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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 17 — Aug. 18, 2008
  • pp: 12899–12904
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Fabrication of photonic crystals with functional defects by one-step holographic lithography

Juntao Li, Yikun Liu, Xiangsheng Xie, Peiqing Zhang, Bing Liang, Li Yan, Jianying Zhou, Gershon Kurizki, Daniel Jacobs, Kam Sing Wong, and Yongchun Zhong  »View Author Affiliations


Optics Express, Vol. 16, Issue 17, pp. 12899-12904 (2008)
http://dx.doi.org/10.1364/OE.16.012899


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Abstract

A one-step introduction of functional defects into a photonic crystal is demonstrated. By using a multi-beam phase-controlled holographic lithography, line-defects in a Bragg structure and embedded waveguides in a two-dimensional photonic crystal are fabricated. Intrinsic defect introduction into a 3-dimensional photonic crystal is also proposed. This technique gives rise to a substantial reduction of the fabrication complexity and a significant improvement on the accuracy of the functional defects in photonic crystals.

© 2008 Optical Society of America

1. Introduction

Photonic crystals (PhCs), proposed in 1987 [1

1. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987). [CrossRef] [PubMed]

, 2

2. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987). [CrossRef] [PubMed]

], have undergone rapid development in recent years. The generation of broadband short light pulses in hollow fibers [3

3. W.H. Reeves, D.V. Skryabin, F. Biancalana, J.C. Knight, P.St.J. Russell, F.G. Omenetto, A. Efimov, and A.J. Taylor, “Transformation and control of ultra-short pulses in dispersion-engineered photonic crystal fibres,” Nature 424, 511–515 (2003). [CrossRef] [PubMed]

], light localization and controlled emissions in PhCs [4

4. J.D. Joannopoulos, P.R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386, 143–149 (1997). [CrossRef]

], and integrated nano-photonics [5

5. R.G. Hunsperger, Integrated Optics (Springer-Verlag Berlin, Heidelberg, Germany, 2002).

] are among important applications of PhCs. These and many other applications require accurate introduction of defects into the PhCs materials, much in the same way as defects are introduced into the semiconductors. There has been a paramount need to develop means to incorporate functional defects directly into PhCs, both effectively and accurately [6

6. P.V. Braun, S.A. Rinne, and F. García-Santamaría, “Introducing defects in 3D photonic crystals: state of the art,” Adv. Mater. 18, 2665–2673 (2006). [CrossRef]

].

Multiple beam holographic lithography [7

7. M. Campbell, D.N. Sharp, M.T. Harrison, R.G. Denning, and A.J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404, 53–56 (2000). [CrossRef] [PubMed]

] has been widely employed to fabricate large size, defect-free PhC templates [8

8. L. Wu, Y. Zhong, C.T. Chen, K.S. Wong, and G.P. Wang, “Fabrication of large area two- and three-dimensional polymer photonic crystals using single refracting prism holographic lithography,” Appl. Phys. Lett. 86, 241102 (2005). [CrossRef]

]. Various techniques exist for introducing functional defects into PhCs generated by holographic lithography. One method is to introduce functional defects via laser writing, after the crystal has already been formed [9

9. N.D. Lai, W.P. Liang, J.H. Lin, and C.C. Hsu, “Rapid fabrication of large-area periodic structures containing well-defined defects by combining holography and mask techniques,” Opt. Express 13, 5331–5337 (2005). [CrossRef] [PubMed]

, 10

10. J. Scrimgeour, D.N. Sharp, C.F. Blanford, O.M. Roche, R.G. Denning, and A.J. Turberfield, “Threedimensional optical lithography for photonic microstructures,” Adv. Mater. 18, 1557–1560 (2006). [CrossRef]

]. However, this technique degrades the resolution and accuracy of the defect, and introduces a costly and complicated second step to the manufacturing process [6

6. P.V. Braun, S.A. Rinne, and F. García-Santamaría, “Introducing defects in 3D photonic crystals: state of the art,” Adv. Mater. 18, 2665–2673 (2006). [CrossRef]

].

Special PhC features can also be introduced in a single step, using multi-beam phase controlled interference holography. With this method, each of the interfering beams, which is large enough in transverse dimension to neglect the propagation diffraction, is controlled using variable phase retardation to determine the interference pattern. This is the space domain analogy of time domain pulse shaping, which was proposed to control physical and chemical processes sometime ago [11

11. A.M. Weiner, “Femtosecond pulse shaping using spatial light modulators” Rev. Sci. Instrum. 71, 1929–1960 (2000). [CrossRef]

], and has given rise to many significant innovations and developments in different branches of science and technology [12

12. H. Rabitz, R. de Vivie-Riedle, M. Motzkus, and K. Kompa, “Chemistry - Whither the future of controlling quantum phenomena?,” Science 288, 824–828 (2000). [CrossRef] [PubMed]

]. In previously reported works, both simulated numerically [13

13. J.W. Rinne and P. Wiltzius, “Design of holographic structures using genetic algorithms,” Opt. express 14, 9909–9916 (2006). [CrossRef] [PubMed]

] and demonstrated experimentally [14

14. T. Kondo, S. Juodkazis, V. Mizeikis, S. Matsuo, and H. Misawa, “Fabrication of three-dimensional periodic microstructures in photoresist SU-8 by phase-controlled holographic lithography,” New J. Phys. 8, 250 (2006). [CrossRef]

, 15

15. X.S. Xie, M. Li, J. Guo, B. Liang, Z.X. Wang, A. Sinistkii, Y. Xiang, and J.Y. Zhou, “Phase manipulated multi-beam holographic lithography for tunable optical lattices,” Opt. Express 15, 7032–7037 (2007). [CrossRef] [PubMed]

], phase control has been used to vary the space group of the generated intensity pattern.

Besides the multi-beam approach, an advanced phase-control holographic lithography has also been used to introduce defects into a PhC in a single step [16

16. S. Jeon, J. Park, R. Cirelli, S. Yang, C.E. Heitzman, P.V. Braun, P.J.A. Kenis, and J.A. Rogers, “Fabricating complex three-dimensional nanostructures with high-resolution conformable phase masks,” Proc. Natl. Acad. Sci. 101, 12428–12433 (2004). [CrossRef] [PubMed]

, 17

17. G. Lee, S.H. Song, C. Oh, and P. Kim, “Arbitrary structuring of two-dimensional photonic crystals by use of phase-only Fourier gratings,” Opt. Lett. 29, 2539–2541 (2004). [CrossRef] [PubMed]

]. This technique is based on the multi-beam diffraction in a phase mask, and it is sometimes called diffraction optical element (DOE). As a result, each pixel must be very small to produce effective diffraction, requiring thousands, even millions of pixels for incorporation defects into a PhC structure via holographic lithography. In this approach, the phase mask needs to have very fine scale in order to produce multiple higher-order diffraction beams. Furthermore, this approach is limited because a particular phase mask is suitable only for one particular structure; and the fabrication of the mask itself may be an extra burden compared with coherent multi-beam interference [16

16. S. Jeon, J. Park, R. Cirelli, S. Yang, C.E. Heitzman, P.V. Braun, P.J.A. Kenis, and J.A. Rogers, “Fabricating complex three-dimensional nanostructures with high-resolution conformable phase masks,” Proc. Natl. Acad. Sci. 101, 12428–12433 (2004). [CrossRef] [PubMed]

, 17

17. G. Lee, S.H. Song, C. Oh, and P. Kim, “Arbitrary structuring of two-dimensional photonic crystals by use of phase-only Fourier gratings,” Opt. Lett. 29, 2539–2541 (2004). [CrossRef] [PubMed]

]. Very recently, a tunable liquid-crystal spatial light modulator (LC-SLM) has been used to circumvent this problem in a similar experiment, which used holographic lithography to manufacture quasicrystals [18

18. G. Zito, B. Piccirillo, E. Santamato, A. Marino, V. Tkachenko, and G. Abbate, “Two-dimensional photonic quasicrystals by single beam computer-generated holography,” Opt. Express 16, 5164–5170 (2008). [CrossRef] [PubMed]

].

In this communication, we report the demonstration of a novel and simple method of one-step introduction of a functional defect into a PhC using multi-beam phase-controlled holographic lithography. A tunable LC-SLM is introduced to control the phases of the multiple beamlets, making the light intensity distribution dynamically reconfigurable; and a genetic algorithm (GA) [19

19. M. Mitchell, An Introduction to Genetic Algorithms (MIT Press, Cambridge, Massachusetts1996).

] is used to find an amplitude and a phase pattern that will achieve the desired optical intensity distribution with a relatively low number of beamlets. This method has the following merits compared to previously employed techniques used to manufacture functional defects in PhCs: (I) far fewer beamlets are employed to insert defects (tens, as opposed to thousands), (II) the LC-SLM means that different PhCs can be quickly manufactured without having to go through an etching process to build a new phase mask.

We fabricated a line-defect in a one-dimensional (1-D) Bragg structure and an embedded waveguide in a two-dimensional (2-D) PhC structure. We also show that more complicated defects in three-dimensional (3-D) PhCs can be achieved. With this multi-beam phase-controlled technique, the defects are intrinsically and conveniently introduced into a PhC.

2. Design and experiment

Holographic lithography is based on the recording of an intensity pattern produced by multi-beam interference. The interference intensity pattern is given by [20

20. L.Z. Cai, X.L. Yang, and Y.R. Wang, “Formation of a microfiber bundle by interference of three noncoplanar beams,” Opt. Lett. 26, 1858–1860 (2001). [CrossRef]

]

I(r,t)=<inEi2>+i<jn2Ei·Ejcos((kikj)·r+(φiφj)),
(1)

with i, j denoting different light beams. E i and φi are the electric field and the initial phase of the beams respectively, and k i is the wave vector. The laser interference pattern can be controlled by changing the polarization and amplitude of E i, the wave vector ki, as well as the phase φi for each of the input light beams. In order to simulate the intensity pattern recorded in the photoresist material-SU8, the effects of the refraction and 40% film shrinkage in axial direction of SU8 are considered in the following simulating [21

21. X. Zhu, Y. Xu, and S. Yang, “Distortion of 3D SU8 Photonic Structures Fabricated by Four-beam Holographic Lithography with Umbrella Configuration”, Opt. Express 15, 16546–16560 (2007). [CrossRef] [PubMed]

]. The GA is used to find the set of E i and φi values that generates the desired multi-beam interference intensity pattern.

Fig. 1. (a) Experimental setup for creating phase-controlled holographic intensity pattern. The beamlets mask setup in front of the LC-SLM for (b) 1-D and (c) 2-D interference patterns. The expanded laser beam is divided into multiple beamlets that pass through or are blocked off the pixel regions 1–9. The arrows represent the polarization of the beams that pass through the mask.

The experimental setup is shown in Fig. 1. The output beam from a continuous-wave Nd:YVO4 laser at 532 nm and with power of 120 mW was divided with a mask to multiple beamlets. The multiple beamlets then passed through a LC-SLM [22

22. A.M. Weiner, D.E. Leaird, J.S. Patel, and J.R. Wullert, “Programmable shaping of femtosecond optical pulses by use of 128-element liquid crystal phase modulator,” IEEE J. Quantum Electron. 28, 908–920 (1992). [CrossRef]

] with each unit pixel area of 2 mm×2 mm. The LC-SLM provides a pixel-dependent arbitrarily phase variable for each beamlets, which was controlled through a multi-channel voltage control unit. The multiple parallel beams were focused with a lens to generate phase-dependent wave-vectors of different directions, and then interfered in the focus region to provide an intensity pattern for holographic lithography. A microscope and a CCD detector were used to monitor the intensity distribution, thereby examing the formation of hologram. The samples used to record the periodic structures were glass substrates coated with photoresist, which contained the resin Epon-SU8 (from Shelld). The exposure time is about 30 s and the processing procedures can be found in Ref. 8

8. L. Wu, Y. Zhong, C.T. Chen, K.S. Wong, and G.P. Wang, “Fabrication of large area two- and three-dimensional polymer photonic crystals using single refracting prism holographic lithography,” Appl. Phys. Lett. 86, 241102 (2005). [CrossRef]

.

A GA is employed to obtain the desired interference fringes for holographic lithography. The “chromosome” is an encoded binary string which includes the values of both the amplitudes E i and the phase φi, where E i is 0 or 1 and φi is arbitrarily changed from 0 to 2π. The polarization of Ei is chosen prior to the simulation (Fig. 1(b)). GAs are good at finding approximations in a wide variety of complex optimization problems and have already been successfully implemented in holographic lithography [13

13. J.W. Rinne and P. Wiltzius, “Design of holographic structures using genetic algorithms,” Opt. express 14, 9909–9916 (2006). [CrossRef] [PubMed]

] and waveguide design [23

23. L. Sanchis, A. Hakansson, D. López-Zanón, J. Bravo-Abad, and J. Sáchez-Dehesa, “Integrated optical devices design by genetic algorithm,” Appl. Phys. Lett. 84, 4460–4462 (2004). [CrossRef]

]. As a notable example, we demonstrate the periodical removal of a line in a 1-D Bragg structure, using an interference pattern discovered by our GA. The target structure is set to produce a line defect in every 4 periods of a Bragg structure. The basic Bragg structure can be achieved by the interference of beam 2 and beam 7 in the mask (Fig. 1(b)). The periodic defect structure can be produced by changing the amplitudes and phases of beams 1–8 via GA. The lattice constant of the defect periods is determined by the smallest wave-vector difference (e.g. the wave-vector difference between beam 2 and beam 3) in the transverse direction.

The GA works as follows. In the first step, chromosomes are randomly generated to form interference intensity patterns by Eq. (1). Then each pattern is compared with the target structure, which is measured with a fitness value defined from the average error between the calculated intensity distribution and the target distribution. The subsequent generations are produced repeatedly by copying, crossing over and mutating the chromosomes until a best fitness value is found [13

13. J.W. Rinne and P. Wiltzius, “Design of holographic structures using genetic algorithms,” Opt. express 14, 9909–9916 (2006). [CrossRef] [PubMed]

]. Using the GA simulation, the final interference pattern distribution is searched and the optimal field distribution is automatically obtained. The GA needs 50 generations and apopulation of 100 (5000 iterations) to reach the designated 1-D structure, with a few minutes of computing time by a personal computer. Note that there can be many possible sets of amplitudes and phases for matching the target. One of the possible simple arrangements of pixels is that the amplitudes of beams 4, 5 and 8 are set to be 0, i.e., pixels 4, 5 and 8 are blocked, and the phases of beams 1, 2, 3, 6, 7 are set to be π, 0, 0, π, 0, respectively (Fig. 1(b)). The intensity pattern gives a 97% match to the target, as shown in Fig. 2(a). It clearly shows that defect lines are introduced into a perfect periodical 1-D Bragg structure. The required experimental setup is simple and can be realized in practice.

Fig. 2. (a) The GA numerical simulation of the light intensity distribution in SU8 for a line defect in the Bragg structure generated by the beamlets mask in Fig. 1(b). One possible combination of the phases is π, 0, 0, π, 0, respectively, for the beamlets 1, 2, 3, 6 and 7. (b) The CCD-recorded intensity patterns in air for the structure. (c) SEM showing the top view of the structure after exposure of the light intensity pattern with a SU8 material by a lens of f=100 mm. Scale bars: 10 µm

With the LC-SLM for the phase control, we are able to generate the desired interference pattern, which is recorded with both a CCD detector and a photoresist material-SU8. Figure 2(b) shows the CCD-recorded intensity distribution, and Fig. 2(c) shows the image of scanning electron micrograph (SEM) of the structure produced in SU8.

The above input beams arrangement can be extended to create an embedded waveguide into a triangular 2-D PhC lattice. The 1D Bragg structure is produced by the interference of beams 2 and 7. A 2-D triangle structure is produced with additional beam 9, which interferes with beams 2 and 7 respectively. Following the same idea, we use non-vanishing amplitude beams 1–3, 6, and 7 to produce the line defect in Bragg structure, then add beam 9 to interfere with these beams to produce the line defect in the 2-D triangle PhC. The phases of beams 1–3, 6 and 7 are the same as in the setting for the 1-D defect PhC, and the phase of beam 9 is 0. Note that the intensity distribution is very similar to the structure of a 2-D PhC with a line defect [24

24. S.G. Johnson, P.R. Villeneuve, S. Fan, and J.D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62, 8212–8222 (2000). [CrossRef]

] and that the structure has a photonic band-gap [25

25. A. Matthews, X.-H. Wang, Y. Kivshar, and M. Gu, “Band-gap properties of two-dimensional low-index photonic crystals,” Appl. Phys. B 81, 189–192 (2005). [CrossRef]

]. Figure 3(b) shows the CCD-recorded intensity patterns, which are very similar to the numerically simulated intensity patterns shown in Fig. 3(a). The micro-structure of the exposed material is shown in the SEM in Fig. 3(c) by lens with f=100 mm, showing an accurately and conveniently fabricated PhCs template.

Fig. 3. (a) The simulated light intensity distribution in SU8 for a line defect in a 2-D triangle PhCs by the beamlets mask in Fig. 1(c). One possible combination of the phases is π, 0, 0, π, 0, 0, respectively, for the beamlets 1, 2, 3, 6, 7 and 9. (b) The CCD-recorded intensity patterns in air of the structure. (c) SEM showing the oblique view of the structure after exposure of the intensity pattern by a lens of f=100 mm. Scale bars: 10 µm.

The ratio of the defect period to the unit lattice period of the PhC is determined by the number of the pixels of the SLM, and a larger ratio can be produced with a finer LC-SLM with more variable pixels. As an example, we show a defect mode in every 8 periods of a 2-D square lattice obtained by a similar GA simulation (Fig. 4).

Fig. 4. (a) The beamlets mask setup for a line defect of every 8 periods in a 2-D square PhC. The focal length of the focusing lens used in simulation equals to 16 unit pixel of the LC-SLM. The phases of beams 1~10 are set to 0, 0.5π, 1.35π, π, 0.4π, 0, 0, 0.5π, 1.35π, π, respectively. The phase of beams 11~20 are the same as beams 1~10. The arrow represent the polarizations of the beams. (b) The simulated light intensity distribution in SU8.

Figure 5 (b) also shows the numerical simulation and the CCD recorded intensity patterns of an embedded plane defect in a 3-D Slanted Pore PhC (a diamond-like structure) [26

26. M. Deubel, M. Wegener, A. Kaso, and S. John, “Direct laser writing and characterization of “Slanted Pore” Photonic Crystals,” Appl. Phys. Lett. 85, 1895–1897 (2004). [CrossRef]

]. As shown in Fig. 5(a), the beamlets passing through the mask are focused by a focusing lens having numerical aperture NA=0.75. However, the limited aperture of the lens does not support an easy setup with a single focusing lens. Hence, in our experiment, two focusing lenses with f=100 mm were used to focus the beamlets of 1~6 and 7~12 respectively. Then these two light paths were overlapped at the focus region of each focusing lens with an angle equal to 98°.

Fig. 5. (a) The beamlets mask setup in front of the LC-SLM for an embedded plane defect in a 3-D Slanted Pore PhC. The focal length of the focusing lens used in simulation equals to 31 unit pixel of the LC-SLM. The phases of beams 1~12 are set to π, 0, 0, π, 0, 0, 0, 1.4π, 0.2π, 0, 0.4π, 1.2π, respectively. The two arrows represent the polarizations of the light beams 1~6 and 7~12 that pass through the mask. (b) The simulation and experiment result of light intensity distribution of the embedded plane defect. The perspective view of the 3-D structure in SU8 is shown at the left, its selected 2-D planes are shown in the middle, which can be viewed as a diamond like structure, and experimental CCD-recorded intensity patterns in air of the corresponding planes are shown at the right.

With more elaborated arrangement of beamlets and the polarization of the light source, more complex structures, such as line defects and point defects in 3-D PhCs with large ratio of the defect period to the base lattice period, can be obtained. In comparison to the defect structure extrinsically introduced into a PhC, the removal of a defect from the PhCs with the one-step holographic lithography will give rise to a much improved accuracy to the defect location as well as negligible disturbance to the PhC structure.

There are also some disadvantages of this experiment setup. First, the overall size of the light field distribution is limited by the focusing area of the lens, which is about 100 µm in diameter. Secondly, the fabricated structure with 5 µm period is still too large to produce a band gap in the telecommunication wavelength. One can use a lens with shorter focal length to obtain smaller period structure at a cost of the overall size of the light field distribution. In our simulation, defect PhCs with period less than 1 µm can be produced by a focusing lens with NA=0.35 (Fig. 4). A 2-D line defect with 3 µm period (not shown here) was also fabricated. We believe that the above limitations can be overcome by using umbrella setups based on the DOE [14

14. T. Kondo, S. Juodkazis, V. Mizeikis, S. Matsuo, and H. Misawa, “Fabrication of three-dimensional periodic microstructures in photoresist SU-8 by phase-controlled holographic lithography,” New J. Phys. 8, 250 (2006). [CrossRef]

] to fabricate a PhC with a much larger size.

3. Conclusion

In conclusion, we demonstrate that multi-beam phase-controlled holographic lithography can be used to fabricate functional defect PhCs structures. Examples of templates for line defects in a Bragg structure, embedded waveguides in a 2-D PhC and embedded plane defect in a 3-D Slanted Pore PhC are presented. We believe that the phase-, amplitude- and polarization-controlled multi-beam holographic lithography will have immediate impact on the fabrication of 1-D, 2-D and 3-D PhCs with functional defects.

Acknowledgments

The authors thank Dr. Y. Xiang for providing the liquid crystal modulator and Y.M. Liang and Y.F. Guan for designing and testing of the power supply driving units. This work is supported by the National Key Basic Research Special Foundation (G2004CB719805), Chinese National Natural Science Foundation (60677051, 10774193). GK and DJ are supported by EC (MIDAS STREP) and DIP. KSW and YZ are partially supported by Research Grants Council of Hong Kong (grant number 603507).

References and Links

1.

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987). [CrossRef] [PubMed]

2.

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987). [CrossRef] [PubMed]

3.

W.H. Reeves, D.V. Skryabin, F. Biancalana, J.C. Knight, P.St.J. Russell, F.G. Omenetto, A. Efimov, and A.J. Taylor, “Transformation and control of ultra-short pulses in dispersion-engineered photonic crystal fibres,” Nature 424, 511–515 (2003). [CrossRef] [PubMed]

4.

J.D. Joannopoulos, P.R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386, 143–149 (1997). [CrossRef]

5.

R.G. Hunsperger, Integrated Optics (Springer-Verlag Berlin, Heidelberg, Germany, 2002).

6.

P.V. Braun, S.A. Rinne, and F. García-Santamaría, “Introducing defects in 3D photonic crystals: state of the art,” Adv. Mater. 18, 2665–2673 (2006). [CrossRef]

7.

M. Campbell, D.N. Sharp, M.T. Harrison, R.G. Denning, and A.J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404, 53–56 (2000). [CrossRef] [PubMed]

8.

L. Wu, Y. Zhong, C.T. Chen, K.S. Wong, and G.P. Wang, “Fabrication of large area two- and three-dimensional polymer photonic crystals using single refracting prism holographic lithography,” Appl. Phys. Lett. 86, 241102 (2005). [CrossRef]

9.

N.D. Lai, W.P. Liang, J.H. Lin, and C.C. Hsu, “Rapid fabrication of large-area periodic structures containing well-defined defects by combining holography and mask techniques,” Opt. Express 13, 5331–5337 (2005). [CrossRef] [PubMed]

10.

J. Scrimgeour, D.N. Sharp, C.F. Blanford, O.M. Roche, R.G. Denning, and A.J. Turberfield, “Threedimensional optical lithography for photonic microstructures,” Adv. Mater. 18, 1557–1560 (2006). [CrossRef]

11.

A.M. Weiner, “Femtosecond pulse shaping using spatial light modulators” Rev. Sci. Instrum. 71, 1929–1960 (2000). [CrossRef]

12.

H. Rabitz, R. de Vivie-Riedle, M. Motzkus, and K. Kompa, “Chemistry - Whither the future of controlling quantum phenomena?,” Science 288, 824–828 (2000). [CrossRef] [PubMed]

13.

J.W. Rinne and P. Wiltzius, “Design of holographic structures using genetic algorithms,” Opt. express 14, 9909–9916 (2006). [CrossRef] [PubMed]

14.

T. Kondo, S. Juodkazis, V. Mizeikis, S. Matsuo, and H. Misawa, “Fabrication of three-dimensional periodic microstructures in photoresist SU-8 by phase-controlled holographic lithography,” New J. Phys. 8, 250 (2006). [CrossRef]

15.

X.S. Xie, M. Li, J. Guo, B. Liang, Z.X. Wang, A. Sinistkii, Y. Xiang, and J.Y. Zhou, “Phase manipulated multi-beam holographic lithography for tunable optical lattices,” Opt. Express 15, 7032–7037 (2007). [CrossRef] [PubMed]

16.

S. Jeon, J. Park, R. Cirelli, S. Yang, C.E. Heitzman, P.V. Braun, P.J.A. Kenis, and J.A. Rogers, “Fabricating complex three-dimensional nanostructures with high-resolution conformable phase masks,” Proc. Natl. Acad. Sci. 101, 12428–12433 (2004). [CrossRef] [PubMed]

17.

G. Lee, S.H. Song, C. Oh, and P. Kim, “Arbitrary structuring of two-dimensional photonic crystals by use of phase-only Fourier gratings,” Opt. Lett. 29, 2539–2541 (2004). [CrossRef] [PubMed]

18.

G. Zito, B. Piccirillo, E. Santamato, A. Marino, V. Tkachenko, and G. Abbate, “Two-dimensional photonic quasicrystals by single beam computer-generated holography,” Opt. Express 16, 5164–5170 (2008). [CrossRef] [PubMed]

19.

M. Mitchell, An Introduction to Genetic Algorithms (MIT Press, Cambridge, Massachusetts1996).

20.

L.Z. Cai, X.L. Yang, and Y.R. Wang, “Formation of a microfiber bundle by interference of three noncoplanar beams,” Opt. Lett. 26, 1858–1860 (2001). [CrossRef]

21.

X. Zhu, Y. Xu, and S. Yang, “Distortion of 3D SU8 Photonic Structures Fabricated by Four-beam Holographic Lithography with Umbrella Configuration”, Opt. Express 15, 16546–16560 (2007). [CrossRef] [PubMed]

22.

A.M. Weiner, D.E. Leaird, J.S. Patel, and J.R. Wullert, “Programmable shaping of femtosecond optical pulses by use of 128-element liquid crystal phase modulator,” IEEE J. Quantum Electron. 28, 908–920 (1992). [CrossRef]

23.

L. Sanchis, A. Hakansson, D. López-Zanón, J. Bravo-Abad, and J. Sáchez-Dehesa, “Integrated optical devices design by genetic algorithm,” Appl. Phys. Lett. 84, 4460–4462 (2004). [CrossRef]

24.

S.G. Johnson, P.R. Villeneuve, S. Fan, and J.D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62, 8212–8222 (2000). [CrossRef]

25.

A. Matthews, X.-H. Wang, Y. Kivshar, and M. Gu, “Band-gap properties of two-dimensional low-index photonic crystals,” Appl. Phys. B 81, 189–192 (2005). [CrossRef]

26.

M. Deubel, M. Wegener, A. Kaso, and S. John, “Direct laser writing and characterization of “Slanted Pore” Photonic Crystals,” Appl. Phys. Lett. 85, 1895–1897 (2004). [CrossRef]

OCIS Codes
(090.0090) Holography : Holography
(230.7370) Optical devices : Waveguides
(260.3160) Physical optics : Interference
(160.5298) Materials : Photonic crystals

ToC Category:
Materials

History
Original Manuscript: June 30, 2008
Revised Manuscript: July 23, 2008
Manuscript Accepted: August 6, 2008
Published: August 8, 2008

Citation
Juntao Li, Yikun Liu, Xiangsheng Xie, Peiqing Zhang, Bing Liang, Li Yan, Jianying Zhou, Gershon Kurizki, Daniel Jacobs, Kam Sing Wong, and Yongchun Zhong, "Fabrication of photonic crystals with functional defects by one-step holographic lithography," Opt. Express 16, 12899-12904 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-17-12899


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