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Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 4 — Feb. 25, 2013
  • pp: 4475–4480

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Broadband frequency tripling in locally ordered nonlinear photonic crystal

Yan Sheng and Wieslaw Krolikowski  »View Author Affiliations


Optics Express, Vol. 21, Issue 4, pp. 4475-4480 (2013)
http://dx.doi.org/10.1364/OE.21.004475


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Abstract

We propose and fabricate a LiNbO3-based nonlinear photonic crystal with locally ordered ferroelectric domains. The nonlinearity modulation provides sets of uniformly distributed reciprocal lattice vectors, ensuring broadband high frequency conversion efficiency. Frequency tripling via cascading is demonstrated in the range of 1400–1830 nm, with energy conversion efficiency up to ∼15%.

© 2013 OSA

1. Introduction

All-optical frequency conversion is of considerable interest for applications ranging from ultrafast spectroscopy to broadband networks and entangled photons sources. Parametric wave interactions in quadratic media have been shown to be particularly well-suited to realize frequency up-conversion via, for instance, sum frequency mixing (SFM, ω1 + ω2 = ω3) [1

E. Mimoun, L. D. Sarlo, J. Zondy, J. Dalibard, and F. Gerbier, “Sum-frequency generation of 589 nm light with near-unit efficiency,” Opt. Express 17, 18684–18691 (2008). [CrossRef]

], and down-conversion via difference frequency generation (DFG, ω1 − ω2 = ω3) [2

S. J. Wagner, B. M. Holmes, U. Younis, I. Sigal, A. S. Helmy, S. J. Aitchison, and D. C. Hutchings, “Difference frequency generation by quasi-phase matching in periodically intermixed semiconductor superlattice waveguides,” IEEE J. Quantum Electron. 47, 834–840 (2011). [CrossRef]

] or spontaneous parametric down conversion (SPDC, ω1 = ω2 + ω3) [3

H. Y. Leng, X. Q. Yu, Y. X. Gong, P. Xu, Z. D. Xie, H. Jin, C. Zhang, and S. N. Zhu, “On-chip steering of entangled photons in nonlinear photonic crystals,” Nature Commun. 2, 429 (2011). [CrossRef]

]. It is also possible to cascade different parametric processes to broaden the spectral range of generated frequencies. For example, the second harmonic generation (SHG, ω1 +ω1 = 2ω1) combined with SFM (ω1 + 2ω1 = 3ω1) has been widely used for third harmonic generation (THG) [4

S. Zhu, Y. Zhu, and N. Ming, “Quasi-phase-matched third-harmoinc generation in a quasi-periodic optical superlattice,” Science 278, 843–846 (1997). [CrossRef]

, 5

N. G. B. Broderick, R. T. Bratfalean, T. M. Montro, and D. J. Richardson, “Temperature and wavelength tuning of second-, third-, and fourth-hamonic generation in a two-dimensional hexagonally poled nonlinear crystal,” J. Opt. Soc. Am. B 19, 2263–2272 (2002). [CrossRef]

].

It is well known that the efficient parametric process requires the matching of phase velocities of interacting waves. This so called phase matching, can be achieved by the quasi-phase matching (QPM) technique [6

J. A. Amstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962). [CrossRef]

, 7

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE. J. Quantum Electron. 28, 2631–2654 (1992). [CrossRef]

] in nonlinear photonic crystals with a spatially modulated second-order nonlinear [or χ(2)] coefficient [8

V. Berger, “Nonlinear photonic crystals,” Phys. Rev. Lett. 81, 4136–4139 (1998). [CrossRef]

–11

A. Arie and N. Voloch, “Periodic, quasi-periodic, and random quadratic nonlinear photonic crystals,” Laser Photon. Rev. 4, 355–373 (2010). [CrossRef]

]. In order to broaden the bandwidth of the nonlinear interactions, the QPM concept has been generalized from simple periodic to disordered nonlinearity modulations [12

M. Baudier-Raybaut, R. Haïdar, Ph. Kupecek, Ph. Lemasson, and E. Rosencher, “Nonlinear optics: disorder is the new order,” Nature (London) 432, 285–286 (2004). [CrossRef]

]. Several types of disordered χ(2) structures have been recently investigated for broadband frequency conversions, including e.g. as-grown SBN [13

M. Horowitz, A. Bekker, and B. Fischer, “Broadband second-harmonic generation in SrxBa1−xNb2O6 by spread spectrum phase matching with controllable domain gratings,” Appl. Phys. Lett. 62, 2619–2621 (1993). [CrossRef]

] and randomly poled LiNbO3 crystals [14

Y. Sheng, D. Ma, M. Ren, W. Chai, Z. Li, K. Koynov, and W. Krolikowski, “Broadband second harmonic generation in one-dimensional randomized nonlinear photonic crystal,” Appl. Phys. Lett. 99, 031108 (2011). [CrossRef]

, 15

I. Varon, G. Porat, and A. Arie, “Controlling the disorder properties of quadratic nonlinear photonic crystals,” Opt. Lett. 36, 3978–3980 (2011). [CrossRef] [PubMed]

].

However, demonstrated so far randomized χ(2) structures are not well suited for broadband cascading of two parametric processes. In most of these structures the reciprocal vectors G⃗ represented by the Fourier transform of the nonlinearity distribution are unevenly redistributed with corresponding Fourier coefficients decreasing quickly with the increase of the magnitude of reciprocal lattice vector. This poses limitation to the conversion efficiency of the cascaded process that typically involves reciprocal G⃗ vectors of very different magnitudes [16

Y. Sheng, S. M. Saltiel, and K. Koynov, “Cascaded third-harmonic generation in a single short-range-ordered nonlinear photonic crystal,” Opt. Lett. 34, 656–658 (2009). [CrossRef] [PubMed]

, 17

W. Wang, V. Roppo, K. Kalinowski, Y. Kong, D. N. Neshev, C. Cojocaru, J. Trull, R. Vilaseca, K. Staliunas, W. Krolikowski, S. M. Saltiel, and Yu. S. Kivshar, “Third-harmonic generation via broadband cascading in disordered quadratic nonlinear media,” Opt. Express 17, 20117–20123 (2009). [CrossRef] [PubMed]

]. Until now the experimental conversion efficiency of broadband cascaded THG using a single crystal has been generally lower than 10%, although the efficiency of a single-wavelength frequency tripling may be as high as 27% [4

S. Zhu, Y. Zhu, and N. Ming, “Quasi-phase-matched third-harmoinc generation in a quasi-periodic optical superlattice,” Science 278, 843–846 (1997). [CrossRef]

].

In this letter we experimentally demonstrate an efficient method for broadband phase matching of cascaded parametric processes, by using LiNbO3 nonlinear photonic crystal with locally ordered ferroelectric domain pattern. The pattern reflects the nonlinearity modulation that serves as a source of a few sets of reciprocal lattice vectors G⃗ with comparable Fourier coefficients, which, subsequently, enables us to realize the broadband third harmonic generation with conversion efficiency up to 15%, significantly higher than previously reported.

2. Design and analysis

The main principle which we need to follow in designing the two-dimensional nonlinear photonic structure is to maximize the nonlinear interaction which is determined by the strength of relevant Fourier coefficients of the spatial nonlinearity modulation. As the former decreases with the order of interaction it is preferential to design the structure employing only the lowest order processes in wave interaction. Moreover, as the THG is formed via cascading of SHG and SFM we must ensure that these two constituent processes involve Fourier coefficients of comparable strengths. In general the design would need to necessarily involve some sort of optimization algorithm involving large number of parameters. Here we show that a simple extension of our earlier concept provides already significant enhancement of the broadband cascading.

The creation of the locally ordered nonlinear photonic structure is depicted in Fig. 1(a). We start with a basic unit consisting of regularly located domains which will determine the positions of maxima in the Fourier space. In generally this basic unit could be of any regular pattern. Here we build upon our previously investigated structure of square lattice. We extend it to two concentric squares. We chose two characteristic lengths (a1 and a2) to ensure that the two constituent processes of the cascading effect involve Fourier coefficients of comparable strengths. Next we build a two-dimensional lattice with period b, and locate the basic units at a random distance d from each lattice point. Finally, we randomly rotate each basic unit around its own center, i.e. the angle of rotation (θ) is taken randomly from 0 and 2π. The resultant pattern possesses no spatial long-range order, but maintains local ordering within the basic unit. The pattern is transformed into a LiNbO3 crystal via electric-field poling technique. The resulting domain structure of the poled crystal with a1 = 8.0 μm, a2 = 19.5 μm, b = 41 μm, and 0 ≤ d ≤ 2.5 μm is shown in Fig. 1(b). These parameters are selected in accordance with the state of the art of the electric poling technique. The whole poled area is 12 mm(x)×8 mm(y)×0.4 mm(z) and the average radius of the individual domains is r0 ≈2.5 μm. The inverted domains in shape of hexagons originating from sixfold structure symmetry of LiNbO3 crystal [18

Y. Sheng, T. Wang, B. Ma, B. Cheng, and D. Zhang, “Anisotropy of domain broadening in periodically poled lithium niobate crystals,” Appl. Phys. Lett. 88, 041121 (2006). [CrossRef]

] are clearly seen on the −z surface of the sample [see the inset of Fig. 1(b)].

Fig. 1 (a) Schematic presentation of the locally order nonlinear photonic structure. (b) Micrograph of the etched +z surface of the LiNbO3 crystal fabricated by electric-field poling technique. The inset shows the enlarged domain pattern on the −z surface.

The domain pattern, and consequently, the distribution of the second-order nonlinearity χ(2) in the locally ordered crystal can be expressed as
g ( x,y)=circ ( x,y)⊗ ∑ m=1M ∑ n=1N ∑ j=12 δ ( x− ( mb+ x mn)− U mnj,y− ( nb+ y mn)− V mnj),
(1)
where
circ ( x,y)= { 1 if ( x2+ y2)2≤ r02 0 otherwise.
(2)
x mn= d mncos θ mn,     y mn= d mnsin θ mn,
(3)
U mnj= ∑ i=03 aj2 [ cos ( θ mn+iπ/2)−sin ( θ mn+iπ/2)], V mnj= ∑ i=03 aj2 [ sin ( θ mn+iπ/2)+cos ( θ mn+iπ/2)],
(4)
with dmn representing the distance from the lattice point (m,n) to the nearest basic unit, θmn being the rotation angle of the unit, and U mnj and V mnj denoting the horizontal and vertical coordinates of the four vertexes of the rotating squares (identified by i = 0, 1, 2, 3) with side length of aj( j = 1, 2), respectively.

Upon taking the Fourier transform of the structure function g(x, y), we obtain the spectrum of reciprocal lattice vectors that can be used for quasi-phase matching of frequency conversion processes. In addition the modulus squared of the Fourier coefficients will determine the strength of nonlinear parametric interaction.

Figure 2(a) displays the calculated Fourier spectrum of the locally ordered structure obtained with our experimentally selected parameters. The continuous distribution of reciprocal lattice vectors in shape of homocentric rings is clearly visible, which comes as a result of the random rotation of the basic units. In fact, the radii and widths of the rings are determined precisely by the local ordering of domains within the basic cell. While this spectrum resembles the one reported earlier [16

Y. Sheng, S. M. Saltiel, and K. Koynov, “Cascaded third-harmonic generation in a single short-range-ordered nonlinear photonic crystal,” Opt. Lett. 34, 656–658 (2009). [CrossRef] [PubMed]

], the amplitude of the Fourier coefficients is now very uniform across the whole spectrum of reciprocal vectors (especially those within the first and second rings) owing to the presence of two characteristic length scales, a1 and a2, within the basic unit. This uniformity of Fourier coefficients allows us to realize a significantly more efficient phase matching of cascaded parametric interaction as long as the constituent processes involve reciprocal wave vector located inside the homocentric rings. In Fig. 2(b), we show the experimentally observed Fourier spectrum of the locally ordered crystal, represented here by the diffraction pattern of a He-Ne laser propagating along z crystallographic axis of the crystal. The result agrees well with the theory. The slight differences can be attributed to the fabrication imperfection of the domain-inverted structures.

Fig. 2 Top row: Theoretical (a) and experimental (b) Fourier spectra of the locally order nonlinear photonic structure. Bottom row depicts radial profiles of the spectra.

3. Results and discussion

To demonstrate the effect of the locally ordered nonlinear photonic crystal on broadband frequency conversion, the cascaded third harmonic generation is experimentally studied using a sample formed by electric poling in LiNbO3 crystal. As a laser source, we use an optical parametric amplifier (Palitra) pumped by a ∼200 femtosecond laser with repetition rate of 1 kHz. The output beam is s-polarized and propagates along the x crystallographic axis of the sample to use the largest nonlinear coefficient d33 of LiNbO3 crystal. The beam is loosely focused with the intensity being adjusted to be below the supercontinuum generation and damage threshold.

In experiment the tuning of the incident laser wavelength continuously from 1.50 to 1.81 μm results in the cascaded third-harmonic emission with its color gradually changing from green to red. The wavelength tuning curve of the third harmonic generation, i.e., the power of the emitted third harmonic vs. fundamental wavelength is depicted in Fig. 3(a), for constant input average power ∼1.3 mW (corresponding peak intensity of 40GW/cm2). It is seen that the emitted third harmonics at longer fundamental wavelengths (1.62–1.79 μm) are stronger than those at the shorter ones (1.44–1.61 μm). This is caused by the participation of different reciprocal lattice vectors in the sum frequency mixing of the cascaded THG. Using the material dispersion data of congruently grown LiNbO3 crystal [19

G. J. Edwards and M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16, 373–375 (1984). [CrossRef]

], we find that the reciprocal lattice vectors from the first two rings (0.26≤ |G| ≤0.48 μm−1 and 0.60 ≤ |G| ≤0.84 μm−1) are mainly responsible for the phase matching of SHG at the whole investigated wavelengths [Fig. 3(b)]. For the following process of SFM, the vectors from the second to fourth rings are involved in both collinear and non-collinear phase matchings in the wavelength range of 1.6–1.8 μm [Fig. 3(c)], while only those from the third and fourth rings (1.28≤ |G| ≤1.41 μm−1 and 1.60≤ |G| ≤1.75 μm−1) allows the phase matchings of 1.4–1.6 μm [Fig. 3(d)]. Since the Fourier coefficients associated with the vectors from the second ring are higher than those from the third and fourth rings (Fig. 2), the corresponding nonlinear interactions are more efficient. The inset in Fig. 3(a) depicts far-field images of the emitted second and third harmonics. Notice the broadening of the emission which is a direct consequence of the ring structure in the reciprocal space (Fig. 2). The emission angles are determined by the intersection of the circle representing wave vectors of the relevant harmonic and the ring of the reciprocal vectors. Our measurements of the emission angle for 6.5° the SHG and 11.9° for THG (at λ1 = 1.45 μm) correspond well to the theoretical values of 6.3° and 10.35°, respectively.The slight differences are resulted from the fact that in the calculation we ignored the contributions of the third and fourth reciprocal rings to the SHG which are much weaker than those of the internal rings.

Fig. 3 (a) The wavelength tuning curve of the cascaded THG in the locally ordered nonlinear photonic crystal. The inset depicts far-field images of the SH and TH beams at λ = 1.45 μm.(b–d) Diagrams of the phase matching in the SHG (b) and SFM (c,d). Graphs in (c) and (d) involve collinear and transversely emitted SH waves, respectively and reciprocal lattice vectors from different domains represented by homocentric rings.

Figure 4 summarizes the experimental observations. Figure 4(a) illustrates the measured spectra of fundamental and second and third harmonics at the λ1=1400.0 nm as a representative for the whole investigated frequency range. In Fig. 4(b) we show the power and conversion efficiency for the third harmonics obtained for λ1=1.62 μm. We obtained an average power of 0.246 mW with 1.605 mW input. After accounting for the Fresnel reflections, the maximum internal conversion efficiency reached 15.3%. For the intermediate process of SHG the maximum conversion efficiency reached about 30%. This high conversion efficiency achieved by femtosecond pulses confirms that our technique is very versatile and is applicable to both CW and short pulse operation. In the former case each constituent nonlinear process (SHG and SFM) utilizes the appropriate reciprocal vectors provided by the nonlinearity modulation. Exactly the same effect takes place in a short pulse regime. However, because of the group-velocity walk-off, the original (i.e. CW) phase matching condition gets modified by the contributions from a term Δk(Ω) proportional to the group delay of fundamental and harmonics. Here we use Ω to designate frequencies of ultrashort-pulse (in the vicinity of central frequency ω0). Taking the SHG as an example, the modification reads Δk (Ω)= [ υg −1 ( 2 ω0)− υg −1 ( ω0)] ( Ω−2 ω0), where υg represents the group velocity of the pulse [20

A. M. Weiner, Ultrafast Optics (John Wiley & Sons, 2009). [CrossRef]

]. In our experimental conditions the contribution to the phase matching due to group velocity mismatch is between one two two orders of magnitude smaller than the term representing central frequencies of the pulses. However, because the locally ordered nonlinearity modulation provides broad continuous bands of the reciprocal vectors, there are always reciprocal vectors available to ensure fulfilment of the modified phase matching condition for all spectral components of the fundamental, second and third harmonics. So each process is taking place in the full phase matching regime, ensuring the high efficiency of the frequency conversion for either CW or short pulses. It should be noted that since the presence of reciprocal vectors ensures the fulfilment of the phase matching, the energy transfer from the fundamental to its harmonics is a monotonic function of the propagation distance and increases with the sample length. However, because of the presence of randomness the actual growth rate will be slower than in case of periodic nonlinearity modulation [17

W. Wang, V. Roppo, K. Kalinowski, Y. Kong, D. N. Neshev, C. Cojocaru, J. Trull, R. Vilaseca, K. Staliunas, W. Krolikowski, S. M. Saltiel, and Yu. S. Kivshar, “Third-harmonic generation via broadband cascading in disordered quadratic nonlinear media,” Opt. Express 17, 20117–20123 (2009). [CrossRef] [PubMed]

].

Fig. 4 (a) Example of spectra of the interacting harmonics for fundamental wavelength λ1 = 1.4 μm; (b) Power (black squares) and conversion efficiency (red dots) of the cascaded third harmonic (λ1 = 1620 nm) vs. the average power of the fundamental wave. (b) The dependence of the power of cascaded third harmonic generation as a function of the incidence angle of the fundamental beam (Pin =1.3 mW).

Figure 4(c) depicts the dependence of the power of the third harmonic on the incident angle of the fundamental beam for an incident power of ∼1.3 mW. It is seen that the emission is not very sensitive to the incident angles. This property is a direct consequence of the isotropic distribution of the reciprocal lattice vectors provided by the nonlinearity modulation. The slight drop of the TH power at angles over 10 degrees comes as a result of larger reflection loss from the surfaces of the crystal.

4. Conclusion

In conclusion, we have designed and fabricated a LiNbO3 nonlinear photonic crystal with locally ordered ferroelectric domains. The complex nonlinearity modulation serves as a source of continuously distributed reciprocal lattice vectors with comparable Fourier coefficients, which, subsequently, leads to the broadband third harmonic generation with increased conversion efficiency. The results show that the locally ordered nonlinear photonic crystal may be applied to efficient broadband frequency conversion devices.

Acknowledgments

This work was supported by the Australian Research Council.

References and links

1.

E. Mimoun, L. D. Sarlo, J. Zondy, J. Dalibard, and F. Gerbier, “Sum-frequency generation of 589 nm light with near-unit efficiency,” Opt. Express 17, 18684–18691 (2008). [CrossRef]

2.

S. J. Wagner, B. M. Holmes, U. Younis, I. Sigal, A. S. Helmy, S. J. Aitchison, and D. C. Hutchings, “Difference frequency generation by quasi-phase matching in periodically intermixed semiconductor superlattice waveguides,” IEEE J. Quantum Electron. 47, 834–840 (2011). [CrossRef]

3.

H. Y. Leng, X. Q. Yu, Y. X. Gong, P. Xu, Z. D. Xie, H. Jin, C. Zhang, and S. N. Zhu, “On-chip steering of entangled photons in nonlinear photonic crystals,” Nature Commun. 2, 429 (2011). [CrossRef]

4.

S. Zhu, Y. Zhu, and N. Ming, “Quasi-phase-matched third-harmoinc generation in a quasi-periodic optical superlattice,” Science 278, 843–846 (1997). [CrossRef]

5.

N. G. B. Broderick, R. T. Bratfalean, T. M. Montro, and D. J. Richardson, “Temperature and wavelength tuning of second-, third-, and fourth-hamonic generation in a two-dimensional hexagonally poled nonlinear crystal,” J. Opt. Soc. Am. B 19, 2263–2272 (2002). [CrossRef]

6.

J. A. Amstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962). [CrossRef]

7.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE. J. Quantum Electron. 28, 2631–2654 (1992). [CrossRef]

8.

V. Berger, “Nonlinear photonic crystals,” Phys. Rev. Lett. 81, 4136–4139 (1998). [CrossRef]

9.

N. G. R Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D.C. Hanna, “Hexagonally poled lithium niobate: A two-dimensional nonlinear photonic crystal,” Phys. Rev. Lett. 84, 4345–4348 (2000). [CrossRef] [PubMed]

10.

R. T. Bratfalean, A. C. Peacock, N. G. R. Broderick, K. Gallo, and R. Lewen, “Harmonic generation in a two-dimensional nonlinear quasi-crystal,” Opt. Lett. 30, 424–426 (2005). [CrossRef] [PubMed]

11.

A. Arie and N. Voloch, “Periodic, quasi-periodic, and random quadratic nonlinear photonic crystals,” Laser Photon. Rev. 4, 355–373 (2010). [CrossRef]

12.

M. Baudier-Raybaut, R. Haïdar, Ph. Kupecek, Ph. Lemasson, and E. Rosencher, “Nonlinear optics: disorder is the new order,” Nature (London) 432, 285–286 (2004). [CrossRef]

13.

M. Horowitz, A. Bekker, and B. Fischer, “Broadband second-harmonic generation in SrxBa1−xNb2O6 by spread spectrum phase matching with controllable domain gratings,” Appl. Phys. Lett. 62, 2619–2621 (1993). [CrossRef]

14.

Y. Sheng, D. Ma, M. Ren, W. Chai, Z. Li, K. Koynov, and W. Krolikowski, “Broadband second harmonic generation in one-dimensional randomized nonlinear photonic crystal,” Appl. Phys. Lett. 99, 031108 (2011). [CrossRef]

15.

I. Varon, G. Porat, and A. Arie, “Controlling the disorder properties of quadratic nonlinear photonic crystals,” Opt. Lett. 36, 3978–3980 (2011). [CrossRef] [PubMed]

16.

Y. Sheng, S. M. Saltiel, and K. Koynov, “Cascaded third-harmonic generation in a single short-range-ordered nonlinear photonic crystal,” Opt. Lett. 34, 656–658 (2009). [CrossRef] [PubMed]

17.

W. Wang, V. Roppo, K. Kalinowski, Y. Kong, D. N. Neshev, C. Cojocaru, J. Trull, R. Vilaseca, K. Staliunas, W. Krolikowski, S. M. Saltiel, and Yu. S. Kivshar, “Third-harmonic generation via broadband cascading in disordered quadratic nonlinear media,” Opt. Express 17, 20117–20123 (2009). [CrossRef] [PubMed]

18.

Y. Sheng, T. Wang, B. Ma, B. Cheng, and D. Zhang, “Anisotropy of domain broadening in periodically poled lithium niobate crystals,” Appl. Phys. Lett. 88, 041121 (2006). [CrossRef]

19.

G. J. Edwards and M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16, 373–375 (1984). [CrossRef]

20.

A. M. Weiner, Ultrafast Optics (John Wiley & Sons, 2009). [CrossRef]

OCIS Codes
(190.2620) Nonlinear optics : Harmonic generation and mixing
(190.7220) Nonlinear optics : Upconversion
(190.4223) Nonlinear optics : Nonlinear wave mixing

ToC Category:
Nonlinear Optics

History
Original Manuscript: December 3, 2012
Revised Manuscript: January 9, 2013
Manuscript Accepted: January 29, 2013
Published: February 13, 2013

Citation
Yan Sheng and Wieslaw Krolikowski, "Broadband frequency tripling in locally ordered nonlinear photonic crystal," Opt. Express 21, 4475-4480 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-4-4475


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References

  1. E. Mimoun, L. D. Sarlo, J. Zondy, J. Dalibard, and F. Gerbier, “Sum-frequency generation of 589 nm light with near-unit efficiency,” Opt. Express17, 18684–18691 (2008). [CrossRef]
  2. S. J. Wagner, B. M. Holmes, U. Younis, I. Sigal, A. S. Helmy, S. J. Aitchison, and D. C. Hutchings, “Difference frequency generation by quasi-phase matching in periodically intermixed semiconductor superlattice waveguides,” IEEE J. Quantum Electron.47, 834–840 (2011). [CrossRef]
  3. H. Y. Leng, X. Q. Yu, Y. X. Gong, P. Xu, Z. D. Xie, H. Jin, C. Zhang, and S. N. Zhu, “On-chip steering of entangled photons in nonlinear photonic crystals,” Nature Commun.2, 429 (2011). [CrossRef]
  4. S. Zhu, Y. Zhu, and N. Ming, “Quasi-phase-matched third-harmoinc generation in a quasi-periodic optical superlattice,” Science278, 843–846 (1997). [CrossRef]
  5. N. G. B. Broderick, R. T. Bratfalean, T. M. Montro, and D. J. Richardson, “Temperature and wavelength tuning of second-, third-, and fourth-hamonic generation in a two-dimensional hexagonally poled nonlinear crystal,” J. Opt. Soc. Am. B19, 2263–2272 (2002). [CrossRef]
  6. J. A. Amstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev.127, 1918–1939 (1962). [CrossRef]
  7. M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE. J. Quantum Electron.28, 2631–2654 (1992). [CrossRef]
  8. V. Berger, “Nonlinear photonic crystals,” Phys. Rev. Lett.81, 4136–4139 (1998). [CrossRef]
  9. N. G. R Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D.C. Hanna, “Hexagonally poled lithium niobate: A two-dimensional nonlinear photonic crystal,” Phys. Rev. Lett.84, 4345–4348 (2000). [CrossRef] [PubMed]
  10. R. T. Bratfalean, A. C. Peacock, N. G. R. Broderick, K. Gallo, and R. Lewen, “Harmonic generation in a two-dimensional nonlinear quasi-crystal,” Opt. Lett.30, 424–426 (2005). [CrossRef] [PubMed]
  11. A. Arie and N. Voloch, “Periodic, quasi-periodic, and random quadratic nonlinear photonic crystals,” Laser Photon. Rev.4, 355–373 (2010). [CrossRef]
  12. M. Baudier-Raybaut, R. Haïdar, Ph. Kupecek, Ph. Lemasson, and E. Rosencher, “Nonlinear optics: disorder is the new order,” Nature (London)432, 285–286 (2004). [CrossRef]
  13. M. Horowitz, A. Bekker, and B. Fischer, “Broadband second-harmonic generation in SrxBa1−xNb2O6 by spread spectrum phase matching with controllable domain gratings,” Appl. Phys. Lett.62, 2619–2621 (1993). [CrossRef]
  14. Y. Sheng, D. Ma, M. Ren, W. Chai, Z. Li, K. Koynov, and W. Krolikowski, “Broadband second harmonic generation in one-dimensional randomized nonlinear photonic crystal,” Appl. Phys. Lett.99, 031108 (2011). [CrossRef]
  15. I. Varon, G. Porat, and A. Arie, “Controlling the disorder properties of quadratic nonlinear photonic crystals,” Opt. Lett.36, 3978–3980 (2011). [CrossRef] [PubMed]
  16. Y. Sheng, S. M. Saltiel, and K. Koynov, “Cascaded third-harmonic generation in a single short-range-ordered nonlinear photonic crystal,” Opt. Lett.34, 656–658 (2009). [CrossRef] [PubMed]
  17. W. Wang, V. Roppo, K. Kalinowski, Y. Kong, D. N. Neshev, C. Cojocaru, J. Trull, R. Vilaseca, K. Staliunas, W. Krolikowski, S. M. Saltiel, and Yu. S. Kivshar, “Third-harmonic generation via broadband cascading in disordered quadratic nonlinear media,” Opt. Express17, 20117–20123 (2009). [CrossRef] [PubMed]
  18. Y. Sheng, T. Wang, B. Ma, B. Cheng, and D. Zhang, “Anisotropy of domain broadening in periodically poled lithium niobate crystals,” Appl. Phys. Lett.88, 041121 (2006). [CrossRef]
  19. G. J. Edwards and M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron.16, 373–375 (1984). [CrossRef]
  20. A. M. Weiner, Ultrafast Optics (John Wiley & Sons, 2009). [CrossRef]

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