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NONLINEAR EFFECTS IN WAVEGUIDE DEVICES
Y. Silberberg, B. Sfez
To cite this version:
Y. Silberberg, B. Sfez. NONLINEAR EFFECTS IN WAVEGUIDE DEVICES. Journal de Physique
Colloques, 1988, 49 (C2), pp.C2-283-C2-287. �10.1051/jphyscol:1988266�. �jpa-00227683�
JOURNAL DE PHYSIQUE
Colloque C2, Suppl6ment au n06, Tome 49, juin 1988
NONLINEAR EFFECTS IN WAVEGUIDE DEVICES
Y. SILBERBERG and B.G. SFEZ
Bell Communications Research, Red Bank, NJ 07701, U.S.A.
Abstract
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We review travelling-wave Kerr-effect waveguide devices for optical switching and processing. We also propose a novel nonlinear waveguide junction device, anddemonstrate its potentially useful characteristics for all-optical switching.
1
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INTRODUCTIONThe interest in nonlinear waveguide devices, which has been growing steadily in recent years, stems from their potential use for ultrafast signal processing. The confinement of light in the small core area, and its diffractionless propagation over long distances increase the efficiency of the nonlinear interaction, and allow the use of relatively weak nonlinearities. These same advantages make the optical fiber one of the most useful nonlinear media, and indeed some of the proposed waveguide devices have been first realized in a fiber-optic form. While still in a less developed state compared with optical fibers, planar waveguide structures offer several
possibilities that are difficult to realize in fibers. Planar structures are more suitable for implementing in different nonlinear materials systems, such as glasses, semiconductors and organic materials. Even materials which are difficult to process into waveguide structures can be considered, for example, as cladding layers. Most attractive, however, is the possibility to generate waveguide structures that have unique nonlinear characteristics, structures that would have been impossible in a fiber device.
Of great importance are devices that could operate at a very high bit rate. This can be achieved in materials where the intensity-dependent refractive indices originate from nonresonant
electronic processes which are usually extremely fast. Transparent materials are less
susceptible to thermal problems which may limit absorptive materials. To benefit from this speed without being limited by transit times, most devices operate in a travelling-wave, or
"pipeline", mode. This implies that while the time required to perform an operation is still the transit time, two consecutive operations can be performed as fast as the nonlinearity and dispersion effects allow, thus the rate can be very high.
In this paper we will describe several all-optical travelling-wave waveguide devices and introduce ,in some more detail a novel device which is based on nonlinear waveguide junctions.
All these devices are assumed to be made in a material with a Kerr-like optical nonlinearity which responds to the instantaneous intensity of light, so that n-n +npI. Other nonlinear devices, such as SHG and parametric oscillator waveguide devices wiyl not be covered here. We also will not address devices with feedback, which are not compatible with pipeline geometry. We want to stress that even without feedback traveling wave devices offer a rich spectrum of nonlinear behavior, although bistability is not possible.
Host proposed waveguide devices operate through a nonlinear phase shift that the propagating mode (or modes) acquires. In these devices the intensities are not strong enough to affect
significantly the guiding structure or the mode shapes. We distinguish between two classes of devices. Interferometric devices, which are a nonlinear analog of electrooptic devices, are reviewed in section 2. Some travelling wave devices exhibit unique nonlinear characteristics which are useful for switching; two of these are discussed in section 3. Many interesting and potentially useful effects can be obtained, however, in a strong signal regime where the light changes the index enough to affect its propagation in a significant way. We will describe some of these works in section 4.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1988266
JOURNAL DE PHYSIQUE
Fig. 1
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Some nonlinear interferometers: (a). A Mach-Zehnder with unequal path-length /3/. (b).An asymmetric M'Z /4/. (c). A three-port MZ logic gate /5/. (d). A nonlinear two-mode interferometer /6/.
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INTERFEROMETRIC DEVICESOne family of proposed waveguide devices for all-optical processing is characterized by a sinusoidal response to the light intensity. The all-optical Kerr gate is based on optically induced birefringance that rotates the polarization of a signal wave. The transmission of the signal through a polarizer depends sinusoidaly on the phase difference induced between two polarization components. Application of the phenomena for ultrafast time division
multiplexing/demultiplexing has been studied by Morioka et a1 /I/, and subpicosecond gating has been demonstrated recently /2/, both using fiber devices.
Similar sinusoidal responses are expected from the several types of Mach-Zehnder devices which have been proposed /3-5/. These all-optical devices operate essentially like their electrooptic counterparts, with the difference that an optically induced phase shift rather than an
electrooptic one affects their output. Some of these devices are shown schematically in Fig. 1.
Simple nonlinear Mach-Zehnder interferometers are 2-port devices, in which asymmetry due to a difference in optical path-length /3/ or different mode size /4/ lead to intensity induced phase shifts between the two arms. These devices are characterized by a sinusoidal transfer function.
Adding two input channels to a symmetric MZ results in a very versatile logic gate /5/. The proposal of reference 5 shown in Fig. lc also requires an electroopticaly induced phase bias.
This device demonstrates the versatility enabled by waveguide structures and material systems.
A third interferometric device that has been proposed for power dependent routing is shown in Fig. Id /6/. This is the all-optical equivalent of an electrooptical device known as the BOA switch /7/. In this device the central region supports two guided modes, which are excited with equal amplitudes through each of the input arms. The device routes the signal according to the nonlinear phase shift induced between the two guided modes of the central region. The response of this device is, again, a sinusoidal function of the input intensity.
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SWITCHING D E V I C Q3.1 Nonlinear directional Couplers
Of all the nonlinear waveguide devices, the nonlinear directional coupler (NLDC) has attracted the most attention. This is possibly due to the fact that the NLDC behaves in a remarkably different way compared with an electrooptical directional coupler, and it can have several unique characteristics that could be useful to optical processing. The use of a directional coupler as a switch was first proposed by Jensen
/a/,
and recently demonstrated in a dual-corefiber /9/ and in a GaAs structure /lo/. In this application, a coupler of one coupling length is used. Low intensity signals are coupled from the input guide to the other waveguide, while high intensity signals bias the coupler and remain in the input guide. In other configurations, the coupler can be used as a high gain amplifier /11/ and as a phase controlled switch, in which a weak control signal can route an intense input /12/.
3.2 Nonlinear waveguide junctions.
We would like to introduce here a novel waveguide structure that is characterized by a very interesting and potentially useful nonlinear response. The structure is based on a waveguide junction, in which two single-mode waveguides converge to form a single two-mode waveguide. Such a structure is known to behave in two distinct ways depending on its symmetry /13/. We have found that asymmetries introduced by nonlinear index changes can drive a symmetric junction to behave like an asymmetric one. Particularly useful is a geometry where the light is coupled to the two-mode region and it is propagating into the diverging guides. We have found this system to have unique routing capabilities: a high intensity signal at the two mode region will tend to route itself to one of the two diverging waveguides with good extinction ratio. This is because the symmetric mode of propagation is extremely unstable, and small perturbations are sufficient to break the symmetry and to direct the entire signal to one branch. This behavior is
demonstrated in Fig. 2 : An intense signal is coupled to the fundamental mode of the two mode section. Without any perturbation, this signal splits evenly between the two output guides, as shown in the center simulation. Slight asymmetry in the field pattern can route the signal to the left or to the right. An addition of a small quantity of the higher order mode is enough to induce the switching. The almost complete switching shown in Fig. 2 is obtained with a control signal which is less than 1% of the switched signal. Figure 3 demonstrates the robustness of this process: the switch is insensitive to the precise value of relative phase between the two modes, and the state is stable also against perturbation of the intensity. This should be contrasted with the very sensitive NLDC device which has been proposed /12/. This process can be the basis for a phase or intensity controlled switching devices, one of which is shown in Fig.
4. Like in most of these devices, the power requirements can be reduced by making the device longer. In the nonlinear junction this means reducing the angle between the guides. Generally speaking, a nonlinear phase accumulation of a few x's over the interaction length is required in order to reach this binary regime.
Fig. 2
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Simulations of high-intensity propagation in a symmetric waveguide junction. The light propagates in two identical waveguide which are diverging fron a single two-mode guide. In the center the input is the symmetric mode of the two-mode region. The two other simulations describe the effect of the addition of a minute amount of the asymmetric mode, 1/200 in intensity, with a relative phase of 0 and 180 degrees.JOURNAL DE PHYSIQUE
RELATIVE PHASE
Fig. 3
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The dependence of the switching shown in Fig. 2 on the relative phase between the two eigenmodes in the two-mode section. The transmission through the left output arm is plotted vs. the relative phase. The odd mode is 1/200 in intensity relative to the even mode. Notethe insensitivity to the precise value of phase and the sharp transition.
LINEAR ' NON-LINEAR
Fig. 4 - A possible all-optical switch based on a nonlinear waveguide junction principle. The linear half prepares the two normal modes in the center, and the nonlinear part performs the switching.
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SELF-TRAPPING IN PLANAR STRUCTURESIn all the devices mentioned so far, the nonlinear index change was small enough so that it could be considered a perturbation over the index profile that determines the waveguide structure. These nonlinear devices operated due to perturbation of the propagation constant of the mode rather then by affecting its shape.
An exciting regime lays beyond this assumption. In an extreme case, one may consider waveguides that are formed solely by light itself. These are self-trapped beams, and they are usually discussed in the context of self-focusing /14/. While self-focusing effects are notoriously unstable in 3-dimensional optics, they are stable when the light is confined to a plane in.a quasi 2-dimensional propagation. A self-trapped beam is a soliton, and the stability of solitons in the time domain is well established. Recently a first demonstration of higher-order solitons formed in nonlinear films were reported /IS/. Solitons also appear in numerical studies of high-intensity propagation in waveguides, and they can be emitted or trapped by waveguides /16/.
Not much has been published or studied about this interesting regime, and its importance will depend on the development of suitable highly nonlinear materials.
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CONCLUSIONSNonlinear waveguide devices have the potential of achieving the speed optical devices could offer. New devices with novel and useful features are being proposed and studied. We have presented here one of these, a new nonlinear waveguide junction switch. These and other devices depend critically on the development of better material systems that will combine higher nonlinearities with minimal absorption.
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