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IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 19, NO. 22, NOVEMBER 15, 2007
A Spatial-Distance-Controllable Demultiplexer Using a Chirped Volume Holographic Grating Duc Dung Do, Nam Kim, Jun Won An, and Kwon Yeon Lee
Abstract—In this letter, we introduce a demultiplexer with a function of controlling spatial distance based on a chirped volume holographic grating. The chirped grating is recorded by illuminating a photopolymer film under the interference of convergent and divergent beams. The theoretical and experimental results show that the position of the focused points of the diffracted beam at the readout stage depends on the distance between the grating and the output lens. This characteristic can be utilized to control the channel spacing and spatial distance in the dense wavelength-division-multiplexing demultiplexer. Index Terms—Demultiplexing, holographic grating. Fig. 1. Chirped grating (a) in the recording and (b) readout schemes.
I. INTRODUCTION
A
demultiplexer based on a transmission volume holographic grating (VHG) has attracted considerable attention [1]. Its advantages over other technologies are that it has low cost, simplicity, and low crosstalk when the channel count increases. In the demultiplexer, a polychromatic beam is diffracted into different directions according to the wavelengths because of the angular dispersion properties of the VHG. A convex lens focuses these separated beams into points, where output fibers are placed, to couple the channels out. From the basic scheme, there have been many efforts to improve the demultiplexer’s performance such as cascading more gratings to expand the channel numbers [2], or using an apodized grating to reduce the crosstalk between the adjacent channels [3]. A chirped VHG in the demultiplexer was reported by Han et al. [4], [5]. They figured out that the chromatic dispersion in the optical communication system could be controllable. In this letter, we describe a spatial characteristic of the demultiplexer in the case of using a chirped VHG instead of a uniform grating. The chirped VHG acts not only as a dispersive element but also as a second lens. Therefore, the spatial distance between the two adjacent channels is controlled by changing the relative distance between the chirped VHG and the lens. As a consequence, a demultiplexer based on the chirped VHG has tunable channel spacing or controllable spatial distance.
Manuscript received June 25, 2007; revised July 24, 2007. This work was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD) (The Regional Research Universities Program/Chungbuk BIT Research-Oriented University Consortium). D. D. Do and N. Kim are with the Department of Computer and Communication Engineering, Chungbuk National University, Chungbuk 361-763, Korea (e-mail:
[email protected]). J. W. An is with the Department of Electrical Engineering, Pennsylvania State University, University Park, PA 16802 USA. K. Y. Lee is with the Department of Electronic Engineering, Sunchon National University, Jonnam 540-742, Korea. Color versions of one or more of the figures in this letter are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/LPT.2007.906051
II. THEORY Fig. 1(a) shows the chirped VHG recording scheme. The two laser beams are cylindrical. The reference beam is convergent and the signal beam is divergent. The lines of focus of these plane, and they beams are symmetrical with respect to the and for the reference are denoted as and signal beams, respectively. The distance from the focused lines to the center of the grating is . The nonparaxial approximated expressions for recording beams with the wavelength are as follows [6]:
(1) where the plus and minus signs are used for the signal and reference beams denoted by subscripts and , respectively, and is a point with coordinates . Since the material used to record hologram is photopolymer which has the thickness of and is of the order of meters and centime100 m, while ters, respectively, then the quadratic factor of in (1) is negligibly small and can be removed. The permittivity index modulation of the material resulting from exposure to the interference of these beams is given approximately by
(2) is the where the asterisk denotes a complex conjugate and to the center of the inclined angle of the line connecting grating. It is clear that the quadratic phase factor of in the approximation (2) gives the linear change of the grating period over the transverse -direction. Therefore, the chirped grating [7]. can act as a cylindrical lens with a focal length of The hologram is illuminated by a plane beam as sketched in Fig. 1(b) and expressed by
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DO et al.: SPATIAL-DISTANCE-CONTROLLABLE DEMULTIPLEXER USING A CHIRPED VHG
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where is the wavelength of the incident field and is the incident angle. To determine the diffraction of the plane wave after it goes through the chirped grating, the first-order Born approximation is used when the permittivity index modulation of the grating is small and the diffraction is weak [8]. The diffracted at the observation point with coordinates field is given by the volume integral (4) where is the volume occupied by the grating. If a convergent lens with a focal length is placed at the origin of the coordi, which is located at a distance far from the nates grating, as shown in Fig. 1(b), the field diffracted from the plane to the one is calculated by the integral for light propagating in free-space as follows: Fig. 2. Spatial distance between the two channels with 0.4-nm channel spacing. The squared dots and the solid line are the experimental and theoretical results, respectively.
(5) where is the distance from the point to the origin . In (5), the Green function—the of the coordinates last exponential function—is also approximated by the nonparaxial approximation, which was used in (1). When the terms in (5) are substituted by expressions (2), (3), and (4), the field diffracted by the VHG can be obtained by calculating the integration. In fact, (5) cannot be solved analytically. However, the diffracted field reaches a maximum when the phase factor in the integrand of (5) is zero. Unfortunately, the conditions for the phase factors relating to x- and y-axes do not coincide due to the fact that the chirped grating acts like a cylindrical lens. This induced the astigmatism to the system. Considering the condition that the phase factor is zero for the x-axis only, we obtain the relationships (6) (7) Equation (6) is similar to the lens equation for a combination of two lenses except for a ratio between the recording and reading wavelengths. This ratio is considered as a focal-length converting coefficient for the diffractive chirped grating lens. Equation (7) shows the position of the focused point of the diffracted beam along the x -axis. If the reading beam incident to , the chirped VHG has two wavelengths that are different by the diffracted beams are focused to the points separated by a , which is derived by differentiating (7). Taking the distance is approximated to be small Bragg mismatch into account, (8) where is the output angle, as shown in Fig. 1(b). It is clear depends on the relative positions bethat the spatial distance tween the chirped VGH and the output lens . Therefore, a tunable channel-spacing demultiplexer can be obtained by moving
the output lens closer to or farther from the grating. When is equal to , the approximation (8) becomes the approximation for the case of a uniform VHG [1]. We carried out experiments to verify this. III. EXPERIMENTS AND RESULTS A chirped VHG was recorded by exposing a 100- m-thick photopolymer film under the interference of two laser beams with a wavelength of 532 nm. Two couples of cylindrical lenses were used in each beam to control the position of the focused lines. The distance from the focused lines to the material was 4 m and the recording angle , at the center of the material film, was 15.7 [Fig. 1(a)]. In the experiment for testing the spatial and spectral characteristics of the chirped VHG system, a collimating lens and an output-focusing lens were used [1]. The output-focusing lens with a focal length of 100 mm transformed the angularly dispersed diffraction beams into a spatial separation where a singlemode fiber was placed. This output fiber was held and moved along the horizontal direction by a motorized fiber alignment unit. The diffraction beam was coupled to the fiber and its spectrum was examined by an optical spectral analyzer. For each distance from the grating to the lens, the spatial distance of two channels with 0.4-nm channel spacing at the 1550-nm region was measured. At the center of the chirped VGH, the Bragg angle, corresponding to a wavelength of 1550 nm was 51.9 . Fig. 2 shows the experimental (squared dots) and theoretical (solid line) results of the dependence of the spatial distance on . When , the measured spatial distance was 68.7 m, and the corresponding theoretical value derived from (8) was 66.1 m. The small difference between the experimental and theoretical results might be due to the approximation applied in the process of obtaining (8) and the misalignment of the focused lines in the grating recording setup. However, the important result is that by shifting the lens, we could change the spatial distance of the two adjacent channels. According to (6), the coupling fiber is also moved to the corresponding position to couple out the power efficiently. The feature of controlling the
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affected by the phase structure of the grating. However, the insertion loss of the system was about 17 dB, which was higher than in that of the uniform grating case. This was because the average diffraction efficiency of the chirped VHG was small due to the linear change of the grating period along the horizontal direction. In addition, the chirped VHG, like a cylindrical lens, changed the incident light in one direction only. Thus, it induced an astigmatic aberration to the overall system, resulting in reducing the coupling efficiency of the output fiber; i.e., the insertion loss increased. We also see that although using a uniform VHG together with a system of two movable lenses can provide the same method to control the spatial distance without the astigmatic aberration, the chirped VHG still has an advantage of controlling the chromatic dispersion, which becomes important when the capacity of a communication channel increases. When we apply the chirped VHG to a real application, the drawbacks of high insertion loss and the aberration caused by the chirped VHG should be overcome. In [4] and [9], other research groups have discussed modeling and designing based on cylindrical lenses and using a tapered waveguide to compensate for the aberration. Therefore, with some additional designs on the out-coupling optics, it is possible that the chirped VHG can be used not only for controlling the chromatic-dispersion characteristic but also for tuning the spatial distance in the demultiplexer. IV. CONCLUSION In this letter, we have presented the spatial and spectral characteristics of a demultiplexer using a chirped VHG. An output beam was focused, not on the focal plane of the lens, but on the plane depending on the distance from the grating to the lens. The experimental results showed that we could use the chirped VHG in a tunable channel-spacing or controllable spatial-distance demultiplexer. REFERENCES Fig. 3. Spectra measured when the output lens was at a distance of 100 mm far from the chirped VHG. (a) Two channels and (b) 51 channels with 0.4-nm channel spacing.
spatial distance can be used in a tunable channel-spacing demultiplexer. For a combination of a chosen lens and a chosen fiber array, using a chirped VHG provides a method to finely tune channel spacing of the output channels. Meanwhile, in the case of the uniform VHG, designing the grating must be done with a good amount of care in order to match the spatial distance of the two channels to the pitch of the fiber array. Fig. 3 shows the spectra response of the chirped grating working as a demultiplexer. The spectra of two center wavelengths of 1550 and 1550.4 nm measured with respect to the output lens position of 100 mm far from the grating is sketched in Fig. 3(a). The bandwidth of 0.13 nm and the crosstalk of about 20 dB were obtained. In the case of 51 channels shown in Fig. 3(b), the uniformity was 3.5 dB. Comparing with the results reported for the uniform VHG case in a previous publication [1], it can be seen that the spectral response was not
[1] J. W. An, N. Kim, and K. Y. Lee, “50 GHz-spaced 42-channel demultiplexer based on the photopolymer volume grating,” Jpn. J. Appl. Phys., vol. 41, no. 6B, pp. 665–666, 2002. [2] J. W. An, D. D. Do, N. Kim, and K. Y. Lee, “Expansion of channel number in optical demultiplexer using cascaded photopolymer volume gratings,” IEEE Photon. Technol. Lett., vol. 18, no. 6, pp. 788–790, Mar. 15, 2006. [3] D. D. Do, N. Kim, J. W. An, and K. Y. Lee, “Effects of apodization on a holographic demultiplexer based on a photopolymer grating,” Appl. Opt., vol. 43, pp. 4520–4526, 2004. [4] S. Han, B. A. Yu, S. Chung, H. Kim, J. Paek, and B. Lee, “Filter characteristics of a chirped volume holographic grating,” Opt. Lett., vol. 29, no. 1, pp. 107–109, 2004. [5] S. H. Han, T. S. Kim, S. W. Chung, and B. H. Lee, “Dispersion characteristics of holographic multiple-channel demultiplexers,” IEEE Photon. Technol. Lett., vol. 16, no. 8, pp. 1879–1881, Aug. 2004. [6] E. B. Champagne, “Nonparaxial imaging, magnification, and aberration properties in holography,” J. Opt. Soc. Amer., vol. 57, pp. 51–55, 1967. [7] B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics. New York: Wiley, 1991, ch. 4. [8] M. Born and E. Wolf, Principles of Optics, 7th (expanded) ed. Cambridge, U.K.: Cambridge Univ. Press, 1999, ch. 13. [9] T. Sugita, K. Hirano, T. Abe, and Y. Itoh, “Aberration properties in a chirped grating for coarse wavelength division demultiplexing,” Appl. Opt., vol. 45, pp. 5597–5607, 2006.
