DOI: 10.1007/s00340-007-2676-9

Appl. Phys. B 87, 603–606 (2007)

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nLasers and OpticsApplied Physics B

y. sheng�

j. doub. chengd. zhang

Effective generation of red-green-bluelaser in a two-dimensional decagonalphotonic superlatticeOptical Physics Lab., Beijing National Laboratory for Condensed Matter Physics,Institute of Physics, Chinese Academy of Sciences, Beijing 100080, P.R. China

Received: 12 February 2007/Revised version: 24 April 2007Published online: 24 May 2007 • © Springer-Verlag 2007

ABSTRACT We demonstrate the effective generation of red, green and blue (RGB)light in a two-dimensional decagonal quasiperiodic LiNbO3 nonlinear crystal. Owingto the unique abundance in reciprocal vectors (RVs), the RGB signals were gener-ated directly by frequency doublings. Thus the conversion efficiencies of the RGBlight were much higher than previously recorded. In addition, the same results wereobtained when the crystal was rotated by integral multiples of π/5. This result willaid in the effective generation of RGB in multiple directions and may have importantapplications in laser-based projection displays.

PACS 42.65.Ky; 42.72.Bj; 42.79.Nv

1 Introduction

The three colors of the red,green and blue laser source are neededmore frequently since most visual col-ors including white light can be pro-duced by combining these three pri-mary colors in the proper proportion.Optical frequency conversion with non-linear optical materials is an import-ant means for achieving such sources.Thus considerable attention has beengiven to this field. For example, ob-servations of quasiphase matching ofRGB using a proton exchanged LiNbO3

waveguide [1] and using a dye-dopedpolymer waveguide [2] were reported.For bulk samples, results were mainlyobtained via sum-frequency mixing,frequency doubling or optical para-metric oscillation following a cascadedsecond-order process [3–10].

However, the cascaded harmonic orsum-frequency generation may be nota good candidate. It usually fails to yielda vigorous output due to its inherentlylow efficiency. As for optical parametricoscillation, additional dielectric coat-

� Fax: +86-10-82649531, E-mail: shengyan@aphy.iphy.ac.cn

ings on the sample’s head faces areneeded to form an optical oscillatorcavity. In addition, it must run at hightemperatures to prevent photorefrac-tive damage. Attempts at the generationof RGB by frequency doublings usinga one-dimensional aperiodic optical su-perlattice have been made [11, 12], butthe efficiency experimentally attainedwas still comparatively low [13]. The in-volved enormous computer proceduresand inevitable deviations between the-oretical design and experiment add tothe complexity in using them as prac-tical devices. Thus the effective gener-ation of the three primary colors is stilla challenge.

In this work, we substituted a two-dimensional decagonal quasiperiodicsuperlattice for the traditional one-di-mensional structure. On the basis ofwhich, plentiful reciprocal vectors wereachieved to produce RGB signals di-rectly by frequency doublings. There-fore, the output efficiency of RGB lightobtained is much higher than previouslydocumented, and no special treatmentis needed. Even though a decagonal

quasicrystal was recently reported asa means to broaden the harmonic tem-perature and wavelength acceptancebandwidth [14], no record of it as a RGBlight generator was found.

2 Experiments

2.1 Structure and diffractionpattern of decagonalquasiperiodic superlattice

The two-dimensional decago-nal quasiperiodic superlattice was fab-ricated by the electric field poling tech-nique in a z-cut LiNbO3 wafer [15].Figure 1 shows the microscopic +z sur-face of the etched sample, in whichthe quasiperiodic geometric tiling withtenfold symmetric axis is displayed. Itwas composed of thin rhombi (with ver-tex angles of 36◦ and 144◦) and thickrhombi (72◦ and 108◦). The side lengthof the rhombi was about a = 13.19 µm.The poled circular cylinders placed atthe vertices of rhombi and their diameterwas about 5.2 µm. No domain mergingwas found across the whole sample of9.5×9.5×0.4 mm3.

Figure 2a is the diffraction patternof the crystal with its local tenfold axisparallel to the incident He-Ne laser.The pattern possesses tenfold rotationalsymmetry, with four series of the mostintense peaks visible. The magnitudeand orientation of the RVs of the internalseries correspond to the inverse of halfthe long diagonal of the thin rhombi.Similarly, the external three series, re-spectively, correspond to half the longdiagonal of the thick rhombi, half theside length, and half the short diagonalof the thin rhombi. We choose the RVsfor the internal series of spots to form

604 Applied Physics B – Lasers and Optics

FIGURE 1 The +z face micrograhps of poledLiNbO3 crystal in a decagonal quasiperiodic man-ner

a basic set ±Fi (i = 1, ..., 5), where

F1 = (1, 0) = (10000)

F2 = (cos(π/5), sin(π/5)) = (01000)

F3 = (cos(2π/5), sin(2π/5))

= (00100)

F4 = (cos(3π/5), sin(3π/5))

= (00010)

F5 = (cos(4π/5), sin(4π/5))

= (00001) .

In the above equations, the vectorsare expressed in both two-dimensionalCartesian coordinates and in a symbolicfive-dimensional vector notation. Themagnitude of each Fi is related to theside length as |Fi | = 2π/(a cos(π/10))

≈ 1.051 × 2π/a [16, 17]. Figure 2b isthe schematic view of part spots in thereciprocal vectors, in which the real-line arrows Fi (i = 1, 2, 3, 4, 5) indicatefive basic reciprocal vectors. When wechoose the basic set of RVs, it is possibleto index the entire diffraction pattern.The intensities of the diffraction peaksrelated to the different prominent series,their indexes and the related elementsof the tiles defining the quasicrystal, areshown in Table 1.

2.2 Experiments of red, greenand blue light generationby frequency doubling

The quasiphase matchingcondition in the frequency doubling pro-cess can be written as ∆k = k2ω −2kω −Gm,n,o,p,q, where ∆k is the wave vectormismatching, kω and k2ω are the wavevectors of fundamental and harmonicwaves, and Gm,n,o,p,q is the reciprocalvector which depends on the combi-nation of the five basic RVs. Different

FIGURE 2 (a) The diffraction patterns of LiNbO3 nonlinear crystal with its local tenfold axis par-allel to the He-Ne beam. (b) Schematic view of the reciprocal vectors. The real-line arrows Fi(i = 1, 2, 3, 4, 5) indicate the five basic reciprocal vectors. The direction of input and output beams isalong reciprocal vector (01011) in the collinear QPM harmonic generations

from the periodic RVs that can be sim-ply indexed with one or two integers, theindexing of the five basic RVs requiresfive integers in a decagonal system.

The performance of the decagonalquasicrystal as a generator of red, greenand blue light was experimentally de-

tected at room temperature. The funda-mental source was a tunable nanosecondoptical parametric oscillator pumped bya Nd:YAG laser. Its repetition rate andpulse width were 10 Hz and 4 ns, respec-tively. The incident fundamental beamwas s-polarized and entering along the

SHENG et al. Effective generation of red-green-blue laser in a two-dimensional decagonal photonic superlattice 605

RV Magnitude Fourier coefficient Associated element of the tile

(10000) 1.000 1.000 Half long diagonal of thin rhombi(01001) 1.176 1.201 Half long diagonal of thick rhombi(00110) 1.902 0.922 Half side length(01111) 3.078 0.343 Half short diagonal of thin rhombi

TABLE 1 Magnitudes and intensities of different Fourier coefficients of the decagonal quasiperiodicstructure

FIGURE 3 Conversion efficiencies of RGB light generation as a function of average input power

RV (01001). It was weakly focused bya 15 cm focal-lens that produced a fo-cal spot with a diameter of 180 µm.When the fundamental beam was at1.249 µm, 1.061 µm and 0.915 µm, re-spectively, the three primary colors weregenerated as their frequency doublings.In these processes the reciprocal vec-tors (01001), (00110) and (01111) wereindividually responsible for the phasematching. The length of RV (00110) islonger than that of (01001) by a factor of(1 +√

5)/2, and (01111) is equal to thesum of (00110) and (01001).

In Fig. 3, the average output poweras a function of average input poweris shown, in which squares, dots andtriangles represent the experimentalvalues of red light at 624.5 nm, greenat 530.5 nm and blue at 457.5 nm, re-spectively. The higher conversion effi-ciencies of 31.8% for the red, 29.6%for green and 11.3% for blue were gen-erated when the average input powerswere 2.44, 2.43 and 2.76 mW, respec-tively. In principle, the second harmonicconversion efficiency increases propor-tionally with the input power and occurswhen using a moderate input. How-ever, in our case the input powers werequite high, so that the harmonic outputs

could be affected by a number of fac-tors. The major factor can be attributedto back conversion, as pointed out byHanna [18]. Meanwhile, the divergenceof input light (a slightly focused beamwas used in our experiment) and thesmall irregular distribution of the re-versed domains (as shown in Fig. 1)could directly impact the phase match-ing condition. All of these result ina saturation effect of the second har-monic output at a higher input power.Such an effect has been observed inexperiments of periodic structures [18,19]. Even though the obtained conver-sion efficiency of blue light was aboutone order of magnitude higher thanpreviously recorded, it is still weakercompared with that of red and green.This may result from the followingtwo factors: the Fourier coefficient ofthe adopted reciprocal vectors and thepoled column diameter of the crystal,which are similar to the phenomenain the two-dimensional periodic poledLiNbO3 [15].

We measured the wavelength ac-ceptance bandwidths around 1.249,1.061 and 0.915 µm with an averagepower of 2.0 mW. The results are shownin Fig. 4. The FWHM of the experimen-

FIGURE 4 The wavelength-tuning responsearound (a) 1.249 µm, (b) 1.061 µm and (c)0.915 µm, respectively

tal curve is 2.0 nm, 1.3 nm and 0.8 nm,respectively.

Another benefit of the decagonalquasiperiodic scheme is that RGB lightcan be generated in multiple direc-

606 Applied Physics B – Lasers and Optics

tions, while only one direction wasavailable in cases of one-dimensionalsuperlattices. For decagonal quasiperi-odic structure, the unique property is itsequality against tenfold axis. The above-mentioned generation of RGB light canbe equally obtained when the crystalis rotated by integral multiples of π/5,which agrees well with the tenfold rota-tional symmetry of the two-dimensionaldecagonal superlattice.

3 Conclusions

In summary, we have demon-strated effective three primary colorscoherent radiation of red at 624.5 nm,green at 530.5 nm and blue at 457.5 nm,by frequency doublings in a decagonalquasiperiodic superlattice. The conver-sion efficiencies were 31.8% for the red,29.6% for the green and 11.3% for theblue. This scheme would be an attractive

way to obtain an effective RGB coherentsource.

ACKNOWLEDGEMENTS The au-thors acknowledge the National Natural ScienceFoundation of China for their financial support(Grant No. 10474135).

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