GRATING COUPLERS - MODERN PHYSICS AT THE BORDER BETWEEN PHYSICS AND ENGINEERING

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1 GRATING COUPLERS - MODERN PHYSICS AT THE BORDER BETWEEN PHYSICS AND ENGINEERING STEFAN STANKOWSKI Physics and Chemistry Department, Biel School of Engineering and Architecture Quellgasse 21, CH-2501 Biel Stefan.Stankowski@hta-bi.bfh.ch Abstract Modern optics is a field which combines basic physics with industrial applications, especially in the domains of telecommunication and sensor development. The grating coupler, an important device of integrated optics, is proposed as a model system. It is particularly appropriate for discussing basic topics such as wave-guiding and diffraction, and can be used for demonstrating important applications. Practical hints are given for the use of grating couplers in laboratory courses. KEYWORDS: integrated optics, grating, waveguide, sensor Introduction Modern optics is one of the fields where basic physics is intimately related to technical applications. On the one hand, there is laser physics, one of the frontiers of nowadays research. But there is a silent revolution going on with other optical components, too: freely propagating beams are replaced by guided waves, and refractive elements such as classical lenses are being replaced by diffractive elements such as diffractive lenses and gratings. Obviously, these new components allow for much higher degrees of integration and miniaturisation. This is a fascinating field, interesting from the point of view of basic physical principles and motivating due to its direct technical applicability. It is unfortunately still under-represented in standard physics textbooks where classical optical instrumentation is described in some length, but wave-guide coupling is not even mentioned. Fortunately, some very good textbooks of "photonics" are now available to which the interested reader may refer [1]. With the present contribution I hope to give some fresh ideas about incorporating more of this subject in physics courses. Grating couplers In this report, I concentrate on one particular optical component which is gaining more and more importance in telecommunication as well as in sensor technology, the grating coupler. This basic element allows in fact to discuss fundamental notions of modern optics. such as guided modes, radiation modes, effective refractive index, evanescent waves, mode conversion and coupling. It is furthermore used in numerous technical applications, a variety of which will be discussed below.

2 For the sake of simplicity, we shall consider planar waveguides (which play an increasingly important role in integrated optoelectronic systems) rather than fibers (in the core of which gratings can be written by UV laser irradiation by today's state of the art). Planar waveguides consist of a very thin (typically nm) layer of silicium-titaniumoxide, tantal oxide, silicium nitrate or other high refractive index material, deposited on a substrate (e.g. a glass wafer). On the upper side, the waveguide may be exposed to air or to other material (e.g. aqueous solution). The refractive indices of the substrate (about 1.5) and the cover (1.0 for air, 1.33 for water) being small with respect to the refractive index of the waveguide material (1.7 to 2.6 typically), total reflection will occur if the incidence angle on the interfaces exceeds the critical angle, sin α critical = n(substrate)/n(guide).different modes can then travel along the waveguide, each of them being characterized by its angle with respect to the central guide axis, x. Tracing zig-zag rays, it should be considered that each ray line represents in fact a wavefront, and that, in order to avoid destructive interference, neigbouring rays going into the same direction should have the same phase. Calculating the travel time difference and applying this principle, one arrives at the equation known as "dispersion relation" of the waveguide, which defines the allowed propagation angles (see standard textbooks for the derivation of this equation [1],[2]). The important result is that only discrete values of the angle are allowed and that there is thus only a discrete number of guided modes. In the small waveguiding structures mentioned above, only very few guided modes are allowed (usually one or two TE and TM modes). In order to excite these modes, light can be directly shone to the cleaved end of the guide (end butt coupling, needs well polished ends and thorough adjustment of the light source) or else be coupled into the waveguide by a prism or a grating. Grating structures are applied to the guide by impressing or etching, or another one of a variety of technologies. Each of these structures can be used for coupling light into as well as coupling it out of the guide. Fundamental optics. Be Χ the angle that a certain mode forms with the central axis of the waveguide. It is customary to characterize this mode by the projection of its wave vector, k, on the central axis, k cos α, and to put this equal to n e k o, where k o = 2π/λ is the wave number in the vacuum and n e is called the effective refractive index. In this way, n e contains all the information about the particular mode in question. The dispersion relation, i.e. the equation which governs the allowed modes, determines the corresponding values of the effective refractive index. It reads: k 0 d (n g 2 - n e 2 ) 1/2 - atan q s [(n e 2 - n s 2 )/(n g 2 - n e 2 )] 1/2 - atan q c [(n e 2 - n c 2 )/(n g 2 - n e 2 )] 1/2 = mπ (1) Here, d is the thickness of the guide, m is an arbitrary integer, and the indices s and c refer to the substrate and the cover material, respectively. (The parametzers q i will be explained shortly). Interestingly, the indices of refraction of the substrate and the cover appear in this relation. The totally reflected wave thus senses the properties of the neighbouring media. In fact, an

3 exponentially decaying part of the wave, the so called evanescent wave, extends into these regions. The dispersion relation further depends on the polarization of the wave. Setting the q i parameters equal to unity, this equation is appropriate for TE waves, having the electrical vector perpendicular to the x-axis. With q i = n g 2 / n i 2 (i = s or c), one obtains the pertinent relation for TM waves which have the magnetic field vector perpendicular to the x-axis. In order to understand the function of the grating, it is convenient to remember standard Fraunhofer diffraction. Maximum light intensity behind a grating of spacing g is found when the condition g sin β = m λ is satisfied (m = integer). The same condition may be rewritten, upon introducing the wave number k = 2π/λ of the light and a similarly defined periodicity number of the grating, K = 2π/g : k sin β - m K = 0 (2) The same relation may be used to discuss diffraction of a guided wave on a grating, with k replaced by n e k 0 : n e k 0 sin β - m K = 0. (3) The angle β is the in-coupling or out-coupling angle (with respect to air). Therefore, once n e is determined, the coupling angle of a given grating can be calculated immediately. It is obviously different for different polarizations of the guided wave (TE or TM). The basic formalism involved so far, implies essentially the condition for total reflection and the formulae for Fraunhofer diffraction. For a full derivation of the "dispersion relation", the phase change upon total reflection is needed (or else the penetration depth of the wave into the neighbouring medium, or the so called Goos-Hähnchen shift). This can be given as additional information if not treated in the standard course. (By the way, the penetration of the wave into the adjacent medium can be directly demonstrated, using cm microwaves totally reflecting on a prism face). Applications The basic property is the in- or out-coupling of a guided mode by the grating, under a welldefined angle. The latter depends on: - the wavelength, allowing for wavelength-selection in add-drop filters - the polarization (TE or TM), allowing for polarization selection - the refractive properties of the cover medium, allowing for sensing. The first two properties are used in telecommunication applications. Gratings serve as highly selective filters for coupling in or out specific wavelengths under a given angle, or to select polarization states. They are also able to reflect a guided mode backwards. The last property is at the basis of sensing applications. A change in the coupling angle is indicative of a change of the refractive index of the cover medium. This may be due to

4 changes in the composition or to changes in environmental parameters, as in temperature sensors (where the temperature change affects the refractive index of the cover medium). Or else, if the cover medium (aqueous solution) contains some molecules such as drugs, environmental agents or biomolecules (pathogens, hormones etc.), their binding to receptors fixed at the waveguide surface can be monitored. This is due to their forming an adlayer at the surface having a distinct refractive index. Even though this adlayer may be as small as some nanometers or even less, the evanescent wave is able to sense it. Falling down exponentially with distance from the surface, the evanescent wave is in fact most sensitive to whatever is closest to the waveguide surface. Unfortunately, the induced changes in the coupling angle are relatively small, and quite sophisticated instrumentation is needed to detect them with high enough precision. This is why many researchers resort to simpler detection schemes, e.g. optically absorbing or fluorescent markers attached to the interesting molecules. The evanescent wave, penetrating into the interface region, can in fact be absorbed or can excite fluorescence. The actual aim is to construct high troughput multicompartment well systems which allow for rapid scanning of high numbers of different biomolecules. Laboratory experiments Using a helium neon laser (of a few milliwatts) as a light source, coupling of a wave into a waveguide can be monitored by eye. It is recommended to use a rotating scale in order to be able to adjust angles carefully and reproducibly. High efficiency grating couplers as used in telecommunication are quite expensive. On the other hand, grating couplers for sensing purposes can be bought for less than 40$ a piece (Microvacuum, Budapest, sold e.g. by ASI, Zurich). Being optimized for sensing, their coupling efficiency is rather low, but sufficient to demonstrate the main phenomena, as outlined below. In-coupling of guided wave: In the simplest mounting, such a chip (48 to 16 mm glass substrate with planar guide and central grating line) is arranged vertically on a turntable or rotating scale, in the beam of the laser. The laser light is directed onto the grating region. Turning carefully, the guided wave is readily seen by eye to pass through the waveguide, as the specific angle is attained (in a darkened room). Polarization selectivity: Turning the laser tube on its axis (if the laser produces a polarized beam) or using polarizers, a different coupling angle will be found for the TE and TM polarizations, respectively. Out-coupling of guided wave: It is also possible to excite the mode by shining the laser beam into the front end of the guide. Careful adjustment is necessary to achieve the necessary alignment, but the chip's cleaved ends are well polished so that end butt coupling is possible. Outcoupling is then readily visible by eye under the specific angle (well-darkened room is required because outcoupling efficiency of these gratings is low). In fact, two different outcoupling angles appear

5 simultaneously if the laser tube is oriented such that the polarization is 45 degrees with respect to the surface of the waveguide. These correspond to the TE and TM waves. Upon turning the laser on its axis, the one or the other polarization signal can be made to disappear. Wavelength dependence: Where a laser of different output wavelength is available (e.g. green), change of the outcoupling angle with the wavelength can be demonstrated. With the biosensor chip, the change in angle is relatively small even for such a big change in wavelength, but telecommunication gratings are optimized for distinct changes in the coupling angle even at small wavelength variations. The functional principle of add-drop-filters should be obvious from these experiments. Though this function cannot be demonstrated convincingly with the Microvacuum/ASI chips, their coupling efficiency being too low. We are currently looking for advantageous sources for high efficiency couplers. These would also allow to demonstrate an effect called "abnormal reflection": If the beam diameter and grating length are big enough (typically, they are), the beam is coupled in and gradually coupled out again, leading to very high reflection (transmission is hindered by destructive interference). Sensor properties: More possibilities exist if the chip is mounted in a horizontal position and illuminated from below by a moveable laser source. In our lab, we use a vertical aluminium plate with a circular slit cut out as a guiding structure for the laser mount. This slit allows to fix, at least approximately, the angular position of the light source. The light impinges from below onto the chip lying on a frame fixed to a rotating scale. With this scale we perform the angular fine adjustment, with the chip remaining in a roughly horizontal position. Putting a stripe of opaque tape on the frame prevents the chip from sliding and facilitates the visualization of guided waves leaking out at the lateral face of the chip. After determination of the coupling angle, a drop of water (or other solution) can be deposited in the grating region. The coupling angle will be seen to change (by about 1 to 2 degrees, with the chips described above) thereby demonstrating the principle of refractive index sensing and biosensors. In research applications, coupling angles can be measured to a precision of 10-5 and better. This allows then to monitor minute changes of the composition of the cover medium, refractive index changes due to temperature variation, adsorption at the waveguide surface of biomolecules etc. In our laboratory, we cannot aim at such high technology applications, but the principle of the technique can well be demonstrated by the kind of experiments discussed. References 1. W. Glaser: "Photonik für Ingenieure", Verlag Technik, Berlin (1997) 2. R.G.Hunsperger: "Integrated Optics", Springer, Berlin (1984)

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