March 15, 2004 / Vol. 29, No. 6 / OPTICS LETTERS
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Experimental characterization of simultaneous spatial and spectral filtering by an optical resonant filter Rabi Rabady and Ivan Avrutsky Department of Electrical and Computer Engineering, Wayne State University, Detroit, Michigan 48202 Received September 12, 2003 Simultaneous spatial and spectral filtering by an optical resonant filter has been characterized experimentally to furnish additional insight into the operation and applications of optical resonant filters. Our experimental study can be useful for applications that depend on spatial filtering, spectral filtering, spatial – spectral filtering, and polarization selectivity. One significant application is the integration of an optical resonant filter with semiconductor lasers to control the spatial – spectral radiation for optimum performance. © 2004 Optical Society of America OCIS codes: 120.2440, 070.6110, 330.6180, 130.3120.
The ability of optical resonant filters (ORFs), also known as waveguide grating mirrors, to provide simultaneous spatial and spectral f iltering makes them attractive for applications in which the ability to select spatial filtering, spectral f iltering, spatial– spectral filtering, or polarization is required. A major application of simultaneous filtering with ORFs is control of spectral and spatial radiation of lasers.1 The potential for ORFs to be integrated
where k is the Bragg coupling coeff icient, L is the period of the sequence of light traveling inside the waveguide,4 s is the grating depth, l is the wavelength, L is the grating period, u is the angle of incidence, m is the diffraction order, and nⴱ is the effective refractive index, which is related to the indices 共n1 , n2 , n3 兲 of the superstrate, the waveguide layer, and the substrate, respectively, and to waveguide thickness d by (for the TE mode; Ref. 9)
æ 兵关n2 2 2 共nⴱ 兲2 兴 关共nⴱ 兲2 2 n1 2 兴其1兾2 1 兵关n2 2 2 共nⴱ 兲2 兴 关共nⴱ 兲2 2 n3 2 兴其1兾2 . 2pd关n2 2 2 共nⴱ 兲2 兴1兾2 苷 tan l n2 2 2 共nⴱ 兲2 2 兵关共nⴱ 兲2 2 n3 2 兴 关共nⴱ 兲2 2 n1 2 兴其1兾2 Ω
with semiconductor lasers in a compact design to produce high laser performance (low beam divergence and radiation spectral width) makes the experiments reported in this Letter useful and significant. The principle of operation of ORFs is anomalous ref lection, as discovered by Wood in 1902.2 Much theoretical and experimental work in this field has been done since then.1 – 8 The ORF is configured as shown in Fig. 1. Two major components, waveguiding and coupling effects, are needed for ORF operation. Waveguiding can be achieved by either of two means: by surface plasmon excitation, as happens on the surface of a metal that has been illuminated by a suitable laser beam, or by incorporation of a dielectric layer that is sandwiched between two media with lower refractive indices than the waveguide’s refractive index. Coupling is achieved by a diffraction grating that is integrated with the waveguide. All the research reported here was based on the second type of waveguiding. The condition for waveguide excitation, which is also the main equation that describes the simultaneous spatial– spectral f iltering, is3 µ
k苷
nⴱ 2 m
l L
∂2
1 sin2 u 苷
µ
lk 4p
∂2
Equation (1) indicates a hyperbolic relation between spectral and spatial filtering. The spectral gap between the lower and upper sections of the hyperbolic curve is a function of Bragg coupling factor k and wavelength l. If k is relatively high, which is so for deep gratings, we f ind a clear split of the two sections of the hyperbolic curve. It is also evident that at normal incidence there are two wavelengths that satisfy Eq. (1). Shallow gratings with relatively low k, however, produce one sharp resonance. This is obvious when k is set to zero and the excitation condition in Eq. (1) is reduced to a linear relation between the spatial 共u兲 and the spectral 共l兲 parameters that is satisfied at normal incidence by a single wavelength: nⴱ 苷 m
l 6 sin u . L
,
共2ps兲2 兵共n2 2 2 共nⴱ 兲2 兲 关共nⴱ兲2 2 n1 2 兴其1兾2 , Ll2
(1)
0146-9592/04/060605-03$15.00/0
(2)
Fig. 1. Structure of the ORF. © 2004 Optical Society of America
(3)
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OPTICS LETTERS / Vol. 29, No. 6 / March 15, 2004
the exposed photoresist film to obtain the grating formation and then hard backed it to enhance its etching resistance before dry etching with Ar and CF4 to transfer the pattern from the photoresist to the waveguide film. A detailed description of the technology for fabricating ORFs with precise positioning of the resonance wavelength can be found in Ref. 3. To study the spatial– spectral characteristics of the fabricated ORF we prepared the optical setup shown in Fig. 2. The spatial f ilter in Fig. 2 is made from an objective lens with 5-mm focal length and a f iber with
Fig. 2. Computer-controlled optical setup for the ORF spatial– spectral characterization.
Fig. 3. Normal-incidence ref lection spectra for ORFs with strong Bragg coupling, weak Bragg coupling, and engineered moderate Bragg coupling.
As we discussed above, two technological components are needed for the fabrication of an ORF, namely, a waveguide f ilm and a grating coupler. We deposited the waveguide film upon a standard BK7 glass substrate whose refractive index (1.51 at l 苷 632.8 nm) was less than the refractive index of the deposited film. A holographic grating 共L 艐 500 nm兲 was then introduced onto the top of the waveguide film. We used rf magnetron sputtering to deposit a mixture of silica and titania for waveguide fabrication. Changing the forward sputtering power of the two magnetrons controls the silica– titania mole ratios and thus the optical constants of the waveguide. To fabricate the grating we spatially f iltered, collimated, and then spatially split a coherent deepultraviolet beam from the second-harmonic generation of an Ar1 laser with 257-nm wavelength into two beams, one delayed from the other within the coherence length of the laser beam. The period of the grating was controlled by the angle of the two coherent interfering beams on the photoresist film; the angle was controlled by a computer-controlled rotation stage with 1023 -degree resolution. A sinusoidal interference pattern was imprinted upon SPR505-A photoresist (ethyl lactate, N-butyl acetate, xylene) f ilm of 艐450-nm thickness. We developed
Fig. 4. Ref lection contours in the spatial –spectral domain for ORFs with (a) strong Bragg coupling, (b) weak Bragg coupling, and (c) the engineered moderate Bragg coupling.
March 15, 2004 / Vol. 29, No. 6 / OPTICS LETTERS
a 60-mm core diameter and can provide an acceptable 0.006-rad spatial f iltering width to characterize the filter’s spectral behavior at any angle. The spectral behavior was captured repeatedly at different angles (0.1 deg apart) about normal incidence. Then we assembled the acquired spectra, after time averaging by the optical spectrum analyzer to suppress noise and overcome the limited power from the white source, and constructed the characteristics of simultaneous spatial– spectral f iltering. Armed with the theory and the technological setup described above, we could control the gratings’ depth by adjusting the photoresists’s thickness, the exposure dose and etching time, and the waveguide’s refractive index by adjusting the forward rf power of the two magnetrons. Figure 3 shows the normal-incidence ref lection spectra for three fabricated filters, one with strong Bragg coupling, which resulted from relatively deep gratings (160– 200-nm depth), one with weak Bragg coupling, which resulted from shallow gratings (30– 80-nm depth), and moderate Bragg coupling, which we engineered by adjusting the grating depth (100–140-nm depth) and the waveguide’s refractive index after observing the normal-incidence ref lection spectra of strong and weak Bragg coupling. Simultaneous spatial– spectral characteristics were later constructed for the three kinds of coupling. Figure 4 shows the ref lection contours in the spectral– spatial domains for an ORF that was fabricated with strong Bragg coupling [Fig. 4(a)] and for an ORF that was fabricated with weak Bragg coupling [Fig. 4(b)]. It is evident that the experimental results shown in Figs. 4(a) and 4(b) are in harmony with the theory described in Eqs. (1) and (3), respectively. Figure 4(c) shows a compromise between the two
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kinds of coupling shown in Figs. 4(a) and 4(b); we intentionally designed the Bragg coupling to cause the resonance peaks to overlap by adjusting the grating depth and the waveguide’s refractive index. We have achieved an experimental characterization of simultaneous spatial –spectral f iltering by optical resonance f ilters for further understanding of the operation and applications of these filters. This study can be useful when one is integrating an ORF with semiconductor lasers to control its spatial–spectral radiation for high performance. Additionally, the close-to-rectangular f iltering prof ile shown by the right curve in Fig. 3 emerged from this study. This profile should yield high bandwidth efficiency for dense wavelength-divison-multiplexing communications. R. Rabady’s e-mail address is
[email protected]. References 1. 2. 3. 4. 5. 6. 7. 8. 9.
I. Avrutsky and R. Rabady, Opt. Lett. 26, 989 (2001). R. W. Wood, Philos. Mag. 4, 393 (1902). R. Rabady and I. Avrutsky, Appl. Opt. 42, 4499 (2003). V. A. Sychugov and J. Ctyroky, Sov. J. Quantum Electron. 12, 392 (1982). A. Hesel and A. Oliner, Appl. Opt. 4, 1275 (1965). R. Magnusson and S. S. Wang, Appl. Phys. Lett. 61, 1022 (1992). D. L. Brundrett, E. N. Glytsis, and T. K. Gaylord, Opt. Lett. 23, 700 (1998). I. Avrutsky, R. Rabady, and K. Zinoviev, presented at the Diffractive Optics and Micro-Optics Meeting DOMO-2002, June 3 – 6, 2002, Tucson, Arizona. A. Yariv, Optical Electronics, 4th ed. (Saunders, Philadelphia, Pa., 1991).
