Multilayer thin-film coatings for optical

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improved significantly in recent years [1, 2, 3, 4]. A wide range of synthesis approaches is available to design multilayer coatings even with complex reflection and transmission profiles such as gain ... band, square-top filters operated at high bit rates [14]. ... parameters (refractive indices, number of layers, incidence angle, ...
Multilayer thin-film coatings for optical communication systems Martina Gerken Lichttechnisches Institut, Universität Karlsruhe (TH), Kaiserstraße 12, 76131 Karlsruhe, Germany Tel.: +49-721-608-2541, Fax: +49-721-358149, Email: [email protected]

David A. B. Miller Edward L. Ginzton Laboratory, Stanford University, Stanford, California 94305

Abstract: Recent developments in thin-film coatings for optical communication systems are reviewed. Particular emphasis is given to thin-film designs with dispersion related to the photonic crystal superprism effect. A single dispersive coating may be used for multiplexing or demultiplexing several wavelength channels by spatial beam shifting. 2004 Optical Society of America

OCIS codes: (310.0310) Thin films, (060.2340) Fiber optics components; (260.2030) Dispersion

1. Introduction In current optical communication systems multilayer thin-film coatings find application in many functions such as antireflection coatings, wavelength division multiplexing (WDM) filters, interleavers, band splitting filters, or gain flattening filters. The fabrication of thin-film coatings is a proven technology and packaging technology has improved significantly in recent years [1, 2, 3, 4]. A wide range of synthesis approaches is available to design multilayer coatings even with complex reflection and transmission profiles such as gain equalizing filters for erbium-doped fiber amplifiers (EDFAs) [1, 5, 6]. Recently, emphasis has been given to designing coatings with a decreased sensitivity to fabrication errors allowing a higher yield [7, 8]. Progress has also been made in thermo-optic and electro-optic tuning of thin-film filters [9, 10, 11]. In the following we will focus on the dispersive properties of thin-film coatings, since these gain importance in the design of filters for dense wavelength division multiplexing (DWDM) systems and are promising for novel multiplexing/demultiplexing and dispersion-compensation components. 2. Temporal Dispersion Compensation Thin-film filters operating in transmission are minimum phase filters and their amplitude and phase response are related through a Hilbert transform (similar to the Kramers-Krönig relations in optics) [12, 13]. Thus, the wavelength-dependent amplitude transmission and phase response cannot be designed independently, leading to chromatic group delay (first derivative of the phase response with respect to frequency) and chromatic dispersion (second derivative of the phase response) effects. Dispersion effects become particularly pronounced for narrowband, square-top filters operated at high bit rates [14]. Dispersion compensation components are necessary for DWDM filters with bandwidths of 50-GHz and smaller [7]. Such compensation components can be realized by thin-film filters operated in reflection, since these are not minimum-phase filters and it is hence possible to design coatings with unity amplitude response and the desired phase characteristics. It has been demonstrated that such all-pass filters can compensate the chromatic dispersion of 50-GHz thin-film filters [15, 16] and 100-GHz fiber Bragg grating filters [17]. Reflective all-pass thin-film filters also have been employed for compensating the chromatic dispersion of optical fibers [18,19,20]. Recently, tunable thin-film dispersion compensators have been realized [11]. 3. Spatial Dispersion for Wavelength Multiplexers and Demultiplexers In the last section we have considered the temporal dispersion characteristics of thin-film filters at normal incidence. Using thin-film coatings at oblique incidence, we obtain spatial dispersion effects as well, i.e., incident beams experience a wavelength-dependent lateral shift. Several groups have shown that periodic photonic crystal structures exhibit wavelength regimes of high spatial dispersion. This photonic crystal “superprism effect” observed in planar [21] and thin-film [22] one-dimensional, in two-dimensional [21,23,24], and in three-dimensional [25] photonic crystals may be used to achieve high dispersion in a compact device. Dispersive thin-film stacks are particularly interesting as cost-effective wavelength multiplexing and demultiplexing devices. In contrast to

traditional thin-film filters, a single such coating is sufficient for demultiplexing several wavelength channels. Fig. 1 shows a schematic of a 4-channel wavelength demultiplexer [26]. Performing multiple bounces off the stack increases the wavelength-dependent spatial shift. We have developed different synthesis algorithms for designing non-periodic thin-film stacks with custom-engineered spatial dispersion properties such as a linear spatial beam shift with wavelength or a step-like spatial shift [27, 28]. Such stacks also exhibit temporal dispersion that is approximately proportional to the spatial dispersion. Mirror

Thin-Film Stack

z y

x

Focussing lens Substrate Mirror Out 4 Out 3 Out 2 Out 1

In

Fig. 1. Schematic of a 4-channel wavelength demultiplexer using a thin-film stack with spatial dispersion.

The number of channels Nchannels that can be demultiplexed is calculated as the total shift in the x-direction divided by the spatial extent per channel [26]. Therefore, the performance of the device is determined by the total spatial shift that can be achieved as well as by how accurately the desired dispersion characteristics are matched. For simple structures, e.g., Fabry-Perot or Gires-Tournois resonators, an analytical relationship exists between the stack parameters (refractive indices, number of layers, incidence angle, polarization), the dispersion profile, and the total spatial shift (or group delay) [11, 17]. Thus, for such simple stacks the performance is related in a straightforward manner to the stack parameters. For general multilayer structures, on the other hand, no analytic model exists. It is expected though that, e.g., a larger number of layers will allow for a larger dispersion or a better matching of the desired dispersion profile. The minimum number of layers necessary to achieve the desired dispersion characteristics is typically found in a trial-and-error approach. In order to speed up the design process and to be able to quickly estimate the feasibility of specific dispersive devices, we developed an empirical model relating the stack parameters to the achievable number of channels for the case of multilayer stacks with constant spatial dispersion. We developed the empirical model by designing and analyzing 623 thin-film stacks composed of different material systems, different stack thicknesses, and for operation at different incidence angles [29]. All designs have a center wavelength of 1550 nm and are operated at ppolarization. We find empirically from these designs that, for a device with a single focussing lens as shown in Fig. 1, the maximum number of channels can be approximated by (1).

N channels ≤ 1 +

L

8

λc ccrosstalk

2 sin (θ )  ∆n 2  π sin (θ ) 1 − 2 2 navg ns  

(1)

In (1) λc is the center wavelength of the device, θ is the incidence angle in vacuum, L is the total stack thickness, ∆n is the refractive index difference between the two stack materials, navg is the arithmetic average of the refractive indices, and ns is the refractive index of the substrate. ccrosstalk determines the crosstalk requirements between adjacent channels. For ccrosstalk=2, the adjacent channel crosstalk is approximately –15 dB, for ccrosstalk=3.2 it is –30 dB, and for ccrosstalk=3.8 it is –40 dB. In this model only the stack thickness and not the number of layers seems to matter. That is somewhat misleading since the layer thickness should likely always be on the order of a quarter wavelength for the class of structures investigated . Using (1) we can estimate that an 8-channel demultiplexer is possible with today’s thin-film deposition technology (λc = 1550 nm, θ = 45º, alternating layers of SiO2 (nL=1.45) and Ta2O5 (nH=2.09) on a quartz substrate (ns=1.52), L = 21 µm, crosstalk of –40dB). A 4-channel demultiplexing has been demonstrated experimentally [26].

4. Conclusions Multilayer thin-film coatings are a proven technology that is employed in many areas of optical communication systems. New developments include the design of filters with a higher tolerance towards fabrication errors, tunable filters, and dispersive filters for dispersion compensation and wavelength multiplexing and demultiplexing. We introduced an empirical model for estimating how many wavelength channels can be demultiplexed using the spatial dispersion of a single thin-film coating. Eight to sixteen channels seem possible in the near future making this a promising component for cost-effective coarse wavelength division multiplexing (CWDM) systems. 5. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17]

[18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29]

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