemeer, "Key trade-offs for second harmonic generation in poled polymers," Appl. Phys. Lett. 69, 1991-1993 (1996). [CrossRef]
  6. M.-s. Kim, J. J. Ju, S. K. Park, J. Y. Do, and M.-H. Lee, "Evaluation of nonlinear optical polymers for secondharmonic generation: toward the balance of absorption and nonlinearity against intrinsic trade-off," Chem. Phys. Lett. 417, 277-281 (2006). [CrossRef]
  7. M. Cha, W. E. Torruellas, G. I. Stegeman, W. H. G. Horsthuis, G. R. Mohlmann, and J. Meth, "Two photon absorption of di-alkyl-amino-nitro-stilbene side chain polymer," Appl. Phys. Lett. 65, 2648-2650 (1994). [CrossRef]
  8. Q. Zhang, M. Canva, and G. Stegeman, "Wavelength dependence of 4-dimethylamino-4???-nitrostilbene polymer thin film photodegradation," Appl. Phys. Lett. 73, 912-914 (1998). [CrossRef]
  9. H. Sato, H. Matsuno, and I. Seo, "Enhancement of Cerenkovian second-harmonic generation power with ultraviolet irradiation-formed nonlinear optical |(2) corrugation and channel waveguide," J. Opt. Soc. Am. B 15, 773-780 (1998). [CrossRef]
  10. J. Y. Do, S. K. Park, J. J. Ju, S. Park, and M.-H. Lee, "Improved electro-optic effect by hyperbranched chromophore structures in side-chain polyimide," Macromol. Chem. Phys. 204, 410-416 (2003). [CrossRef]
  11. S. K. Park, J. Y. Do, J.-J. Ju, S. Park, M.-s. Kim, and M.-H. Lee, "Transparent nonlinear optical polymers for all-optical wavelength converters in optical fiber communications," Macromol. Rapid Commun. 24, 772-777 (2003). [CrossRef]
  12. J. Y. Do and J. J. Ju, "Polyester dendrimers carrying NLO chromophores: synthesis and optical characterization," Macromol. Chem. Phys. 206, 1326-1331 (2005). [CrossRef]
  13. S. K. Park, J. Y. Do, J. J. Ju, S. Park, M.-s. Kim, and M.-H. Lee, "Nonlinear optical polymer applicable for all-optical wavelength converters in communications bands near 1.5 ?m," Mater. Lett. 59, 2872-2875 (2005). [CrossRef]
  14. S. K. Park, J. Y. Do, J. J. Ju, S. Park, M.-s. Kim, and M.-H. Lee, "Polyamic alkyl ester system promising for side-chain electro-optic polymer," React. Funct. Polym. 66, 974-983 (2006). [CrossRef]
  15. J. J. Ju, J. Kim, J. Y. Do, M.-s. Kim, S. K. Park, S. Park, and M.-H. Lee, "Second-harmonic generation in periodically poled nonlinear polymer waveguides," Opt. Lett. 29, 89-91 (2004). [CrossRef] [PubMed]
  16. J. J. Ju, S. K. Park, S. Park, J. Kim, M.-s. Kim, M.-H. Lee, and J. Y. Do, "Wavelength conversion in nonlinear optical polymer waveguides," Appl. Phys. Lett. 88, 241106-1-241106-3 (2006). [CrossRef]
  17. M.-s. Kim, J. J. Ju, S. K. Park, J. Y. Do, and M.-H. Lee, "Balancing the trade-off between absorption and nonlinearity in NLO polymers for practical applications," Proc. SPIE 5935, 593509-1-593509-8 (2005). [CrossRef]
  18. M. H. Chou, I. Brener, M. M. Fejer, E. E. Chaban, and S. B. Christman, "1.5-?m-band wavelength conversion based on cascaded second-order nonlinearity in LiNbO3 waveguides," IEEE Photon. Technol. Lett. 11, 653-655 (1999). [CrossRef]
  19. M.-s. Kim, J. J. Ju, S. K. Park, J. Y. Do, and M.-H. Lee, "Absorption effects on second-harmonic generation and cascaded wavelength conversion in nonlinear optical polymers," J. Nonlinear Opt. Phys. Mater. 13, 367-371 (2004). [CrossRef]
  20. M.-s. Kim, J. T. Ahn, J. Kim, J. J. Ju, and M.-H. Lee, "Chromatic dispersion compensation via mid-span spectal inversion with periodically poled LiNbO3 wavelength converter at low pump power," ETRI J. 27, 312-318 (2005). [CrossRef]
  21. L. Zhang, A. Shirakawa, S. Morita, and T. Kobayahsi, "Nonlinear phase shift and detuning by second- and thirdorder nonlinearities," Jpn. J. Appl. Phys. 36, Part 2, L1294-L1296 (1997). [CrossRef]
  22. B. Boulanger, J. P. Feve, P. Delarue, I. Rousseau, and G. Marnier, "Cubic optical nonlinearity in KTiOPO4," J. Phys. B: At. Mol. Opt. Phys. 32, 475-488 (1999). [CrossRef]
  23. M.-s. Kim and C. S. Yoon, "Full characterization of third harmonic generation in CsLiB6O10 (CLBO) crystals," in Technical Digest of the 4th Pacific Rim Conference on Lasers and Electro-Optics (Institute of Electrical and Electronics Engineers, Piscataway, 2001), Vol. II, pp. 398-399.
  24. H. Tan, G. P. Banfi, and A. Tomaselli, "Optical frequency mixing through cascaded second-order processes in ? -barium borate," Appl. Phys. Lett. 63, 2472-2474 (1993). [CrossRef]
  25. M.-s. Kim and C. S. Yoon, "Theoretical analysis of third-harmonic generation via direct third-order and cascaded second-order processes in CsLiB6O10 crystals," Phys. Rev. A 65, 033831-1-033831-9 (2002). [CrossRef]
  26. S. Park, J. J. Ju, J. Y. Do, S. K. Park, and M.-H. Lee, "Thermal bias operation in electro-optic polymer modulators," Appl. Phys. Lett. 83, 827-829 (2003). [CrossRef]
  27. S. Park, J. J. Ju, J. Y. Do, S. K. Park, and M.-H. Lee, "Thermal stability enhancement of electrooptic polymer modulator," IEEE Photon. Technol. Lett. 16, 93-95 (2004). [CrossRef]
  28. S. Park, J. J. Ju, J. Y. Do, S. K. Park, J. T. Ahn, S.-I. Kim, and M.-H. Lee, "16-arrayed electrooptic polymer modulator," IEEE Photon. Technol. Lett. 16, 1834-1836 (2004). [CrossRef]
  29. J. Kim, J. J. Ju, and M.-s. Kim, "Distributions of electric field and induced nonlinearity in periodic poling," Jpn. J. Appl. Phys. 42, Part 1, 7304-7312 (2003). [CrossRef]

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