Diffraction gratings are among the most venerable tools of optical physics, with the first gratings produced in the mid-1700s. They are used in chemical analysis, astronomic spectroscopy, light-based communications, and other applications. Unlike a prism, diffraction gratings operate by interference effects as incident light impinges on rulings or grooves cut or etched onto the grating surface. Over the last 10 years, advances in fabrication techniques—many by our own group—have made possible gratings of unprecedented groove depth and density. These gratings offer new efficiencies, for example, in transmissivity, beam splitting, bandpass filtering, and polarization separation.
High density refers to the groove-to-groove distance or period. Groove depth is defined by the gratings' depth-to-period ratio. We reasoned that optimizing the groove depth to bring the grating period close to the wavelength of the incident light should enable novel functions. Our group faced two fundamental challenges concerning deep-etched, high-density gratings. The first was theoretical: How would such gratings perform? As a practical matter, only when we were fairly sure that the effort would produce useful new devices did we try to fabricate them. Fabrication was the second challenge. Which techniques and materials would be needed to make these gratings? We settled on fused silica, an excellent optical material with good thermal stability, high transmission at our wavelengths of interest, and a high laser-damage threshold. However, fused silica is hard and difficult to etch. Developing ways to work with it took considerable time and experimentation.
For the first challenge, it is necessary to understand exactly what is going on inside the grating. Rigorous coupled wave analysis3,4 is one of the most widely used numerical methods for predicting the performance of gratings, but it is computationally intensive and yields an approximation. If we had a better model of the diffraction mechanism, it would be much easier to design a practical deep-etched grating. The eigenfunction or modal method, first proposed by Botten,5 is a powerful method for revealing the diffraction mechanism by defining the modes within a grating design. We feel that Botten's method has not received enough attention in the 30 years since it was formulated. Tishchenko6 developed the modal method and later Clausnitzer7 presented a simplified version, which illustrated clearly that the diffraction can be simply described by a sine (or cosine) function for a subwavelength, low-contrast grating.
We further developed the simplified modal method to illustrate a series of novel and interesting optical functions of deep-etched, high-density, fused-silica gratings.8–13 We used the overlap integral and even and odd modes to reach simplified equations,11 including those for triangular10 and sinusoidal grooves.14,15 We obtained unified designs of these gratings16 by defining the ratios of period-to-wavelength and depth-to-wavelength, which can be shown clearly using the effective-mode indices of the method.
With that knowledge, we developed several applications for deep-etched, high-density, fused-silica gratings, including high-efficiency polarizers,8 a 1×2 beam splitter,9 a 1×3 beam splitter,17 and other designs. The gratings also offer highly efficient diffraction at the minus-one diffraction order with polarization-independence over a wide spectrum.18,19 In fabricating devices like these, it is a real technical challenge to achieve narrow (smaller than several hundred nanometers) and deep (>1μm) grooves on practically sized substrates with diameters in the tens of centimeters. Eventually, we employed several procedures, including fringe recording of holographic interference, lithographic developing, and dry etching using an inductively coupled plasma (ICP) facility. Over 10 years, we successfully made a series of deep-etched fused-silica gratings one by one.1,2,8–25 We found that ICP for etching the grating is a crucial step.
In conclusion, deep-etched, fused silica gratings have shown a series of novel functions that include high-efficiency polarization-independent diffraction, polarization beam splitting, and two- and three-port beam splitting. These functions will enable us to develop new optical devices as well as other practical applications in optical-fiber communications, spectrometry, femtosecond laser-pulse compression, and carrier-envelope phase-stabilized laser systems.26
1. J. Zheng, C. Zhou, E. Dai, Double-line-density gratings structure for compression and generation of double femtosecond laser pulses, JOSA B 24, pp. 979-984, 2007.
2. W. Jia, C. Zhou, J. Feng, E. Dai, Miniature pulse compressor of deep-etched gratings, Appl. Opt. 32, pp. 6058-6063, 2008.
3. M. G. Moharam, E. B. Grann, D. A. Pommet, T. K. Gaylord, Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings, JOSA A 12, pp. 1068-1076, 1995.
4. P. Lalanne, G. M. Morris, Highly improved convergence of the coupled-wave method for TM polarization, JOSA A 13, pp. 779-784, 1996.
5. I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andrewartha, The dielectric lamellar diffraction grating, Opt. Acta 28, pp. 413-428, 1981.
6. A. V. Tishchenko, Phenomenological representation of deep and high contrast lamellar gratings by means of the modal method, Opt. Quantum Electron. 37, pp. 309-330, 2005.
7. T. Clausnitzer, T. Kämpfe, E. B. Kley, A. Tünnermann, U. Peschel, A. V. Tishchenko, O. Parriaux, An intelligible explanation of highly-efficient diffraction in deep dielectric rectangular transmission gratings, Opt. Express 13, pp. 10448-10456, 2005.
8. B. Wang, C. Zhou, S. Wang, J. Feng, Polarizing beam splitter of deep-etched fused-silica grating, Opt. Lett. 32, pp. 1299-1301, 2007.
9. B. Wang, C. Zhou, J. Zheng, J. Feng, Wideband two-port beam splitter of a binary fused-silica phase grating, Appl. Opt. 47, pp. 4004-4008, 2008.
10. J. Zheng, C. Zhou, J. Feng, B. Wang, Polarizing beam splitter of deep-etched triangular-groove fused silica gratings, Opt. Lett. 33, pp. 1554-1556, 2008.
11. J. Zheng, C. Zhou, B. Wang, J. Feng, Beam splitting of low-contrast binary gratings under the second Bragg angle incidence, JOSA A 25, pp. 1075, 2008.
12. J. Zheng, C. Zhou, J. Feng, H. Cao, P. Lv, Polarizing beam splitter of two-layer dielectric rectangular transmission gratings in Littrow mounting, Opt. Commun. 282, pp. 3069-3075, 2009.
13. J. Zheng, C. Zhou, J. Feng, A metal-mirror-based reflecting polarizing beam splitter, J. Opt. A: Pure Appl. Opt. 11, pp. 015710, 2009.
14. J. Feng, C. Zhou, H. Cao, P. Lv, Deep-etched sinusoidal polarizing beam splitter grating, Appl. Opt. 49, pp. 1739-1743, 2010.
15. J. Feng, C. Zhou, H. Cao, P. Lu, Unified design of sinusoidal-groove, fused-silica grating, Appl. Opt. 49, pp. 5697-5704, 2010.
16. P. Lv, C. Zhou, J. Feng, H. Cao, Unified design of wavelength-independent deep-etched fused-silica gratings, Opt. Commun. 283, pp. 4135-4140, 2010.
17. J. Feng, C. Zhou, B. Wang, J. W. Jia, H. Cao, P. Lv, Three-port beam splitter of a binary fused silica grating, Appl. Opt. 47, pp. 6638-6643, 2008.
18. S. Wang, C. Zhou, Y. Zhang, H. Ru, Deep etched high-density fused silica transmission gratings with high efficiency at wavelength of 1550nm, Appl. Opt. 45, pp. 2567-2571, 2006.
19. H. Cao, C. Zhou, J. Feng, P. Lv, J. Ma, Design and fabrication of a polarization-independent wideband transmission fused-silica grating, Appl. Opt. 49, pp. 4108-4112, 2010.
20. S. Wang, C. Zhou, H. Ru, Y. Zhang, Optimized condition for etching fused silica phase gratings with inductively coupled plasma technology, Appl. Opt. 44, pp. 4429-4434, 2005.
21. J. Feng, C. Zhou, J. Zheng, H. Cao, P. Lv, Dual-function beam splitter of a subwavelength fused silica grating, Appl. Opt. 48, pp. 2697-2701, 2009.
22. J. Feng, C. Zhou, J. Zheng, B. Wang, Modal analysis of deep-etched low-contrast two-port beam splitter grating, Opt. Commun. 281, pp. 5298-5301, 2008.
23. J. Feng, C. Zhou, J. Zheng, H. Cao, P. Lv, Design and fabrication of a polarization-independent two-port beam splitter, Appl. Opt. 48, pp. 5636-5641, 2009.
24. H. Cao, C. Zhou, J. Feng, J. Ma, Polarization-independent triangular-groove fused-silica gratings with high efficiency at a wavelength of 1550nm, Opt. Commun. 283, pp. 4271-4273, 2010.
25. T. Wu, C. Zhou, J. Zheng, J. Feng, H. Cao, L. Zhu, W. Jia, Generation of double femtosecond pulses by using two transmissive gratings, Appl. Opt. 49, pp. 4506-4513, 2010.
26. C. Zhou, Deep-etched fused silica grating and applications, Proc. SPIE
7848, pp. 78480R, 2010. doi:10.1117/12.869033