## Electrically and optically controlled cross-polarized wave conversion

Optics Express, Vol. 16, Issue 5, pp. 3083-3100 (2008)

http://dx.doi.org/10.1364/OE.16.003083

Acrobat PDF (291 KB)

### Abstract

Light wave propagation in third-order nonlinear media with applied external electric field is investigated. Interplay between the nonlinear electro-optic and all-optical effects is examined theoretically. Energy exchange between the orthogonal light polarizations, the cross polarization conversion, results. The assisting external field acts as either the effect-enhancing or functionality-controlling parameter. Various materials such as silica glass, silicon, other bulk and quantum well semiconductors, organic materials, and particle-doped nanostructures are referred to as possible candidates for device implementations. Numerical estimates of achievable parameters in a selected suitable material are discussed.

© 2008 Optical Society of America

## 1. Introduction

1. E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maak, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. **6**, 69–82 (2000). [CrossRef]

2. M. M. Fejer, “Nonlinear optical frequency conversion,” Physics Today **47**, 25–32 (1994). [CrossRef]

7. M. Cada, “Switching mirror in the CdTe-based photonic crystal,” Appl. Phys. Lett. **87**, 11101–11102 (2005). [CrossRef]

8. E. Garmire, “Resonant optical nonlinearities in semiconductors”, IEEE J. Sel. Top. Quantum Electron. **6**, 1094–1110 (2000). [CrossRef]

^{(3)}

*EEE*, where χ

^{(3)}is the nonlinear susceptibility tensor and

*E*is the electric field vector of the participating fields (e.g. optical mode, external optical control), is engaged in a device functionality as an intensity-dependent refractive index change of a waveguide material.

*E*, do not necessarily have to be all contributors from optical modes or controlling optical signals, as is the case in optical solitons, four-wave mixing or all-optical switching. An externally applied electric field can play a role of one or more constituting field contributors in this term. They can also be information-carrying signals while participating in a given functionality.

9. K. L. Sala, “Nonlinear refractive-index phenomena in isotropic media subjected to a dc electric field: Exact solutions,” Phys. Rev. A. **29**, 1944–1954 (1984). [CrossRef]

10. P. G. Kazansky and V. Pruneri, “Electric-field poling of quasi-matched optical fibers,” J. Opt. Soc. Am. B **14**, 3170–3179 (1997). [CrossRef]

12. R. H. Stolen, J. Botineau, and A. Ashkin, “Intensity discrimination of optical pulses with birefringent fibers,” Opt. Lett. **7**, 512–516 (1982). [CrossRef] [PubMed]

14. J. M. Dziedzic, R.H. Stolen, and A. Ashkin, “Optical Kerr effect in long fibers,” Appl. Opt. **20**, 1403–1411 (1981). [CrossRef] [PubMed]

15. B. Nickolaus, D. Grischkowsky, and A.C. Balant, “Optical pulse reshaping based on the nonlinear birefringence of single-mode optical fibers,” Opt. Lett. **8**, 189–193 (1983). [CrossRef]

12. R. H. Stolen, J. Botineau, and A. Ashkin, “Intensity discrimination of optical pulses with birefringent fibers,” Opt. Lett. **7**, 512–516 (1982). [CrossRef] [PubMed]

17. M. Hofer, M.E. Fermann, M.E. Haberl, M.H. Ober, and A.J. Schmidt, “Mode locking with cross-phase and self-phase modulation,” Opt. Lett. **16**, 502–506 (1991). [CrossRef] [PubMed]

_{2}-based CdTe-nanoparticle-doped, some plastics, and other materials are mentioned. It is known that the size, the density and the shape of nanoparticles embedded in a base material can modify molecular [19] and/or atomic [20

20. A. Wadehra and S. K. Gish, “A density functional theory-based chemical potential equalization approach to molecular polarizability,” J. Chem. Sci. **117**, 401–409 (2005). [CrossRef]

21. S. Ohtsuka, T. Koyama, K. Tsunemoto, H. Nagata, and S. Tanaka, “Nonlinear optical properties of CdTe microcrystallites doped glasses fabricated by laser evaporation method,” Appl. Phys. Lett. **61**, 2953–2954 (1992). [CrossRef]

## 2. Theory

## 2.1 Governing equations

*and*

**E***, in a notoriously known form [22]:*

**H***, can be written out consisting of linear and nonlinear terms:*

**P**^{(i)}are the linear,

*i*=

*1*, and the nonlinear,

*i*=

*2*,

*3*,…, susceptibilities, respectively. Combining Eqs. (1) and (2) yields the known vector wave equation:

*ε*=

*ε*(1+χ

_{o}^{(1)})=

*n*

^{2}

*is the material permittivity and*

_{L}*n*is its linear refractive index. The double curl operator, ∇×∇×, in Eq. (3) becomes the simpler Laplace operator, Δ, in a homogeneous medium. In a third-order nonlinear medium, the nonlinear polarization is usually written out in the Cartesian coordinates using the 81 components of the fourth-ranked susceptibility tensor, χ

_{L}^{(3)}, as [23]:

*i*∈{

*x*,

*y*,

*z*}.

^{(3)}has 21 nonzero components, of which only 3 are independent due to symmetry. One can obtain the following relationships [24

24. C. C. Shang and H. Hsu, “The spatial symmetric forms of third-order nonlinear susceptibility,” IEEE J. Quantum Electron. **23**, 177–179 (1987). [CrossRef]

_{xxx}. The vector wave equation (3) can be simplified into a scalar wave equation under certain assumptions, for example, a TE mode propagation in a planar waveguide or a linearly-polarized mode traveling in a fiber. The latter is a well-studied subject whereby the scalar polarization is written as

*I*is the light intensity and

*Z*is the free space impedance. This thus indicates an intensity-dependent field via the intensity-dependent refractive index,

_{0}*n*, that is

*n*=

*n*+

_{L}*n*, where

_{NL}I*n*is the known nonlinear refractive index coefficient for a given material. The scalar approximation leads then to the nonlinear wave equation. It can be solved approximately for some situations, the most known being the spatial soliton in optical fibers [25]. For this approximate case specifically, it is incorrectly called in literature the nonlinear Schrödinger equation due to its similar form. However, Schrödinger himself did not derive any nonlinear equation. In 1925 he formulated a linear motion equation for a free particle [26].

_{NL}*P*=

_{NL}*ε*

_{0}χ

^{(3)}

*EEE*, does not necessarily have to be considered only as a refractive index change with intensity of light. An externally applied electric field can play a role of one or more constituting field contributors,

*E*, in this term. This can lead to different situations yielding various interesting effects.

## 2.2 Propagation expressions

*ω*, propagating along the z-axis, and having generally all field components,

*E*,

_{x}*E*and

_{y}*E*:

_{z}*γ*=

*e*

^{j(ωt-kz)}, * means complex conjugate,

*k*=

*ωn*/

_{L}*c*is the propagation constant, and

*c*is the speed of light in vacuum. An external electric field,

*x*-axis. The induced nonlinear polarization, using Eq. (6), is then given by:

*e*

^{2}=

*e*

^{2}

*+*

_{x}*e*

^{2}

*+*

_{y}*e*

^{2}

*and |*

_{z}*e*|

^{2}=

*e*

_{x}e^{*}

*+*

_{x}*e*

_{y}*e*

^{*}

*+*

_{y}*e*

_{z}*e*

^{*}

*. The complex conjugate terms are omitted in Eq. (8) for simplicity but have been taken into account in derivations.*

_{z}*ω*, 2

*ω*, 3

*ω*. In a dispersive medium, which is usually the case, the terms at harmonic frequencies, 2

*ω*, 3

*ω*suffer from the phase mismatch unless some of the known techniques for phase matching is employed. This can include periodic perturbation of the dielectric constant or the boundary, or periodic modulation of the nonlinear properties of the waveguide material. In this work, we are interested only in the fundamental frequency terms at

*ω*, and thus the harmonic terms as well as the dc terms are omitted in the further analysis. The non-zero components of the nonlinear polarization at

*ω*thus are:

*e*(

_{x}*z*),

*e*(

_{x}*z*) and

*e*(

_{z}*z*). The spatial dependence on transversal coordinates,

*x*,

*y*, is omitted for simplicity and because it is not relevant in the analysis. For small nonlinearity, the longitudinal variations of the mutual power coupling factors in Eq. (9) can also be neglected; therefore, one can set approximately:

*e*(

_{x}*e*

_{x}e^{*}

*),*

_{x}*e*(

_{y}*e*

_{y}e^{*}

*), and*

_{y}*e*(

_{z}*e*

_{z}e^{*}

*), as well as to cross-phase polarization modulation amongst the three polarization components, i.e.*

_{z}*e*(

_{x}*e*

_{y}e^{*}

*+*

_{y}*e*

_{z}e^{*}

*),*

_{z}*e*(

_{y}*e*

_{x}e^{*}

*+*

_{x}*e*

_{z}e^{*}

*), and*

_{z}*e*(

_{z}*e*

_{x}e^{*}

*+*

_{x}*e*

_{y}e^{*}

*). The second term describes an external-field-controlled propagating field.*

_{y}## 2.3 Field solutions

*k*=

_{0}*ε*, and

_{0}Z_{0}*e*(0) and,

_{x}*e*

_{y,z}(0) are the field’s initial amplitudes.

*n*

_{EXT}E^{2}

_{ext}, with:

*L*required for a

_{π}*π*- phase shift in the form:

*E*≪

^{2}_{ext}*e*, which corresponds to approximately

^{2}_{x,y,z}*1- mW*of optical power in a

*10 - µm*cross-section waveguide and about

^{2}*E*>

_{ext}*1V*/

*µm*, one can neglect the all-optical effects and thus make the external electric field the dominating control parameter.

*n*and

_{NL}*n*in Eqs. (15)–(17), respectively, would be quite different.

_{EXT}*Fm3m*), gallium arsenide, indium phosphide or silicon (GaAs, InP, Si, space group

*F*-

*43m*), the tensor χ

^{(3)}has 21 nonzero components, of which only 4 are independent. Relationships similar to those in Eq. (5) can be derived as follows [24

24. C. C. Shang and H. Hsu, “The spatial symmetric forms of third-order nonlinear susceptibility,” IEEE J. Quantum Electron. **23**, 177–179 (1987). [CrossRef]

_{xxx}and

*φ*=(χ

_{xxy}+χ

_{xyxy}+χ

_{xyyx})/χ

_{xxx}.

*|*

**e**_{x}^{2}) and the cross-phase polarization modulation (proportional to

*φ*(|

*|*

**e**_{y}^{2}+|

*|*

**e**_{z}^{2})) are separated and modified in their strengths as a result of two effective susceptibility coefficients (χ and χ·

*φ*) governing the interaction. The field solutions are basically identical to those in Eq. (14) except that the light intensity is modified due to the difference between the self-phase and cross-phase modulation terms. It assumes the form:

*n*, remains the same, and so as the external-electric-field-assisted effect (

_{NL}*n*). It is interesting to note that the dispersive properties of χ with respect to optical versus electrical fields’ values, as discussed above, might be properly accounted for in a similar manner as in this case where χ and

_{EXT}*φ*·χ appear in the equations together.

## 2.4 Power exchange expressions

*x*component and with coupling only to/from the

*y*component of the mode for simplicity and without losing the generality of the solution, one writes:

*γ*has been omitted for simplicity as well.

**e**_{x,y}|, are functions of the distance

*z*. To obtain a solution to Eq. (26), one can divide the whole process into a series of local processes where in each single local process, the light waves magnitudes, |

**e**_{x,y}|, are

*z*- independent. This kind of partition of the whole process is valid as long as a change in

*z*is small enough so the interaction strength can be considered constant for the amplitude changes (not the phase changes, of course). The interaction strength depends on the non-linearity, χ, the external electric field,

*E*, and the initial light polarization magnitudes. One can thus assume that the light propagation magnitudes, │

_{ext}

**e**_{x,y}|, are

*z*- independent. Then the solution to Eq. (26) for each local process leads to a local coupled-field solution whereby evaluating the integral in Eq. (26) for constant light magnitudes is possible. Choosing the integration constant to be equal to

*E*

^{2}

_{ext}=(i.e.

*ω*=0), thus leaving in only the self-phase and cross-phase polarization modulation terms, as expected. Also, the new amplitude term assumes a value of unity, as it is supposed to under the same condition of zero external electric field.

*y*- component:

*p*and

_{x}*p*, such that

_{y}*p*+

_{x}*p*=

_{y}*p*, where

_{T}*p*[

_{T}*mW*/

*µm*

^{2}] is the total (constant) power in the wave per cross-sectional area. We also define the term with the superscript “

*i*” as the one associated with the

*i*-

*th*local process, i.e.

*p*

_{i}^{x,y}=

*p*

_{x,y}, at the

*i*-

*th*process. The local power densities can then be expressed as:

*|*

**e**_{x}^{2}and |

*|*

**e**_{y}^{2}in the exponents of Eq. (31) using powers

*p*and

_{x}*p*again, one can obtain two local coupled power equations:

_{y}*p*

^{i+1}

_{x,y}-

*p*

^{i}_{x,y}, is very small for a very small value of (

*f*·

*p*

^{i}_{x,y}). In the infinitezimal limit one can write (

*f*·

*p*

^{i}_{x,y})→

*d*(

*f*·

*p*

_{x,y}) and thus justify the approximation

*p*

^{i+1}

_{x,y}-

*p*

^{i}_{x,y}→

*d*(

*p*

_{x,y}). The following differential equations then replace the difference ones in (34):

*p*and

^{0}_{x}*p*as initial values of

^{0}_{y}*p*and

_{x}*p*, respectively, yields the following global coupled power expressions:

_{y}*p*+

_{x}*p*=

_{y}*p*, in Eq. (36) allows one to find the decoupled global analytical expressions for both power quantities in the form:

_{T}*p*=

^{N}_{x}*p*/

^{0}_{x}*p*and

_{T}*p*=

^{N}_{y}*p*/

^{0}_{y}*p*are the normalized power densities, which basically determine the initial power percentage distribution between the mode components. The power densities in Eq. (37) can also be expressed in a completely uncoupled form:

_{T}*f*in Eq. (33) correspond to the minima of

*p*, while the maxima of

_{x}*f*determine

*p*maxima with the first one being the largest. An interplay between the external electric field,

_{x}*E*, and the distance,

_{ext}*z*, then produces an optimal condition for the maximum power exchange between the mode components, although there is no absolute maximum. The power density maximum condition dictated by the distance comes from the condition that

*sin*(2

*ϕ z*)=0. The maximum dictated by the external field is determined from the condition that (2

*ϕ z*)·

*sin*(2

*ϕ z*)+cos(2

*ϕ z*)-1=0. For the first (largest) maximum, these conditions yield a hyperbola in 3-D for

*f*(

*z*,

*E*), described by the two equations in the

_{ext}*z*-

*E*coordinate system:

_{ext}*decreasing*of the external field causes an

*increase*in the maximum value of the power exchange; however, at the price of a longer propagation distance required. This is a direct consequence of the fact that the

*f*function does not have a global maximum, except at infinity (i.e. for

*z*=∞ or

*E*=0), and behaves as a 3-D hyperbola according to Eq. (39).

_{ext}*E*, or alternatively for a given

_{ext}*z*, a maximum of the power exchange can always be found, while the stronger the nonlinearity χ, the shorter the distance is required for the same power exchange and the same external field. The value of the power exchange maximum increases more less linearly with the total power in the mode. For example, for

*p*=1

_{T}*mW*/

*µm*

^{2},

*E*=1

_{ext}*V*/

*µm*, χ=0.12

*µm*

^{2}/

*V*

^{2}, and an equal initial distribution of the power between the mode components, the maximum achievable power exchange is over 10 %.

## 3. Numerical considerations

*and χ*

^{Re}_{ijkl}*, corresponding to the phase and loss effects, respectively. Both contributions should be considered in numerical estimates; however, the values of χ*

^{Im}_{ijkl}*are not usually readily available or are not even known. Thus the nonlinear loss is often not considered and only the phase effects are included in estimates or device designs.*

^{Im}_{ijkl}7. M. Cada, “Switching mirror in the CdTe-based photonic crystal,” Appl. Phys. Lett. **87**, 11101–11102 (2005). [CrossRef]

8. E. Garmire, “Resonant optical nonlinearities in semiconductors”, IEEE J. Sel. Top. Quantum Electron. **6**, 1094–1110 (2000). [CrossRef]

28. J. Loicq, Y. Renotte, J.-L. Delplancke, and Y. Lion, “Non-linear optical measurements and crystalline characterization of CdTe nanoparticles produced by the ‘electropulse’ technique,” New J. Phys. **6**, 1–13 (2004). [CrossRef]

29. Y. P. Rakovich, M. V. Artemyev, A. G. Rolo, M. I. Vasilevskiy, and M. J. M. Gomes, “Third-order optical nonlinearity in thin films of CdS nanocrystals,” Phys. Stat. Sol. **224**, 319–324 (2001). [CrossRef]

30. G. V. Prakash, M. Cazzanelli, Z. Gaburro, L. Pavesi, F. Iacona, G. Franzo, and F. Priolo, “Nonlinear optical properties of silicon nanocrystals grown by plasma-enhanced chemical vapor deposition,” J. Appl. Phys. **91**, 4607–4615 (2002). [CrossRef]

31. H. Rajagopalan, P. Vippa, and M. Thakur, “Quadratic electro-optic effect in a nano-optical material based on the nonconjugated conductive polymer Poly (β-pinene),” Appl. Phys. Lett , **88**, 331091–331093 (2006). [CrossRef]

*W*/

*µm*

^{2}] and 9%, respectively.

*E*

_{ext(1)}=0.8

*V*/

*µm*,

*E*

_{ext(2)}=2

*V*/

*µm*, and

*E*

_{ext(3)}=3

*V*/

*µm*respectively. It can be seen from figure 1, as mentioned before, that decreasing the external field causes an increase in the maximum value of CPC.

*V*/

*µm*and the total optical power is 0.101 [

*W*/

*µm*

^{2}]. The initial power percentage in the

*x*- component is the determining parameter of the CPC in this case. The values are

*P*

_{I%(1)}=0.001,

*P*

_{I%(2)}=0.5,

*P*

_{I%(3)}=0.9,

*P*

_{I%(4)}=0.99.

*P*, while keeping the external field and the initial power percentage constant. The external electric field is 2

_{T}*V*/

*µm*, and the initial power percentage in the

*x*- component is 0.2. The total launched optical power is the determining parameter of the CPC in this case with its values taken as

*P*

_{T(1)}=0.448

*mW*/

*µm*

^{2},

*P*

_{T(2)}=0.011

*W*/

*µm*

^{2},

*P*

_{T(3)}=0.101

*W*/

*µm*

^{2},

*P*

_{T(4)}=1.01

*W*/

*µm*

^{2}.

## 4. Summary

## 5. Conclusions

## Acknowledgments

## References and links

1. | E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maak, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. |

2. | M. M. Fejer, “Nonlinear optical frequency conversion,” Physics Today |

3. | M. Cada, “Nonlinear optical devices,” Optica Pura i Aplicada |

4. | R. Ramaswami and K. N. Sivarajan, Optical networks (Morgan Kaufman, New York, 2002). |

5. | G. P. Agrawal, Nonlinear fiber optics (Academic Press, New York, 2001). |

6. | R. P. Khare, Fiber optics and optoelectronics (Oxford University Press, London, 2004). |

7. | M. Cada, “Switching mirror in the CdTe-based photonic crystal,” Appl. Phys. Lett. |

8. | E. Garmire, “Resonant optical nonlinearities in semiconductors”, IEEE J. Sel. Top. Quantum Electron. |

9. | K. L. Sala, “Nonlinear refractive-index phenomena in isotropic media subjected to a dc electric field: Exact solutions,” Phys. Rev. A. |

10. | P. G. Kazansky and V. Pruneri, “Electric-field poling of quasi-matched optical fibers,” J. Opt. Soc. Am. B |

11. | J. Kerr, Phil. Mag. J. Sci., ser. Fourth50, (1875). |

12. | R. H. Stolen, J. Botineau, and A. Ashkin, “Intensity discrimination of optical pulses with birefringent fibers,” Opt. Lett. |

13. | M. Horowitz and Y. Silberberg, “Nonlinear filtering by use of intensity-dependent polarization rotation in birefringent fibers,” Opt. Lett. |

14. | J. M. Dziedzic, R.H. Stolen, and A. Ashkin, “Optical Kerr effect in long fibers,” Appl. Opt. |

15. | B. Nickolaus, D. Grischkowsky, and A.C. Balant, “Optical pulse reshaping based on the nonlinear birefringence of single-mode optical fibers,” Opt. Lett. |

16. | H.G. Winful and A. Hu,“Intensity discrimination with twisted birefingent optical fibers,” Opt. Lett. |

17. | M. Hofer, M.E. Fermann, M.E. Haberl, M.H. Ober, and A.J. Schmidt, “Mode locking with cross-phase and self-phase modulation,” Opt. Lett. |

18. | H. A. Haus, E.P. Ippen, and K. Tamura, “Additive-pulse modelocking in fiber lasers,” IEEE J. Quantum Electron. |

19. | F. Torrens, “Molecular polarizability of semiconductor clusters and nanostructures,” Ninth Foresight Conference on Molecular Nanotechnology, November 2001. |

20. | A. Wadehra and S. K. Gish, “A density functional theory-based chemical potential equalization approach to molecular polarizability,” J. Chem. Sci. |

21. | S. Ohtsuka, T. Koyama, K. Tsunemoto, H. Nagata, and S. Tanaka, “Nonlinear optical properties of CdTe microcrystallites doped glasses fabricated by laser evaporation method,” Appl. Phys. Lett. |

22. | A. Yariv, Optical electronics in modern communications (Oxford ser. Elec. Comp. Eng., London, 1997). |

23. | R. W. Boyd, Nonlinear optics (Academic Press, New York, 1992). |

24. | C. C. Shang and H. Hsu, “The spatial symmetric forms of third-order nonlinear susceptibility,” IEEE J. Quantum Electron. |

25. | E. Infeld and G. Rowlands, Nonlinear waves, solitons and chaos (Cambridge University Press, London, 2000). |

26. | S. Brandt and H. D. Dahmen: The picture book of quantum mechanics (Springer Verlag, New York, 1995). |

27. | M. J. Weber, Handbook of optical materials (CRC Press, Washington D.C., 2003). |

28. | J. Loicq, Y. Renotte, J.-L. Delplancke, and Y. Lion, “Non-linear optical measurements and crystalline characterization of CdTe nanoparticles produced by the ‘electropulse’ technique,” New J. Phys. |

29. | Y. P. Rakovich, M. V. Artemyev, A. G. Rolo, M. I. Vasilevskiy, and M. J. M. Gomes, “Third-order optical nonlinearity in thin films of CdS nanocrystals,” Phys. Stat. Sol. |

30. | G. V. Prakash, M. Cazzanelli, Z. Gaburro, L. Pavesi, F. Iacona, G. Franzo, and F. Priolo, “Nonlinear optical properties of silicon nanocrystals grown by plasma-enhanced chemical vapor deposition,” J. Appl. Phys. |

31. | H. Rajagopalan, P. Vippa, and M. Thakur, “Quadratic electro-optic effect in a nano-optical material based on the nonconjugated conductive polymer Poly (β-pinene),” Appl. Phys. Lett , |

32. | Q. Chen, L. Kuang, E. H. Sargent, and Z. Y. Wang, “Ultrafast nonresonant third-order optical nonlinearity of fullerene-containing polyurethane films at telecommunication wavelengths,” Opt. Lett. , |

33. | M. Qasymeh, M. Cada, and S. Ponomarenko, “Quadratic electro-optic Kerr effect: Applications to photonic devices,” sub. IEEE J. Quantum Electron. (2007). |

34 . | M. Qasymeh and M. Cada, “Re-configurable all-optical devices based on electrically controlled cross-polarization wave conversion,” ISDRS, College Park, MD, USA (2007). |

35 . | M. Qasymeh, M. Cada, S. Ponomarenko, and J. Pistora, “Application of DC-electric field assistance to optical multistability,” ISMOT, Rome, Italy (2007). |

**OCIS Codes**

(190.3270) Nonlinear optics : Kerr effect

(230.4320) Optical devices : Nonlinear optical devices

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: November 28, 2007

Revised Manuscript: February 7, 2008

Manuscript Accepted: February 12, 2008

Published: February 20, 2008

**Citation**

Michael Cada, Montasir Qasymeh, and Jaromir Pistora, "Electrically and optically controlled cross-polarized wave conversion," Opt. Express **16**, 3083-3100 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-5-3083

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### References

- E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maak, D. V. Attanasio, D. J. Fritz, G. J. McBrien and D. E. Bossi, "A review of lithium niobate modulators for fiber-optic communications systems," IEEE J. Sel. Top. Quantum Electron. 6, 69-82 (2000). [CrossRef]
- M. M. Fejer, "Nonlinear optical frequency conversion," Physics Today 47, 25-32 (1994). [CrossRef]
- M. Cada, "Nonlinear optical devices," Optica Pura i Aplicada 38, 1-11 (2005).
- R. Ramaswami and K. N. Sivarajan, Optical networks (Morgan Kaufman, New York, 2002).
- G. P. Agrawal, Nonlinear fiber optics (Academic Press, New York, 2001).
- R. P. Khare, Fiber optics and optoelectronics (Oxford University Press, London, 2004).
- M. Cada, "Switching mirror in the CdTe-based photonic crystal," Appl. Phys. Lett. 87, 11101-2 (2005). [CrossRef]
- E. Garmire, "Resonant optical nonlinearities in semiconductors", IEEE J. Sel. Top. Quantum Electron. 6, 1094-1110 (2000). [CrossRef]
- K. L. Sala, "Nonlinear refractive-index phenomena in isotropic media subjected to a dc electric field: Exact solutions," Phys. Rev. A. 29, 1944-1954 (1984). [CrossRef]
- P. G. Kazansky and V. Pruneri, "Electric-field poling of quasi-matched optical fibers," J. Opt. Soc. Am. B 14, 3170-3179 (1997). [CrossRef]
- J. Kerr, Phil. Mag. J. Sci., ser. Fourth 50, (1875).
- R. H. Stolen, J. Botineau, and A. Ashkin, "Intensity discrimination of optical pulses with birefringent fibers," Opt. Lett. 7, 512-516 (1982). [CrossRef] [PubMed]
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