Abstract

A microfabricated compound eye, comparable to a natural compound eye shows a spherical arrangement of integrated optical units called artificial ommatidia. Each consists of a self-aligned microlens and waveguide. The increase of waveguide length is imperative to obtain high resolution images through an artificial compound eye for wide field-of -view imaging as well as fast motion detection. This work presents an effective method for increasing the waveguide length of artificial ommatidium using a laser induced self-writing process in a photosensitive polymer resin. The numerical and experimental results show the uniform formation of waveguides and the increment of waveguide length over 850 µm.

© 2009 Optical Society of America

1. Introduction

A recently developed artificial compound eye (ACE) has a huge potential for a wide field-of-view imaging and fast motion detection in a small form factor [1, 2]. A natural compound eye consists of a number of photoreception units called by ommatidia. Each single ommatidium comprises a light-diffracting facet lens, a crystalline cone, a light-guiding rhabdom, and photoreceptor cells. A single ommatidium can be anatomically and optically mimicked by a self-aligned microlens and waveguide as shown in Fig. 1(a). The integrated optical unit can also offer small angular acceptance similar to that of a natural ommatidium due to the lens-waveguide coupling theory [3, 4]. Herein, high coupling efficiency between a microlens and a waveguide was demonstrated by a microlens-induced self-writing process in a photosensitive polymer resin. However, the waveguide length is still not enough for high resolution and wide field-of-view imaging through an ACE due to UV exposure with polychromatic light source [1]. The spatial profiles coming from the short waveguides become broaden and then result in image blurring on image sensor arrays. On the other hand, longer waveguides secure the narrow spatial profiles all the way down to the image sensor arrays and enable high resolution imaging through an ACE as shown in Fig. 1(b). In a variety of photosensitive polymer resins, the formation of a self-written waveguide to tens of millimeters in length has been successfully demonstrated by a laser induced self-writing process. However, a liquid-phase cladding surrounding a solid-phase core restricts the practical use in integrated optoelectronic applications [59]. This work will introduce a laser-induced and microlens-assisted self-writing process for creating solid-phased waveguide structures with long waveguide length for high resolution artificial compound eye optical systems.

 

Fig. 1. A schematic diagram of (a) a single ommatidium as an optical unit of an artificial compound eye and (b) the effect of the waveguide length for high resolution wide field-of-view imaging through an artificial compound eye.

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2. Numerical analysis of a laser induced self-writing process

The limitation in the growth of waveguide length in an ACE results from incoherence nature of light from a mercury lamp. Polychromatic waves passing through a microlens are focused at different positions due to chromatic dispersion. The absorption coefficient of a photosensitive polymer resin varies with wavelength [10]. Depending on wavelength, the light is focused at slightly different positions and individual wavelength induces self-focusing under UV exposure over the threshold dose due to local index change. In the early stage of self-focusing with polychromatic light, shorter wavelength with higher absorption contributes to self-focusing followed by longer wavelengths. Incoherence of the self-focusing events by polychromatic waves results in broadening waveguide diameter as well as restricting the waveguide length [11]. In particular, a self-written waveguide induced by the shorter wavelength with higher absorption may disturb that of the longer wavelength and eventually result in high coupling loss between a microlens and a waveguide as well as more diffraction. On the other hand, a monochromatic and coherent light maximizes the irradiation energy at a single focal point of a microlens and it also secures the uniform intensity distribution during UV exposure. Therefore, a laser as a light source helps obtain uniform and long waveguides inside an ACE.

 

Fig. 2. FD-BPM analysis of a coherent light based self-writing process in SU-8 with respect to different UV exposure energy: (a) Exposure energy: 3Eth (b) Exposure energy: 9Eth (c) Exposure energy: 18Eth.

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A FD-BPM (finite difference-beam propagation method) based numerical analysis, which deals with interaction between the refractive index and phase of light over spatial propagation with time, shows that a laser induced self-writing process effectively increases the waveguide length in a photosensitive polymer (SU-8 2050, MicroChem). For the numerical analysis of a self-writing process in a photosensitive polymer resin, a polymer model as described in earlier work is used as follows [5].

Δn(x,y,z,t)=Δn0{1exp[1U00tτE(t)2dt]}

, where Δn′ is the refractive index difference due to photo-crosslinking and, Δn0′ is the saturation value of the refractive index, U0 is the critical exposure energy for polymerization, t is the exposure duration, τ is the radical lifetime of a monomer and |E(t)| is the amplitude of the electric field. The initial refractive index and saturation index for a UV sensitive polymer model are set by 1.584 and 1.605, respectively [1]. The absorption coefficient is also set by 0.001 µm-1 at a wavelength of 380 nm [10].

Figure 2 demonstrates the waveguide formation assisted by a microlens, depending on UV exposure dose (λ=377 nm). It is clearly shown that the length of a polymer waveguide self-written by the local change in refractive index increases with exposure dose. UV light impinges onto a microlens made of a photosensitive polymer resin, over the threshold energy (Eth), self-focusing due to local index change starts at the focal point of the microlens. The polymer portion with locally high index corresponds to the core of the polymer waveguide. The waveguide length significantly increases up to the penetration depth of the polymer resin. In the numerical analysis, a self-writing process was conducted by 1 mm in propagation direction and thermal diffusion during exposure is not considered in the analysis. The result also shows the effect of waveguide length for high resolution imaging using a compound eye. The electric field magnitudes and spatial distributions are calculated at the position of 800 µm apart from microlens and significantly changed with waveguide length. The result explains that long waveguides contribute to spatial field confinement with high intensity and also prevent optical crosstalk with a neighbor waveguide for high resolution artificial compound eye optical systems.

3. Microfabrication process

For the long waveguide formation, a thick photosensitive polymer resin with microlens arrays is prepared by the following methods as outlined in Fig. 3. First, monolithic honeycomb packed photoresist (AZ1512, AZ Electronic Materials) microlens arrays (DL=28 µm, F/1.8) with low Fresnel number (NF<10) are fabricated by a resist melting process. The microlens template is replicated by polydimethylsiloxane (PDMS) elastomer after anti-stiction coating (IHP-1000, APP Co., Ltd.) and then polymer (SU-8 2050, MicroChem) microlens arrays are once again recast from the PDMS template. Finally, polymeric artificial ommatidia are formed by a self-writing process using UV laser light source with a wavelength of 377 nm (i-PULSE 375, TOPTICA Photonics AG).

 

Fig. 3. Microfabrication procedures of artificial ommatidia in a UV sensitive polymer resin (SU-8).

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4. Experimental results and discussion

The beam propagation through the microfabricated artificial ommatidia was characterized with a modified confocal laser scanning microscope under the illumination of 532 nm as described in the previous work [1]. Note that the optical characterization was done by coupling a light of 532 nm through the self-aligned microlens and waveguide, while the waveguides were self-written by 377 nm. Figure 4 shows the comparison of 3D optical sectioning images with the beam propagation of visible light between through self-aligned microlens and waveguide arrays and only through microlens arrays. The lateral optical sections of 75 µm x 75 µm were stacked along the propagation direction (z-axis) over a range of 500 µm with the interval of 5 µm. The lateral intensity distributions at three different positions (z=100 µm, 200 µm and 300 µm) are also shown. It is demonstrated that the incident beam impinged on the microlens is coupled and then propagated through the waveguide. The measured coupling loss between a microlens and a waveguide is 0.22 dB, which is defined by the ratio of areal intensity at the focal plane of the microlens to that at the waveguide core located at a distance z=100 µm from the microlens focus. In contrast, the beam impinged on a microlens without a self-written waveguide severely diffracts. Especially for a self-aligned microlens and waveguide, the result also shows that the focal length of the microlens increases due to the formation of a polymer cone during the self-writing process. In other words, local polymerization by focused UV light starts to increase the refractive index and therefore the focal length increases until the complete formation of the waveguide.

 

Fig. 4. 3D optical sectioning of coupled light (λ=532 nm) using a modified confocal laser scanning microscopy through (a) only microlenses and (b) self-aligned microlens and waveguides.

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The waveguide length and diameter were measured at half-maximum of the peak intensity and 1/e2 of the peak intensity of the coupled laser light (λ=532 nm), respectively. Figure 5 demonstrates the waveguide length increases under different UV exposure dose (λ=377 nm) with a constant irradiation power (100 µW) in SU-8. The optical characterization was done by coupling a visible light (λ=532 nm) through the self-aligned microlens and waveguide with a modified confocal laser scanning microscope. Below the threshold energy of UV exposure the visible light impinged onto microlens severely diffracts due to lack of the waveguide. However, above the threshold energy, the self-focusing overcomes the light diffraction through a microlens and then forms the waveguide with constant diameter in the SU-8 polymer resin. Consequently, it also suppresses the mutual diffraction between microlenses. The results obviously show the waveguide length increases over 500 µm with the exposure dose of 152.6 mJ·cm-2 under the constant UV irradiation power.

 

Fig. 5. Longitudinal increment of microlens induced self-written waveguides exposed by different exposure doses under a constant irradiation power.

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Figure 6 shows the effects of irradiation laser power and exposure dose on the waveguide lengths and core diameters of the SU-8 self-written waveguides. The experiment was conducted with two different modes: the first mode was done by a constant exposure power (100 µW) with different exposure durations of 4~84 sec, i.e., UV energy of 12.7 mJ·cm-2 to 267.1 mJ·cm-2 and the second mode was done by a constant exposure dose (76.2 mJ·cm-2) with different powers of 70~1200 µW, i.e., UV irradiation intensities of 2.2 mW·cm-2 to 38.2 mW·cm-2. The evolution of the waveguide length and core diameter under two modes was compared in detail.

In the constant exposure power mode, the increment of waveguide length is more sensitive to the exposure duration, compared to that of waveguide diameter. The results show the waveguide length increases from 80 µm to 850 µm, which only results from the physical limit of the prepared polymer resin thickness. The exposure dose for the maximum length corresponds to 267.1 mJ·cm-2 under a constant UV irradiation power of 100 µW. The waveguide diameter also increases with exposure duration but the increment becomes saturated at the exposure dose above 150 mJ·cm-2. The saturated diameter is about 9.5 µm, which is determined at the 1/e2 of the maximum output intensity. The results summarize the control of exposure duration under a constant power helps increase waveguide length without the enlargement of waveguide diameter. The numerical result also shows the waveguide increases up to 1 mm in length due to the limit of the penetration depth of UV light at 377 nm in SU-8.

In the constant exposure dose mode, the increase of irradiation power also affects the physical dimensions of the self-written waveguide. Under the exposure dose of 76.2 mJ·cm-2 over threshold energy, both the length and diameter of a waveguide increase with irradiation power. Particularly, the waveguide diameter keeps broadening up to 11 µm at the irradiation power of 1200 µW. Unlike the first mode, the second mode shows the further increment of the diameter, which seems due to thermal diffusion of the photo-acid generator in SU-8 or high order nonlinear terms in the refractive index under the relatively high power irradiation.

In summary, the increase of the exposure duration under a constant low irradiation laser power is more desirable for achieving the long waveguide formation during a self-writing process since it can minimize coupling with the increment of the diameter.

 

Fig. 6. The effects of exposure dose and irradiation power on thewaveguide lengths and core diameters of self-written waveguides: (a) the length and diameter of a self-written waveguide (b) different exposure durations under a constant exposure power, and (c) different irradiation powers under a constant exposure dose.

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6. Conclusion

This work demonstrates an effective method for increasing the waveguide length over 850 µm in an artificial ommatidium with a laser-induced and microlens-assisted self-writing process. From the experimental results, the control of exposure duration under a constant low laser power is more desirable for achieving long waveguides without the increment of waveguide diameter. This method will be employed with spherical arrangements to obtain wide FOV image with high resolution through an ACE in the near future.

Acknowledgements

This work was supported by the Korea Science and Engineering Foundation (KOSEF) grant funded by the Korea government (MOST) (No. 2008-2003551).

References and links

1. K. H. Jeong, J. Kim, and L. P. Lee, “Biologically inspired artificial compound eyes,” Science 312, 557–561 (2006). [CrossRef]   [PubMed]  

2. L. P. Lee and R. Szema, “Inspirations from biological optics for advanced photonic systems,” Science 310, 1148–1150 (2005). [CrossRef]   [PubMed]  

3. D. G. Stavenga, “Angular and spectral sensitivity of fly photoreceptors. I. Integrated facet lens and rhabdomere optics,” J. Comp. Physiol. A 189, 1–17 (2003).

4. J. Y. Kim, K. H. Jeong, and L. P. Lee, “Artificial ommatidia by self-aligned microlenses and waveguides,” Opt. Lett. 30, 5–7 (2005). [CrossRef]   [PubMed]  

5. A. S. Kewitsch and A. Yariv, “Self-focusing and self-trapping of optical beams upon photopolymerization,” Opt. Lett. 21, 24–26 (1996). [CrossRef]   [PubMed]  

6. S. Shoji and S. Kawata, “Optically-induced growth of fiber patterns into a photopolymerizable resin,” Appl. Phys. Lett. 75, 737–739 (1999). [CrossRef]  

7. K. Dorkenoo, O. Cregut, L. Mager, F. Gillot, C. Carre, and A. Fort, “Quasi-solitonic behavior of self-written waveguides created by photopolymerization,” Opt. Lett. 27, 1782–1784 (2002). [CrossRef]  

8. R. Bachelot, C. Ecoffet, D. Deloeil, P. Royer, and D. J. Lougnot, “Integration of micrometer-sized polymer elements at the end of optical fibers by free-radical photopolymerization,” Appl. Opt. 40, 5860–5871 (2001). [CrossRef]  

9. A. B. Villafranca and K. Saravanamuttu, “An Experimental Study of the Dynamics and Temporal Evolution of Self-Trapped Laser Beams in a Photopolymerizable Organosiloxane,” J. Phys. Chem. C 112, 17388–17396 (2008). [CrossRef]  

10. Z. G. Ling, K. Lian, and L. Jian, “Improved patterning quality of SU-8 microstructures by optimizing the exposure parameters, Proc. SPIE 3999, 1019–1027 (2000). [CrossRef]  

11. J. H. Zhang and K. Saravanamuttu, “The dynamics of self-trapped beams of incoherent white light in a free-radical photopolymerizable medium,” J. Am. Chem. Soc. 128, 14913–14923 (2006). [CrossRef]   [PubMed]  

References

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  1. K. H. Jeong, J. Kim, and L. P. Lee, "Biologically inspired artificial compound eyes," Science 312, 557-561 (2006).
    [CrossRef] [PubMed]
  2. L. P. Lee and R. Szema, "Inspirations from biological optics for advanced photonic systems," Science 310, 1148-1150 (2005).
    [CrossRef] [PubMed]
  3. D. G. Stavenga, "Angular and spectral sensitivity of fly photoreceptors. I. Integrated facet lens and rhabdomere optics," J. Comp. Physiol. A 189, 1-17 (2003).
  4. J. Y. Kim, K. H. Jeong, and L. P. Lee, "Artificial ommatidia by self-aligned microlenses and waveguides," Opt. Lett. 30, 5-7 (2005).
    [CrossRef] [PubMed]
  5. A. S. Kewitsch and A. Yariv, "Self-focusing and self-trapping of optical beams upon photopolymerization," Opt. Lett. 21, 24-26 (1996).
    [CrossRef] [PubMed]
  6. S. Shoji and S. Kawata, "Optically-induced growth of fiber patterns into a photopolymerizable resin," Appl. Phys. Lett. 75, 737-739 (1999).
    [CrossRef]
  7. K. Dorkenoo, O. Cregut, L. Mager, F. Gillot, C. Carre, and A. Fort, "Quasi-solitonic behavior of self-written waveguides created by photopolymerization," Opt. Lett. 27, 1782-1784 (2002).
    [CrossRef]
  8. R. Bachelot, C. Ecoffet, D. Deloeil, P. Royer, and D. J. Lougnot, "Integration of micrometer-sized polymer elements at the end of optical fibers by free-radical photopolymerization," Appl. Opt. 40, 5860-5871 (2001).
    [CrossRef]
  9. A. B. Villafranca, and K. Saravanamuttu, "An Experimental Study of the Dynamics and Temporal Evolution of Self-Trapped Laser Beams in a Photopolymerizable Organosiloxane," J. Phys. Chem. C 112, 17388-17396 (2008).
    [CrossRef]
  10. Z. G. Ling, K. Lian, and L. Jian, "Improved patterning quality of SU-8 microstructures by optimizing the exposure parameters, Proc. SPIE 3999,1019-1027 (2000).
    [CrossRef]
  11. J. H. Zhang and K. Saravanamuttu, "The dynamics of self-trapped beams of incoherent white light in a free-radical photopolymerizable medium," J. Am. Chem. Soc. 128, 14913-14923 (2006).Q1
    [CrossRef] [PubMed]

2006 (2)

K. H. Jeong, J. Kim, and L. P. Lee, "Biologically inspired artificial compound eyes," Science 312, 557-561 (2006).
[CrossRef] [PubMed]

J. H. Zhang and K. Saravanamuttu, "The dynamics of self-trapped beams of incoherent white light in a free-radical photopolymerizable medium," J. Am. Chem. Soc. 128, 14913-14923 (2006).Q1
[CrossRef] [PubMed]

2005 (2)

L. P. Lee and R. Szema, "Inspirations from biological optics for advanced photonic systems," Science 310, 1148-1150 (2005).
[CrossRef] [PubMed]

J. Y. Kim, K. H. Jeong, and L. P. Lee, "Artificial ommatidia by self-aligned microlenses and waveguides," Opt. Lett. 30, 5-7 (2005).
[CrossRef] [PubMed]

2003 (1)

D. G. Stavenga, "Angular and spectral sensitivity of fly photoreceptors. I. Integrated facet lens and rhabdomere optics," J. Comp. Physiol. A 189, 1-17 (2003).

2002 (1)

2001 (1)

2000 (2)

A. B. Villafranca, and K. Saravanamuttu, "An Experimental Study of the Dynamics and Temporal Evolution of Self-Trapped Laser Beams in a Photopolymerizable Organosiloxane," J. Phys. Chem. C 112, 17388-17396 (2008).
[CrossRef]

Z. G. Ling, K. Lian, and L. Jian, "Improved patterning quality of SU-8 microstructures by optimizing the exposure parameters, Proc. SPIE 3999,1019-1027 (2000).
[CrossRef]

1999 (1)

S. Shoji and S. Kawata, "Optically-induced growth of fiber patterns into a photopolymerizable resin," Appl. Phys. Lett. 75, 737-739 (1999).
[CrossRef]

1996 (1)

Bachelot, R.

Carre, C.

Cregut, O.

Deloeil, D.

Dorkenoo, K.

Ecoffet, C.

Fort, A.

Gillot, F.

Jeong, K. H.

K. H. Jeong, J. Kim, and L. P. Lee, "Biologically inspired artificial compound eyes," Science 312, 557-561 (2006).
[CrossRef] [PubMed]

J. Y. Kim, K. H. Jeong, and L. P. Lee, "Artificial ommatidia by self-aligned microlenses and waveguides," Opt. Lett. 30, 5-7 (2005).
[CrossRef] [PubMed]

Jian, L.

Z. G. Ling, K. Lian, and L. Jian, "Improved patterning quality of SU-8 microstructures by optimizing the exposure parameters, Proc. SPIE 3999,1019-1027 (2000).
[CrossRef]

Kawata, S.

S. Shoji and S. Kawata, "Optically-induced growth of fiber patterns into a photopolymerizable resin," Appl. Phys. Lett. 75, 737-739 (1999).
[CrossRef]

Kewitsch, A. S.

Kim, J.

K. H. Jeong, J. Kim, and L. P. Lee, "Biologically inspired artificial compound eyes," Science 312, 557-561 (2006).
[CrossRef] [PubMed]

Kim, J. Y.

Lee, L. P.

K. H. Jeong, J. Kim, and L. P. Lee, "Biologically inspired artificial compound eyes," Science 312, 557-561 (2006).
[CrossRef] [PubMed]

L. P. Lee and R. Szema, "Inspirations from biological optics for advanced photonic systems," Science 310, 1148-1150 (2005).
[CrossRef] [PubMed]

J. Y. Kim, K. H. Jeong, and L. P. Lee, "Artificial ommatidia by self-aligned microlenses and waveguides," Opt. Lett. 30, 5-7 (2005).
[CrossRef] [PubMed]

Lian, K.

Z. G. Ling, K. Lian, and L. Jian, "Improved patterning quality of SU-8 microstructures by optimizing the exposure parameters, Proc. SPIE 3999,1019-1027 (2000).
[CrossRef]

Ling, Z. G.

Z. G. Ling, K. Lian, and L. Jian, "Improved patterning quality of SU-8 microstructures by optimizing the exposure parameters, Proc. SPIE 3999,1019-1027 (2000).
[CrossRef]

Lougnot, D. J.

Mager, L.

Royer, P.

Saravanamuttu, K.

J. H. Zhang and K. Saravanamuttu, "The dynamics of self-trapped beams of incoherent white light in a free-radical photopolymerizable medium," J. Am. Chem. Soc. 128, 14913-14923 (2006).Q1
[CrossRef] [PubMed]

A. B. Villafranca, and K. Saravanamuttu, "An Experimental Study of the Dynamics and Temporal Evolution of Self-Trapped Laser Beams in a Photopolymerizable Organosiloxane," J. Phys. Chem. C 112, 17388-17396 (2008).
[CrossRef]

Shoji, S.

S. Shoji and S. Kawata, "Optically-induced growth of fiber patterns into a photopolymerizable resin," Appl. Phys. Lett. 75, 737-739 (1999).
[CrossRef]

Stavenga, D. G.

D. G. Stavenga, "Angular and spectral sensitivity of fly photoreceptors. I. Integrated facet lens and rhabdomere optics," J. Comp. Physiol. A 189, 1-17 (2003).

Szema, R.

L. P. Lee and R. Szema, "Inspirations from biological optics for advanced photonic systems," Science 310, 1148-1150 (2005).
[CrossRef] [PubMed]

Villafranca, A. B.

A. B. Villafranca, and K. Saravanamuttu, "An Experimental Study of the Dynamics and Temporal Evolution of Self-Trapped Laser Beams in a Photopolymerizable Organosiloxane," J. Phys. Chem. C 112, 17388-17396 (2008).
[CrossRef]

Yariv, A.

Zhang, J. H.

J. H. Zhang and K. Saravanamuttu, "The dynamics of self-trapped beams of incoherent white light in a free-radical photopolymerizable medium," J. Am. Chem. Soc. 128, 14913-14923 (2006).Q1
[CrossRef] [PubMed]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

S. Shoji and S. Kawata, "Optically-induced growth of fiber patterns into a photopolymerizable resin," Appl. Phys. Lett. 75, 737-739 (1999).
[CrossRef]

J. Am. Chem. Soc. (1)

J. H. Zhang and K. Saravanamuttu, "The dynamics of self-trapped beams of incoherent white light in a free-radical photopolymerizable medium," J. Am. Chem. Soc. 128, 14913-14923 (2006).Q1
[CrossRef] [PubMed]

J. Comp. Physiol. A (1)

D. G. Stavenga, "Angular and spectral sensitivity of fly photoreceptors. I. Integrated facet lens and rhabdomere optics," J. Comp. Physiol. A 189, 1-17 (2003).

Opt. Lett. (3)

Proc. SPIE (2)

A. B. Villafranca, and K. Saravanamuttu, "An Experimental Study of the Dynamics and Temporal Evolution of Self-Trapped Laser Beams in a Photopolymerizable Organosiloxane," J. Phys. Chem. C 112, 17388-17396 (2008).
[CrossRef]

Z. G. Ling, K. Lian, and L. Jian, "Improved patterning quality of SU-8 microstructures by optimizing the exposure parameters, Proc. SPIE 3999,1019-1027 (2000).
[CrossRef]

Science (2)

K. H. Jeong, J. Kim, and L. P. Lee, "Biologically inspired artificial compound eyes," Science 312, 557-561 (2006).
[CrossRef] [PubMed]

L. P. Lee and R. Szema, "Inspirations from biological optics for advanced photonic systems," Science 310, 1148-1150 (2005).
[CrossRef] [PubMed]

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Figures (6)

Fig. 1.
Fig. 1.

A schematic diagram of (a) a single ommatidium as an optical unit of an artificial compound eye and (b) the effect of the waveguide length for high resolution wide field-of-view imaging through an artificial compound eye.

Fig. 2.
Fig. 2.

FD-BPM analysis of a coherent light based self-writing process in SU-8 with respect to different UV exposure energy: (a) Exposure energy: 3Eth (b) Exposure energy: 9Eth (c) Exposure energy: 18Eth.

Fig. 3.
Fig. 3.

Microfabrication procedures of artificial ommatidia in a UV sensitive polymer resin (SU-8).

Fig. 4.
Fig. 4.

3D optical sectioning of coupled light (λ=532 nm) using a modified confocal laser scanning microscopy through (a) only microlenses and (b) self-aligned microlens and waveguides.

Fig. 5.
Fig. 5.

Longitudinal increment of microlens induced self-written waveguides exposed by different exposure doses under a constant irradiation power.

Fig. 6.
Fig. 6.

The effects of exposure dose and irradiation power on thewaveguide lengths and core diameters of self-written waveguides: (a) the length and diameter of a self-written waveguide (b) different exposure durations under a constant exposure power, and (c) different irradiation powers under a constant exposure dose.

Equations (1)

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Δ n ( x , y , z , t ) = Δ n 0 { 1 exp [ 1 U 0 0 t τ E ( t ) 2 d t ] }

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