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Bragg reflectors as small as optical waveguides can be used at the intersections of waveguides as spectral filters, beam splitters, or beam combiners. We present the concept of fabricating small Bragg reflectors in photorefractive waveguides and show the spectral selectivity of these micro-Bragg reflectors fabricated in a lithium niobate crystal. We also show that we can fabricate waveguide structures simultaneously with the micro-Bragg reflector, by using a crystal whose c-axis is directed 45 degree off the optical axis of the fabrication beam. The reflectivity of the micro-Bragg reflector was smaller than 0.01 and was not large enough for the immediate use.
©1998 Optical Society of America
1. Introduction
A promising solution to massively parallel signal interconnection for the next-generation signal processors is the optical interconnection. One approach to massively parallel optical interconnection is based on free-space optics and the other is based on guided optics. Possible advantages of guided optics are the absence of diffraction and easy isolation of signals. Optical 3-D waveguides can be fabricated by moving a focused spot of a strong laser beam in photorefractive (PR) materials[1–3]. The fabrication technique has been improved[4] and even an array of waveguides can be fabricated[5]. Although photorefractive waveguides have a problem of volatility, it is worth studying the photorefractive waveguides because of their easiness of fabrication, tangibility of their structures. Note that it is possible to fix photorefractive effects[6]. The tangibility can also be utilized for optical dynamic interconnections[7]. If Bragg reflectors as small as the waveguides can be fabricated in photorefractive media, they can be used as spectral filters, beam splitters, or beam combiners along with the waveguides or network of waveguides. Small complex optical systems such as a very small interferometer can be made. If such optical systems are fabricated in glass[8], they can be used permanently.
We propose in Section 2 the concept of small Bragg reflector[9] in a lithium niobate crystal and show the results of fabrication experiments. We confirmed the spectral selectivity of the micro-Bragg reflector fabricated within the waveguide structures.
2. Micro-Bragg reflector in photoreferactive waveguide
The concept of a micro-Bragg reflector is explained referring to Fig. 1. During fabrication of a photorefractive waveguide by a microscope objective, L1, standing waves are formed near the focus of the fabrication beam by introducing another counter-propagating convergent beam formed by a lens, L2. Then a small Bragg reflector is fabricated near the common focus of the two beams. The resultant small Bragg reflector can be used as a wavelength-selective reflector, a partial reflector, or even a coupler between a guided mode and a free-space beam. The wavelength-selectivity and reflectivity may be controlled by the number of fringes that constitute the reflector and the change of refractive index.
If the small Bragg grating is fabricated at the intersection of two photorefractive waveguides, it can couple the guided modes in the two waveguides[10]. The Bragg grating may be used as a beam splitter and a beam combiner, and a very small interferometer may be composed of the photorefractive waveuguides and the micro-Bragg partial reflector.
Bragg reflectors are fabricated by an optical system shown in Fig. 2. Counter-propagating convergent beams formed by using a light beam from a dye laser (580 nm) illuminate the photorefractive lithium niobate crystal. To reduce photorefractive effects during exposure, we used linearly polarized light and chose the ordinary ray for the fabrication in the crystal. A small Bragg reflector is formed by the standing waves near the common focus. During exposure, the crystal was kept stationary. When one of the beams is stopped and the crystal is moved, an optical waveguide is formed. In this case, the crystal is moved during exposure along the optical axis. The c-axis of the crystal is directed 45 degrees off the optical axis. Figure 3 shows the wavelength selectivity of the reflectance of a Bragg reflector fabricated by us. The maximum reflectance of this reflector was 0.06. The strong selectivity indicates the formation of periodic structure, while the extreme selectivity implies the formation of too long Bragg reflector. The length of this Bragg reflector is estimated at 1.5 mm. This is the experimental result of the longest reflector that we made.
If we assume reasonable refractive index change[3] of 1.2 × 10-3 in the Bragg reflector and assume 200 periods of the grating along the optical axis, we can expect reflectance of 0.47 from the coupled mode theory for the Bragg reflectors. We may expect some higher index change and anticipate much higher reflectance. The smaller reflectance of the present reflector than those expected may be ascribed to the aberrations near the foci and the reduced fringe contrast caused by the amplitude-mismatch between the counter-propagating convergent beams. The photorefractive effect may also distort the wavefront of the fabrication beams during exposure. Perfect resolution to these problems is quite difficult and was not pursued in this paper.
The Bragg reflector was incorporated into a waveguide. Figure 4 (a) shows the near field pattern of an end face of a waveguide with the Bragg reflector. Cross section of this near field pattern is plotted in Fig. 4 (b). The figure shows that the light is well confined within the waveguide. Figure 5 indicates the spectral transmittance of the waveguide plotted as a function of deviation of the probe wavelength from the fabrication wavelength. It was confirmed that spectral reflectance also have the similar wavelength selectivity.
Fig. 4 Near field pattern at the end face of the waveguide; (a) intensity distribution and (b) cross-section
The results of trials to obtain smaller or shorter Bragg reflectors, namely micro-Bragg reflectors, are shown in Fig. 6. We found that the reflectance and spectral selectivity of the fabricated Bragg reflectors are not simple functions of exposures. The normalized spectral reflectances are plotted as a function of relative wavelength. The fabrication process is not yet understood well. We only present here the results of three reflectors. The measures of spectral selectivity, Δλ/λ, range from 10-4 to 10-3. These values imply the lengths of reflectors of 150 to 1500 μm. The maximum reflectance ranges from 1.9 × 10-3 to 8.2 × 10-3. This range of reflectance is insufficient for the immediate practical use.
It has recently been reported that a waveguide can be fabricated in silica glass by using ultrashort pulses from a Ti-sapphire laser[8]. The refractive index change is reported as high as 0.01 to 0.035. If ultrashort pulses are used to fabricate micro-Bragg reflector within the waveguide, the length of the Bragg reflector, and hence the spectral selectivity, can precisely be controlled by the duration of the laser pulse. If we use 100-fs pulses, we will readily be able to fabricate a micro-Bragg reflector that has the spectral selectivity of Δλ/λ ~ 1/50 and 50% peak reflectivity.
3. Conclusion
Bragg reflectors as small as the waveguides can be used as spectral filters, beam splitters, or beam combiners along with the waveguides or the network of waveguides. Small complex optical systems such as a very small interferometer can be made in the photorefractive media. We confirmed the spectral selectivity of this micro-Bragg reflector by using light from a tunable dye laser. We also confirmed that we can fabricate waveguide structures simultaneously with the micro-Bragg reflector, by using a lithium niobate crystal whose c-axis is directed 45 degree off the optical axis of the fabrication beam. Unfortunately, however, the reflectivity of the micro-Bragg reflector was smaller than 0.01 and is not large enough for the immediate use. The structure of the Bragg reflector was too long unexpectedly. An alternative approach to use ultrashort pulses with a silica glass has been suggested. Experiments along this line is under way.
References and links
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9. K. Itoh, W. Watanabe, K. Ikezawa, and Y. Furuya, “Micro-Bragg reflectors in photorefractive 3-D waveguides,” Proc. SPIE, to appear.
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